Fair Market Rents Trend

Component Modeling

Technical Report

Alternative Methods for

Calculating Fair Market Rents

in Rental Markets with

Rapidly Rising Rents

U.S. Department of Housing and Urban Development | Office of Policy Development and Research

DISCLAIMER The contents of this report are the views of the author and do not necessarily reflect the views or policies of the U.S. Department of Housing and Urban Development or the U.S. Government.

Fair Market Rents Trend Component Modeling Technical Report

Alternative Methods for Calculating Fair Market Rents in Rental Markets with Rapidly Rising Rents

UrbanSim Inc.

and Terner Center

April 2022

Alternative Methods for Calculating Fair Market Rents

Table of Contents

List of Exhibits .............................................................................................................................................. iii

Executive Summary ...................................................................................................................................... iv

Introduction .................................................................................................................................................. 1

Alternative Calculations to Account for Areas with Rapidly Rising Rents .................................................... 2

Rapidly Rising Rent Analysis ........................................................................................................................ 22

Final Considerations and Next Steps .......................................................................................................... 39

Appendix A: Model Estimations and Forecast Evaluations......................................................................... 44

Appendix B: Summary of Rapidly Rising Rent Analysis ............................................................................. 150

Appendix C: Alternative Data Set Analysis ................................................................................................ 158

Appendix D: Summary of Augmented Dickey-Fuller Tests ....................................................................... 167

Appendix E: Rapidly Rising Rents Dashboard ........................................................................................... 168

References ................................................................................................................................................ 220

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Alternative Methods for Calculating Fair Market Rents

List of Exhibits

Exhibit 1. Rent CPI Variables ....................................................................................................................... 3

Exhibit 2. Fuel CPI Variables ....................................................................................................................... 4

Exhibit 3. Rent CPI Model Variables ........................................................................................................... 8

Exhibit 4. Lag-Length Selection for Rent CPI Models ................................................................................. 8

Exhibit 5. Rent CPI VECM Model Cointegration Test .............................................................................. 10

Exhibit 6. Rent CPI Forecast Evaluation Approach—VECM and ARIMA (2019Q2–2020Q4) ................ 12

Exhibit 7. Rent CPI Forecast Evaluation Approach—VECM and HUD ARDL (2018Q2–2019Q4) ........ 13

Exhibit 8. Rent CPI Forecast Evaluation Approach—VECM and HUD ARDL (2019Q2–2020Q4) ........ 15

Exhibit 9. Fuel and Utilities CPI Model Variables ..................................................................................... 17

Exhibit 10. Lag-Length Selection for Fuel and Utilities CPI Models ......................................................... 17

Exhibit 11. Fuel and Utilities CPI VECM Model Cointegration Test ........................................................ 19

Exhibit 12. Fuel and Utilities CPI Forecast Evaluation Approach—RMSE Fuel and Utilities CPI ........... 20

Exhibit 13. Denver Error-Correction Term ................................................................................................. 24

Exhibit 14. Log of Denver Rent-to-Income Ratio ...................................................................................... 25

Exhibit 15. Denver Business-Cycle Component ......................................................................................... 26

Exhibit 16. Denver Model Comparison: Error-Correction, Band-Pass, and Rent-to-Income Ratio.. ......... 27

Exhibit 17. Deviations from Rent Trend by Metro Area ............................................................................ 30

Exhibit 18. Rate of Change of Deviations from Rent Trend ....................................................................... 31

Exhibit 19. Comparison of HUD 50th Percentile Rents and Apartment List Rents ................................... 33

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Alternative Methods for Calculating Fair Market Rents

Executive Summary

The U.S. Department of Housing and Urban Development (HUD) estimates Fair Market Rents (FMRs) to inform reimbursement rates for federal housing assistance programs. FMRs are calculated for more than 600 metropolitan areas and 2,000 non-metropolitan areas. FMRs consist of base rent derived from the American Community Survey (ACS), an inflation factor that is used to bring base values to current values, and a trend factor (forecast) that is used to bring current values to future values. (The expected change in the gross rent index divided by the current gross rent index is calculated as the trend factor.) The gross rent index consists of two components. The Rent of Primary Residence and the Fuels and Utilities Consumer Price Index (CPI) factors are modeled using time series econometric approaches to forecast seven quarters into the future. HUD has investigated alternative approaches to developing the trend component models.

In addition, HUD has recognized that rapidly rising rents introduce further challenges to the calculation and application of FMRs and the possibility of increased discrepancies between FMRs and the ability of households to gain access to affordable housing. This research builds upon earlier work done.

UrbanSim Inc. and the Terner Center have introduced a multivariate, cointegration approach to modeling the FMR trend factor components and taken a statistical approach to define markets that may be experiencing rapidly rising rents. The multivariate time series approach to modeling both the rent and the fuel and utilities components of the CPI have promising in-sample forecasting results and introduce an additional layer of economic theory into the existing methodology. Identifying areas with rapidly rising rents is inherently a difficult problem but using a set of data-driven statistical methods—including bandpass filters, cointegration, and rent ratios—and alternative rent data sources—such as Apartment List—

has helped pinpoint periods when rents have risen rapidly and outpaced their fundamentals. Decomposing rents into both long-run trends and cyclical components using band-pass filters is a promising approach to identifying where rising rents have historically occurred but also could help identify areas where rents are rising rapidly in real time.

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Alternative Methods for Calculating Fair Market Rents

Introduction

HUD must forecast Fair Market Rents (FMRs) several quarters in advance because of the lag between when rents are updated and when HUD needs the FMR values reset. HUD’s current methodology for updating FMR is to use a trend factor that is applied to each metropolitan area in the United States. The trend factor models are specified using an ARIMA(X) time series approach. Producing more accurate trend forecasts is increasingly important in the current market environment, in which numerous geographies have experienced rapidly rising rents throughout the past business cycle, and COVID-19-related economic impacts may have had exceptional and unexpected consequences on local rental markets. This report will summarize the theory and preliminary results to updating the Rent of Primary Residence Consumer Price Index (CPI) component and the Fuels and Utilities CPI component and will introduce a statistical approach to helping identify markets with rapidly rising rents.

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Alternative Methods for Calculating Fair Market Rents

Alternative Calculations to Account for Areas with Rapidly Rising Rents

Variables

Dependent Variables

The dependent variables modeled include the Rent of Primary Residence Consumer Price Index (CPI) and the Fuels and Utilities CPI. Both variables originated from the Bureau of Labor Statistics (BLS). The Rent CPI is based on a repeat survey of rental housing units. Adjustments for age and vacancies are made to the series over time. The geographic coverage for each CPI component included Alaska, Atlanta, Chicago, Baltimore, Boston, Dallas, Denver, Detroit, Honolulu, Houston, Los Angeles, Miami, Minneapolis, New York/New Jersey, Philadelphia, Phoenix, San Francisco, San Diego, Seattle, St. Louis, Tampa, and Washington, D.C. There was no attempt to seasonally adjust the price series before estimation and forecast evaluation.

Additional Variables

The econometric approach originally proposed by UrbanSim and the Terner Center was a multivariate vector autoregression (VAR) and extensions to that model that included cointegrating vectors (vector error correction model [VECM]). The approach would be used for both the Rent and Fuel CPI components. These models would be extensions to both autoregressive integrated moving average (ARIMA) models and prior research projects that included additional exogenous variables acting as structural drivers of both components. VAR models are extensions of ARIMA models, in which every variable is regressed on the same number of lags of itself and lags of each variable included in the specification. All variables are treated endogenously. Variable selection for each CPI component was based on the economic theory of underlying supply and demand driver for each variable. A subset of those variables was used for final specifications.

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Alternative Methods for Calculating Fair Market Rents

Rent of Primary Residence CPI Model Variables

Variables for inclusion in the Rent CPI model included housing variables such as Federal Housing Finance Agency (FHFA) home price indices, inventory, and housing permits. Demographic variables included population and number of households. Employment variables included labor force, nonfarm payrolls, and employment counts from the Quarterly Census of Employment and Wages. Per capita personal income was used as an overall proxy for income measures. Those variables represent common supply and demand drivers that align with economic and real estate theory and are used in many applied forecasting models. In addition, when developing error-correction models, one is looking for variables that may share long-run equilibrium relationships, such as prices and income or rents and prices.

Variables are listed in exhibit 1.

Exhibit 1. Rent CPI Variables

Variable

Source

Periodicity

Geography

Purpose

House Price

FHFA

Monthly

MSA

Proxy for price

Index

Unemployment

BLS

Monthly

MSA

Proxy for labor

Rate

market slack

Nonfarm

BLS

Monthly

MSA

Proxy for labor

Payrolls

market

Population

Census

Annual

MSA

Proxy for

demographics

Labor Force

BLS

Monthly

MSA

Proxy for labor

for dynamics

Personal

BEA

Annual

MSA

Proxy for

Income per

income

Capita

dynamics

Housing

Realtor.com

Monthly

CBSA

Proxy for

Inventory

housing

inventory

Mortgage Rates

Freddie Mac

Weekly

National

Proxy for

financing costs

Housing Permits

Census

Monthly

MSA

Proxy for

building activity

BEA = Bureau of Economic Analysis. BLS = Bureau of Labor Statistics. CBSA = core-based statistical area. FHFA = Federal Housing Finance Agency. MSA = metropolitan statistical area.

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Alternative Methods for Calculating Fair Market Rents

Fuel and Utility CPI Model Variables

Variables for inclusion in the Fuel CPI component included West Texas Intermediate (WTI) crude oil prices, natural gas prices, electricity prices, and the U.S. Producer Price Index (PPI). Including energy prices with the Fuel CPI was an attempt to capture underlying drivers of the Fuel CPI, similar to modeling oil prices with gasoline and jet fuel, as done when estimating the crack spread in energy trading. The motivation lies in the derived demand that may exist in the underlying input prices. In addition, the PPI could be tested separately as an overall raw material proxy. Literature that modeled the CPI and PPI as a VAR tested the theory of cost push versus demand pull inflation (Baumeister, Kilian, and Zhou, 2017).

Said differently, do consumer prices drive producer prices or vice versa—or both? Exhibit 2 lists the variables.

Exhibit 2. Fuel CPI Variables

Variable

Source

Periodicity

Geography

Purpose

WTI Crude

EIA

Monthly

NA

Oil Price

Price

Henry Hub

EIA

Monthly

NA

Natural Gas

Natural Gas

U.S. Average

EIA

Monthly

NA

Electricity

Electricity Price

Price

EIA = U.S. Energy Information Administration. NA = not applicable. WTI = West Texas Intermediate.

Econometric Methodology

The proposed econometric methodology builds upon prior research by introducing a multivariate time series approach to forecasting both CPI series. This approach can be used to measure whether a local multivariate approach outperforms the current ARIMA forecasting approach. VAR models are widely used in macroeconomic forecasting and have demonstrated forecasting performance in short- to medium-term horizons (Sims, 1980). As an example, suppose one was interested in forecasting both inflation and employment for a given metropolitan statistical area (MSA). The inflation equation would be a function 4

Alternative Methods for Calculating Fair Market Rents

of the same number of lags of both inflation and employment, and a symmetric equation would be estimated for employment. VAR models can be generalized to more than two variables.

• VAR models are transparent in methodology and rely on well-known estimation methods, such as ordinary least squares and maximum likelihood; more complicated systems estimators are unnecessary.

• All variables are treated endogenously, eliminating the need for producing exogenous forecasts for independent variables in a traditional structural approach, thus reducing the risk of bias in variable selection. Often, this method also better represents the true relationship between variables.

• The interaction of variables in VAR models may better represent local economic conditions through both supply and demand variables rather than relying on ARIMA models, as was done in prior research.

• VARs can be augmented with error-correction terms, which introduce a statistical long-run relationship into the model that can act as an equilibrium adjustment term.

The theory of cointegration has been a widely used econometric technique in developing real estate models. Cointegration is defined as two or more variables sharing a statistical, long-run relationship.

More specifically, cointegration allows for two variables to vary over the short run but requires a long-run equilibrium relationship to be maintained (Granger, 1974). Real estate models often have been based on a long-run relationship existing between prices and income. One might expect that the two variables could diverge over a business cycle but eventually reestablish an equilibrium in the long run.

CPI Modeling Approach

Estimating and forecasting with VAR/VECM model follows a routinized approach similar to that of estimating an ARIMA model:

1. Model specification and variable selection/transformation.

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Alternative Methods for Calculating Fair Market Rents

2. VAR estimation and lag-length selection.

3. Cointegration test.

4. VECM estimation and results.

5. In-sample forecast and evaluation/model revision.

6. Future out-of-sample forecasting.

7. Model revision based on incoming data and expert opinion.

Specifying VAR models relies on underlying theoretical and applied knowledge of what variables to include. Choosing variables for a VAR model cannot be performed in an automated fashion, such as a stepwise regression in an ordinary least squares (OLS) single equation approach. Such approaches should be used with caution, as they can result in specifications with little to no economic theory. Additional factors must be considered when specifying augmented vector autoregression to include error-correction terms. The econometrician first must identify a set of two or more variables that he or she believes should have a long-run statistical relationship, which can be done using commonly used cointegration tests. A prerequisite is that all variables considered for a VECM model be unit root processes, which is tested using the augmented Dickey-Fuller unit root test (Dickey and Fuller, 1979).

Once a set of two or more variables is selected for estimation, lag selection is performed on the VAR

model. Commonly employed information criteria are used to evaluate multiple lag specifications. The two most common measures are the Akaike information criterion (AIC) and the Schwarz information criteria (SIC). The two measures present theoretical tradeoffs between them that result in both choosing robust lag lengths, just under different assumptions. Both measures are approximately correct according to a different goal and a different set of asymptotic assumptions. The AIC criteria were used throughout the modeling process.

After lag selection was performed and a VAR was estimated, cointegration tests were performed to detect the presence of statistical long-run relationships between variables in the set. The Johansen procedure was used throughout the modeling process (Johansen, 1991). It is the most widely used and one of the most 6

Alternative Methods for Calculating Fair Market Rents

accepted multivariate cointegration tests. The test will detect n-1 possible cointegrating relationships in a group of n variables. If more than one long-run relationship is found, the modeler determines, through theory and expertise, what each cointegrating relationship represents.

The estimated VAR model is augmented with the cointegrating equations and reestimated as a VECM

model. Both long-run cointegrating equations in levels are estimated alongside short-run equations in first differences that act to pick deviations from the theoretical long-run relationship. Coefficients are evaluated for both sign and statistical significance.

Forecasting the performance of each VECM was tested by benchmarking the VECM models against ARIMA models estimated by UrbanSim using auto-selection procedures. The auto-selection procedure followed a set of steps that included (1) transforming the variable into logs if needed, (2) differencing up to two times depending on the results of an ADF unit root test, (3) estimating up to an AR(4) MA(4) model by iterating over every combination and returning the model with the lowest AIC measure, and (4) forecasting seven quarters in-sample to provide a comparison to the VECM in-sample forecast. Forecast evaluation was performed by comparing the VECM model to both the ARIMA model and a simple weighted combination of the two. Precedent in the literature suggests that an ensemble approach to forecasting can reduce overall forecasting errors. The root mean squared error (RMSE) was used as the primary measure. The advantages of RMSE include (1) the errors are squared, penalizing outliers; and (2) the error is reported in native units of the dependent variable.

Rent of Primary Residence Model

The Rent CPI modeling process followed the steps laid out in the previous section. The first step was variable selection and model specification. As stated earlier, no agreed-upon way exists to choose a set of variables for a VAR model; the modeler must rely on a combination of economic theory and applied expertise. In addition, the desire to estimate a VECM model requires the modeler to develop and test a hypothesis of possible statistical relationships that should hold in the long run, according to theory.

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Alternative Methods for Calculating Fair Market Rents

An attempt was made at the outset of the Rent CPI modeling process to find a parsimonious set of variables that have strong economic linkages to the Rent CPI and could be used into the future if HUD

chooses to operationalize multivariate models in the FMR process. After analyzing statistical correlations to avoid severe multicollinearity among choice variables and unit root tests to ensure that all included variables are nonstationary and, therefore, able to be modeled as a cointegrating vector, the FHFA all-transaction home price index and per capita disposable personal income were chosen to be included in the VECM models; appendix D summarizes the stationarity tests. In addition, the metro-level consumer price index for all items was used to generate both real home price and real income variables for use in the VECM models. The home price index was included as a supply-side proxy for the housing market, and the per capita disposable personal income variable is a demand-side proxy for households. Exhibit 3

displays the variables, sources, and frequencies.

Exhibit 3. Rent CPI Model Variables

Variable

Source

Frequency

Rent of Primary Residence CPI

BLS

Monthly, Bimonthly

All-Transactions House Price Index

FHFA

Quarterly

State Per Capita Disposable Personal Income

BEA

Quarterly, Annual

Consumer Price Index—MSA

BLS

Biannual, Annual

BEA = Bureau of Economic Analysis. BLS = Bureau of Labor Statistics. CPI = Consumer Price Index. FHFA = Federal Housing Finance Agency. Following the choice of variables to include in the VECM models, estimation and lag-length selection were performed. The Akaike information criteria were used for lag selection for all Rent CPI models. Lag selection results are shown in exhibit 4. As a comparison, the Schwarz information criteria would have selected almost all models with only one lag, which was thought to be overly restrictive in the modeling process.

Exhibit 4. Lag-Length Selection for Rent CPI Models

Area

Lag-Length—AIC Measure

Alaska

5

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Alternative Methods for Calculating Fair Market Rents

Atlanta

5

Baltimore

4

Boston

5

Chicago

5

Dallas

5

Denver

5

Detroit

4

Honolulu

5

Houston

5

Los Angeles

6

Miami

4

Minneapolis

5

New York/New Jersey

5

Philadelphia

5

Phoenix

5

San Diego

5

San Francisco

5

Seattle

5

St. Louis

7

Tampa

4

Washington, DC

4

AIC = Akaike information criterion. CPI = Consumer Price Index.

Source: Author’s calculations

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Alternative Methods for Calculating Fair Market Rents

The definition of cointegration states that two or more nonstationary variables may be combined in a linear combination that results in a stationary process. Variables considered for the Rent CPI VECM

model must be nonstationary or a unit-root process so that they can be combined in a cointegrating model.

Augmented Dickey-Fuller (ADF) unit root tests were performed on all variables included in the VECM

models. The null hypothesis of the ADF is that the variable has a unit root. All variables failed to reject the null hypothesis with very small (in absolute values) ADF tau statistics. This result is to be expected, as all variables considered have a pronounced trend in the time series.

Johansen cointegration tests were run on each VECM model to confirm the presence of cointegration between the variables; the results appear in exhibit 5. With three variables included in each VAR model, at most, two long-term equilibrium relationships can exist.

Exhibit 5. Rent CPI VECM Model Cointegration Test

Area

# of Cointegrating Relationships

Probability Value

Null Hypothesis: No Cointegration

Alaska

1

0.02

Atlanta

1

0.00

Baltimore

1

0.06

Boston

1

0.00

Chicago

1

0.03

Dallas

1

0.11

Denver

1

0.00

Detroit

1

0.01

Honolulu

1

0.10

Houston

1

0.03

Los Angeles

1

0.08

Miami

1

0.04

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Alternative Methods for Calculating Fair Market Rents

Minneapolis

1

0.00

New York

1

0.01

Philadelphia

1

0.00

Phoenix

2

0.00, 0.00

San Diego

1

0.06

San Francisco

1

0.01

Seattle

0

0.29

St. Louis

1

0.11

Tampa

1

0.03

Washington, DC

1

0.02

CPI = Consumer Price Index. VECM = vector error correction model.

After performing unit root tests on all included variables, performing lag selection using the AIC

measure, and testing for the presence of cointegration using the Johansen procedure, the VECM models were estimated for each metro area. A training set was estimated from the earliest available data point, which varied from 1985 to 1990 depending on the region, through 2019Q1. The period of 2019Q2

through 2020Q4 was used as a test set for in-sample forecasting and evaluation. The auto-specification procedure for benchmark ARIMA models was also completed at this step. Complete estimation results for both ARIMA and VECM models can be found in appendix A.

The forecast evaluation relied on the mean absolute percentage error because it allows for easy comparison across regions. The VECM model was compared with the auto-selected ARIMA specification and an equally weighted forecast combination. Building ensembles of different forecast methodologies can result in an overall smaller mean absolute percentage error (MAPE) and take advantage of multiple modeling methodologies. Appendix A shows the full forecast evaluation results, and exhibit 6 displays a summary of each regional forecasting model.

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Exhibit 6. Rent CPI Forecast Evaluation Approach—VECM and ARIMA (2019Q2–2020Q4) MAPE

MAPE

Area

MAPE VECM

ARIMA

Combination

Alaska

1.21

1.29

1.28

Atlanta

0.63

1.07

0.42

Baltimore

2.41

5.73

3.21

Boston

1.24

3.48

2.36

Chicago

0.97

1.82

1.57

Dallas

1.28

2.61

1.91

Denver

0.37

0.80

0.58

Detroit

0.75

0.45

0.52

Honolulu

1.83

1.20

1.51

Houston

0.55

1.09

0.68

Los Angeles

1.02

0.53

0.69

Miami

1.07

1.20

1.14

Minneapolis

1.20

0.43

0.81

New York/New Jersey

0.57

0.87

0.58

Philadelphia

0.64

0.37

0.34

Phoenix

2.63

2.16

2.40

San Diego

0.73

0.73

0.73

San Francisco

2.49

2.63

2.56

Seattle

1.02

1.62

0.89

St. Louis

0.90

1.11

1.04

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Alternative Methods for Calculating Fair Market Rents

Tampa

1.04

0.64

0.84

Washington, DC

0.97

2.21

1.56

ARIMA = autoregressive integrated moving average. CPI = Consumer Price Index. MAPE = mean absolute percentage error. Q

= quarter. VECM = vector error correction model.

Note: The lowest mean absolute percentage error is shown in bold, indicating the highest accuracy model for each area.

The forecast evaluation resulted in 13 of 22 metro-area VECM models outperforming the ARIMA models in an eight-quarter in-sample forecast on an absolute basis. Six of the ARIMA models outperform the VECM models, and three of the simple mean combination models outperform both the VECM and ARIMA models.

A second forecasting exercise was completed to evaluate the VECM approach against autoregressive distributed lag models (ARDLs) that followed a similar specification as the local versions of existing HUD models. As discussed in a 2019 2M research report, the HUD local ARDL models were estimated with local exogenous factors that included Census Bureau local permit data and BLS local employment data. All 22 regions were specified in first differences and included a first-order moving average (MA[1]) term to help capture the time series dynamics of the rent series and two lags of both permit and employment data to capture local economic dynamics. All models were estimated from the beginning of the sample, which varied by region through 2018Q1. The in-sample forecast evaluation was performed over the sample of 2018Q2 through 2019Q4, excluding any effects from the COVID-19 pandemic. In addition, without having the exogenous forecasts for permits and employment that HUD would have included over the time horizon, the estimated ARDL models rely on the actual, observed data for all exogenous variables. Forecast evaluation results are shown in exhibit 7.

Exhibit 7. Rent CPI Forecast Evaluation Approach—VECM and HUD ARDL (2018Q2–2019Q4) Area

MAPE VECM MAPE HUD

Alaska

0.69

1.99

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Alternative Methods for Calculating Fair Market Rents

Atlanta

1.93

2.21

Baltimore

1.28

1.14

Boston

0.60

0.94

Chicago

0.52

0.22

Dallas

1.66

0.92

Denver

0.22

0.81

Detroit

0.46

1.05

Honolulu

0.49

0.63

Houston

0.82

1.29

Los Angeles

0.74

1.34

Miami

0.70

0.56

Minneapolis

1.01

1.49

New York/New Jersey

1.15

0.86

Philadelphia

0.55

0.32

Phoenix

2.27

2.12

San Diego

2.59

0.11

San Francisco

1.57

1.49

Seattle

0.63

0.96

St. Louis

0.41

0.59

Tampa

1.48

1.30

Washington, DC

1.16

1.78

ARDL = autoregressive distributed lag models. CPI = Consumer Price Index. MAPE = mean absolute percentage error. Q =

quarter. VECM = vector error correction model.

Note: The lowest mean absolute percentage error is shown in bold, indicating the highest accuracy model for each area.

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The VECM model outperformed the HUD ARDL model in 12 of 22 regions based on root mean squared error over the 2018-through-2019 period.

A second forecast evaluation was performed with the VECM and HUD ARDL models over the in-sample period of 2019Q2 through 2020Q4. This in-sample evaluation includes the onset of the COVID-19

pandemic. The HUD ARDL models are specified with the same exogenous variables, and actual observed data are used to drive the forecast over the horizon. This method contrasts with what exogenous forecasts HUD would have used in 2019 before knowing of the oncoming pandemic. Exhibit 8 shows the forecast results.

Exhibit 8. Rent CPI Forecast Evaluation Approach—VECM and HUD ARDL (2019Q2–2020Q4) Area

MAPE VECM MAPE HUD

Alaska

1.59

2.33

Atlanta

1.17

2.43

Baltimore

3.31

3.79

Boston

0.35

0.97

Chicago

0.33

0.16

Dallas

2.61

1.36

Denver

1.15

0.61

Detroit

1.01

1.58

Honolulu

2.57

2.65

Houston

1.68

1.63

Los Angeles

0.85

1.52

Miami

1.92

1.80

Minneapolis

1.37

1.56

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Alternative Methods for Calculating Fair Market Rents

New York/New Jersey

0.53

0.74

Philadelphia

0.33

1.21

Phoenix

2.07

2.46

San Diego

0.23

1.19

San Francisco

1.91

2.14

Seattle

1.04

1.45

St. Louis

0.78

1.01

Tampa

0.36

1.34

Washington, DC

0.37

0.55

ARDL = autoregressive distributed lag models. CPI = Consumer Price Index. MAPE = mean absolute percentage error. Q =

quarter. VECM = vector error correction model.

Note: The lowest mean absolute percentage error is shown in bold, indicating the highest accuracy model for each area.

The VECM model outperformed the HUD ARDL model in 18 of 22 regions based on root mean squared error over the 2019-through-2020, period which included the onset of the COVID-19 pandemic.

Utilities and Fuels CPI Component Model

The Fuel CPI modeling process followed a similar process as the Rent CPI modeling exercise. The first step was variable selection and model specification. As stated earlier, no agreed-upon way exists to choose a set of variables for a VAR model. The modeler must rely on a combination of economic theory and applied expertise. In addition, the desire to estimate a VECM model requires the modeler to develop and test a hypothesis of possible statistical relationships that should hold in the long run according to theory. That process was performed using the Johansen cointegration test, with results reported in Exhibit 11.

The Fuels and Utilities CPI component has underlying subcomponents that represent household energy prices for electricity and fuels. Precedent exists for modeling crude oil prices in a VAR representation, 16

Alternative Methods for Calculating Fair Market Rents

with products derived from crude, such as gasoline, kerosene, and jet fuel (Baumeister, Kilian, and Zhou, 2017). Working from that approach, it was thought that modeling the Fuel CPI component with individual energy prices such as natural gas, electricity, and crude oil could provide increased information to the models. The Producer Price Index is also included to transform nominal prices into real prices for the model process.

Exhibit 9. Fuel and Utilities CPI Model Variables

Variable

Source

Frequency

Fuel and Utilities CPI

BLS

Monthly, Bimonthly

Henry Hub Natural Gas Price

EIA

Monthly

Electricity per kWh, U.S. City Average

EIA

Monthly

WTI Crude Oil Price

EIA

Monthly

Producer Price Index: All Commodities

BLS

Monthly

BLS = Bureau of Labor Statistics. CPI = Consumer Price Index. EIA = U.S. Energy Information Administration. kWh =

kilowatt-hour. WTI = West Texas Intermediate.

Following the choice of variables to include in the VECM models, estimation and lag-length selection were performed. The Akaike information criteria were used for lag selection for all Fuel and Utilities CPI models. Lag-length selection results are shown in exhibit 10.

Exhibit 10. Lag-Length Selection for Fuel and Utilities CPI Models Area

Lag-Length—AIC Measure

Alaska

4

Atlanta

3

Baltimore

6

Boston

4

Chicago

5

Dallas

4

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Alternative Methods for Calculating Fair Market Rents

Denver

4

Detroit

2

Honolulu

2

Houston

3

Los Angeles

3

Miami

2

Minneapolis

4

New York/New Jersey

4

Philadelphia

4

Phoenix

4

San Diego

4

San Francisco

2

Seattle

2

St. Louis

6

Tampa

4

Washington, DC

5

AIC = Akaike information criterion. CPI = Consumer Price Index.

The definition of cointegration states that two or more nonstationary variables may be combined in a linear combination that results in a stationary process. Variables considered for the Fuel and Utilities CPI VECM model must be nonstationary or a unit root process so that they can be combined in a cointegrating model. Augmented Dickey-Fuller (ADF) unit root tests were performed on all variables included in the VECM models. The null hypothesis of the ADF is that the variable has a unit root. All variables failed to reject the null hypothesis with very small (in absolute values) ADF tau statistics—a result that was expected because all variables considered have a pronounced trend in the time series.

18

Alternative Methods for Calculating Fair Market Rents

Johansen cointegration tests were run on each VECM model to confirm the presence of cointegration between the variables (exhibit 11). With three variables included in each VAR model, two long-term equilibrium relationships can exist at most.

Exhibit 11. Fuel and Utilities CPI VECM Model Cointegration Test Area

# of Cointegrating Relationships

Probability Value

Null Hypothesis: No Cointegration

Alaska

0

0.54

Atlanta

1

0.09

Baltimore

~1

0.11

Boston

~1

0.13

Chicago

~1

0.12

Dallas

~1

0.11

Denver

1

0.06

Detroit

1

0.01

Honolulu

~1

0.14

Houston

1

0.08

Los Angeles

0

0.49

Miami

1

0.04

Minneapolis

0

0.42

New York/New

1

0.01

Jersey

Philadelphia

1

0.05

Phoenix

0

0.17

San Diego

1

0.06

San Francisco

~1

0.11

St. Louis

~1

0.14

19

Alternative Methods for Calculating Fair Market Rents

Seattle

0

0.14

Tampa

1

0.08

Washington, DC

1

0.01

* Because the ADF test results were inconclusive, a 10-percent p-value was used as a threshold for cointegration. ~ =

approximately.

CPI = Consumer Price Index. MAPE = mean absolute percentage error. Q = quarter. VECM = vector error correction model.

After performing unit root tests on all included variables, performing lag selection using the AIC

measure, and testing for the presence of cointegration using the Johansen procedure, we estimated the VECM models for each region. A training set was estimated from the earliest available data point, which varied from 1985 through 1990 depending on the region, through 2018Q4; 2019Q1 through 2020Q4 was used as a test set for in-sample forecasting and evaluation. The auto-specification procedure for benchmark ARIMA models was also completed at this step. Appendix A presents complete estimation results for both ARIMA and VECM models.

The forecast evaluation relied on the root mean squared error. The VECM model was compared with the auto-selected ARIMA specification and an equally weighted forecast combination. Many ways can be used to develop combination forecasts, but equally weighting the two has been shown to be as effective in lowering the MAPE as any other statistical approach. Appendix A presents the full forecast evaluation results. Exhibit 12 shows a summary of each regional forecasting model.

Exhibit 12. Fuel and Utilities CPI Forecast Evaluation Approach—RMSE Fuel and Utilities CPI Area

MAPE VECM MAPE ARIMA

Combination

Alaska

2.75

2.23

2.44

Atlanta

3.45

1.89

2.27

Baltimore

0.87

0.96

0.90

Boston

7.42

3.60

5.51

20

Alternative Methods for Calculating Fair Market Rents

Chicago

0.87

7.72

4.03

Dallas

3.27

2.61

2.76

Denver

5.68

2.66

3.95

Detroit

3.65

2.53

3.01

Honolulu

2.43

9.36

5.55

Houston

4.52

4.02

4.27

Los Angeles

0.73

0.96

0.81

Miami

0.74

1.46

1.03

Minneapolis

0.99

0.54

0.77

New York/New Jersey

4.36

4.76

4.40

Philadelphia

1.22

1.07

1.14

Phoenix

6.95

8.01

7.48

San Diego

2.68

5.65

4.01

San Francisco

1.14

0.72

0.77

Seattle

3.32

2.84

3.08

St. Louis

8.92

10.97

9.33

Tampa

2.46

1.91

2.19

Washington, DC

3.21

2.98

3.01

ARIMA = autoregressive integrated moving average. CPI = Consumer Price Index. MAPE = mean absolute percentage error. Q

= quarter. RMSE = root mean squared error. VECM = vector error correction model.

Note: The lowest mean absolute percentage error is shown in bold, indicating the highest accuracy model for each area.

The forecast evaluation resulted in 8 of 22 metro-area VECM models outperforming the ARIMA models in an eight-quarter in-sample forecast on an absolute basis. Thirteen of the ARIMA models outperformed the VECM models, and one of the combination models outperformed both the VECM and ARIMA models.

21

Alternative Methods for Calculating Fair Market Rents

Rapidly Rising Rent Analysis

Statistical Approach

The pace of rental price appreciation in many metro and sub-metro areas has become an issue of concern for low-income families and policymakers. As with any issue, being able to accurately define the problem is a crucial first step in implementing an effective response. Identifying metro areas with above-trend rent growth is a difficult problem to solve. We implemented a statistical approach, letting the data inform the problem rather than making assumptions that could be clouded with bias or judgment. Three approaches were tested: a cointegration model to try to identify periods of disequilibrium in rental market fundamentals, rent-to-income ratios, and decomposing rent series into cyclical and trend components using band-pass filters. All three methods are described below. Ultimately, the band-pass filter approach was chosen as the most robust and was implemented on an alternative rent data set originating from Apartment List. This dataset is released monthly and, after investigation, is believed it to be more representative of real-time market conditions.

The first approach used was to identify disequilibrium in FMR metro markets by relying on the theory of cointegration and estimate statistical, long-run regression models. The model took the form of an ordinary least squares (OLS) regression and followed the well-known Engel-Granger (1987) two-step procedure.

The dependent variable was a measure of rental prices proxied by metro-level personal shelter consumer prices indices. The independent variables included a combination of fundamental supply and demand factors for the rental real estate market, including, but not limited to, measures of income, housing activity, population and household totals, and other long-term measures of real estate markets. When variables are expressed in level form, the equation represents the long-run equilibrium relationship between the prices and the included set of independent variables. The residual from the resulting regression represents the amount of variation in the dependent variable not explained by the specification.

In that case, the residual represents deviations from long-run equilibrium in prices. The residual can be standardized and compared across metro regions to identify markets that display prices above or below 22

Alternative Methods for Calculating Fair Market Rents

equilibrium. Advantages to this approach include relying on well-known statistical methods that are transparent and reproducible with publicly available data; representing the market as a combination of long-run supply and demand drivers rooted in underlying real estate economic theory; using long-standing, proven econometric methodologies, such as cointegration and error correction; and the ability to compare across multiple MSA markets with similar data driving each estimation.

The second approach was deriving rent-to-income ratios using the CPI primary rent and real personal disposable income series. Although this approach is not as econometrically involved as the Engel-Granger approach, it can be used to help identify current states of rental markets with respect to economic fundamentals. This approach can also be used to help verify the results from other approaches.

The third approach was to use band-pass (BP) filters to statistically decompose rent series into a long-run structural trend and a number of underlying cyclical series (Baxter and King, 1995). For example, a common approach is to use BP filters to decompose real gross domestic product (GDP) into a trend component that is thought to represent potential GDP and a business-cycle component with a periodicity of 2 to 8 years, which represents deviations from the long run. This approach has advantages when dealing with trending time series, such as the Rent of Primary Residence CPI component. The Christiano-Fitzgerald Asymmetric filter was used to decompose quarterly Rent CPI series into trend and business-cycle components (Christiano and Fitzgerald, 1999). Housing makes a significant contribution to overall U.S. economic growth, so looking at the business-cycle frequency is a starting point for this type of analysis.

Summary of Results

The first approach used was the Engel-Granger cointegration approach. Ordinary least squares regressions were run on the log of all Rent CPI series. Independent variables included the log of real per capita disposable income and the log of real home prices. Dickey-Fuller unit root tests were performed on the residuals to check for stationarity. If stationarity was found, the residuals could be interpreted as the long-23

Alternative Methods for Calculating Fair Market Rents

run error-correction mechanism with respect to the underlying linear estimation. All residual graphs are shown in appendix B. The scaling was normalized so that interpretation would be units of standard deviation. Using this framework, one could look at periods when the relationship increased 2 or more standard deviations, toward a value of positive 1 or 2, at which the relationship historically would begin to mean revert. Exhibit 13 illustrates the error-correction term for Denver as an example.

Exhibit 1. Denver Error-Correction Term

Denver error-correction term

2

1

0

-1

-2

-31985 1990 1995 2000 2005 2010 2015 2020

Source: Author’s calculations

The residual was assumed to be stationary based on the unit root tests. The residual or error-correction term hit the lowest point at roughly 2 standard deviations below the mean and then had a 4-standard-deviation move, from -2 toward +2, over the period of 2007Q2 through 2010Q2. This relationship must be interpreted as the equilibrium relationship between rent, income, and home prices. The specification could be changed to include other fundamental long-run drivers, but the requirement of the error-term being stationary is necessary for interpretation as a mean-reverting term. To identify periods of rising rents, the error-correction term could transform into first differences to determine if it is increasing or decreasing and then transformed into second differences to determine if it is increasing or decreasing at an 24

Alternative Methods for Calculating Fair Market Rents

increasing or decreasing rate. Doing so can capture the idea of acceleration in prices and determine whether rents are in a state of “rapid increase.”

Rent-to-income ratios were calculated for metro regions as additional way to look at relative changes and help understand periods, for example, when rents increased much faster than income. Rent-to-income ratios for all 22 regions demonstrated an outpacing of rental price appreciation relative to real incomes, which should not be surprising given the stagnation in real wages and incomes over the past two decades.

Exhibit 14 shows the log of rent-to-income ratio for Denver.

Exhibit 2. Log of Denver Rent-to-Income Ratio

Log Denver Rent-to-Income Ratio

.3

.2

.1

.0

-.1

-.2

-.3

-.4

-.5

-.61985 1990 1995 2000 2005 2010 2015 2020

Source: Author’s calculations

The third approach discussed was using band-pass filters to isolate the underlying long-run trend from higher frequency cyclical movements in rental prices. Those techniques have been widely used in applied macroeconomics and finance to analyze the business cycle (BC) of an underlying economy. The advantage of using band-pass filters is the ability to separate a trending variable from its underlying cyclical movements. Many macroeconomic variables including the CPI and its components almost appear to monotonically increase, making any determination of whether prices are rising or rapidly rising difficult to determine. The Christiano-Fitzgerald asymmetric filter was applied to the log of the Rent CPI 25

Alternative Methods for Calculating Fair Market Rents

series to specifically isolate a cycle of 2 to 8 years in length. The 2- to 8-year frequency is commonly used for business-cycle analysis and has been used to look at housing and its relationship to the broader macroeconomy. The chart for all business-cycle rent components is shown in appendix B. Continuing with Denver as an example, exhibit 3.3 shows the business-cycle component.

Exhibit 3. Denver Business-Cycle Component

Denver Business-Cycle Component

.03

.02

.01

.00

-.01

-.02

-.03

96

98

00

02

04

06

08

10

12

14

16

18

20

Source: Author’s calculations

The graph represents deviations from the filtered long-run trend in the underlying data. When the component is above the zero axis, the Denver rent CPI can be said to be increasing in an above-trend way.

Determining if the business-cycle component is increasing or decreasing at an increasing or decreasing rate can help determine if prices are in a state of rapidly rising rents.

The first and second differences were taken to understand when each of the three residual series is increasing or decreasing at an increasing or decreasing rate. All three methods can be compared to see where they align. Exhibit 16 displays a snapshot of the Denver region. The first column is the error-correction term, followed by the band-pass filter cycle, and finally the rent-to-income ratio. At the peak of the housing boom in the mid-2000s, all three methods were signaling that rents were increasing at an 26

Alternative Methods for Calculating Fair Market Rents

increasing rate. The middle column shows that after the onset of the Great Recession, the cyclical component turned sharply to a state of decreasing at an increasing rate, picking up the relation to the overall business cycle. Dashboards for all 22 metro areas are shown in appendix C.

Exhibit 16. Denver Model Comparison: Error-Correction, Band-Pass, and Rent-to-Income Ratio D = Decreasing at a decreasing rate. R = Increasing at a decreasing rate. RD = Decreasing at an increasing rate. RR = Increasing at an increasing rate.

Source: Author’s calculations

As an alternative case, all metro areas picked up the downturn in the economy and rental market because of the coronavirus pandemic. In almost all cases, all three signals turned negative and many to rapidly decreasing rental prices throughout all of 2020.

All three approaches to statistically identifying periods of rapidly rising rents are data-driven in their approach and provide insights into how various fundamentals drive rental markets. After analyzing how each method compared across metropolitan areas, the band-pass filtering approach was selected as the most robust and consistent for identifying when markets are experiencing extreme movements in price.

27

Alternative Methods for Calculating Fair Market Rents

BP filters do not rely on estimating any structural equations and focus on only how cyclical components of trending series move. One advantage of this approach is that it can be updated frequently without needing other exogenous variables for analysis. Band-pass filtering also showed a more consistent result across periods when compared with the cointegration and rent-to-income ratio approaches. The BP

approach can identify periods of rapidly rising and falling rents without the frequent reversals seen in both of the other approaches.

Alternative Data Sets and Case Study

Additional datasets were analyzed to look for differences in how rent prices evolve over time. We compared REIS, Craigslist, Apartment List, and Zillow rent data with the Rent CPI series for a set of metro areas. One noticeable difference was that the alternative data seemed to react in a much more pronounced way than the Rent CPI data to the COVID-19 pandemic. The difference, of course, could be explained in the way the data are calculated, but it does give a very different picture of how rents have evolved since the pandemic began. A notable point is that most of these alternative datasets are derived from real-time market conditions for rental contracts or listings rather than a survey-based method.

Apartment List data are available monthly starting in 2017 and include all 22 metro regions covered in this study. The entire Apartment List database covers state, region, metro, and city-level geographies. 1

The band-pass filter approach to identifying areas with rapidly rising rents could be implemented below FMR-designated geographies. Those data were used for an additional case study within the BP filter framework and analyzing how the most current Apartment List data compares with the recently released FY22 FMR calculations.

The Christiano-Fitzgerald band-pass filter was applied to the log of all 22 Apartment List rent series. The same underlying assumptions of nonstationarity were used in the calculation. The decomposition included 1 For a more detailed description of the Apartment List data, see https://www.apartmentlist.com/research/rent-

estimate-methodology.

28

Alternative Methods for Calculating Fair Market Rents

the entire monthly sample from January 2017 through September 2021. Exhibit 17 illustrates the business-cycle component for each metro area, and exhibit 18 shows the rate of change of the business-cycle component. All graphs are shaded to highlight when the pandemic began.

29

Alternative Methods for Calculating Fair Market Rents

Exhibit 17. Deviations from Rent Trend by Metro Area

Anchorage

Atlanta

Baltimore

.02

.04

.04

.01

.00

.02

.00

.00

-.04

-.01

-.02

-.02

-.08

-.04

-.03

-.12

-.06

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Boston

Chicago

Dallas

.04

.02

.04

.02

.00

.00

.00

-.02

-.04

-.02

-.04

-.04

-.08

-.06

-.06

-.12

-.08

-.08

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Denver

Detroit

Honolulu

.04

.04

.06

.02

.02

.04

.00

.02

-.02

.00

.00

-.04

-.02

-.06

-.02

-.08

-.04

-.04

-.10

-.06

-.06

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Houston

Los Angeles

Miami

.04

.02

.04

.02

.00

.00

.00

-.02

-.04

-.02

-.04

-.04

-.06

-.08

-.06

-.08

-.12

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Minneapolis

New York/New jersey

Philadelphia

.04

.04

.04

.02

.02

.02

.00

.00

.00

-.02

-.02

-.02

-.04

-.04

-.06

-.04

-.06

-.08

-.06

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Phoenix

San Diego

Seattle

.04

.04

.04

.02

.00

.00

.00

-.04

-.02

-.04

-.04

-.08

-.08

-.06

-.12

-.08

-.12

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

San Francisco

St. Louis

Tampa

.08

.04

.08

.04

.02

.04

.00

.00

.00

-.04

-.04

-.08

-.02

-.08

-.12

-.04

-.12

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Washington D.C.

.04

.02

.00

-.02

-.04

-.06

-.08

2017

2018

2019

2020

2021

2022

Source: Author’s calculations

30

Alternative Methods for Calculating Fair Market Rents

Exhibit 18. Rate of Change of Deviations from Rent Trend

Anchorage

Atlanta

Baltimore

.006

.015

.012

.004

.010

.008

.002

.005

.004

.000

.000

.000

-.002

-.005

-.004

-.004

-.010

-.008

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Boston

Chicago

Dallas

.02

.015

.015

.01

.010

.010

.005

.005

.00

.000

.000

-.01

-.005

-.005

-.02

-.010

-.010

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Denver

Detroit

Honolulu

.015

.008

.012

.010

.004

.008

.005

.004

.000

.000

.000

-.005

-.004

-.004

-.010

-.008

-.008

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Houston

Los Angeles

Miami

.010

.015

.02

.005

.010

.01

.005

.000

.00

.000

-.005

-.005

-.01

-.010

-.010

-.02

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Minneapolis

New York/New Jersey

Philadelphia

.008

.015

.012

.010

.004

.008

.005

.004

.000

.000

.000

-.005

-.004

-.010

-.004

-.008

-.015

-.008

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Phoenix

San Diego

Seattle

.020

.015

.02

.015

.010

.01

.010

.005

.005

.00

.000

.000

-.01

-.005

-.005

-.010

-.010

-.02

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

San Francisco

St. Louis

Tampa

.02

.008

.03

.01

.004

.02

.01

.00

.000

.00

-.01

-.004

-.01

-.02

-.008

-.02

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

2017

2018

2019

2020

2021

2022

Washington D.C.

.015

.010

.005

.000

-.005

-.010

-.015

2017

2018

2019

2020

2021

2022

31

Alternative Methods for Calculating Fair Market Rents

Source: Author’s calculations

The first graph containing the business-cycle component for each of the 22 metros highlights the cyclical nature of rents as the pandemic began in 2020. The deviations from trend ranged from -2 to -12 percent in some areas. What is consistent is the cyclical downturn in all 22 areas and the subsequent acceleration in the business-cycle components beginning in early 2021. Most of the 22 areas had moved back into above-trend growth (where the cyclical component moved above the zero line) by the third quarter of 2021.

The second graph contains the rate of change (first difference) of the business-cycle components, which is equivalent to measuring the acceleration of the cyclical components and is used to identify areas with rapidly rising rents. If a metro area’s cyclical component is increasing at an increasing rate, rents are assumed to be rapidly rising. The second graph highlights that most of the 22 areas were experiencing acceleration in the business-cycle component throughout the first half of 2022.

Combining the band-pass filtering methodology with a monthly, market-derived dataset such as Apartment List could help identify periods of rapidly rising rents that could inform and update FMRs that are in place until the next forecast cycle is completed. An additional advantage to the Apartment List data is that they cover state, regional, metro, and city-level geographies for more than 500 rental markets, which would give HUD the ability to identify smaller areas experiencing rising rents with real-time data.

That component highlights the flexibility of using the band-pass approach, which requires only a single time series of rents for any area under analysis.

The Apartment List data are current through September 2021. The September two-bedroom rent can be compared with the HUD FY22 50-percent FMRs as currently calculated to determine any significant differences. Exhibit 19 contains the HUD two-bedroom FY22 FMR, Apartment List September 2021

two-bedroom rent, and the percentage difference.

32

Alternative Methods for Calculating Fair Market Rents

Exhibit 19. Comparison of HUD 50th Percentile Rents and Apartment List Rents Metro Area

HUD FY22 50th

Apartment List Sept. Percentage Difference

Percentile Rent 2-Bed

2021 Rent 2-Bed ($)

(%)

($)

Anchorage

1,335

1,503

-12.58

Atlanta

1,397

1,548

-10.10

Baltimore

1,518

1,680

-10.67

Boston

2,583

2,004

22.41

Chicago

1,456

1,373

5.70

Dallas

1,477

1,429

3.24

Denver

1,800

1,746

3.00

Detroit

1,162

1,148

1.20

Los Angeles

2,255

2,088

7.41

Miami

1,814

1,895

-4.44

Minneapolis

1,432

1,312

8.37

New York/New Jersey

2,505

1,873

25.22

Philadelphia

1,399

1,413

-1.00

Phoenix

1,417

1,687

-19.05

San Diego

2,433

2,298

5.55

Seattle

2,185

1,904

12.86

St. Louis

1,015

1,112

-9.55

Tampa

1,452

1,697

-16.87

Washington, DC

1,927

1,891

1.86

FMR = Fair Market Rent. FY = fiscal year.

Source: HUD, Apartment List

33

Alternative Methods for Calculating Fair Market Rents

Eight of 19 Apartment List metro rents were greater than the HUD FY22 calculated FMRs as of September 2021. The percentage difference for the eight metro areas ranged from 1 to 19 percent above HUD FMR values. Considering that those differences were calculated in September 2021, the acceleration in rents according to the Apartment List data could increase, albeit at a slower rate, but continue to create an even larger gap between HUD FMRs and market list rents. That discrepancy in market rents between datasets presents an opportunity to align—in real time—HUD FMRs and current pricing. A mechanism could be developed wherein the Apartment List monthly data are continuously updated and analyzed using the band-pass filter technique. If the acceleration in rents (the rate of change in the business-cycle component) is found to be increasing for some given number of months—say, 4 to 7

months—then an adjustment can be made to FMRs to align the static FMRs more closely with current market conditions. That effort could potentially prevent housing authorities from being required to undertake costly surveys to submit a request for an increase in local FMRs. In addition, that approach might be timelier to the needs of households looking for affordable housing. A fully outlined example is shown below.

Hypothetical Rent Adjustment Process:

1. Obtain updated monthly Apartment List rental data for current month.

2. Transform the monthly time series into the natural log.

3. Implement the Christiano-Fitzgerald Asymmetric BP filter with business-cycle frequency.

4. Take the first difference of the business-cycle component.

5. Compare with last month(s) to verify whether prices continue to accelerate.

6. If persistent acceleration triggers a threshold of 4 months or more, adjust FMRs upward.

34

Alternative Methods for Calculating Fair Market Rents

Conclusions

Making material improvements to two separate components of the HUD FMR trend market could have great importance for the way housing program voucher assignment and, ultimately, access to affordable housing are determined. In addition, developing statistical methodology to help identify markets that might be experiencing rapidly rising rents complements the trend factor modeling for the FMR update.

The approach undertaken here was to test the efficacy and accuracy of multivariate time series approaches to modeling the Rent of Primary Residence CPI component and the Fuels and Utilities CPI component.

The working hypothesis was that adding in additional economic drivers to model each component could produce more accurate forecasts and include economic theory in the modeling approach.

The econometric methodology used for this study included modeling the two CPI components in a vector autoregression/vector error correction framework. Those models treat all variables as endogenous and focus more on the underlying statistical properties and interaction of the data rather than trying to model the components as single equations with exogenous supply-and-demand relationships being estimated. In addition to using a VAR approach, another statistical approach was tested and implemented where appropriate. The theory of cointegration allows two or more stochastic time series to be modeled together, resulting in a long-run equilibrium relationship that results in variables not being able to diverge in the long run.

The Rent of Primary Residence CPI component was modeled as a VECM for 22 metro areas across the United States. Variables included in the VECM models included the Rent CPI component, a measure of real home prices, and a measure of real disposable personal income per capita. Long-run cointegrating relationships were found in all but one metro area and implemented in the model. Training and test sets were identified, and a seven-quarter in-sample forecast was used to evaluate the accuracy of the VECM

model, benchmarked against both pure time series ARIMA models and autoregressive distributed lag models (ARDL), following HUD’s approach to including local exogenous factors. The multivariate 35

Alternative Methods for Calculating Fair Market Rents

VECM model was evaluated against both an ARIMA time series model and an ARDL HUD model over the in-sample forecast horizon of 2018 through 2019. That timeframe was chosen to test the models in a more “normal” economic environment as compared with the current pandemic-driven environment. The VECM model outperformed the ARIMA model in 14 of 22 metro areas and the HUD ARDL model in 12

of 22 areas. The VECM was also evaluated against the HUD ARDL model over the period of 2019

through 2020, which included the pandemic. The VECM model outperformed the HUD ARDL model in 18 of 22 metro areas.

The Fuel and Utilities CPI component has been modeled in the past as a pure time series model with little improvement offered from including an additional regressor to the ARIMA(X) models. We proposed the VAR/VECM approach for the Fuel CPI component. The hypothesis was that individual energy prices may have explanatory power in helping explain past and future Fuel and Utilities CPI movements.

Variables under consideration included WTI crude, Henry Hub natural gas prices, and U.S. city average electricity prices. Ultimately, natural gas and electricity prices were used in the VECM models. The WTI price was entering early VAR specification, with little to no interaction with the other three variables. All variables under consideration were unit root processes and could be considered for cointegrating relationships with the VECM framework. Identifying strong statistical cointegrating relationships was much more difficult. Many of the regions’ cointegration tests were only significant at the 10-percent level or slightly higher. We decided that cointegrating relationships would still be imposed on those models that fell within that range. For any model that was outside the near-10-percent range, a VAR in first differences was estimated and used for the forecast evaluation. Eight of 22 VECM models outperformed the ARIMA models, which was not surprising due to the weaker statistical relationships that emerged in the VECM modeling process. The Fuel and Utilities CPI component has volatility that was difficult to characterize as purely seasonal; therefore, adjusting for seasonality did not improve the VECM model performance. The VECM model was not evaluated against any HUD-specific models for the fuel and utilities component because a similar ARIMA approach has been used by HUD.

36

Alternative Methods for Calculating Fair Market Rents

Identifying markets with rapidly rising rents was an additional research question to be investigated. Not only is this issue important for how the HUD FMR program addresses people’s needs, it also can help inform the approaches taken in setting the FMR through the trend factor modeling process. We investigated various statistical approaches to help better understand this question, including a fundamental approach using cointegration theory to model the equilibrium state of a rental market, calculating rent-to-income ratios, and using statistical decomposition techniques to isolate trend and cyclical components in trending rent series. Ultimately, the band-pass filtering approach was chosen as the most robust and offering the most flexibility for the research questions at hand.

Multiple alternative datasets were evaluated. Monthly market rent data from Apartment List were used in a case to study to implement the band-pass filtering approach to identifying markets with rapidly rising rents and using that information as an adjustment mechanism for published HUD FMRs. We outlined a workflow that included using the recuring monthly Apartment List data to determine if a market is

“rapidly rising” and then adjusting HUD FMRs to close the gap. That new approach could complement the way housing authorities currently perform surveys and make requests for FMR increases when they identify markets that have experienced accelerating prices. In addition, the alternative dataset is available for 500 cities and all 50 states, allowing for the implementation of robust statistical tools at a small geographic level.

The work done in this modeling project offers new and possibly improved methods for updating the FMR

trend factor components. More work could be done testing additional variables that could help improve the forecasting performance. In addition, smoothing techniques could be applied to the Fuel CPI component to model the underlying trend and improve the interaction with the energy prices used in this analysis. Identifying past periods of rapidly rising rents across metro regions is possible with a combination of statistical tools, implementing newer machine learning algorithms to large datasets of real-time data, which could help identify whether an area is currently in a period of rapidly rising rents.

Further research could be directed at better understanding the differences between both publicly available 37

Alternative Methods for Calculating Fair Market Rents

and proprietary datasets on rent prices. This modeling effort has revealed significant differences in price movements depending on which source is being evaluated, which could provide additional improvement to the overall FMR modeling process, especially in smaller areas where government data are not available on a real- or near-time basis.

38

Alternative Methods for Calculating Fair Market Rents

Final Considerations and Next Steps

2019 Senate Committee on Appropriations Report (S. Rept. 116-109)

“The Committee is concerned that where there is a significant fluctuation in local rental market conditions, HUD’s published fair market rents do not reflect the increased need in rental subsidy and the associated operating costs. As a result, some PHAs are conducting independent market surveys to more accurately reflect local market conditions for HUD’s review and consideration. However, some rental market surveys can be costly and an unviable option for PHAs that lack the expertise and capacity.

This is particularly true for smaller PHAs in markets where the local fair market rents are outpacing HUD’s annual determination of FMRs.”

COVID-19 Impact

In the intervening time since the Senate’s report, the issuance of the NOFA for this study (6/2/2020), and the selection of the research teams (11/30/2020), the COVID-19 pandemic has continued to have an impact on the economy, rental housing costs, utility costs, and inflation. The Census Bureau announced in November 2021 that as a result of the pandemic impacts on the American Community Survey (ACS), the 2020 ACS 1-year data do not meet its data quality standards (U.S. Census Bureau, 2022, n.d.). The pandemic may have similar impacts on 2021 ACS 1-year data and possibly into 2022 and beyond.

Inflation has also been increasing rapidly and, according to the January 2022 Department of Labor report increased in December 2021, at the fastest rate in 40 years. Increases in rental housing costs typically begin slowly and remain high once they rise. Even without the ACS 1-year data quality issue described above, the current Consumer Price Index (CPI) methodology used to calculate FY 2022 Fair Market Rents (FMRs), which includes Rent of Primary Residence, does not pick up those inflationary impacts in real time because it is only produced every 6 months. The ACS 1-year data used for the CPI calculations will continue to pose an issue at a minimum for FY 2023 and FY 2024 FMRs.

39

Alternative Methods for Calculating Fair Market Rents

Alternative Methodologies

The opportunity and necessity to do something different on an ongoing rather than a temporary basis clearly exist. HUD has publicly stated as much, and with the December 9, 2021, issuance of HUD Notice 2021-34 (Expedited Regulatory Waivers for the Public Housing and Housing Choice Voucher [including Mainstream and Mod Rehab] Programs) affirmatively identified 227 rental market areas with significant rental market fluctuations and provided an expedited waiver process for PHAs to request an exception payment standard up to 120 percent of the FMRs but only through December 31, 2022. To develop a more permanent solution, the study team has concluded the following:

• The Department’s FMR calculations would benefit from the use of real-time data sources and the improved FMR calculation methodology described in this study as an alternative to the existing CPI calculation. All three approaches to statistically identifying periods of rapidly rising rents—

bandpass filter, cointegration, and rent-to-income ratios—are data-driven in their approach and provide insights into how various factors drive rental markets. After analyzing how each method compared across metropolitan areas, the band-pass filtering approach appeared to be the most robust and consistent for identifying when markets are experiencing extreme movements in price.

• The Department, by statue, has to produce and publish FMRs once a year. However, this study’s alternative data sources and methods could also be used on a rolling basis for HUD approval of exception payment standards for PHAs’ voucher programs and then incorporated into the formulation of the following years’ FMRs. PIH Notice 2021-34 could serve as a template for implementation, as follows:

On a quarterly basis, the Department would determine eligible FMR areas with significant rental market fluctuations or rapidly rising rents by comparing alternative FMRs using this study’s data sources, methods, and attendant recommendations by using private-sector data sources covering the FMR area(s), such as ApartmentList.com. Where use of the average private-sector rent data and study methodology 40

Alternative Methods for Calculating Fair Market Rents

demonstrate FMR increases at or above a certain percentage threshold (for example, 5 or 10 percent), the Department would deem those areas as “FMR Area Determined to Have Significant Rental Market Fluctuations,” as one of its three criteria to meet for expedited exception payment standard waiver request submissions and evaluations. Using the Department’s identical approach under PIH Notice 2021-34 with the study’s alternative modifications would provide an immediate and possible rolling measure throughout each year of applicable FMRs that would be outside the “basic range” (90 through 110 percent of FMRs) and therefore justify expedited exception payment standard waiver submissions and review.

• These recommendations are consistent with Section 8(c)(1) of the U.S. Housing Act of 1937, which require HUD to calculate FMRs annually based “on the most recent available data” (42

USC 1437f).

Implementation

Alternative Final FMR Increases Would Take Effect upon Publication: Under the alternative FMR

data sources and methods, all of the results of all FMR increases would take effect , including those with local CPI replacement data, upon publication. This recommendation conforms with the Department’s existing regulatory and policy treatment of annual FMR increases, which would remain in place.

Alternative Final FMR Decreases of No More than 10 Percent Would Take Effect upon Publication: 24 CFR 888.113(b) limits decreases in the annual change in FMRs to no more than 10

percent. This regulatory treatment would remain in place under the alternative FMR.

Possible Areas for Further Study or Review

The Department could also study and possibly use a modified version of these alternative data sources and methods in place of not only the CPI factor but also the Recent Mover Adjustment Factor, ACS 5-year 2-Bedroom Adjusted Standard Quality Gross Rent Factor, and Trend Factor Type and Small Area FMR calculations.

41

Alternative Methods for Calculating Fair Market Rents

Recent Mover Adjustment Factor

As previously noted, the ACS 1-year data are insufficient to capture rapidly rising rents compared with the more recent 12-month, 15-month, 18-month, or 24 month “recent mover” data from FMR

reevaluations and appeals, which has been historically true before and after HUD’s data sources and method rulemaking improvements over the past several years. The Department could compare and possibly replace the ACS 1-year data with data from the most recent 12-month, 15-month, or 18-month period available before its issuance of proposed FMRs, using the ApartmentList.com data or other similar sources.

ACS 5-Year Factor and Trend Factor

HUD contracted with 2M Research for a study titled Deriving Local Trend Factors for Fair Market Rent Estimation, which was published in March 2019 (2M Research, 2019). On the basis of the study’s findings and HUD’s rulemaking, some of the improvements were proposed2 and later adopted, starting with the Department’s FY 2020 FMRs. 3 As a result of the study’s findings, HUD replaced the national trend factor with local and regional trend factors. HUD’s replacement of its previous trend factor helped address current market conditions, including those in which rent prices are escalating rapidly.

The Phase II analysis of that report suggested that localization of trend factors is feasible and, in certain areas, may lead to more accurate trend factors and will improve the accuracy of FMRs. The Axiometrics data, although appealing, is based on a limited number of apartment sites, and the monthly series is relatively short. The ApartmentList.com monthly dataset, unlike Axiometrics data, is based on the universe of apartment units and is derived from real-time market conditions for rental contracts rather than a survey-based method like ACS data. The entire ApartmentList.com database also covers state, 2 “Proposed Changes to the Methodology Used for Estimating Fair Market Rents.” Published in the Federal Register as 84 Fed. Reg., 26141–26144.

3 “Fair Market Rents for the Housing Choice Voucher Program, Moderate Rehabilitation Single Room Occupancy Program, and Other Programs Fiscal Year 2020.” FR–6161–N–02. 2019-18608.pdf (govinfo.gov)

42

Alternative Methods for Calculating Fair Market Rents

region, metro, and city-level geographies. The Department could further examine the potential of the ApartmentList.com database in improving predictions of FMR in metro areas.

Small Area FMRs (SAFMRs)

The study team is aware that outside the Census Bureau for ZIP Code Tabulation Areas (ZCTAs), the Department currently uses a considerable number of data sources and methods for formulation of FMRs, which are also used as components of the existing Small Area FMR (SAFMR) calculations. The Department may wish to consider where a methodology intersection exists between the FMRs and the SAFMRs and whether the ApartmentList.com and utility data alternatives employed in this study could be used for the existing FMR-based elements of the SAFMR calculations instead.

43

Alternative Methods for Calculating Fair Market Rents

Appendix A: Model Estimations and Forecast Evaluations

Alaska

Vector Error Correction Estimates

Sample (adjusted): 1996Q3 2018Q4

Included observations: 90 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_ALAS(-1))

1.000000

LOG(RINCOME_ALAS... -2.129231

(0.15490)

[-13.7457]

LOG(RHPRIC_ALAS(-1)) -0.346758

(0.11777)

[ -2.94444]

C

6.578377

R-squared

0.812884

0.481473

0.340851

Adj. R-squared

0.771873

0.367824

0.196380

Sum sq. resids

0.000344

0.003607

0.009076

S.E. equation

0.002172

0.007029

0.011150

F-statistic

19.82080

4.236469

2.359302

Log likelihood

433.6142

327.9090

286.3848

Akaike AIC

-9.258092

-6.909088

-5.986328

Schwarz SC

-8.785906

-6.436902

-5.514142

Mean dependent

0.006137

0.003899

0.003224

S.D. dependent

0.004547

0.008841

0.012438

44

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(RENT_ALAS)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q4

Included observations: 95

Convergence achieved after 27 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.900044

0.202201

4.451235

0.0000

AR(1)

1.311725

0.150824

8.697076

0.0000

AR(2)

-0.538509

0.146773

-3.668998

0.0004

MA(1)

0.389484

0.099862

3.900220

0.0002

MA(2)

-1.158313

0.113859

-10.17326

0.0000

MA(3)

0.203316

0.123914

1.640782

0.1045

MA(4)

0.803141

0.097149

8.267146

0.0000

SIGMASQ

0.092430

0.015466

5.976190

0.0000

R-squared

0.825842 Mean dependent var

0.931419

Adjusted R-squared

0.811829 S.D. dependent var

0.732372

S.E. of regression

0.317693 Akaike info criterion

0.716689

Sum squared resid

8.780834 Schwarz criterion

0.931752

Log likelihood

-26.04271 Hannan-Quinn criter.

0.803590

F-statistic

58.93506 Durbin-Watson stat

1.869544

Prob(F-statistic)

0.000000

45

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_ALAS_A

45.55066

0.0066

RENT_ALAS_V

35.43657

0.0095

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

5.887818

0.0042

0.9979

0.0021

Sq Error

2.539083

0.0640

0.9680

0.0320

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_ALAS_A

4.669243 4.030663 2.021409 1.994290 0.011553 5.108689

RENT_ALAS_V

3.936904 3.175732 1.594002 1.574667 0.009761 4.320455

Simple mean

4.294964 3.603197 1.807705 1.784726 0.010638 4.705738

Forecast Comparison Graph

210

208

206

204

202

200

198 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_ALAS

RENT_ALAS_A

RENT_ALAS (C_ALAS)

Simple mean

46

Alternative Methods for Calculating Fair Market Rents

Atlanta:

Vector Error Correction Estimates

Sample (adjusted): 1986Q1 2018Q4

Included observations: 81 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_ATL(-1))

1.000000

LOG(RINCOME_ATL(-1))

-2.058413

(0.16266)

[-12.6543]

LOG(RHPRICE_ATL(-1))

-0.481410

(0.16689)

[-2.88459]

C

5.155842

R-squared

0.606062

0.627844

0.699016

Adj. R-squared

0.456638

0.486681

0.584849

Sum sq. resids

0.003988

0.001378

0.007941

S.E. equation

0.008292

0.004874

0.011701

F-statistic

4.055975

4.447662

6.122771

Log likelihood

286.7812

329.8232

258.8897

Akaike AIC

-6.513115

-7.575881

-5.824438

Schwarz SC

-5.833210

-6.895976

-5.144532

Mean dependent

0.005767

0.002729

0.002212

S.D. dependent

0.011249

0.006803

0.018160

47

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_ATL)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 111

Convergence achieved after 8 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.010705

0.003574

2.994922

0.0034

AR(1)

0.157395

0.092536

1.700909

0.0919

AR(2)

0.306839

0.067684

4.533385

0.0000

AR(3)

-0.082684

0.118316

-0.698843

0.4862

AR(4)

0.361024

0.081768

4.415251

0.0000

SIGMASQ

0.000115

1.28E-05

8.958149

0.0000

R-squared

0.364082 Mean dependent var

0.008900

Adjusted R-squared

0.333800 S.D. dependent var

0.013496

S.E. of regression

0.011016 Akaike info criterion

-6.105857

Sum squared resid

0.012742 Schwarz criterion

-5.959396

Log likelihood

344.8751 Hannan-Quinn criter.

-6.046442

F-statistic

12.02311 Durbin-Watson stat

1.915574

48

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_ATL_V

0.631977

0.4569

RENT_ATL_A

13.74701

0.0100

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-1.374736

0.2116

0.1058

0.8942

Sq Error

-1.544491

0.1664

0.0832

0.9168

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_ATL_V

2.293374 1.903201 0.638614 0.641581 0.003883 0.650854

RENT_ATL_A

3.854335 3.222705 1.075973 1.067915 0.006471 1.068486

Simple mean

1.508189 1.249091 0.420217 0.419526 0.002543 0.423210

Forecast Comparison Graph

320

300

280

260

240 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_ATL

RENT_ATL (CE_ATL)

RENT_ATL_A

Simple mean

49

Alternative Methods for Calculating Fair Market Rents

Baltimore

Vector Error Correction Estimates

Sample (adjusted): 1999Q1 2018Q2

Included observations: 78 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_BAL(-1))

1.000000

LOG(RINCOME_BAL(-1)) -3.855242

(0.33221)

[-11.6048]

LOG(RHPRICE_BAL(-1))

0.199718

(0.11674)

[ 1.71077]

C

15.37901

R-squared

0.342677

0.236377

0.592870

Adj. R-squared

0.244569

0.122403

0.532105

Sum sq. resids

0.003036

0.002577

0.012742

S.E. equation

0.006732

0.006201

0.013790

F-statistic

3.492862

2.073962

9.756679

Log likelihood

285.3235

291.7260

229.3868

Akaike AIC

-7.033936

-7.198104

-5.599661

Schwarz SC

-6.701580

-6.865747

-5.267305

Mean dependent

0.009418

0.003064

0.003956

S.D. dependent

0.007745

0.006620

0.020160

50

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_BAL)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1998Q2 2018Q2

Included observations: 81

Convergence achieved after 6 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.009454

0.000979

9.659102

0.0000

AR(1)

0.437531

0.093128

4.698174

0.0000

AR(2)

-0.461934

0.101065

-4.570666

0.0000

AR(3)

0.266164

0.102760

2.590150

0.0115

SIGMASQ

4.32E-05

7.55E-06

5.723120

0.0000

R-squared

0.246950 Mean dependent var

0.009458

Adjusted R-squared

0.207316 S.D. dependent var

0.007620

S.E. of regression

0.006784 Akaike info criterion

-7.081564

Sum squared resid

0.003498 Schwarz criterion

-6.933758

Log likelihood

291.8033 Hannan-Quinn criter.

-7.022262

F-statistic

6.230720 Durbin-Watson stat

1.944266

Prob(F-statistic)

0.000217

51

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_BAL_A

91.21358

0.0002

RENT_BAL_V

192.9742

0.0000

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-3.028704

0.0231

0.0116

0.9884

Sq Error

-2.720041

0.0346

0.0173

0.9827

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_BAL_A

6.848337 5.545568 1.522629 1.505443 0.009373 4.438792

RENT_BAL_V

8.892730 7.229195 1.984691 1.955457 0.012134 5.775879

Simple mean

7.854543 6.276358 1.722911 1.700117 0.010734 5.098680

Forecast Comparison Graph

390

380

370

360

350

340

330

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

2016

2017

2018

2019

2020

RENT_BAL

RENT_BAL_A

RENT_BAL (CE_BAL)

Simple mean

52

Alternative Methods for Calculating Fair Market Rents

Boston:

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_BOS(-1))

1.000000

LOG(RINCOME_BOS(-1)) -1.744261

(0.06830)

[-25.5387]

LOG(RHPRICE_BOS(-1)) -0.307258

(0.05945)

[-5.16823]

C

4.144789

R-squared

0.414463

0.663965

0.731082

Adj. R-squared

0.334390

0.618012

0.694307

Sum sq. resids

0.007198

0.002123

0.011364

S.E. equation

0.007843

0.004259

0.009855

F-statistic

5.176046

14.44864

19.87977

Log likelihood

468.5956

550.4132

437.9986

Akaike AIC

-6.740233

-7.961390

-6.283561

Schwarz SC

-6.372597

-7.593754

-5.915925

Mean dependent

0.008668

0.003975

0.003059

S.D. dependent

0.009614

0.006891

0.017825

53

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_BOS,2)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q3 2018Q4

Included observations: 154

Convergence achieved after 27 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-9.81E-05

0.000260

-0.376582

0.7070

AR(1)

-0.991263

0.006127

-161.7970

0.0000

MA(1)

-0.215759

0.082596

-2.612210

0.0099

MA(2)

-0.822241

0.071180

-11.55151

0.0000

MA(3)

0.368648

0.086144

4.279444

0.0000

MA(4)

0.304325

0.068415

4.448201

0.0000

SIGMASQ

9.06E-05

8.38E-06

10.80518

0.0000

R-squared

0.729970 Mean dependent var

9.21E-05

Adjusted R-squared

0.718949 S.D. dependent var

0.018377

S.E. of regression

0.009742 Akaike info criterion

-6.354506

Sum squared resid

0.013952 Schwarz criterion

-6.216462

Log likelihood

496.2969 Hannan-Quinn criter.

-6.298433

F-statistic

66.23078 Durbin-Watson stat

1.949906

Prob(F-statistic)

0.000000

54

Alternative Methods for Calculating Fair Market Rents

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_BOS_V

13.01435

0.0113

RENT_BOS_A

241.9841

0.0000

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-5.138722

0.0013

0.0007

0.9993

Sq Error

-3.329822

0.0126

0.0063

0.9937

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_BOS_V

4.869779 4.603662 1.249625 1.241018 0.006594 1.750959

RENT_BOS_A

14.04020 12.87119 3.484416 3.414471 0.018799 5.099799

Simple mean

9.423546 8.737426 2.367020 2.335211 0.012689 3.415835

Forecast Comparison Graph

400

380

360

340

320 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_BOS

RENT_BOS (CE_BOS)

RENT_BOS_A

Simple mean

55

Alternative Methods for Calculating Fair Market Rents

Dallas:

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_DAL(-1))

1.000000

LOG(RINCOME_DAL(-1)) -1.329742

(0.08388)

[-15.8532]

LOG(RHPRICE_DAL(-1))

-0.260749

(0.10913)

[-2.38942]

C

1.691189

R-squared

0.351637

0.554781

0.546328

Adj. R-squared

0.262971

0.493897

0.484287

Sum sq. resids

0.007238

0.004180

0.010596

S.E. equation

0.007865

0.005977

0.009516

F-statistic

3.965896

9.112018

8.805961

Log likelihood

468.2189

505.0012

442.6875

Akaike AIC

-6.734611

-7.283600

-6.353545

Schwarz SC

-6.366975

-6.915964

-5.985909

Mean dependent

0.006699

0.003810

0.001110

S.D. dependent

0.009162

0.008402

0.013252

56

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_DAL)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 155

Convergence achieved after 201 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.008295

0.001639

5.059621

0.0000

AR(1)

-0.573466

0.076886

-7.458629

0.0000

AR(2)

0.773007

0.090216

8.568396

0.0000

AR(3)

-0.072509

0.099937

-0.725545

0.4693

AR(4)

-0.489949

0.093602

-5.234363

0.0000

MA(1)

0.530853

48.31357

0.010988

0.9912

MA(2)

-0.711802

84.00603

-0.008473

0.9933

MA(3)

0.530856

78.39426

0.006772

0.9946

MA(4)

0.999998

235.9915

0.004237

0.9966

SIGMASQ

0.000107

0.002106

0.050903

0.9595

R-squared

0.338699 Mean dependent var

0.008263

Adjusted R-squared

0.297653 S.D. dependent var

0.012775

S.E. of regression

0.010706 Akaike info criterion

-6.093756

Sum squared resid

0.016620 Schwarz criterion

-5.897406

Log likelihood

482.2661 Hannan-Quinn criter.

-6.014003

F-statistic

8.251634 Durbin-Watson stat

1.943366

Prob(F-statistic)

0.000000

57

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_DAL_V

11.42477

0.0149

RENT_DAL_A

7.187462

0.0365

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-6.373901

0.0004

0.0002

0.9998

Sq Error

-4.346105

0.0034

0.0017

0.9983

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_DAL_V

4.316429 3.674193 1.285603 1.296911 0.007697 1.521532

RENT_DAL_A

8.034022 7.437187 2.617630 2.658024 0.014429 2.851531

Forecast Comparison Graph

300

280

260

240

220 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_DAL

RENT_DAL (CE_DAL)

RENT_DAL_A

Simple mean

58

Alternative Methods for Calculating Fair Market Rents

Denver:

Vector Error Correction Estimates

Sample (adjusted): 1986Q3 2018Q4

Included observations: 130 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_DEN(-1))

1.000000

LOG(RINCOME_DEN(-1)) -15.58382

(3.21545)

[ -4.84654]

LOG(RHPRICE_DEN(-1)) -9.732707

(1.67891)

[-5.79704]

C

-89.94895

R-squared

0.889714

0.602447

0.585827

Adj. R-squared

0.874099

0.546157

0.527183

Sum sq. resids

0.000689

0.003947

0.010847

S.E. equation

0.002469

0.005910

0.009797

F-statistic

56.97578

10.70244

9.989555

Log likelihood

605.1720

491.6951

425.9795

Akaike AIC

-9.048800

-7.303002

-6.291992

Schwarz SC

-8.673814

-6.928017

-5.917007

Mean dependent

0.008261

0.003084

0.004643

S.D. dependent

0.006958

0.008772

0.014248

59

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_DEN)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1985Q1 2018Q4

Included observations: 136

Convergence achieved after 7 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.008017

0.002302

3.482884

0.0007

AR(1)

0.738090

0.064495

11.44417

0.0000

AR(2)

0.276202

0.110113

2.508348

0.0134

AR(3)

0.129568

0.145331

0.891536

0.3743

AR(4)

-0.245824

0.080674

-3.047125

0.0028

SIGMASQ

7.17E-06

9.12E-07

7.862088

0.0000

R-squared

0.846009 Mean dependent var

0.008097

Adjusted R-squared

0.840087 S.D. dependent var

0.006850

S.E. of regression

0.002739 Akaike info criterion

-8.904165

Sum squared resid

0.000975 Schwarz criterion

-8.775666

Log likelihood

611.4832 Hannan-Quinn criter.

-8.851946

F-statistic

142.8416 Durbin-Watson stat

1.861394

Prob(F-statistic)

0.000000

60

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_DEN_V

51.56764

0.0004

RENT_DEN_A

67.83486

0.0002

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-3.082178

0.0178

0.0089

0.9911

Sq Error

-1.936651

0.0940

0.0470

0.9530

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_DEN_V

1.794248 1.228874 0.370655 0.369219 0.002723 1.281357

RENT_DEN_A

3.695088 2.684212 0.809901 0.803815 0.005596 2.641441

Simple mean

2.741494 1.953213 0.589261 0.585907 0.004156 1.959104

Forecast Comparison Graph

350

340

330

320

310

300

290 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_DEN

RENT_DEN (_DEN_B)

RENT_DEN_A

Simple mean

61

Alternative Methods for Calculating Fair Market Rents

Detroit:

Vector Error Correction Estimates

Sample (adjusted): 1985Q2 2018Q4

Included observations: 135 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_DET(-1))

1.000000

LOG(RINCOME_DET(-1)) -2.256159

(0.15762)

[-14.3136]

LOG(RHPRICE_DET(-1))

0.436874

(0.08612)

[ 5.07291]

C

6.549442

R-squared

0.260205

0.427976

0.639976

Adj. R-squared

0.180723

0.366519

0.601296

Sum sq. resids

0.006886

0.004151

0.018667

S.E. equation

0.007544

0.005857

0.012421

F-statistic

3.273758

6.963812

16.54532

Log likelihood

475.5816

509.7495

408.2651

Akaike AIC

-6.838246

-7.344437

-5.840964

Schwarz SC

-6.536958

-7.043149

-5.539676

Mean dependent

0.006519

0.003122

0.002980

S.D. dependent

0.008334

0.007359

0.019671

62

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(RENT_DET)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 155

Convergence achieved after 17 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

1.160387

0.153662

7.551576

0.0000

AR(1)

0.397697

0.189420

2.099556

0.0375

MA(1)

-0.433969

0.184955

-2.346349

0.0203

MA(2)

-0.016197

0.074543

-0.217278

0.8283

MA(3)

0.026373

0.083165

0.317117

0.7516

MA(4)

0.289696

0.086954

3.331615

0.0011

SIGMASQ

1.597729

0.178997

8.925998

0.0000

R-squared

0.094298 Mean dependent var

1.137845

Adjusted R-squared

0.057581 S.D. dependent var

1.332491

S.E. of regression

1.293560 Akaike info criterion

3.399959

Sum squared resid

247.6480 Schwarz criterion

3.537404

Log likelihood

-256.4968 Hannan-Quinn criter.

3.455786

F-statistic

2.568199 Durbin-Watson stat

1.986862

Prob(F-statistic)

0.021421

63

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_DET_V

1.365324

0.2869

RENT_DET_A

1.115452

0.3316

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

1.260599

0.2478

0.8761

0.1239

Sq Error

1.354311

0.2177

0.8911

0.1089

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_DET_V

2.363391 2.054555 0.758504 0.754967 0.004361 0.945846

RENT_DET_A

1.529954 1.227330 0.453382 0.454314 0.002834 0.617122

Simple mean

1.518163 1.417241 0.524598 0.523982 0.002807 0.612607

Forecast Comparison Graph

280

270

260

250

240 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_DET

RENT_DET (CE_DET)

RENT_DET_A

Simple mean

64

Alternative Methods for Calculating Fair Market Rents

Honolulu:

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_HON(-1))

1.000000

LOG(RINCOME_HON(-1)) 1.049293

(0.72604)

[ 1.44524]

LOG(RHPRICE_HON(-1)) -1.876770

(0.28422)

[-6.60319]

C

-11.52515

R-squared

0.905122

0.645925

0.601157

Adj. R-squared

0.892147

0.597505

0.546614

Sum sq. resids

0.000725

0.001501

0.023333

S.E. equation

0.002489

0.003581

0.014122

F-statistic

69.75989

13.33991

11.02177

Log likelihood

622.4117

573.6386

389.7952

Akaike AIC

-9.035996

-8.308039

-5.564108

Schwarz SC

-8.668360

-7.940403

-5.196471

Mean dependent

0.007993

0.002265

0.005850

S.D. dependent

0.007578

0.005645

0.020973

65

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_HON)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1984Q2 2018Q4

Included observations: 139

Convergence achieved after 125 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.008051

0.003249

2.477711

0.0145

AR(1)

-0.084354

0.081930

-1.029589

0.3051

AR(2)

0.181659

0.099682

1.822375

0.0707

AR(3)

0.221055

0.122347

1.806789

0.0731

AR(4)

0.408591

0.073487

5.560037

0.0000

MA(1)

1.014108

4259.984

0.000238

0.9998

MA(2)

1.014106

6062.239

0.000167

0.9999

MA(3)

0.999995

10179.19

9.82E-05

0.9999

SIGMASQ

5.41E-06

0.011313

0.000478

0.9996

R-squared

0.902242 Mean dependent var

0.008115

Adjusted R-squared

0.896226 S.D. dependent var

0.007467

S.E. of regression

0.002406 Akaike info criterion

-9.078173

Sum squared resid

0.000752 Schwarz criterion

-8.888171

Log likelihood

639.9330 Hannan-Quinn criter.

-9.000961

F-statistic

149.9771 Durbin-Watson stat

2.073851

Prob(F-statistic)

0.000000

66

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_HON_V

189.0363

0.0000

RENT_HON_A

88.51229

0.0001

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

3.066967

0.0181

0.9909

0.0091

Sq Error

2.078474

0.0763

0.9619

0.0381

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_HON_V

8.474540 6.284118 1.839697 1.870125 0.012806 2.169584

RENT_HON_A

5.690673 4.122726 1.206450 1.219810 0.008569 1.451632

Simple mean

7.074495 5.184238 1.517205 1.538194 0.010672 1.808523

Forecast Comparison Graph

350

340

330

320

310

300 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_HON

RENT_HON (CE_HON)

RENT_HON_A

Simple mean

67

Alternative Methods for Calculating Fair Market Rents

Houston:

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_HOU(-1))

1.000000

LOG(RINCOME_HOU(-1)) -1.456060

(0.20694)

[-7.03602]

LOG(RHPRICE_HOU(-1)) -0.407013

(0.22286)

[-1.82628]

C

2.442646

R-squared

0.301219

0.493374

0.417036

Adj. R-squared

0.205659

0.424091

0.337314

Sum sq. resids

0.008649

0.005371

0.013216

S.E. equation

0.008598

0.006775

0.010628

F-statistic

3.152150

7.121213

5.231147

Log likelihood

456.2855

488.2124

427.8806

Akaike AIC

-6.556500

-7.033021

-6.132546

Schwarz SC

-6.188864

-6.665384

-5.764909

Mean dependent

0.007361

0.003822

0.001934

S.D. dependent

0.009647

0.008928

0.013056

68

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_HOU)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 155

Convergence achieved after 110 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.007344

0.000423

17.36014

0.0000

AR(1)

0.447743

0.083229

5.379672

0.0000

AR(2)

1.308352

0.081999

15.95576

0.0000

AR(3)

-0.372238

0.093298

-3.989776

0.0001

AR(4)

-0.459069

0.089924

-5.105076

0.0000

MA(1)

-0.768534

73.33089

-0.010480

0.9917

MA(2)

-0.784085

14.45584

-0.054240

0.9568

MA(3)

0.768535

71.38801

0.010766

0.9914

MA(4)

-0.215915

32.38733

-0.006667

0.9947

SIGMASQ

0.000124

0.005287

0.023537

0.9813

R-squared

0.417957 Mean dependent var

0.007785

Adjusted R-squared

0.381830 S.D. dependent var

0.014669

S.E. of regression

0.011533 Akaike info criterion

-5.981302

Sum squared resid

0.019287 Schwarz criterion

-5.784952

Log likelihood

473.5509 Hannan-Quinn criter.

-5.901549

F-statistic

11.56917 Durbin-Watson stat

1.984925

Prob(F-statistic)

0.000000

69

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_HOU_V

0.035047

0.8577

RENT_HOU_A

3.582755

0.1072

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-4.399388

0.0032

0.0016

0.9984

Sq Error

-3.331562

0.0126

0.0063

0.9937

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_HOU_V

1.766428 1.461466 0.551808 0.551046 0.003318 0.522468

RENT_HOU_A

3.042610 2.904132 1.090830 1.094861 0.005738 1.139875

Simple mean

2.118893 1.820610 0.686964 0.687777 0.003988 0.705700

Forecast Comparison Graph

280

270

260

250

240 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_HOU

RENT_HOU (CE_HOU)

RENT_HOU_A

Simple mean

70

Alternative Methods for Calculating Fair Market Rents

Los Angeles:

Vector Error Correction Estimates

Sample (adjusted): 1996Q3 2018Q4

Included observations: 90 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_LA(-1))

1.000000

LOG(RINOME_LA(-1))

-2.355012

(0.24864)

[-9.47153]

LOG(RHPRICE_LA(-1))

-0.541792

(0.09780)

[-5.53952]

C

6.745448

R-squared

0.781346

0.636483

0.854440

Adj. R-squared

0.733422

0.556808

0.822537

Sum sq. resids

0.000504

0.002174

0.009349

S.E. equation

0.002627

0.005458

0.011317

F-statistic

16.30379

7.988506

26.78204

Log likelihood

416.5005

350.6825

285.0496

Akaike AIC

-8.877789

-7.415167

-5.956657

Schwarz SC

-8.405603

-6.942981

-5.484470

Mean dependent

0.009623

0.003279

0.006735

S.D. dependent

0.005087

0.008198

0.026864

71

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(RENT_LA)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q4

Included observations: 95

Convergence achieved after 8 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

2.421947

0.939463

2.578011

0.0116

AR(1)

0.750318

0.101620

7.383537

0.0000

AR(2)

-0.164550

0.120125

-1.369828

0.1741

AR(3)

0.349645

0.074262

4.708237

0.0000

SIGMASQ

0.538070

0.065622

8.199536

0.0000

R-squared

0.744516 Mean dependent var

2.288049

Adjusted R-squared

0.733161 S.D. dependent var

1.458933

S.E. of regression

0.753633 Akaike info criterion

2.344130

Sum squared resid

51.11664 Schwarz criterion

2.478545

Log likelihood

-106.3462 Hannan-Quinn criter.

2.398444

F-statistic

65.56817 Durbin-Watson stat

1.869976

Prob(F-statistic)

0.000000

72

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_LA_A

0.077158

0.7992

RENT_LA_V

1.734135

0.2794

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-1.557231

0.1944

0.0972

0.9028

Sq Error

-1.265542

0.2744

0.1372

0.8628

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_LA_A

0.545109 0.434799 0.110842 0.110861 0.000703 0.129611

RENT_LA_V

1.021389 0.788434 0.201651 0.201990 0.001319 0.244708

Simple mean

0.705732 0.495800 0.127008 0.127168 0.000911 0.169103

Forecast Comparison Graph

420

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360

340

320 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_LA

RENT_LA_A

RENT_LA (ICE_LA)

Simple mean

73

Alternative Methods for Calculating Fair Market Rents

Miami:

Vector Error Correction Estimates

Sample (adjusted): 1985Q2 2018Q4

Included observations: 135 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_MIA(-1))

1.000000

LOG(RINCOME_MIA(-1))

-35.78269

(8.12411)

[-4.40451]

LOG(RHPRICE_MIA(-1))

11.70248

(2.78813)

[ 4.19725]

C

180.0218

R-squared

0.296012

0.447379

0.599627

Adj. R-squared

0.220377

0.388006

0.556612

Sum sq. resids

0.009421

0.005404

0.043530

S.E. equation

0.008824

0.006683

0.018967

F-statistic

3.913687

7.535116

13.93988

Log likelihood

454.4272

491.9360

351.1143

Akaike AIC

-6.524847

-7.080533

-4.994286

Schwarz SC

-6.223560

-6.779245

-4.692998

Mean dependent

0.008315

0.002507

0.004676

S.D. dependent

0.009993

0.008543

0.028485

74

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_MIA)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 155

Convergence achieved after 16 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.009370

0.002086

4.493001

0.0000

AR(1)

0.799589

0.090253

8.859445

0.0000

MA(1)

-0.839504

0.106634

-7.872791

0.0000

MA(2)

0.070826

0.061759

1.146817

0.2533

MA(3)

0.179782

0.071714

2.506947

0.0133

SIGMASQ

0.000132

8.44E-06

15.59602

0.0000

R-squared

0.089350 Mean dependent var

0.008914

Adjusted R-squared

0.058792 S.D. dependent var

0.012062

S.E. of regression

0.011702 Akaike info criterion

-6.017403

Sum squared resid

0.020405 Schwarz criterion

-5.899593

Log likelihood

472.3487 Hannan-Quinn criter.

-5.969551

F-statistic

2.923894 Durbin-Watson stat

1.964227

Prob(F-statistic)

0.015080

75

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_MIA_V

39.36325

0.0008

RENT_MIA_A

48.99126

0.0004

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-2.703067

0.0305

0.0153

0.9847

Sq Error

-2.410766

0.0467

0.0234

0.9766

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_MIA_V

3.758380 3.505322 1.077397 1.074559 0.005775 1.759710

RENT_MIA_A

4.237616 3.917749 1.203371 1.198648 0.006507 2.006509

Simple mean

3.994764 3.711535 1.140384 1.136640 0.006136 1.881696

Forecast Comparison Graph

340

330

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280 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_MIA

RENT_MIA (CE_MIA)

RENT_MIA_A

Simple mean

76

Alternative Methods for Calculating Fair Market Rents

Minneapolis:

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_MIN_V

330.5244

0.0000

RENT_MIN_A

159.4966

0.0000

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

4.176599

0.0042

0.9979

0.0021

Sq Error

2.562384

0.0374

0.9813

0.0187

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_MIN_V

4.285384 3.575609 1.203962 1.214316 0.007371 1.450153

RENT_MIN_A

1.585515 1.293454 0.435035 0.436441 0.002716 0.536292

Simple mean

2.935069 2.434532 0.819499 0.824338 0.005038 0.993115

Forecast Comparison Graph

310

300

290

280

270

260

250 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_MIN

RENT_MIN (CE_MIN)

RENT_MIN_A

Simple mean

77

Alternative Methods for Calculating Fair Market Rents

New York/New Jersey:

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_NYNJ(-1))

1.000000

LOG(RINCOME_NYNJ(-1)) 0.392171

(0.57711)

[ 0.67954]

LOG(RHPRICE_NYNJ(-1)) -1.828266

(0.31379)

[-5.82649]

C

-7.791747

R-squared

0.417357

0.589082

0.750705

Adj. R-squared

0.337680

0.532888

0.716613

Sum sq. resids

0.002163

0.003078

0.011981

S.E. equation

0.004299

0.005129

0.010119

F-statistic

5.238071

10.48304

22.02022

Log likelihood

549.1550

525.5001

434.4565

Akaike AIC

-7.942613

-7.589554

-6.230694

Schwarz SC

-7.574976

-7.221917

-5.863057

Mean dependent

0.009455

0.003703

0.003860

S.D. dependent

0.005283

0.007505

0.019009

78

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_NYNJ,2)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q3 2018Q4

Included observations: 154

Convergence achieved after 104 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-8.67E-05

7.70E-05

-1.125675

0.2622

AR(1)

-1.289865

0.163804

-7.874417

0.0000

AR(2)

-1.512411

0.084962

-17.80104

0.0000

AR(3)

-1.133690

0.164383

-6.896615

0.0000

AR(4)

-0.331509

0.076088

-4.356920

0.0000

MA(1)

0.311377

4.926920

0.063199

0.9497

MA(2)

0.383120

1.288210

0.297405

0.7666

MA(3)

-0.165582

10.62494

-0.015584

0.9876

MA(4)

-0.621946

48.84732

-0.012732

0.9899

SIGMASQ

2.16E-05

0.000366

0.058976

0.9531

R-squared

0.582294 Mean dependent var

-3.09E-05

Adjusted R-squared

0.556187 S.D. dependent var

0.007216

S.E. of regression

0.004807 Akaike info criterion

-7.729155

Sum squared resid

0.003328 Schwarz criterion

-7.531951

Log likelihood

605.1450 Hannan-Quinn criter.

-7.649051

F-statistic

22.30444 Durbin-Watson stat

1.971309

Prob(F-statistic)

0.000000

79

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_NYNJ_V

14.28053

0.0092

RENT_NYNJ_A

0.456994

0.5242

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-1.676192

0.1376

0.0688

0.9312

Sq Error

-1.456012

0.1887

0.0944

0.9056

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_NYNJ_V

2.709068 2.319197 0.571646 0.571583 0.003345 1.306948

RENT_NYNJ_A

3.733015 3.558492 0.878472 0.882741 0.004628 1.789140

Simple mean

2.624613 2.358847 0.583448 0.585350 0.003247 1.263116

Forecast Comparison Graph

420

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370 III IV I II III IV I II III IV I II III IV I II III IV

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2017

2018

2019

2020

RENT_NYNJ

RENT_NYNJ (E_NYNJ)

RENT_NYNJ_A

Simple mean

80

Alternative Methods for Calculating Fair Market Rents

Philadelphia:

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_PHIL(-1))

1.000000

LOG(RINCOME_PHIL(-1)) 0.025402

(0.34760)

[ 0.07308]

LOG(RHPRICE_PHIL(-1)) -1.320528

(0.22906)

[-5.76500]

C

-5.737019

R-squared

0.286564

0.422485

0.646676

Adj. R-squared

0.189000

0.343508

0.598358

Sum sq. resids

0.004423

0.002382

0.011071

S.E. equation

0.006149

0.004512

0.009727

F-statistic

2.937189

5.349500

13.38380

Log likelihood

501.2142

542.6843

439.7483

Akaike AIC

-7.227078

-7.846035

-6.309676

Schwarz SC

-6.859441

-7.478398

-5.942040

Mean dependent

0.007319

0.004015

0.004516

S.D. dependent

0.006828

0.005569

0.015349

81

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(RENT_PHIL)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 155

Convergence achieved after 17 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

1.489867

0.161318

9.235568

0.0000

AR(1)

0.778739

0.136596

5.701055

0.0000

MA(1)

-0.798758

0.150917

-5.292710

0.0000

MA(2)

0.003370

0.100966

0.033377

0.9734

MA(3)

0.169894

0.077528

2.191384

0.0300

SIGMASQ

1.295261

0.140612

9.211588

0.0000

R-squared

0.068077 Mean dependent var

1.478161

Adjusted R-squared

0.036804 S.D. dependent var

1.182753

S.E. of regression

1.160784 Akaike info criterion

3.175560

Sum squared resid

200.7655 Schwarz criterion

3.293370

Log likelihood

-240.1059 Hannan-Quinn criter.

3.223412

F-statistic

2.176887 Durbin-Watson stat

1.997017

Prob(F-statistic)

0.059686

82

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_PHIL_V

3.057870

0.1309

RENT_PHIL_A

2.015179

0.2055

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

1.241974

0.2542

0.8729

0.1271

Sq Error

1.447297

0.1911

0.9045

0.0955

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_PHIL_V

2.456461 2.048350 0.649652 0.646659 0.003895 1.109222

RENT_PHIL_A

1.312898 1.167195 0.371817 0.372333 0.002091 0.577155

Simple mean

1.281053 1.096966 0.349287 0.348597 0.002036 0.545302

Forecast Comparison Graph

330

320

310

300

290

280 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_PHIL

RENT_PHIL (E_PHIL)

RENT_PHIL_A

Simple mean

83

Alternative Methods for Calculating Fair Market Rents

Phoenix:

Vector Error Correction Estimates

Sample (adjusted): 2003Q3 2018Q4

Included observations: 62 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_PHO(-1))

1.000000

LOG(RINCOME_PHO(-1)) -3.628374

(0.40974)

[-8.85527]

LOG(RHPRICE_PHO(-1))

0.202112

(0.08345)

[ 2.42206]

C

15.79268

R-squared

0.861498

0.859337

0.797430

Adj. R-squared

0.812253

0.809324

0.725404

Sum sq. resids

0.000615

0.000478

0.019223

S.E. equation

0.003697

0.003259

0.020668

F-statistic

17.49407

17.18213

11.07156

Log likelihood

269.1688

276.9944

162.4676

Akaike AIC

-8.134479

-8.386915

-4.692502

Schwarz SC

-7.551232

-7.803669

-4.109256

Mean dependent

0.006890

0.002729

0.004392

S.D. dependent

0.008533

0.007463

0.039442

84

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_PHO)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 2002Q2 2018Q4

Included observations: 67

Convergence achieved after 188 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.006621

0.003003

2.204430

0.0315

AR(1)

-0.013174

0.237583

-0.055448

0.9560

AR(2)

1.531069

0.225275

6.796435

0.0000

AR(3)

0.007311

0.175782

0.041593

0.9670

AR(4)

-0.727335

0.169929

-4.280232

0.0001

MA(1)

0.896063

269.9761

0.003319

0.9974

MA(2)

-0.859583

34.70091

-0.024771

0.9803

MA(3)

-0.454618

185.9386

-0.002445

0.9981

MA(4)

0.321705

51.22167

0.006281

0.9950

SIGMASQ

1.28E-05

0.003874

0.003294

0.9974

R-squared

0.810527 Mean dependent var

0.006602

Adjusted R-squared

0.780610 S.D. dependent var

0.008268

S.E. of regression

0.003873 Akaike info criterion

-8.027725

Sum squared resid

0.000855 Schwarz criterion

-7.698666

Log likelihood

278.9288 Hannan-Quinn criter.

-7.897515

F-statistic

27.09265 Durbin-Watson stat

1.933690

Prob(F-statistic)

0.000000

85

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_PHO_V

91.63344

0.0001

RENT_PHO_A

76.73806

0.0001

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

6.815671

0.0002

0.9999

0.0001

Sq Error

3.560322

0.0092

0.9954

0.0046

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_PHO_V

5.320176 4.486780 2.636932 2.685884 0.016154 2.369397

RENT_PHO_A

4.533593 3.689891 2.163748 2.199035 0.013732 2.014631

Simple mean

4.924042 4.088336 2.400340 2.442126 0.014933 2.190722

Forecast Comparison Graph

180

170

160

150

140

130 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_PHO

RENT_PHO (CE_PHO)

RENT_PHO_A

Simple mean

86

Alternative Methods for Calculating Fair Market Rents

San Diego:

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_SD(-1))

1.000000

LOG(RINCOME_SD(-1))

-1.978266

(0.42111)

[-4.69777]

LOG(RHPRICE_SD(-1))

-0.827885

(0.16300)

[-5.07918]

C

4.717653

R-squared

0.897975

0.704714

0.719358

Adj. R-squared

0.884023

0.664333

0.680980

Sum sq. resids

0.000499

0.001884

0.021038

S.E. equation

0.002065

0.004013

0.013409

F-statistic

64.36137

17.45159

18.74387

Log likelihood

647.4333

558.3943

396.7339

Akaike AIC

-9.409453

-8.080511

-5.667670

Schwarz SC

-9.041816

-7.712875

-5.300033

Mean dependent

0.008864

0.002754

0.005044

S.D. dependent

0.006063

0.006926

0.023741

87

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_SD)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1984Q2 2018Q4

Included observations: 139

Convergence achieved after 70 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.013278

0.004824

2.752607

0.0068

AR(1)

-0.055778

0.110871

-0.503091

0.6158

AR(2)

0.232885

0.142283

1.636771

0.1041

AR(3)

0.205072

0.151577

1.352926

0.1784

AR(4)

0.519034

0.104961

4.945005

0.0000

MA(1)

1.015962

0.068730

14.78201

0.0000

MA(2)

0.953494

0.085305

11.17741

0.0000

MA(3)

0.918176

0.068666

13.37161

0.0000

SIGMASQ

3.92E-06

5.82E-07

6.738452

0.0000

R-squared

0.918461 Mean dependent var

0.009549

Adjusted R-squared

0.913443 S.D. dependent var

0.006962

S.E. of regression

0.002048 Akaike info criterion

-9.436936

Sum squared resid

0.000545 Schwarz criterion

-9.246934

Log likelihood

664.8671 Hannan-Quinn criter.

-9.359725

F-statistic

183.0413 Durbin-Watson stat

2.087989

Prob(F-statistic)

0.000000

88

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_SD_V

320.9701

0.0000

RENT_SD_A

114.2780

0.0000

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-0.148850

0.8859

0.4429

0.5571

Sq Error

-1.135714

0.2935

0.1467

0.8533

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_SD_V

3.475661 2.990817 0.731529 0.727975 0.004273 1.273499

RENT_SD_A

3.843126 3.025501 0.737903 0.733583 0.004725 1.408788

Simple mean

3.650973 3.008159 0.734716 0.730807 0.004489 1.338424

Forecast Comparison Graph

440

420

400

380

360

340 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_SD

RENT_SD (ICE_SD)

RENT_SD_A

Simple mean

89

Alternative Methods for Calculating Fair Market Rents

Seattle

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 85 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_SEA(-1))

1.000000

LOG(RINCOME_SEA(-1)) -16.92373

(5.78918)

[ -2.92334]

LOG(RHPRICE_SEA(-1))

-7.304502

(1.95219)

[-3.74170]

C

-93.81802

R-squared

0.538868

0.682704

0.812632

Adj. R-squared

0.430366

0.608046

0.768545

Sum sq. resids

0.003481

0.003196

0.005928

S.E. equation

0.007155

0.006856

0.009336

F-statistic

4.966445

9.144433

18.43264

Log likelihood

308.7745

312.4013

286.1489

Akaike AIC

-6.865281

-6.950620

-6.332915

Schwarz SC

-6.376751

-6.462089

-5.844385

Mean dependent

0.009422

0.000150

0.003238

S.D. dependent

0.009479

0.010950

0.019407

90

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_SEA)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 111

Convergence achieved after 120 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.008773

0.001060

8.277006

0.0000

AR(1)

1.668273

0.123663

13.49046

0.0000

AR(2)

-0.707599

0.126015

-5.615204

0.0000

MA(1)

-1.487387

67.39254

-0.022070

0.9824

MA(2)

0.401524

35.52413

0.011303

0.9910

MA(3)

0.588418

62.58543

0.009402

0.9925

MA(4)

-0.502553

77.68049

-0.006469

0.9949

SIGMASQ

5.39E-05

0.000852

0.063310

0.9496

R-squared

0.366918 Mean dependent var

0.009252

Adjusted R-squared

0.323893 S.D. dependent var

0.009272

S.E. of regression

0.007624 Akaike info criterion

-6.796313

Sum squared resid

0.005987 Schwarz criterion

-6.601031

Log likelihood

385.1954 Hannan-Quinn criter.

-6.717093

F-statistic

8.528020 Durbin-Watson stat

1.958949

Prob(F-statistic)

0.000000

91

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_SEA_V

2.981810

0.1350

RENT_SEA_A

47.53959

0.0005

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-1.076023

0.3176

0.1588

0.8412

Sq Error

-1.349561

0.2192

0.1096

0.8904

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_SEA_V

4.686035 4.024815 1.026110 1.018936 0.005887 1.347080

RENT_SEA_A

7.706430 6.507417 1.624531 1.641678 0.009795 2.185628

Simple mean

3.920964 3.556351 0.897354 0.897935 0.004954 1.106458

Forecast Comparison Graph

420

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380

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340

320 III IV I II III IV I II III IV I II III IV I II III IV

2016

2017

2018

2019

2020

RENT_SEA

RENT_SEA (CE_SEA)

RENT_SEA_A

Simple mean

92

Alternative Methods for Calculating Fair Market Rents

San Francisco

Vector Error Correction Estimates

Sample (adjusted): 1985Q3 2018Q4

Included observations: 134 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_SF(-1))

1.000000

LOG(RINCOME_SF(-1))

7.985885

(2.64190)

[ 3.02278]

LOG(RHPRICE_SF(-1))

-4.472673

(0.97387)

[-4.59269]

C

-47.18365

R-squared

0.525702

0.605147

0.707362

Adj. R-squared

0.460841

0.551151

0.667343

Sum sq. resids

0.004015

0.002836

0.020791

S.E. equation

0.005858

0.004923

0.013330

F-statistic

8.105035

11.20707

17.67573

Log likelihood

507.6990

530.9945

397.5240

Akaike AIC

-7.323866

-7.671560

-5.679462

Schwarz SC

-6.956230

-7.303923

-5.311826

Mean dependent

0.010061

0.002759

0.008252

S.D. dependent

0.007978

0.007349

0.023113

93

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_SF)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1980Q2 2018Q4

Included observations: 155

Convergence achieved after 38 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.012809

0.003215

3.983885

0.0001

AR(1)

-0.935974

0.049661

-18.84724

0.0000

AR(2)

0.774095

0.077463

9.993053

0.0000

AR(3)

0.883429

0.041269

21.40647

0.0000

MA(1)

1.213180

0.096866

12.52434

0.0000

MA(2)

-0.185834

0.159727

-1.163448

0.2465

MA(3)

-0.461350

0.094611

-4.876273

0.0000

SIGMASQ

4.93E-05

5.17E-06

9.547453

0.0000

R-squared

0.481889 Mean dependent var

0.011788

Adjusted R-squared

0.457217 S.D. dependent var

0.009791

S.E. of regression

0.007213 Akaike info criterion

-6.955814

Sum squared resid

0.007649 Schwarz criterion

-6.798734

Log likelihood

547.0756 Hannan-Quinn criter.

-6.892012

F-statistic

19.53182 Durbin-Watson stat

1.941783

Prob(F-statistic)

0.000000

94

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_SF_V

19.25504

0.0046

RENT_SF_A

27.76010

0.0019

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-1.148249

0.2886

0.1443

0.8557

Sq Error

-1.493222

0.1790

0.0895

0.9105

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_SF_V

13.75523 11.58199 2.495962 2.453135 0.014701 2.990321

RENT_SF_A

14.75520 12.23688 2.635007 2.585960 0.015758 3.198584

Simple mean

14.24024 11.90944 2.565484 2.519698 0.015214 3.091501

Forecast Comparison Graph

500

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380 III IV I II III IV I II III IV I II III IV I II III IV

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2018

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2020

RENT_SF

RENT_SF (ICE_SF)

RENT_SF_A

Simple mean

95

Alternative Methods for Calculating Fair Market Rents

St. Louis

Vector Error Correction Estimates

Sample (adjusted): 1996Q4 2018Q4

Included observations: 89 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_STLOUIS(-1)) 1.000000

LOG(RINCOME_STL(-1))

-2.066163

(0.14596)

[-14.1556]

LOG(RHPRICE_STL(-1))

-0.402874

(0.11865)

[-3.39546]

C

5.429538

R-squared

0.609766

0.538809

0.667819

Adj. R-squared

0.502310

0.411814

0.576348

Sum sq. resids

0.000370

0.001179

0.003621

S.E. equation

0.002315

0.004134

0.007244

F-statistic

5.674582

4.242762

7.300939

Log likelihood

425.1323

373.5273

323.5951

Akaike AIC

-9.104097

-7.944434

-6.822362

Schwarz SC

-8.544853

-7.385190

-6.263118

Mean dependent

0.005788

0.003216

0.002195

S.D. dependent

0.003281

0.005390

0.011130

96

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_STLOUIS)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q4

Included observations: 95

Convergence achieved after 20 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.005921

0.000576

10.28078

0.0000

AR(1)

-0.286216

0.155208

-1.844081

0.0685

AR(2)

-0.397569

0.160388

-2.478796

0.0151

MA(1)

1.880496

0.062021

30.32048

0.0000

MA(2)

0.894060

0.063419

14.09765

0.0000

SIGMASQ

3.41E-06

4.44E-07

7.675288

0.0000

R-squared

0.658529 Mean dependent var

0.005768

Adjusted R-squared

0.639346 S.D. dependent var

0.003176

S.E. of regression

0.001907 Akaike info criterion

-9.539197

Sum squared resid

0.000324 Schwarz criterion

-9.377899

Log likelihood

459.1118 Hannan-Quinn criter.

-9.474020

F-statistic

34.32745 Durbin-Watson stat

1.584418

Prob(F-statistic)

0.000000

97

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_STLOUIS_A

1.226429

0.3489

RENT_STLOUIS_V

0.714006

0.4602

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

4.672922

0.0095

0.9953

0.0047

Sq Error

2.851362

0.0463

0.9768

0.0232

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_STLOUIS_A

3.908381 3.672613 1.497300 1.484657 0.007880 1.772121

RENT_STLOUIS_V

3.177764 2.932226 1.195702 1.187328 0.006417 1.482179

Simple mean

3.539020 3.302420 1.346501 1.336125 0.007141 1.626149

Forecast Comparison Graph

260

250

240

230

220 III IV I II III IV I II III IV I II III IV I II III IV

2016

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2018

2019

2020

RENT_STLOUIS

RENT_STLOUIS_A

RENT_STLOUIS (CE_STL)

Simple mean

98

Alternative Methods for Calculating Fair Market Rents

Tampa

Vector Error Correction Estimates

Sample (adjusted): 1988Q2 2018Q4

Included observations: 123 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_TAM(-1))

1.000000

LOG(RINCOME_TAM(-1)) -28.28390

(6.30307)

[-4.48732]

LOG(RHPRICE_TAM(-1))

2.000708

(1.89509)

[ 1.05573]

C

143.8020

R-squared

0.750858

0.625771

0.614766

Adj. R-squared

0.721144

0.581138

0.568821

Sum sq. resids

0.000728

0.004101

0.023558

S.E. equation

0.002584

0.006134

0.014701

F-statistic

25.26932

14.02043

13.38039

Log likelihood

565.7822

459.4499

351.9388

Akaike AIC

-8.972068

-7.243088

-5.494940

Schwarz SC

-8.651982

-6.923002

-5.174854

Mean dependent

0.007708

0.001270

0.001755

S.D. dependent

0.004894

0.009478

0.022389

A

99

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_TAM)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1987Q2 2018Q4

Included observations: 127

Convergence achieved after 286 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.007885

0.001483

5.318221

0.0000

AR(1)

-0.178892

0.083711

-2.137026

0.0347

AR(2)

0.109605

0.119897

0.914163

0.3625

AR(3)

0.184270

0.130730

1.409544

0.1613

AR(4)

0.244194

0.087661

2.785659

0.0062

MA(1)

1.032143

265.7213

0.003884

0.9969

MA(2)

1.032140

395.8760

0.002607

0.9979

MA(3)

0.999996

640.4021

0.001562

0.9988

SIGMASQ

4.95E-06

0.000206

0.024064

0.9808

R-squared

0.784962 Mean dependent var

0.007708

Adjusted R-squared

0.770384 S.D. dependent var

0.004816

S.E. of regression

0.002308 Akaike info criterion

-9.149656

Sum squared resid

0.000628 Schwarz criterion

-8.948099

Log likelihood

590.0031 Hannan-Quinn criter.

-9.067766

F-statistic

53.84268 Durbin-Watson stat

2.012722

Prob(F-statistic)

0.000000

100

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_TAM_V

147.0837

0.0000

RENT_TAM_A

192.4001

0.0000

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

3.949182

0.0055

0.9972

0.0028

Sq Error

2.437615

0.0449

0.9775

0.0225

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_TAM_V

3.466734 2.932658 1.040256 1.047749 0.006275 1.172032

RENT_TAM_A

2.133225 1.821201 0.646230 0.649063 0.003853 0.722530

Simple mean

2.799464 2.376930 0.843243 0.848124 0.005062 0.947117

Forecast Comparison Graph

290

280

270

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230 III IV I II III IV I II III IV I II III IV I II III IV

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2018

2019

2020

RENT_TAM

RENT_TAM (CE_TAM)

RENT_TAM_A

Simple mean

101

Alternative Methods for Calculating Fair Market Rents

Washington DC

Vector Error Correction Estimates

Sample (adjusted): 1999Q1 2018Q4

Included observations: 80 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(RENT_DC(-1))

1.000000

LOG(RINCOME_DC(-1))

-1.660789

(0.19227)

[-8.63762]

LOG(RHPRICE_DC(-1))

-0.168668

(0.07568)

[-2.22858]

C

3.776893

R-squared

0.476026

0.263285

0.640342

Adj. R-squared

0.400088

0.156515

0.588217

Sum sq. resids

0.001083

0.005012

0.016567

S.E. equation

0.003961

0.008523

0.015495

F-statistic

6.268593

2.465903

12.28488

Log likelihood

334.8979

273.6033

225.7786

Akaike AIC

-8.097448

-6.565083

-5.369465

Schwarz SC

-7.769919

-6.237554

-5.041936

Mean dependent

0.008988

0.003920

0.006224

S.D. dependent

0.005114

0.009280

0.024147

102

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(RENT_DC,2)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1998Q3 2018Q4

Included observations: 82

Convergence achieved after 117 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

-0.000103

3.02E-05

-3.397305

0.0011

AR(1)

0.291053

0.157596

1.846831

0.0688

AR(2)

-0.954352

0.041391

-23.05719

0.0000

AR(3)

0.361861

0.154145

2.347533

0.0216

MA(1)

-0.843704

340.5570

-0.002477

0.9980

MA(2)

0.843699

421.2788

0.002003

0.9984

MA(3)

-0.999996

898.9993

-0.001112

0.9991

SIGMASQ

1.43E-05

0.002886

0.004956

0.9961

R-squared

0.444384 Mean dependent var

-0.000105

Adjusted R-squared

0.391826 S.D. dependent var

0.005105

S.E. of regression

0.003981 Akaike info criterion

-8.025030

Sum squared resid

0.001173 Schwarz criterion

-7.790228

Log likelihood

337.0262 Hannan-Quinn criter.

-7.930761

F-statistic

8.455078 Durbin-Watson stat

2.001843

Prob(F-statistic)

0.000000

103

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2019Q1 2020Q4

Included observations: 8

Evaluation sample: 2019Q1 2020Q4

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

RENT_DC_A

45.78543

0.0066

RENT_DC_V

17.48993

0.0249

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

1.062348

0.3480

0.8260

0.1740

Sq Error

1.357908

0.2460

0.8770

0.1230

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

RENT_DC_A

2.343733 1.668093 0.448890 0.450879 0.003193 0.947617

RENT_DC_V

0.808615 0.736041 0.200472 0.200374 0.001099 0.288643

Simple mean

1.429282 1.162462 0.313909 0.314555 0.001945 0.571811

Forecast Comparison Graph

390

380

370

360

350

340 III IV I II III IV I II III IV I II III IV I II III IV

2016

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2018

2019

2020

RENT_DC

RENT_DC_A

RENT_DC (ICE_DC)

Simple mean

104

Alternative Methods for Calculating Fair Market Rents

Atlanta

Vector Error Correction Estimates

Sample (adjusted): 1999Q1 2018Q1

Included observations: 77 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_ATL(-1))

1.000000

LOG(NATGAS(-1))

0.382400

(0.04580)

[ 8.35007]

LOG(ELEC(-1))

-1.456730

(0.09458)

[-15.4017]

C

-9.134612

R-squared

0.851910

0.334142

0.841251

Adj. R-squared

0.829472

0.233255

0.817199

Sum sq. resids

0.060909

1.958511

0.018223

S.E. equation

0.030379

0.172263

0.016617

F-statistic

37.96744

3.312029

34.97517

Log likelihood

165.7157

32.09913

212.1728

Akaike AIC

-4.018589

-0.548029

-5.225269

Schwarz SC

-3.683759

-0.213200

-4.890439

Mean dependent

0.009102

0.006146

0.006059

S.D. dependent

0.073565

0.196728

0.038864

105

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_ATL)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1998Q2 2018Q2

Included observations: 81

Convergence achieved after 104 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.009276

0.005998

1.546385

0.1264

AR(1)

-0.997035

0.015098

-66.03790

0.0000

AR(2)

-0.995646

0.017201

-57.88170

0.0000

AR(3)

-0.997341

0.005482

-181.9261

0.0000

MA(1)

1.379325

0.134787

10.23335

0.0000

MA(2)

1.274408

0.195834

6.507598

0.0000

MA(3)

1.243886

0.167223

7.438469

0.0000

MA(4)

0.404205

0.109307

3.697895

0.0004

SIGMASQ

0.000969

0.000132

7.342620

0.0000

R-squared

0.820545 Mean dependent var

0.009988

Adjusted R-squared

0.800605 S.D. dependent var

0.073930

S.E. of regression

0.033012 Akaike info criterion

-3.767790

Sum squared resid

0.078466 Schwarz criterion

-3.501740

Log likelihood

161.5955 Hannan-Quinn criter.

-3.661047

F-statistic

41.15183 Durbin-Watson stat

2.186887

Prob(F-statistic)

0.000000

106

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_ATL_V

0.022193

0.8874

UTIL_ATL_A

0.794845

0.4135

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

4.393868

0.0046

0.9977

0.0023

Sq Error

2.494371

0.0469

0.9766

0.0234

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_ATL_V

12.07970 10.17313 3.453975 3.371961 0.019921 0.570998

UTIL_ATL_A

6.963056 5.592218 1.891998 1.868683 0.011613 0.329948

Simple mean

9.077420 6.705208 2.272964 2.226657 0.015054 0.429949

Forecast Comparison Graph

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UTIL_ATL

UTIL_ATL (E RGAS)

UTIL_ATL_A

Simple mean

107

Alternative Methods for Calculating Fair Market Rents

Chicago

Vector Error Correction Estimates

Sample (adjusted): 1998Q3 2018Q1

Included observations: 79 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_CHI(-1))

1.000000

LOG(GAS(-1))

0.045744

(0.04373)

[ 1.04599]

LOG(E(-1))

-0.908960

(0.06235)

[-14.5792]

C

-7.148573

R-squared

0.684988

0.453516

0.915261

Adj. R-squared

0.603695

0.312488

0.893393

Sum sq. resids

0.094921

1.616194

0.010156

S.E. equation

0.039128

0.161455

0.012799

F-statistic

8.426137

3.215783

41.85373

Log likelihood

153.5080

41.53413

241.7882

Akaike AIC

-3.455898

-0.621117

-5.690841

Schwarz SC

-2.946017

-0.111236

-5.180960

Mean dependent

0.006158

0.003980

0.005513

S.D. dependent

0.062154

0.194720

0.039200

108

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_CHI)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 183 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.007002

0.000924

7.580150

0.0000

AR(1)

0.284026

0.079178

3.587166

0.0006

AR(2)

-0.015223

0.000269

-56.49452

0.0000

AR(3)

-0.627652

0.136931

-4.583695

0.0000

AR(4)

0.671596

0.271428

2.474308

0.0154

MA(1)

-0.272133

1.640889

-0.165845

0.8687

MA(2)

0.000291

0.228890

0.001273

0.9990

MA(3)

0.271657

0.993543

0.273423

0.7852

MA(4)

-0.999763

9.677144

-0.103312

0.9180

SIGMASQ

0.001818

0.002774

0.655346

0.5141

R-squared

0.464977 Mean dependent var

0.006243

Adjusted R-squared

0.406963 S.D. dependent var

0.058609

S.E. of regression

0.045134 Akaike info criterion

-3.139545

Sum squared resid

0.169078 Schwarz criterion

-2.867222

Log likelihood

155.9888 Hannan-Quinn criter.

-3.029589

F-statistic

8.014843 Durbin-Watson stat

1.737386

Prob(F-statistic)

0.000000

109

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_CHI_V

1.284317

0.3085

UTIL_CHI_A

7.431395

0.0415

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-5.059871

0.0023

0.0012

0.9988

Sq Error

-3.596849

0.0114

0.0057

0.9943

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_CHI_V

2.087913 1.814351 0.876181 0.876218 0.005032 1.062651

UTIL_CHI_A

17.07687 16.00680 7.724727 7.401186 0.039687 12.24761

Simple mean

9.095844 8.351153 4.031098 3.937241 0.021525 6.568658

Forecast Comparison Graph

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2020

UTIL_CHI

UTIL_CHI (GAS RE)

UTIL_CHI_A

Simple mean

110

Alternative Methods for Calculating Fair Market Rents

Boston

Vector Error Correction Estimates

Sample (adjusted): 1998Q2 2018Q1

Included observations: 80 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_BOS(-1))

1.000000

LOG(GAS(-1))

-0.153925

(0.04845)

[-3.17690]

LOG(E(-1))

-1.656714

(0.07337)

[-22.5801]

C

-8.692369

R-squared

0.702254

0.399058

0.908794

Adj. R-squared

0.643607

0.280691

0.890829

Sum sq. resids

0.094581

1.777566

0.010960

S.E. equation

0.037856

0.164112

0.012886

F-statistic

11.97428

3.371353

50.58716

Log likelihood

156.0981

38.75619

242.3073

Akaike AIC

-3.552452

-0.618905

-5.707684

Schwarz SC

-3.135597

-0.202050

-5.290829

Mean dependent

0.011240

0.004268

0.005734

S.D. dependent

0.063411

0.193501

0.039001

111

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_BOS)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q4

Included observations: 95

Convergence achieved after 163 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.009443

0.005955

1.585707

0.1164

AR(1)

0.005908

0.011137

0.530539

0.5971

AR(2)

-0.999939

0.000739

-1352.957

0.0000

MA(1)

0.402243

14.62346

0.027507

0.9781

MA(2)

1.002726

66.28978

0.015126

0.9880

MA(3)

0.395342

40.58853

0.009740

0.9923

SIGMASQ

0.001473

0.010269

0.143450

0.8863

R-squared

0.636528 Mean dependent var

0.009237

Adjusted R-squared

0.611746 S.D. dependent var

0.063999

S.E. of regression

0.039878 Akaike info criterion

-3.445312

Sum squared resid

0.139941 Schwarz criterion

-3.257131

Log likelihood

170.6523 Hannan-Quinn criter.

-3.369273

F-statistic

25.68493 Durbin-Watson stat

1.933443

Prob(F-statistic)

0.000000

112

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_BOS_V

1.952593

0.2212

UTIL_BOS_A

5.784938

0.0612

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

3.567642

0.0118

0.9941

0.0059

Sq Error

3.159600

0.0196

0.9902

0.0098

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_BOS_V

26.47990 21.76591 7.426230 7.036262 0.043404 1.595107

UTIL_BOS_A

14.00512 10.59277 3.608919 3.499219 0.023392 0.846727

Simple mean

20.06844 16.17934 5.517574 5.292005 0.033205 1.211037

Forecast Comparison Graph

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UTIL_BOS

UTIL_BOS (ELECT)

UTIL_BOS_A

Simple mean

113

Alternative Methods for Calculating Fair Market Rents

Dallas

Vector Error Correction Estimates

Sample (adjusted): 1998Q2 2018Q1

Included observations: 80 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_DAL(-1))

1.000000

LOG(GAS(-1))

-0.257029

(0.03471)

[-7.40557]

LOG(E(-1))

-1.128367

(0.05785)

[-19.5056]

C

-7.368546

R-squared

0.722030

0.409609

0.896581

Adj. R-squared

0.667278

0.293320

0.876210

Sum sq. resids

0.059407

1.746356

0.012427

S.E. equation

0.030002

0.162665

0.013722

F-statistic

13.18735

3.522336

44.01373

Log likelihood

174.6994

39.46473

237.2807

Akaike AIC

-4.017485

-0.636618

-5.582017

Schwarz SC

-3.600630

-0.219764

-5.165162

Mean dependent

0.007492

0.004268

0.005734

S.D. dependent

0.052013

0.193501

0.039001

114

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(UTIL_DAL)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence not achieved after 500 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

1.118524

0.979098

1.142403

0.2565

AR(1)

-0.944092

0.061743

-15.29071

0.0000

AR(2)

-0.998609

0.015429

-64.72280

0.0000

AR(3)

-0.945106

0.061128

-15.46098

0.0000

MA(1)

1.168960

14.45059

0.080894

0.9357

MA(2)

1.297003

98.20726

0.013207

0.9895

MA(3)

1.181647

123.2902

0.009584

0.9924

MA(4)

0.319158

37.36947

0.008541

0.9932

SIGMASQ

46.52758

3052.042

0.015245

0.9879

R-squared

0.440807 Mean dependent var

1.155737

Adjusted R-squared

0.387550 S.D. dependent var

9.171109

S.E. of regression

7.177233 Akaike info criterion

6.951051

Sum squared resid

4327.065 Schwarz criterion

7.196142

Log likelihood

-314.2239 Hannan-Quinn criter.

7.050012

F-statistic

8.277053 Durbin-Watson stat

2.034441

Prob(F-statistic)

0.000000

115

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_DAL_V

3.683734

0.1130

UTIL_DAL_A

0.039884

0.8496

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

1.302498

0.2405

0.8797

0.1203

Sq Error

0.752776

0.4801

0.7600

0.2400

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_DAL_V

8.573861 8.051352 3.278759 3.340827 0.017781 1.930412

UTIL_DAL_A

7.671192 6.449111 2.619438 2.666535 0.015827 1.733639

Simple mean

7.821000 6.803948 2.762135 2.813457 0.016178 1.790958

Forecast Comparison Graph

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UTIL_DAL

UTIL_DAL (GAS RE)

UTIL_DAL_A

Simple mean

116

Alternative Methods for Calculating Fair Market Rents

Denver

Vector Error Correction Estimates

Sample (adjusted): 1997Q4 2018Q1

Included observations: 82 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_DEN(-1))

1.000000

LOG(GAS(-1))

0.188158

(0.06930)

[ 2.71528]

LOG(E(-1))

-0.940580

(0.15684)

[-5.99692]

C

-7.523256

R-squared

0.614591

0.349228

0.472664

Adj. R-squared

0.578133

0.287668

0.422780

Sum sq. resids

0.039357

1.974251

0.069680

S.E. equation

0.023062

0.163337

0.030686

F-statistic

16.85768

5.673014

9.475411

Log likelihood

196.9608

36.43477

173.5401

Akaike AIC

-4.608801

-0.693531

-4.037564

Schwarz SC

-4.373999

-0.458729

-3.802762

Mean dependent

0.007972

0.002434

0.003824

S.D. dependent

0.035506

0.193528

0.040389

117

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(UTIL_DEN)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 52 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

1.309189

0.149528

8.755466

0.0000

AR(1)

0.656551

0.075081

8.744587

0.0000

MA(1)

0.945876

19.32708

0.048940

0.9611

MA(2)

-0.999988

23.84679

-0.041934

0.9666

MA(3)

-0.945864

11.66451

-0.081089

0.9356

SIGMASQ

6.564962

70.49408

0.093128

0.9260

R-squared

0.819755 Mean dependent var

1.289280

Adjusted R-squared

0.809396 S.D. dependent var

6.067818

S.E. of regression

2.649098 Akaike info criterion

5.004119

Sum squared resid

610.5415 Schwarz criterion

5.167513

Log likelihood

-226.6915 Hannan-Quinn criter.

5.070093

F-statistic

79.13547 Durbin-Watson stat

1.825054

Prob(F-statistic)

0.000000

118

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_DEN_V

18.91634

0.0074

UTIL_DEN_A

30.47822

0.0027

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

2.166986

0.0734

0.9633

0.0367

Sq Error

2.100051

0.0805

0.9598

0.0402

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_DEN_V

15.38560 13.61650 5.682550 5.497318 0.031190 3.135693

UTIL_DEN_A

7.770974 6.447592 2.669221 2.674178 0.016127 1.238224

Simple mean

10.68477 9.489271 3.951384 3.881742 0.021914 2.061326

Forecast Comparison Graph

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UTIL_DEN

UTIL_DEN (GAS RE)

UTIL_DEN_A

Simple mean

119

Alternative Methods for Calculating Fair Market Rents

Detroit

Vector Error Correction Estimates

Sample (adjusted): 1997Q3 2020Q1

Included observations: 91 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_DET(-1))

1.000000

LOG(RGAS(-1))

-15.36472

(21.9507)

[-0.69997]

LOG(RE(-1))

-747.0334

(215.732)

[ -3.46278]

C

5384.876

R-squared

0.114648

0.127790

0.283284

Adj. R-squared

0.073469

0.087222

0.249948

Sum sq. resids

0.061197

2.522122

0.038216

S.E. equation

0.026676

0.171251

0.021080

F-statistic

2.784130

3.150026

8.497929

Log likelihood

203.2322

34.02862

224.6552

Akaike AIC

-4.356752

-0.637992

-4.827588

Schwarz SC

-4.218793

-0.500032

-4.689628

Mean dependent

0.007864

-0.006143

-0.000852

S.D. dependent

0.027713

0.179247

0.024340

120

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(UTIL_DET)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 23 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

1.453160

0.603561

2.407645

0.0182

AR(1)

0.019751

0.091530

0.215787

0.8297

AR(2)

-0.910758

0.073464

-12.39740

0.0000

MA(1)

0.093133

0.117061

0.795587

0.4284

MA(2)

0.829508

0.117392

7.066165

0.0000

SIGMASQ

26.79411

3.090216

8.670626

0.0000

R-squared

0.118090 Mean dependent var

1.442652

Adjusted R-squared

0.067406 S.D. dependent var

5.541855

S.E. of regression

5.351820 Akaike info criterion

6.261405

Sum squared resid

2491.852 Schwarz criterion

6.424799

Log likelihood

-285.1553 Hannan-Quinn criter.

6.327379

F-statistic

2.329908 Durbin-Watson stat

2.152597

Prob(F-statistic)

0.049087

121

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_DET_V

0.266872

0.6275

UTIL_DET_A

1.351548

0.2975

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

3.266878

0.0171

0.9914

0.0086

Sq Error

2.722249

0.0345

0.9827

0.0173

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_DET_V

10.20383 9.038486 3.655071 3.570990 0.020032 1.641452

UTIL_DET_A

7.537979 6.231502 2.537275 2.491006 0.014895 1.200225

Simple mean

8.766258 7.412332 3.010235 2.947509 0.017266 1.404944

Forecast Comparison Graph

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2020

UTIL_DET

UTIL_DET (GAS RE)

UTIL_DET_A

Simple mean

122

Alternative Methods for Calculating Fair Market Rents

Honolulu

Vector Error Correction Estimates

Sample (adjusted): 1997Q4 2018Q2

Included observations: 83 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_HON(-1))

1.000000

LOG(RGAS(-1))

-1.279043

(0.33901)

[ -3.77293]

LOG(RE(-1))

-9.836193

(3.34852)

[-2.93748]

C

-72.39858

R-squared

0.667496

0.243299

0.326307

Adj. R-squared

0.636462

0.172674

0.263429

Sum sq. resids

0.056883

2.016876

0.035239

S.E. equation

0.027540

0.163987

0.021676

F-statistic

21.50869

3.444927

5.189524

Log likelihood

184.5802

36.49566

204.4523

Akaike AIC

-4.254946

-0.686642

-4.733790

Schwarz SC

-4.021804

-0.453501

-4.500648

Mean dependent

0.011307

-0.004095

-0.001200

S.D. dependent

0.045676

0.180290

0.025257

123

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_HON)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 17 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.010216

0.006678

1.529915

0.1297

MA(1)

1.754519

0.165845

10.57929

0.0000

MA(2)

0.343141

0.239884

1.430444

0.1562

MA(3)

-0.724849

0.206424

-3.511460

0.0007

MA(4)

-0.287723

0.163625

-1.758426

0.0822

SIGMASQ

0.000397

4.51E-05

8.788294

0.0000

R-squared

0.785081 Mean dependent var

0.010994

Adjusted R-squared

0.772730 S.D. dependent var

0.043198

S.E. of regression

0.020594 Akaike info criterion

-4.775625

Sum squared resid

0.036897 Schwarz criterion

-4.612232

Log likelihood

228.0666 Hannan-Quinn criter.

-4.709652

F-statistic

63.56088 Durbin-Watson stat

1.891398

Prob(F-statistic)

0.000000

124

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_HON_V

28.41013

0.0031

UTIL_HON_A

10.39915

0.0233

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-8.928509

0.0001

0.0001

0.9999

Sq Error

-3.485731

0.0131

0.0065

0.9935

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_HON_V

11.27237 9.102948 2.434228 2.475346 0.015270 1.320707

UTIL_HON_A

37.16865 34.96684 9.368782 9.892696 0.052358 4.720249

Simple mean

23.39795 20.76654 5.558280 5.761357 0.032315 2.891542

Forecast Comparison Graph

380

360

340

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300

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IV

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2017

2018

2019

2020

UTIL_HON

UTIL_HON (GAS RE)

UTIL_HON_A

Simple mean

125

Alternative Methods for Calculating Fair Market Rents

Houston

Vector Error Correction Estimates

Sample (adjusted): 1998Q1 2018Q2

Included observations: 82 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_HOU(-1))

1.000000

LOG(RGAS(-1))

0.183493

(0.51489)

[ 0.35637]

LOG(RE(-1))

-15.70069

(4.71227)

[ -3.33188]

C

110.1646

R-squared

0.480110

0.344206

0.316082

Adj. R-squared

0.406886

0.251841

0.219756

Sum sq. resids

0.137779

1.739795

0.035602

S.E. equation

0.044052

0.156538

0.022393

F-statistic

6.556734

3.726572

3.281361

Log likelihood

145.5888

41.61808

201.0725

Akaike AIC

-3.282655

-0.746782

-4.635914

Schwarz SC

-2.959802

-0.423930

-4.313061

Mean dependent

0.005978

-0.005445

-0.001007

S.D. dependent

0.057200

0.180977

0.025351

126

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(UTIL_HOU)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 32 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.806407

0.946844

0.851679

0.3968

AR(1)

-0.525209

0.234584

-2.238892

0.0278

AR(2)

-1.025619

0.032636

-31.42560

0.0000

AR(3)

-0.425994

0.229154

-1.858983

0.0665

MA(1)

0.879950

0.190080

4.629367

0.0000

MA(2)

1.036424

0.114240

9.072318

0.0000

MA(3)

0.670911

0.179626

3.735037

0.0003

SIGMASQ

45.75013

6.150821

7.438052

0.0000

R-squared

0.320781 Mean dependent var

0.858108

Adjusted R-squared

0.264845 S.D. dependent var

8.251612

S.E. of regression

7.075028 Akaike info criterion

6.858308

Sum squared resid

4254.762 Schwarz criterion

7.076166

Log likelihood

-310.9113 Hannan-Quinn criter.

6.946273

F-statistic

5.734819 Durbin-Watson stat

2.031997

Prob(F-statistic)

0.000019

127

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_HOU_V

0.353473

0.5780

UTIL_HOU_A

1.212471

0.3210

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

0.638984

0.5464

0.7268

0.2732

Sq Error

0.523167

0.6196

0.6902

0.3098

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_HOU_V

9.713977 8.197337 4.523841 4.488189 0.026802 0.951414

UTIL_HOU_A

9.049008 7.383059 4.026729 4.056146 0.025143 0.880219

Simple mean

9.247176 7.786710 4.273301 4.271715 0.025604 0.904457

Forecast Comparison Graph

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150

140

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2016

2017

2018

2019

2020

UTIL_HOU

UTIL_HOU (GAS RE)

UTIL_HOU_A

Simple mean

128

Alternative Methods for Calculating Fair Market Rents

Miami

Vector Error Correction Estimates

Sample (adjusted): 1997Q4 2018Q2

Included observations: 83 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_MIA(-1))

1.000000

LOG(RGAS(-1))

31.31014

(35.6213)

[ 0.87897]

LOG(RE(-1))

-982.1091

(339.748)

[-2.89070]

C

-7051.688

R-squared

0.308747

0.222348

0.322738

Adj. R-squared

0.244230

0.149767

0.259527

Sum sq. resids

0.039570

2.072719

0.035426

S.E. equation

0.022969

0.166242

0.021733

F-statistic

4.785508

3.063454

5.105723

Log likelihood

199.6423

35.36225

204.2330

Akaike AIC

-4.617888

-0.659331

-4.728507

Schwarz SC

-4.384747

-0.426190

-4.495365

Mean dependent

0.004784

-0.004095

-0.001200

S.D. dependent

0.026421

0.180290

0.025257

129

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(UTIL_MIA)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 89 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.680742

0.458836

1.483630

0.1416

AR(1)

1.528862

0.064763

23.60708

0.0000

AR(2)

-0.925098

0.066955

-13.81668

0.0000

MA(1)

-1.495044

56.88823

-0.026280

0.9791

MA(2)

0.756257

77.36991

0.009775

0.9922

MA(3)

0.387380

16.09735

0.024065

0.9809

MA(4)

-0.280570

23.16708

-0.012111

0.9904

SIGMASQ

11.58448

832.6966

0.013912

0.9889

R-squared

0.217826 Mean dependent var

0.709314

Adjusted R-squared

0.153411 S.D. dependent var

3.869315

S.E. of regression

3.560166 Akaike info criterion

5.514507

Sum squared resid

1077.356 Schwarz criterion

5.732365

Log likelihood

-248.4246 Hannan-Quinn criter.

5.602472

F-statistic

3.381634 Durbin-Watson stat

1.973588

Prob(F-statistic)

0.003122

130

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_MIA_V

18.43529

0.0078

UTIL_MIA_A

0.778170

0.4181

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-2.074409

0.0834

0.0417

0.9583

Sq Error

-1.501271

0.1840

0.0920

0.9080

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_MIA_V

1.953885 1.339365 0.747508 0.743395 0.005430 1.075093

UTIL_MIA_A

3.063848 2.636108 1.463298 1.471709 0.008564 1.728723

Simple mean

2.293943 1.851990 1.030306 1.030642 0.006394 1.285437

Forecast Comparison Graph

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175

170

165

160

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I

II

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IV

I

2016

2017

2018

2019

2020

UTIL_MIA

UTIL_MIA (GAS RE)

UTIL_MIA_A

Simple mean

131

Alternative Methods for Calculating Fair Market Rents

Philadelphia

Vector Error Correction Estimates

Sample (adjusted): 1998Q2 2018Q2

Included observations: 81 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_PHIL(-1))

1.000000

LOG(RGAS(-1))

0.047029

(0.38470)

[ 0.12225]

LOG(RE(-1))

-10.58755

(2.94434)

[ -3.59589]

C

72.21650

R-squared

0.666998

0.344205

0.366088

Adj. R-squared

0.602386

0.216961

0.243091

Sum sq. resids

0.024246

1.705942

0.032111

S.E. equation

0.019023

0.159568

0.021892

F-statistic

10.32309

2.705079

2.976382

Log likelihood

213.6808

41.40942

202.3029

Akaike AIC

-4.930389

-0.676776

-4.649453

Schwarz SC

-4.516534

-0.262920

-4.235598

Mean dependent

0.005764

-0.002657

-0.000548

S.D. dependent

0.030168

0.180324

0.025163

132

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_PHIL)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 52 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.005638

0.003430

1.643657

0.1040

AR(1)

-0.694609

0.179743

-3.864460

0.0002

AR(2)

-0.680723

0.177122

-3.843242

0.0002

AR(3)

-0.657469

0.167227

-3.931583

0.0002

AR(4)

0.296324

0.159261

1.860619

0.0663

MA(1)

0.966420

0.128165

7.540421

0.0000

MA(2)

0.851819

0.151332

5.628814

0.0000

MA(3)

0.701746

0.103806

6.760175

0.0000

SIGMASQ

0.000435

6.17E-05

7.055843

0.0000

R-squared

0.497324 Mean dependent var

0.005822

Adjusted R-squared

0.449450 S.D. dependent var

0.029578

S.E. of regression

0.021947 Akaike info criterion

-4.673523

Sum squared resid

0.040460 Schwarz criterion

-4.428432

Log likelihood

226.3188 Hannan-Quinn criter.

-4.574562

F-statistic

10.38819 Durbin-Watson stat

1.990021

Prob(F-statistic)

0.000000

133

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_PHIL_V

0.030054

0.8692

UTIL_PHIL_A

0.478993

0.5197

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

1.046795

0.3355

0.8322

0.1678

Sq Error

1.008704

0.3521

0.8240

0.1760

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_PHIL_V

3.116373 2.598663 1.221292 1.225680 0.007391 1.089042

UTIL_PHIL_A

2.765644 2.280009 1.073557 1.074436 0.006554 0.957001

Simple mean

2.918201 2.439336 1.147425 1.150044 0.006918 1.016681

Forecast Comparison Graph

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2017

2018

2019

2020

UTIL_PHIL

UTIL_PHIL (GAS RE)

UTIL_PHIL_A

Simple mean

134

Alternative Methods for Calculating Fair Market Rents

New York

Vector Error Correction Estimates

Sample (adjusted): 1998Q2 2018Q2

Included observations: 81 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_NY(-1))

1.000000

LOG(RGAS(-1))

-1.009016

(0.26531)

[ -3.80312]

LOG(RE(-1))

-3.866921

(2.08379)

[ -1.85572]

C

26.84237

R-squared

0.531075

0.339352

0.329601

Adj. R-squared

0.440090

0.211166

0.199524

Sum sq. resids

0.057580

1.718566

0.033959

S.E. equation

0.029316

0.160157

0.022513

F-statistic

5.836927

2.647349

2.533884

Log likelihood

178.6514

41.11081

200.0363

Akaike AIC

-4.065467

-0.669403

-4.593490

Schwarz SC

-3.651611

-0.255547

-4.179634

Mean dependent

0.006615

-0.002657

-0.000548

S.D. dependent

0.039178

0.180324

0.025163

135

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_NY)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 92 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.006603

0.004710

1.402042

0.1646

AR(1)

0.180680

0.165878

1.089235

0.2792

AR(2)

0.069250

0.063842

1.084702

0.2812

AR(3)

-0.872019

1.308907

-0.666219

0.5071

AR(4)

0.239411

0.491548

0.487055

0.6275

MA(1)

-0.087159

0.051941

-1.678052

0.0971

MA(2)

-0.089148

0.051959

-1.715740

0.0899

MA(3)

0.997928

0.001714

582.2854

0.0000

SIGMASQ

0.000904

0.000144

6.270713

0.0000

R-squared

0.332176 Mean dependent var

0.006231

Adjusted R-squared

0.268573 S.D. dependent var

0.037000

S.E. of regression

0.031644 Akaike info criterion

-3.896163

Sum squared resid

0.084110 Schwarz criterion

-3.651073

Log likelihood

190.1716 Hannan-Quinn criter.

-3.797202

F-statistic

5.222694 Durbin-Watson stat

1.925221

Prob(F-statistic)

0.000026

136

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_NY_V

2.136196

0.2037

UTIL_NY_A

44.01341

0.0012

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-0.875706

0.4149

0.2074

0.7926

Sq Error

-1.130583

0.3014

0.1507

0.8493

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_NY_V

9.288154 8.526364 4.365017 4.260731 0.023258 3.004394

UTIL_NY_A

10.35783 9.304840 4.765654 4.629082 0.025810 3.394171

Simple mean

9.702106 8.600348 4.408854 4.288930 0.024235 3.184732

Forecast Comparison Graph

220

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200

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170

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2017

2018

2019

2020

UTIL_NY

UTIL_NY (GAS RE)

UTIL_NY_A

Simple mean

137

Alternative Methods for Calculating Fair Market Rents

San Francisco

Vector Error Correction Estimates

Sample (adjusted): 1997Q4 2018Q2

Included observations: 83 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_SF(-1))

1.000000

LOG(RGAS(-1))

0.224027

(1.00688)

[ 0.22250]

LOG(RE(-1))

-29.14489

(9.89743)

[-2.94469]

C

-217.2111

R-squared

0.241107

0.206813

0.397744

Adj. R-squared

0.170277

0.132783

0.341533

Sum sq. resids

0.077634

2.114124

0.031502

S.E. equation

0.032173

0.167894

0.020495

F-statistic

3.404025

2.793616

7.075956

Log likelihood

171.6738

34.54140

209.1041

Akaike AIC

-3.943948

-0.639552

-4.845881

Schwarz SC

-3.710807

-0.406411

-4.612740

Mean dependent

0.011655

-0.004095

-0.001200

S.D. dependent

0.035321

0.180290

0.025257

138

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_SF)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q3

Included observations: 94

Convergence achieved after 280 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.011725

0.000856

13.70373

0.0000

AR(1)

0.588449

0.095444

6.165387

0.0000

AR(2)

-0.746000

0.059533

-12.53091

0.0000

AR(3)

0.799701

0.103270

7.743769

0.0000

MA(1)

-0.562579

137.3761

-0.004095

0.9967

MA(2)

0.562574

157.8631

0.003564

0.9972

MA(3)

-0.999991

518.3279

-0.001929

0.9985

SIGMASQ

0.000821

0.093027

0.008822

0.9930

R-squared

0.322556 Mean dependent var

0.010815

Adjusted R-squared

0.267415 S.D. dependent var

0.034992

S.E. of regression

0.029950 Akaike info criterion

-4.010398

Sum squared resid

0.077144 Schwarz criterion

-3.793947

Log likelihood

196.4887 Hannan-Quinn criter.

-3.922968

F-statistic

5.849673 Durbin-Watson stat

2.063916

Prob(F-statistic)

0.000014

139

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_SF_V

0.618249

0.4673

UTIL_SF_A

4.103345

0.0987

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

0.982881

0.3636

0.8182

0.1818

Sq Error

1.109168

0.3098

0.8451

0.1549

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_SF_V

5.953861 4.691385 1.147910 1.137444 0.007167 0.702203

UTIL_SF_A

3.849321 2.991940 0.722332 0.724040 0.004662 0.441980

Simple mean

4.020194 3.174803 0.777495 0.773714 0.004854 0.475566

Forecast Comparison Graph

440

420

400

380

360

340

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IV

I

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III

IV

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2016

2017

2018

2019

2020

UTIL_SF

UTIL_SF (GAS RE)

UTIL_SF_A

Simple mean

140

Alternative Methods for Calculating Fair Market Rents

San Diego

Vector Error Correction Estimates

Sample (adjusted): 1998Q2 2018Q2

Included observations: 81 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_SD(-1))

1.000000

LOG(RGAS(-1))

1.009910

(0.58452)

[ 1.72776]

LOG(RE(-1))

-19.60210

(6.12496)

[ -3.20037]

C

141.4624

R-squared

0.687830

0.358476

0.331309

Adj. R-squared

0.627259

0.234001

0.201563

Sum sq. resids

0.016516

1.668817

0.033873

S.E. equation

0.015701

0.157822

0.022485

F-statistic

11.35588

2.879911

2.553516

Log likelihood

229.2299

42.30052

200.1396

Akaike AIC

-5.314319

-0.698778

-4.596040

Schwarz SC

-4.900464

-0.284923

-4.182185

Mean dependent

0.012514

-0.002657

-0.000548

S.D. dependent

0.025716

0.180324

0.025163

141

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: D(UTIL_SD)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1995Q2 2018Q2

Included observations: 93

Convergence achieved after 8 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

2.409791

1.081131

2.228954

0.0283

MA(1)

1.762817

0.098875

17.82877

0.0000

MA(2)

0.775180

0.104372

7.427102

0.0000

SIGMASQ

4.951118

0.520830

9.506207

0.0000

R-squared

0.740534 Mean dependent var

2.237140

Adjusted R-squared

0.731788 S.D. dependent var

4.391964

S.E. of regression

2.274564 Akaike info criterion

4.589258

Sum squared resid

460.4540 Schwarz criterion

4.698187

Log likelihood

-209.4005 Hannan-Quinn criter.

4.633240

F-statistic

84.67063 Durbin-Watson stat

1.940482

Prob(F-statistic)

0.000000

142

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_SD_V

2.667567

0.1633

UTIL_SD_A

0.536441

0.4968

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-2.282064

0.0626

0.0313

0.9687

Sq Error

-2.293348

0.0617

0.0308

0.9692

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_SD_V

11.14760 9.959233 2.896812 2.910988 0.016332 0.552315

UTIL_SD_A

19.92825 18.91822 5.605189 5.457071 0.028607 1.391166

Simple mean

14.44626 13.59587 4.012291 3.959588 0.020949 0.923746

Forecast Comparison Graph

380

360

340

320

300

280

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

2016

2017

2018

2019

2020

UTIL_SD

UTIL_SD (GAS RE)

UTIL_SD_A

Simple mean

143

Alternative Methods for Calculating Fair Market Rents

Phoenix

Vector Error Correction Estimates

Sample (adjusted): 2003Q2 2018Q2

Included observations: 61 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_PHO(-1))

1.000000

LOG(RGAS(-1))

0.518929

(0.07969)

[ 6.51220]

LOG(RE(-1))

-0.154497

(0.69432)

[-0.22252]

C

-4.182353

R-squared

0.809651

0.339693

0.375769

Adj. R-squared

0.757002

0.157055

0.203109

Sum sq. resids

0.012892

1.069967

0.027319

S.E. equation

0.016562

0.150882

0.024109

F-statistic

15.37810

1.859925

2.176352

Log likelihood

171.5367

36.76375

148.6318

Akaike AIC

-5.165137

-0.746352

-4.414158

Schwarz SC

-4.680674

-0.261890

-3.929695

Mean dependent

0.007091

-0.019400

0.000236

S.D. dependent

0.033598

0.164337

0.027007

144

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_PHO)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 2002Q2 2018Q2

Included observations: 65

Convergence achieved after 45 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.006787

0.002642

2.568451

0.0128

AR(1)

-0.166542

0.079673

-2.090326

0.0409

AR(2)

-0.216600

0.149794

-1.445980

0.1535

AR(3)

-0.192680

0.105779

-1.821538

0.0736

AR(4)

0.736134

0.136078

5.409655

0.0000

SIGMASQ

0.000249

3.64E-05

6.856441

0.0000

R-squared

0.765757 Mean dependent var

0.006735

Adjusted R-squared

0.745906 S.D. dependent var

0.032885

S.E. of regression

0.016577 Akaike info criterion

-5.176943

Sum squared resid

0.016212 Schwarz criterion

-4.976230

Log likelihood

174.2506 Hannan-Quinn criter.

-5.097749

F-statistic

38.57501 Durbin-Watson stat

2.043276

Prob(F-statistic)

0.000000

145

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_PHO_V

3.722335

0.1116

UTIL_PHO_A

0.385865

0.5617

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

-1.090769

0.3172

0.1586

0.8414

Sq Error

-1.565720

0.1685

0.0842

0.9158

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_PHO_V

13.03059 11.17856 6.957643 6.640920 0.038509 1.385745

UTIL_PHO_A

16.07758 12.79538 8.010103 7.534994 0.047282 1.716062

Simple mean

14.49804 11.98697 7.483873 7.094289 0.042742 1.547366

Forecast Comparison Graph

190

180

170

160

150

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

2016

2017

2018

2019

2020

UTIL_PHO

UTIL_PHO (GAS RE)

UTIL_PHO_A

Simple mean

146

Alternative Methods for Calculating Fair Market Rents

Seattle

Vector Error Correction Estimates

Sample (adjusted): 1998Q4 2018Q2

Included observations: 79 after adjustments

Standard errors in ( ) & t-statistics in [ ]

Cointegrating Eq:

CointEq1

LOG(UTIL_SEA(-1))

1.000000

LOG(RGAS(-1))

-0.683007

(1.75938)

[-0.38821]

LOG(RE(-1))

-43.13133

(18.1025)

[ -2.38262]

C

306.9067

R-squared

0.301263

0.228192

0.297041

Adj. R-squared

0.232374

0.152098

0.227735

Sum sq. resids

0.023255

1.998944

0.035534

S.E. equation

0.018098

0.167792

0.022371

F-statistic

4.373133

2.998825

4.285947

Log likelihood

209.0652

33.13859

192.3189

Akaike AIC

-5.090258

-0.636420

-4.666301

Schwarz SC

-4.850314

-0.396476

-4.426357

Mean dependent

0.010436

-0.001753

-0.000388

S.D. dependent

0.020657

0.182221

0.025457

147

Alternative Methods for Calculating Fair Market Rents

Dependent Variable: DLOG(UTIL_SEA)

Method: ARMA Maximum Likelihood (BFGS)

Sample: 1998Q2 2018Q2

Included observations: 81

Convergence achieved after 48 iterations

Coefficient covariance computed using outer product of gradients Variable

Coefficient

Std. Error

t-Statistic

Prob.

C

0.009701

0.002479

3.913105

0.0002

AR(1)

-0.904571

0.170833

-5.295051

0.0000

AR(2)

-0.958104

0.080775

-11.86140

0.0000

AR(3)

-0.831574

0.167013

-4.979111

0.0000

MA(1)

1.330474

0.218874

6.078712

0.0000

MA(2)

1.208821

0.247569

4.882768

0.0000

MA(3)

0.864688

0.267496

3.232525

0.0019

MA(4)

0.303003

0.138192

2.192629

0.0316

SIGMASQ

0.000261

4.25E-05

6.145313

0.0000

R-squared

0.411031 Mean dependent var

0.009791

Adjusted R-squared

0.345590 S.D. dependent var

0.021190

S.E. of regression

0.017142 Akaike info criterion

-5.161944

Sum squared resid

0.021157 Schwarz criterion

-4.895894

Log likelihood

218.0587 Hannan-Quinn criter.

-5.055201

F-statistic

6.280934 Durbin-Watson stat

1.977945

Prob(F-statistic)

0.000004

148

Alternative Methods for Calculating Fair Market Rents

Forecast Evaluation

Sample: 2018Q3 2020Q1

Included observations: 7

Evaluation sample: 2018Q3 2020Q1

Number of forecasts: 3

Combination tests

Null hypothesis: Forecast i includes all information contained in others Forecast

F-stat

F-prob

UTIL_SEA_V

5.985870

0.0582

UTIL_SEA_A

22.61483

0.0051

Diebold-Mariano test (HLN adjusted)

Null hypothesis: Both forecasts have the same accuracy

Accuracy

Statistic

<> prob

> prob

< prob

Abs Error

1.874945

0.1099

0.9450

0.0550

Sq Error

1.681786

0.1436

0.9282

0.0718

Evaluation statistics

Forecast

RMSE

MAE

MAPE

SMAPE

Theil U1

Theil U2

UTIL_SEA_V

9.982453 9.021538 3.327277 3.261092 0.018136 2.812011

UTIL_SEA_A

8.456982 7.708422 2.840637 2.793068 0.015401 2.383774

Simple mean

9.187936 8.364980 3.083957 3.027834 0.016712 2.588910

Forecast Comparison Graph

290

280

270

260

250

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

II

III

IV

I

2016

2017

2018

2019

2020

UTIL_SEA

UTIL_SEA (GAS RE)

UTIL_SEA_A

Simple mean

149

Alternative Methods for Calculating Fair Market Rents

Appendix B: Summary of Rapidly Rising Rent Analysis

Error-Correction Residual (Normalized Scaling)

Atlanta

Dallas

2

2

1

1

0

0

-1

-1

-2

-2

-3

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Denver

Detroit

2

3

1

2

0

1

-1

0

-2

-1

-3

-2

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Honolulu

Houston

2

3

1

2

0

1

-1

0

-2

-1

-3

-2

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Miami

Minneapolis

3

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

150

Alternative Methods for Calculating Fair Market Rents

Error-Correction Residual (Normalized Scaling)

New York/New Jersey

Philadelphia

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3

-4

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Phoenix

San Diego

2

3

1

2

0

1

-1

0

-2

-1

-3

-2

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Seattle

San Francisco

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Tampa

2

1

0

-1

-280 85 90 95 00 05 10 15 20 25 30

151

Alternative Methods for Calculating Fair Market Rents

Band-Pass Filter 2-8 Year Component (Normalized Scaling)

Atlanta

Boston

3

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

98 00 02 04 06 08 10 12 14 16 18 20

98 00 02 04 06 08 10 12 14 16 18 20

Dallas

Denver

3

3

2

2

1

1

0

0

-1

-2

-1

-3

-2

98 00 02 04 06 08 10 12 14 16 18 20

98 00 02 04 06 08 10 12 14 16 18 20

Detroit

Houston

3

2

2

1

1

0

0

-1

-1

-2

-3

-2

98 00 02 04 06 08 10 12 14 16 18 20

98 00 02 04 06 08 10 12 14 16 18 20

Miami

Minneapolis

3

3

2

2

1

1

0

0

-1

-1

-2

-2

-3

-3

98 00 02 04 06 08 10 12 14 16 18 20

98 00 02 04 06 08 10 12 14 16 18 20

152

Alternative Methods for Calculating Fair Market Rents

Band-Pass Filter 2-8 Year Component (Normalized Scaling)

Honolulu

New York/New Jersey

.03

.015

.02

.010

.01

.005

.00

.000

-.01

-.02

-.005

-.03

-.010

98 00 02 04 06 08 10 12 14 16 18 20

98 00 02 04 06 08 10 12 14 16 18 20

Philadelphia

Phoenix

.015

.04

.010

.02

.005

.00

.000

-.02

-.005

-.010

-.04

-.015

-.06

98 00 02 04 06 08 10 12 14 16 18 20

98 00 02 04 06 08 10 12 14 16 18 20

San Diego

San Francisco

.020

.04

.015

.03

.010

.02

.005

.01

.000

.00

-.005

-.01

-.010

-.02

-.015

-.03

98 00 02 04 06 08 10 12 14 16 18 20

98 00 02 04 06 08 10 12 14 16 18 20

Tampa

.03

.02

.01

.00

-.01

-.02

-.03 98 00 02 04 06 08 10 12 14 16 18 20

153

Alternative Methods for Calculating Fair Market Rents

Rent-to-Real Income Ratio

Atlanta

Boston

1.5

1.4

1.4

1.2

1.3

1.0

1.2

0.8

1.1

0.6

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Dallas

Denver

1.3

1.4

1.2

1.2

1.1

1.0

1.0

0.8

0.9

0.8

0.6

0.7

0.4

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Detroit

Honolulu

1.3

1.8

1.2

1.6

1.1

1.4

1.0

1.2

0.9

1.0

0.8

0.8

0.7

0.6

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Houston

Miami

1.2

1.8

1.1

1.6

1.0

1.4

0.9

1.2

0.8

1.0

0.7

0.8

0.6

0.6

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

154

Alternative Methods for Calculating Fair Market Rents

Rent-to-Real Income Ratio

Minneapolis

New York/New Jersey

1.3

1.8

1.2

1.6

1.1

1.4

1.0

1.2

0.9

1.0

0.8

0.8

0.7

0.6

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Philadelphia

Phoenix

1.5

.52

1.4

.48

1.3

1.2

.44

1.1

.40

1.0

.36

0.9

0.8

.32

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

San Diego

Seattle

2.0

2.5

1.8

1.6

2.0

1.4

1.5

1.2

1.0

1.0

0.8

0.6

0.5

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

San Francisco

Tampa

2.4

1.6

2.0

1.4

1.2

1.6

1.0

1.2

0.8

0.8

0.6

0.4

0.4

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

155

Alternative Methods for Calculating Fair Market Rents

Rent-to-Real Home Price Ratio

Atlanta

Boston

3.4

1.4

3.2

1.2

3.0

2.8

1.0

2.6

0.8

2.4

0.6

2.2

2.0

0.4

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Dallas

Denver

2.8

2.8

2.6

2.4

2.4

2.0

2.2

1.6

2.0

1.8

1.2

1.6

0.8

1.4

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Detroit

Honolulu

4.5

4.4

4.0

4.0

3.5

3.6

3.0

3.2

2.5

2.8

2.0

2.4

1.5

2.0

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Houston

Miami

2.4

3.2

2.0

2.8

2.4

1.6

2.0

1.2

1.6

0.8

1.2

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

156

Alternative Methods for Calculating Fair Market Rents

Rent-to-Real Home Price Ratio

Minneapolis

New York/New Jersey

3.2

4.0

2.8

3.5

3.0

2.4

2.5

2.0

2.0

1.6

1.5

1.2

1.0

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

Philadelphia

Phoenix

3.2

1.0

0.9

2.8

0.8

2.4

0.7

0.6

2.0

0.5

1.6

0.4

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

San Diego

Seattle

4.0

4.5

3.5

4.0

3.5

3.0

3.0

2.5

2.5

2.0

2.0

1.5

1.5

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

San Francisco

Tampa

3.6

2.50

3.2

2.25

2.00

2.8

1.75

2.4

1.50

2.0

1.25

1.6

1.00

80

85

90

95

00

05

10

15

20

25

30

80

85

90

95

00

05

10

15

20

25

30

157

Alternative Methods for Calculating Fair Market Rents

Appendix C: Alternative Data Set Analysis

158

Alternative Methods for Calculating Fair Market Rents

159

Alternative Methods for Calculating Fair Market Rents

160

Alternative Methods for Calculating Fair Market Rents

161

Alternative Methods for Calculating Fair Market Rents

162

Alternative Methods for Calculating Fair Market Rents

163

Alternative Methods for Calculating Fair Market Rents

164

Alternative Methods for Calculating Fair Market Rents

165

Alternative Methods for Calculating Fair Market Rents

166

Alternative Methods for Calculating Fair Market Rents

Appendix D: Summary of Augmented Dickey-Fuller Tests

Null Hypothesis: Unit root (individual unit root process)

Sample: 2014M01 2021M12

Exogenous variables: Individual effects

Automatic selection of maximum lags

Automatic lag length selection based on SIC: 0 to 6

Total (balanced) observations: 2112

Cross-sections included: 24

Method

Statistic

Prob.**

Im, Pesaran and Shin W-stat

5.81046

1.0000

** Probabilities are computed assuming asympotic normality

Intermediate ADF test results

Max

Series

t-Stat

Prob.

E(t) E(Var) Lag

Lag

Obs

CUSR0000S... -1.2201 0.6628 -1.505 0.769

3

11

88

CUUR0100S... -1.3569 0.5998 -1.527 0.748

1

11

88

CUUR0200S... 1.5029 0.9992 -1.527 0.748

1

11

88

CUUR0300S... -0.9573 0.7652 -1.529 0.735

0

11

88

CUUR0400S... -0.8102 0.8111 -1.527 0.748

1

11

88

CUURA100...

-2.1808 0.2147 -1.529 0.735

0

11

88

CUURA101...

-2.6276 0.0913 -1.529 0.735

0

11

88

CUURA102...

0.2708 0.9755 -1.529 0.735

0

11

88

CUURA103...

-0.2552 0.9261 -1.529 0.735

0

11

88

CUURA200...

1.0699 0.9970 -1.527 0.748

1

11

88

CUURA208...

0.8333 0.9941 -1.463 0.811

6

11

88

CUURA300...

-3.0029 0.0385 -1.529 0.735

0

11

88

CUURA316...

-1.0527 0.7312 -1.529 0.735

0

11

88

CUURA318...

-3.3745 0.0145 -1.529 0.735

0

11

88

CUURA319...

0.2999 0.9771 -1.529 0.735

0

11

88

CUURA320...

-2.6337 0.0901 -1.529 0.735

0

11

88

CUURA400...

-1.4994 0.5294 -1.508 0.759

2

11

88

CUURA422...

-3.0579 0.0336 -1.529 0.735

0

11

88

CUURA423...

-1.8851 0.3378 -1.529 0.735

0

11

88

CUURX000...

2.4050 1.0000 -1.527 0.748

1

11

88

CUURX100...

2.1279 0.9999 -1.529 0.735

0

11

88

CUURX200...

2.1013 0.9999 -1.529 0.735

0

11

88

CUURX300...

1.5198 0.9993 -1.529 0.735

0

11

88

CUURX400...

1.7590 0.9997 -1.529 0.735

0

11

88

Average

-0.5010

-1.524 0.744

167

Alternative Methods for Calculating Fair Market Rents

Appendix E: Rapidly Rising Rents Dashboard

D = Decreasing at a decreasing rate. R = Increasing at a decreasing rate. RD = Decreasing at an increasing rate. RR = Increasing at an increasing rate.

Alaska

Error-Correction

Band-Pass

Income

1995Q1 D

D

D

1995Q2 RR

RR

RR

1995Q3 RR

RR

RR

1995Q4 R

RR

R

1996Q1 RR

RR

RR

1996Q2 R

R

R

1996Q3 RR

R

RR

1996Q4 RD

R

RD

1997Q1 RD

RD

RD

1997Q2 D

RD

D

1997Q3 D

RD

RR

1997Q4 RD

RD

RD

1998Q1 RD

D

RD

1998Q2 D

D

D

1998Q3 RD

D

RD

1998Q4 D

RR

RR

1999Q1 RR

RR

RR

1999Q2 RD

R

RD

1999Q3 RD

R

RD

1999Q4 D

RD

D

2000Q1 RD

RD

RD

2000Q2 D

RD

D

2000Q3 RD

D

RD

2000Q4 D

D

D

2001Q1 RR

RR

RR

2001Q2 R

RR

RR

2001Q3 R

RR

RR

2001Q4 RR

RR

RR

2002Q1 RR

RR

RR

2002Q2 R

R

R

2002Q3 R

R

R

2002Q4 R

R

RR

2003Q1 R

R

R

2003Q2 RR

RD

RR

2003Q3 RR

RD

RR

2003Q4 R

RD

R

2004Q1 R

RD

R

2004Q2 RD

RD

RD

2004Q3 RR

RD

RD

168

Alternative Methods for Calculating Fair Market Rents

2004Q4 RD

D

RD

2005Q1 RD

D

RD

2005Q2 RR

D

RR

2005Q3 RR

RR

RR

2005Q4 R

RR

R

2006Q1 RD

RR

R

2006Q2 RD

R

RD

2006Q3 RD

R

RD

2006Q4 RD

R

RD

2007Q1 D

RD

RD

2007Q2 D

RR

D

2007Q3 D

RR

RR

2007Q4 RD

RR

RD

2008Q1 RD

RR

RD

2008Q2 RR

RR

RR

2008Q3 RR

R

RR

2008Q4 R

R

R

2009Q1 RR

R

RR

2009Q2 R

RD

R

2009Q3 RR

RD

RR

2009Q4 R

D

R

2010Q1 RD

D

RD

2010Q2 D

RD

D

2010Q3 RD

RD

D

2010Q4 D

RD

RR

2011Q1 D

RD

RR

2011Q2 D

RD

R

2011Q3 RD

D

RD

2011Q4 RR

D

RR

2012Q1 RR

D

RR

2012Q2 RR

RR

RR

2012Q3 RR

RR

RR

2012Q4 RR

RR

RR

2013Q1 RR

RR

RR

2013Q2 R

RR

R

2013Q3 R

RR

R

2013Q4 RD

RR

R

2014Q1 RD

RR

RD

2014Q2 D

RR

D

2014Q3 RR

R

RR

2014Q4 RD

R

R

2015Q1 RD

R

RD

2015Q2 D

RD

D

2015Q3 D

RD

RD

2015Q4 RR

RD

RR

169

Alternative Methods for Calculating Fair Market Rents

2016Q1 RR

RD

RR

2016Q2 R

RD

R

2016Q3 RR

RD

RR

2016Q4 RD

RD

RD

2017Q1 RD

RD

RD

2017Q2 D

D

D

2017Q3 RD

D

D

2017Q4 D

RR

D

2018Q1 RD

RR

RD

2018Q2 D

RR

D

2018Q3 RR

R

RR

2018Q4 RD

R

R

2019Q1 RD

RD

RD

2019Q2 D

RD

D

2019Q3 RD

RD

RD

2019Q4 RD

RD

RD

2020Q1 RD

D

RD

2020Q2 RR

RR

RD

2020Q3 RD

RD

D

2020Q4 RD

RD

RD

Atlanta Error-Correction Band-Pass

Income

2000Q1 RD

RR

RR

2000Q2 D

RR

R

2000Q3 RR

RR

RR

2000Q4 RR

RR

RR

2001Q1 RR

RR

RR

2001Q2 R

RR

R

2001Q3 RD

R

R

2001Q4 RR

R

RR

2002Q1 RR

R

RR

2002Q2 R

RD

R

2002Q3 RD

RD

RD

2002Q4 D

D

D

2003Q1 RR

RD

RR

2003Q2 RD

RD

RD

2003Q3 RD

RD

RD

2003Q4 D

RD

D

2004Q1 D

D

D

2004Q2 RD

D

RD

170

Alternative Methods for Calculating Fair Market Rents

2004Q3 RD

D

RD

2004Q4 D

D

D

2005Q1 RR

D

RR

2005Q2 RD

RD

RD

2005Q3 RD

RD

RD

2005Q4 D

D

RR

2006Q1 RD

D

RD

2006Q2 D

D

D

2006Q3 RR

RR

RR

2006Q4 RR

RR

RR

2007Q1 R

RR

R

2007Q2 RR

RR

RR

2007Q3 RR

RR

RR

2007Q4 R

R

R

2008Q1 R

R

R

2008Q2 R

RD

R

2008Q3 RD

RD

RD

2008Q4 D

D

D

2009Q1 RR

D

RR

2009Q2 R

RR

R

2009Q3 RR

RR

RD

2009Q4 RD

RD

RD

2010Q1 RR

RD

RR

2010Q2 RD

RD

RD

2010Q3 RD

RD

RD

2010Q4 D

D

D

2011Q1 RD

D

RD

2011Q2 D

RR

D

2011Q3 RD

RR

RD

2011Q4 RR

R

RR

2012Q1 R

R

R

2012Q2 RD

RD

RD

2012Q3 RR

RD

RR

2012Q4 RR

RR

RR

2013Q1 RR

RR

RR

2013Q2 R

RR

R

2013Q3 R

RR

R

2013Q4 RD

R

R

2014Q1 RD

R

RD

2014Q2 D

RD

RR

2014Q3 RD

RD

RD

2014Q4 RD

RR

RD

2015Q1 RD

RR

RD

2015Q2 D

R

RR

2015Q3 RR

RD

RR

171

Alternative Methods for Calculating Fair Market Rents

2015Q4 R

RD

R

2016Q1 RR

RD

RR

2016Q2 RR

D

RR

2016Q3 RR

RR

RR

2016Q4 R

RR

R

2017Q1 R

R

R

2017Q2 RR

RD

RR

2017Q3 R

RD

R

2017Q4 R

RD

R

2018Q1 RD

D

R

2018Q2 D

D

RR

2018Q3 RR

RR

RR

2018Q4 RR

RR

RR

2019Q1 RR

RR

R

2019Q2 R

R

RR

2019Q3 R

R

R

2019Q4 RD

R

R

2020Q1 RD

R

RD

2020Q2 D

RD

D

2020Q3 D

RD

D

2020Q4 D

RD

RR

Baltimore Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RD

1995Q3 RD

RD

RD

1995Q4 RD

RD

RD

1996Q1 RD

RD

RD

1996Q2 RD

RD

RD

1996Q3 RD

RD

RD

1996Q4 RD

RD

RD

1997Q1 RD

RD

RD

1997Q2 RD

RD

RD

1997Q3 RD

RD

RD

1997Q4 RD

RD

RD

1998Q1 RR

RR

RR

1998Q2 RD

R

RD

1998Q3 D

R

RR

1998Q4 D

R

RR

1999Q1 D

RD

R

1999Q2 RD

RD

R

1999Q3 RD

RD

RD

172

Alternative Methods for Calculating Fair Market Rents

1999Q4 RD

D

D

2000Q1 RD

D

RD

2000Q2 D

D

D

2000Q3 D

RR

RR

2000Q4 RR

RR

RR

2001Q1 RR

RR

RR

2001Q2 R

R

R

2001Q3 RD

R

RR

2001Q4 RD

R

RR

2002Q1 RR

R

RR

2002Q2 RR

RR

RR

2002Q3 R

RR

R

2002Q4 RR

RR

RR

2003Q1 RR

R

RR

2003Q2 RD

R

R

2003Q3 RR

R

RR

2003Q4 RR

RD

RR

2004Q1 RD

RD

RD

2004Q2 D

RD

RD

2004Q3 RR

RD

RR

2004Q4 RR

RD

RR

2005Q1 R

D

R

2005Q2 RD

D

R

2005Q3 RR

D

RR

2005Q4 R

RR

R

2006Q1 RD

RR

R

2006Q2 RR

RR

RR

2006Q3 RR

RR

RR

2006Q4 RD

R

R

2007Q1 RR

R

RR

2007Q2 R

RD

R

2007Q3 RD

RD

RR

2007Q4 RR

D

RR

2008Q1 RD

D

RD

2008Q2 RR

RR

RR

2008Q3 RR

RR

RR

2008Q4 RD

RR

RD

2009Q1 RR

R

RR

2009Q2 R

R

R

2009Q3 R

RD

R

2009Q4 R

RD

R

2010Q1 RD

RD

RD

2010Q2 RD

RD

D

2010Q3 D

D

RD

2010Q4 D

D

RR

173

Alternative Methods for Calculating Fair Market Rents

2011Q1 RD

D

RD

2011Q2 RR

RR

RR

2011Q3 R

RR

R

2011Q4 RR

RR

RR

2012Q1 R

RR

R

2012Q2 R

R

R

2012Q3 RR

R

RR

2012Q4 RR

R

RR

2013Q1 RR

RD

RR

2013Q2 RD

RD

RD

2013Q3 RR

RD

RR

2013Q4 RR

D

RR

2014Q1 RD

D

RD

2014Q2 D

RR

RD

2014Q3 RD

RR

RR

2014Q4 RD

RR

RR

2015Q1 RD

R

RD

2015Q2 RR

R

RR

2015Q3 RD

R

RD

2015Q4 RD

RD

RD

2016Q1 D

RD

D

2016Q2 RR

RD

RR

2016Q3 RD

D

RR

2016Q4 D

D

R

2017Q1 RR

RR

RR

2017Q2 R

RR

RR

2017Q3 RD

RR

RD

2017Q4 D

R

RD

2018Q1 RR

R

RR

2018Q2 RR

R

RR

2018Q3 R

R

R

2018Q4 RD

RD

RD

2019Q1 D

RD

RR

2019Q2 RD

RD

RD

2019Q3 RD

RD

D

2019Q4 D

D

D

2020Q1 RD

D

RD

2020Q2 RR

RR

RD

2020Q3 RD

RD

D

2020Q4 RD

RD

RD

Boston Error-

Band-Pass

Income

Correction

174

Alternative Methods for Calculating Fair Market Rents

1995Q1 D

D

D

1995Q2 RD

RR

RD

1995Q3 D

R

RR

1995Q4 D

RR

R

1996Q1 RR

RR

RR

1996Q2 R

RR

R

1996Q3 RD

R

R

1996Q4 D

R

RR

1997Q1 RR

RD

RR

1997Q2 RD

RD

RD

1997Q3 RD

D

RD

1997Q4 RR

D

RR

1998Q1 RD

RR

R

1998Q2 D

RD

RR

1998Q3 D

RD

RR

1998Q4 RD

RD

RD

1999Q1 D

RD

RD

1999Q2 RD

D

RD

1999Q3 D

D

RR

1999Q4 D

RR

RR

2000Q1 RD

R

RD

2000Q2 D

RD

RD

2000Q3 D

RD

RR

2000Q4 RR

D

RR

2001Q1 RR

RR

R

2001Q2 RR

RR

RR

2001Q3 R

RR

R

2001Q4 RR

R

RR

2002Q1 RR

R

RR

2002Q2 R

R

R

2002Q3 RR

R

RR

2002Q4 R

R

R

2003Q1 R

R

R

2003Q2 R

RD

R

2003Q3 RR

RD

RR

2003Q4 RD

D

R

2004Q1 RD

D

RD

2004Q2 D

RD

RR

2004Q3 RD

RD

R

2004Q4 RD

RD

RD

2005Q1 RR

RD

RR

2005Q2 R

D

R

2005Q3 RD

D

RD

2005Q4 RD

D

RD

2006Q1 RD

D

D

175

Alternative Methods for Calculating Fair Market Rents

2006Q2 D

RR

D

2006Q3 D

RR

RR

2006Q4 RD

RR

R

2007Q1 RD

RR

RD

2007Q2 RR

R

RR

2007Q3 RR

R

RR

2007Q4 R

RD

RR

2008Q1 RR

D

RR

2008Q2 RR

RR

RR

2008Q3 R

RR

RR

2008Q4 RR

RR

RR

2009Q1 RR

R

R

2009Q2 R

RD

RD

2009Q3 R

RD

RR

2009Q4 RD

RD

RD

2010Q1 RD

D

RD

2010Q2 D

D

D

2010Q3 D

D

D

2010Q4 D

RD

RR

2011Q1 RR

RD

RD

2011Q2 RD

D

RD

2011Q3 D

RR

RR

2011Q4 RR

RR

RR

2012Q1 RD

RR

RD

2012Q2 RR

R

RR

2012Q3 RR

RD

RR

2012Q4 R

RD

R

2013Q1 RR

D

RR

2013Q2 R

RR

R

2013Q3 R

RR

R

2013Q4 RD

R

R

2014Q1 RD

RD

RD

2014Q2 RD

RD

RD

2014Q3 D

D

D

2014Q4 RD

D

RD

2015Q1 RD

RR

RD

2015Q2 D

R

D

2015Q3 D

RD

RR

2015Q4 RD

RD

RD

2016Q1 RR

D

RR

2016Q2 RD

D

R

2016Q3 RR

RD

RR

2016Q4 RD

RD

RD

2017Q1 RR

RD

RR

2017Q2 RD

D

R

176

Alternative Methods for Calculating Fair Market Rents

2017Q3 RR

RR

RR

2017Q4 RR

RR

RR

2018Q1 R

RR

R

2018Q2 RD

R

RR

2018Q3 RR

R

RR

2018Q4 R

RD

R

2019Q1 RR

RD

R

2019Q2 RD

RD

RD

2019Q3 RD

D

RR

2019Q4 RD

D

RD

2020Q1 RD

RR

RD

2020Q2 RD

RD

D

2020Q3 RD

RD

D

2020Q4 RD

RD

RD

Chicago Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RR

1995Q3 RD

RD

RD

1995Q4 RD

RD

RD

1996Q1 D

D

D

1996Q2 RR

D

RR

1996Q3 RD

RR

R

1996Q4 RR

RR

RR

1997Q1 RR

RR

R

1997Q2 RD

R

RD

1997Q3 RR

R

RR

1997Q4 RD

RD

R

1998Q1 RD

D

RD

1998Q2 RR

RR

RR

1998Q3 RD

RR

R

1998Q4 RD

R

RD

1999Q1 RR

RD

RR

1999Q2 R

RD

R

1999Q3 RD

RD

RD

1999Q4 RD

RD

RD

2000Q1 D

D

D

2000Q2 RR

D

RR

2000Q3 RD

RR

R

2000Q4 RR

RR

RR

2001Q1 RR

RR

RR

2001Q2 R

R

R

177

Alternative Methods for Calculating Fair Market Rents

2001Q3 R

R

R

2001Q4 RD

R

R

2002Q1 RR

RD

RR

2002Q2 RR

RD

RR

2002Q3 RD

D

RD

2002Q4 RR

D

RR

2003Q1 R

D

R

2003Q2 RD

RR

R

2003Q3 RR

RD

RR

2003Q4 RD

RD

RD

2004Q1 RD

RD

RD

2004Q2 RR

RD

RR

2004Q3 R

D

RR

2004Q4 RD

D

R

2005Q1 D

D

RR

2005Q2 RR

RD

RR

2005Q3 R

RD

R

2005Q4 RD

RD

R

2006Q1 RD

RD

RD

2006Q2 D

D

D

2006Q3 D

RR

RR

2006Q4 RD

RR

RD

2007Q1 RR

RR

RR

2007Q2 RR

RR

RR

2007Q3 RD

R

R

2007Q4 RR

R

RR

2008Q1 R

R

R

2008Q2 RR

RD

RR

2008Q3 R

RD

R

2008Q4 RD

RD

RD

2009Q1 RR

D

RR

2009Q2 R

D

R

2009Q3 R

D

R

2009Q4 R

RD

R

2010Q1 RD

RD

RD

2010Q2 RD

RD

RD

2010Q3 RD

RD

RD

2010Q4 D

D

D

2011Q1 RR

D

RR

2011Q2 RR

D

RR

2011Q3 RD

RR

RD

2011Q4 RD

RR

D

2012Q1 D

R

D

2012Q2 D

R

RD

2012Q3 RD

R

RD

178

Alternative Methods for Calculating Fair Market Rents

2012Q4 D

RR

RR

2013Q1 RR

RR

RR

2013Q2 R

RR

R

2013Q3 RD

RR

RD

2013Q4 RD

RR

RD

2014Q1 D

R

RR

2014Q2 RR

RR

RR

2014Q3 RD

RR

RD

2014Q4 RD

RR

RD

2015Q1 RD

RR

RD

2015Q2 RR

R

RR

2015Q3 RD

R

R

2015Q4 RD

RD

RD

2016Q1 RR

RD

RR

2016Q2 R

RD

R

2016Q3 RD

RD

RD

2016Q4 RR

D

RR

2017Q1 R

D

R

2017Q2 RD

D

R

2017Q3 RD

RR

RR

2017Q4 RD

RR

RD

2018Q1 RD

R

RD

2018Q2 D

RD

RR

2018Q3 RD

RD

RD

2018Q4 D

D

D

2019Q1 RR

D

RR

2019Q2 R

RR

R

2019Q3 RD

RR

RD

2019Q4 RD

R

RD

2020Q1 D

R

D

2020Q2 RR

RR

RD

2020Q3 RD

RD

D

2020Q4 RD

RD

RD

Dallas

Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RD

1995Q3 D

D

RR

1995Q4 RR

D

RR

1996Q1 RR

RD

R

1996Q2 RD

RD

RD

1996Q3 RD

RD

RD

179

Alternative Methods for Calculating Fair Market Rents

1996Q4 D

D

RR

1997Q1 RD

D

RD

1997Q2 D

RR

RR

1997Q3 D

RR

RR

1997Q4 RD

RR

RR

1998Q1 RD

RR

RD

1998Q2 D

R

RR

1998Q3 RD

RD

RR

1998Q4 RR

RD

RR

1999Q1 RR

RD

RR

1999Q2 R

D

R

1999Q3 RD

D

R

1999Q4 RR

RR

RR

2000Q1 RD

RR

RD

2000Q2 RR

RD

RR

2000Q3 RR

RD

R

2000Q4 RD

RD

R

2001Q1 D

D

RR

2001Q2 RR

RR

RR

2001Q3 RR

RR

R

2001Q4 RR

RR

RR

2002Q1 RR

R

RR

2002Q2 R

R

R

2002Q3 RD

R

RD

2002Q4 RR

R

RR

2003Q1 RR

RD

RR

2003Q2 RD

RD

RD

2003Q3 RD

RD

RD

2003Q4 RD

RD

RD

2004Q1 D

RD

D

2004Q2 RD

D

RD

2004Q3 D

D

D

2004Q4 D

D

RR

2005Q1 RD

RR

RD

2005Q2 RD

R

RD

2005Q3 D

R

D

2005Q4 D

R

D

2006Q1 RD

RR

RD

2006Q2 D

RR

D

2006Q3 D

RR

D

2006Q4 RD

R

RD

2007Q1 D

R

RR

2007Q2 RR

RR

RR

2007Q3 RD

RR

RD

2007Q4 D

RR

RR

180

Alternative Methods for Calculating Fair Market Rents

2008Q1 RD

RR

RD

2008Q2 RR

R

RR

2008Q3 RR

R

RR

2008Q4 RR

R

RR

2009Q1 RR

R

RR

2009Q2 R

R

R

2009Q3 R

RD

R

2009Q4 RD

RD

RD

2010Q1 RD

RD

RD

2010Q2 D

RD

RD

2010Q3 D

D

D

2010Q4 D

D

D

2011Q1 D

D

D

2011Q2 RR

RR

RR

2011Q3 RD

RR

R

2011Q4 RR

RR

RR

2012Q1 RD

R

R

2012Q2 D

R

RR

2012Q3 RR

R

RR

2012Q4 RR

R

RR

2013Q1 RR

RD

RR

2013Q2 RD

RD

RD

2013Q3 RR

D

RR

2013Q4 RD

D

RD

2014Q1 RD

RR

RD

2014Q2 D

RR

RR

2014Q3 RD

R

R

2014Q4 D

R

RR

2015Q1 RR

RD

RR

2015Q2 RR

RD

RR

2015Q3 RR

D

RR

2015Q4 RR

RD

R

2016Q1 RR

RD

RR

2016Q2 R

RD

R

2016Q3 R

D

R

2016Q4 R

RR

RR

2017Q1 RD

RR

RD

2017Q2 RR

RR

RR

2017Q3 R

R

R

2017Q4 RR

R

RR

2018Q1 RD

RD

R

2018Q2 RR

RD

RR

2018Q3 RD

RD

R

2018Q4 RD

D

RD

2019Q1 RR

D

RR

181

Alternative Methods for Calculating Fair Market Rents

2019Q2 R

D

R

2019Q3 RR

D

RR

2019Q4 RD

D

RD

2020Q1 RR

RR

RR

2020Q2 RD

RD

RD

2020Q3 RD

RD

RD

2020Q4 D

RD

D

Wash DC Error-

Band-Pass

Income

Correction

1998Q1 RR

RR

RR

1998Q2 RD

RD

R

1998Q3 D

RD

RD

1998Q4 D

RD

RD

1999Q1 RR

RD

RR

1999Q2 RD

RD

R

1999Q3 RD

D

RR

1999Q4 RD

D

RD

2000Q1 RD

D

RD

2000Q2 D

RR

D

2000Q3 D

RR

RR

2000Q4 RR

RR

RR

2001Q1 RR

RR

RR

2001Q2 R

RR

R

2001Q3 R

R

RR

2001Q4 R

R

R

2002Q1 RR

R

RR

2002Q2 R

R

R

2002Q3 R

R

RR

2002Q4 R

RD

R

2003Q1 RR

RD

RR

2003Q2 RD

RD

RD

2003Q3 D

RD

RR

2003Q4 RD

RD

RD

2004Q1 RD

D

RD

2004Q2 D

D

D

2004Q3 D

D

D

2004Q4 RR

D

RR

2005Q1 RR

D

RR

2005Q2 RD

D

R

2005Q3 RR

RR

RR

2005Q4 R

RR

RR

2006Q1 RD

RR

R

182

Alternative Methods for Calculating Fair Market Rents

2006Q2 D

RR

RR

2006Q3 RR

R

RR

2006Q4 RD

R

R

2007Q1 RD

R

RD

2007Q2 D

RD

RR

2007Q3 RD

RD

RD

2007Q4 RR

RR

RR

2008Q1 RR

RR

RR

2008Q2 R

RR

R

2008Q3 RR

RR

RR

2008Q4 RD

R

RD

2009Q1 RR

R

RR

2009Q2 R

RD

R

2009Q3 R

RD

R

2009Q4 RD

RD

RD

2010Q1 RD

RD

RD

2010Q2 D

D

RD

2010Q3 D

D

D

2010Q4 D

D

RR

2011Q1 RD

D

RD

2011Q2 RR

RR

RR

2011Q3 RR

RR

RR

2011Q4 RR

RR

RR

2012Q1 RR

RR

RR

2012Q2 R

RR

R

2012Q3 RR

RR

RR

2012Q4 RR

R

RR

2013Q1 RR

R

RR

2013Q2 RD

RD

RD

2013Q3 RR

RD

RR

2013Q4 RD

RD

RD

2014Q1 RD

D

RD

2014Q2 D

D

RD

2014Q3 D

RR

D

2014Q4 RD

RR

RD

2015Q1 RD

RR

RD

2015Q2 D

R

RR

2015Q3 RD

R

RD

2015Q4 RD

RD

RD

2016Q1 D

RD

D

2016Q2 RR

RD

RR

2016Q3 R

D

R

2016Q4 RR

RR

RR

2017Q1 RR

RR

RR

183

Alternative Methods for Calculating Fair Market Rents

2017Q2 RD

RR

R

2017Q3 RR

RR

RR

2017Q4 RR

R

RR

2018Q1 R

R

R

2018Q2 R

RD

R

2018Q3 R

RD

RR

2018Q4 RD

RD

R

2019Q1 D

D

R

2019Q2 RR

D

RR

2019Q3 RD

D

R

2019Q4 D

RR

RR

2020Q1 RD

RR

RD

2020Q2 RR

RR

RD

2020Q3 RD

RD

D

2020Q4 RD

RD

RD

Denver Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RR

RD

RR

1995Q3 RR

D

RR

1995Q4 RR

RR

RR

1996Q1 RR

RR

RR

1996Q2 R

R

R

1996Q3 R

RD

R

1996Q4 RD

RD

R

1997Q1 RR

RD

RR

1997Q2 RD

D

R

1997Q3 RD

D

R

1997Q4 RD

D

R

1998Q1 RD

D

RD

1998Q2 D

D

RR

1998Q3 RD

RR

RR

1998Q4 D

RR

RR

1999Q1 RR

RR

RR

1999Q2 RD

RR

R

1999Q3 RD

RR

R

1999Q4 D

RR

R

2000Q1 RD

RR

RD

2000Q2 D

RR

RR

2000Q3 D

RR

RR

2000Q4 RR

R

RR

2001Q1 RR

R

RR

184

Alternative Methods for Calculating Fair Market Rents

2001Q2 R

R

R

2001Q3 RR

RR

R

2001Q4 RR

RR

R

2002Q1 RR

R

RR

2002Q2 R

R

R

2002Q3 R

RD

R

2002Q4 R

RD

R

2003Q1 RD

RD

RD

2003Q2 D

D

D

2003Q3 RD

D

RD

2003Q4 RD

D

RD

2004Q1 RD

D

RD

2004Q2 D

D

D

2004Q3 RD

D

D

2004Q4 D

RR

D

2005Q1 D

RR

D

2005Q2 RD

RR

RD

2005Q3 RD

R

RD

2005Q4 D

R

RD

2006Q1 D

RD

RD

2006Q2 D

D

D

2006Q3 D

RR

D

2006Q4 RD

RR

D

2007Q1 RD

RR

RD

2007Q2 RR

R

RR

2007Q3 RR

R

RR

2007Q4 R

RR

RR

2008Q1 RR

RR

RR

2008Q2 R

RR

RR

2008Q3 RR

R

RR

2008Q4 R

R

RR

2009Q1 RR

R

RR

2009Q2 R

RD

R

2009Q3 R

RD

R

2009Q4 R

RD

R

2010Q1 R

RD

R

2010Q2 RR

RD

RR

2010Q3 RD

RD

RD

2010Q4 D

D

RD

2011Q1 RD

D

RD

2011Q2 RR

D

D

2011Q3 RD

RD

D

2011Q4 D

RD

D

2012Q1 D

D

RD

2012Q2 D

D

RR

185

Alternative Methods for Calculating Fair Market Rents

2012Q3 D

RR

RR

2012Q4 RR

RR

RR

2013Q1 RR

RR

RR

2013Q2 RD

R

R

2013Q3 RD

R

R

2013Q4 D

R

R

2014Q1 RD

R

RD

2014Q2 D

RR

RR

2014Q3 D

RR

RR

2014Q4 D

R

RR

2015Q1 RD

R

RR

2015Q2 RD

RR

RR

2015Q3 D

RR

RR

2015Q4

RR

RR

2016Q1 RR

RR

RR

2016Q2 R

R

R

2016Q3 RD

R

R

2016Q4 D

RD

R

2017Q1 RD

RD

RD

2017Q2 D

D

RR

2017Q3 D

D

R

2017Q4 RD

D

R

2018Q1 RD

D

R

2018Q2 D

RD

RR

2018Q3 D

RD

RR

2018Q4 RR

RD

RR

2019Q1 RD

RD

R

2019Q2 D

RD

RR

2019Q3 RR

D

RR

2019Q4 R

D

RR

2020Q1 RR

RR

RD

2020Q2 RD

RD

D

2020Q3 RD

RD

RD

2020Q4 RD

RD

RD

Detroit Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RD

1995Q3 D

D

D

1995Q4 RR

RR

RR

1996Q1 RR

RR

R

1996Q2 RD

RR

R

186

Alternative Methods for Calculating Fair Market Rents

1996Q3 RD

R

R

1996Q4 D

RD

RR

1997Q1 D

RD

RR

1997Q2 RD

RD

RD

1997Q3 D

D

D

1997Q4 D

RR

D

1998Q1 RD

RR

RD

1998Q2 D

R

RR

1998Q3 RR

R

RR

1998Q4 RD

RD

R

1999Q1 D

RD

RD

1999Q2 RD

D

RR

1999Q3 RR

RR

RR

1999Q4 RR

RR

R

2000Q1 RD

R

R

2000Q2 D

RD

RD

2000Q3 RR

RD

RR

2000Q4 RR

D

RR

2001Q1 RR

D

RR

2001Q2 R

D

R

2001Q3 RD

RD

R

2001Q4 RR

RD

RR

2002Q1 RR

RR

RR

2002Q2 R

RR

RD

2002Q3 RR

RR

RR

2002Q4 RR

R

RR

2003Q1 R

R

R

2003Q2 RD

RD

RD

2003Q3 RD

RD

D

2003Q4 D

RD

D

2004Q1 D

D

D

2004Q2 RR

D

RR

2004Q3 RD

RD

RD

2004Q4 RD

RD

D

2005Q1 RR

D

RR

2005Q2 RD

D

RD

2005Q3 RR

RR

RR

2005Q4 RR

RR

RR

2006Q1 R

R

R

2006Q2 RD

R

RD

2006Q3 RD

R

RD

2006Q4 RR

RR

RR

2007Q1 R

RR

R

2007Q2 R

RR

R

2007Q3 RD

R

RD

187

Alternative Methods for Calculating Fair Market Rents

2007Q4 D

RD

RD

2008Q1 RD

RD

D

2008Q2 RR

D

RR

2008Q3 R

D

RD

2008Q4 RR

RR

RR

2009Q1 RR

RR

RR

2009Q2 R

R

R

2009Q3 R

RD

RD

2009Q4 RD

RD

RD

2010Q1 RD

D

RD

2010Q2 D

D

D

2010Q3 D

RR

D

2010Q4 D

RR

D

2011Q1 RD

R

RD

2011Q2 RR

RD

RR

2011Q3 RD

RR

R

2011Q4 RR

RR

RR

2012Q1 RD

RR

RD

2012Q2 D

R

RR

2012Q3 RR

R

RR

2012Q4 RR

RD

R

2013Q1 RR

RD

RR

2013Q2 RD

D

R

2013Q3 RD

RR

RR

2013Q4 RR

RR

RR

2014Q1 RD

RD

RD

2014Q2 RD

RD

RD

2014Q3 RD

RD

RD

2014Q4 RD

D

RD

2015Q1 RD

D

RD

2015Q2 D

RR

D

2015Q3 RR

RR

RR

2015Q4 RD

R

R

2016Q1 RR

RD

RR

2016Q2 R

RD

R

2016Q3 RR

D

RR

2016Q4 R

RR

R

2017Q1 RR

RR

RR

2017Q2 RR

RD

RR

2017Q3 R

RD

R

2017Q4 RD

RR

R

2018Q1 RR

RR

RR

2018Q2 R

RR

R

2018Q3 RD

R

RR

2018Q4 RR

RD

RR

188

Alternative Methods for Calculating Fair Market Rents

2019Q1 RR

RD

R

2019Q2 RD

D

RD

2019Q3 RR

RR

RR

2019Q4 RD

RR

RR

2020Q1 RD

RD

RD

2020Q2 D

D

RD

2020Q3 D

RD

D

2020Q4 D

RD

D

Honolulu Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RR

RD

RR

1995Q3 RR

D

RR

1995Q4 RR

RR

RR

1996Q1 RR

RR

RR

1996Q2 R

R

R

1996Q3 RR

R

RD

1996Q4 R

R

RD

1997Q1 RD

RD

RD

1997Q2 RR

D

D

1997Q3 RD

RR

RD

1997Q4 RD

RR

RD

1998Q1 D

RR

D

1998Q2 RD

RR

RD

1998Q3 RD

RR

RD

1998Q4 D

RR

RD

1999Q1 RD

RR

D

1999Q2 RD

R

RD

1999Q3 RR

R

RD

1999Q4 RD

RD

RD

2000Q1 RD

RD

RD

2000Q2 RR

D

D

2000Q3 RD

RR

D

2000Q4 D

RR

D

2001Q1 RD

RR

RR

2001Q2 D

RR

RD

2001Q3 RD

R

D

2001Q4 D

R

D

2002Q1 RD

R

RD

2002Q2 D

R

RR

2002Q3 RD

R

RR

2002Q4 D

RD

RR

189

Alternative Methods for Calculating Fair Market Rents

2003Q1 RD

RD

RR

2003Q2 RD

RD

R

2003Q3 RD

RD

R

2003Q4 RD

D

R

2004Q1 RD

D

RD

2004Q2 D

RD

RR

2004Q3 RD

RD

RR

2004Q4 D

RD

RR

2005Q1 RD

D

RD

2005Q2 D

D

RR

2005Q3 RD

RR

RR

2005Q4 D

RR

RR

2006Q1 RR

RR

RR

2006Q2 R

R

R

2006Q3 R

R

R

2006Q4 RR

R

R

2007Q1 R

R

RR

2007Q2 RR

R

R

2007Q3 R

RD

R

2007Q4 RR

RD

R

2008Q1 R

RD

R

2008Q2 RR

RD

RR

2008Q3 R

D

RR

2008Q4 R

D

RR

2009Q1 R

RR

RR

2009Q2 RR

RD

R

2009Q3 R

RD

R

2009Q4 R

RD

R

2010Q1 RD

RD

RD

2010Q2 RR

D

RR

2010Q3 RR

D

RR

2010Q4 RR

RR

RR

2011Q1 RR

RR

RR

2011Q2 R

R

R

2011Q3 RR

R

R

2011Q4 RR

R

R

2012Q1 R

RR

R

2012Q2 RR

R

RR

2012Q3 R

R

RR

2012Q4 R

RD

RR

2013Q1 RR

RD

RR

2013Q2 RD

D

R

2013Q3 RD

D

R

2013Q4 RD

RR

RD

2014Q1 RD

RR

RD

190

Alternative Methods for Calculating Fair Market Rents

2014Q2 D

R

D

2014Q3 D

R

D

2014Q4 RD

R

D

2015Q1 D

RR

RD

2015Q2 D

RR

D

2015Q3 RD

R

RR

2015Q4 D

RD

RR

2016Q1 RD

RD

RR

2016Q2 RR

D

R

2016Q3 RD

RR

RR

2016Q4 RR

RR

RR

2017Q1 RR

RR

RR

2017Q2 RD

R

R

2017Q3 D

RD

R

2017Q4 RD

RD

R

2018Q1 D

RD

RD

2018Q2 RD

D

RR

2018Q3 RR

D

R

2018Q4 RR

D

R

2019Q1 RD

D

RR

2019Q2 RR

D

R

2019Q3 RD

D

R

2019Q4 D

RR

R

2020Q1 RD

RR

RD

2020Q2 RD

RR

RD

2020Q3 RR

R

RD

2020Q4 RD

R

RD

Houston Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RR

RD

1995Q3 RR

R

RR

1995Q4 RD

R

RD

1996Q1 RD

R

RD

1996Q2 D

RR

D

1996Q3 RD

RR

D

1996Q4 RD

R

RD

1997Q1 RD

R

RD

1997Q2 D

RD

D

1997Q3 D

RD

RD

1997Q4 RD

RR

RD

1998Q1 RD

RR

RD

191

Alternative Methods for Calculating Fair Market Rents

1998Q2 D

RR

RR

1998Q3 D

R

RR

1998Q4 RD

R

RD

1999Q1 RR

RD

RR

1999Q2 RD

RD

R

1999Q3 D

RD

R

1999Q4 D

D

RR

2000Q1 RD

RD

RD

2000Q2 D

RD

RR

2000Q3 RR

RD

RR

2000Q4 R

D

R

2001Q1 RD

D

R

2001Q2 RR

RR

RR

2001Q3 R

RR

RR

2001Q4 R

R

R

2002Q1 RR

R

RR

2002Q2 RR

R

RR

2002Q3 RR

RR

RR

2002Q4 R

RR

R

2003Q1 R

R

R

2003Q2 RR

R

RR

2003Q3 R

RD

R

2003Q4 RR

RD

R

2004Q1 RR

RD

RR

2004Q2 RD

D

RD

2004Q3 RD

D

D

2004Q4 D

D

D

2005Q1 D

RD

D

2005Q2 RD

RD

RD

2005Q3 RD

RD

RD

2005Q4 D

D

D

2006Q1 RD

RR

RD

2006Q2 D

RR

RR

2006Q3 RD

RR

RD

2006Q4 D

R

D

2007Q1 RR

RD

RR

2007Q2 RD

RD

RD

2007Q3 RD

D

RD

2007Q4 D

D

D

2008Q1 RD

RR

RD

2008Q2 RR

RR

RR

2008Q3 RR

RR

RR

2008Q4 RR

R

RR

2009Q1 RR

R

RR

2009Q2 R

RD

R

192

Alternative Methods for Calculating Fair Market Rents

2009Q3 RR

RD

RR

2009Q4 R

D

R

2010Q1 RD

D

RD

2010Q2 D

RD

D

2010Q3 RD

RD

RD

2010Q4 D

RD

D

2011Q1 RD

RD

RD

2011Q2 RD

D

D

2011Q3 D

D

D

2011Q4 D

RR

D

2012Q1 RR

RR

RR

2012Q2 RD

RR

RR

2012Q3 RD

R

RD

2012Q4 RR

R

RR

2013Q1 RR

R

RR

2013Q2 R

R

R

2013Q3 RD

RD

R

2013Q4 D

RD

RR

2014Q1 RD

RD

RD

2014Q2 RR

D

RR

2014Q3 RD

RR

R

2014Q4 RR

RR

RR

2015Q1 RD

RR

R

2015Q2 RR

RR

RR

2015Q3 RR

R

RR

2015Q4 R

R

R

2016Q1 RR

R

RR

2016Q2 R

R

R

2016Q3 R

RD

R

2016Q4 RR

RD

RR

2017Q1 RD

RD

RD

2017Q2 D

D

D

2017Q3 D

D

D

2017Q4 D

D

D

2018Q1 RD

D

RD

2018Q2 D

RD

RR

2018Q3 D

RD

R

2018Q4 RD

RD

RD

2019Q1 D

D

D

2019Q2 RR

RR

RR

2019Q3 RD

RR

R

2019Q4 RD

RR

RD

2020Q1 D

RR

D

2020Q2 RD

RD

RD

2020Q3 D

RD

RD

193

Alternative Methods for Calculating Fair Market Rents

2020Q4 D

RD

RR

LA

Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RD

1995Q3 D

RD

RD

1995Q4 D

RD

D

1996Q1 D

D

D

1996Q2 D

D

D

1996Q3 D

D

RR

1996Q4 RD

D

RD

1997Q1 RR

D

RR

1997Q2 RD

D

RD

1997Q3 D

D

RR

1997Q4 RD

D

RD

1998Q1 RD

RR

RD

1998Q2 D

RR

D

1998Q3 D

RR

RR

1998Q4 D

RR

RR

1999Q1 RR

R

RR

1999Q2 RD

R

R

1999Q3 RD

R

RR

1999Q4 RD

RD

RD

2000Q1 RD

RD

RD

2000Q2 D

D

RR

2000Q3 RR

RR

RR

2000Q4 RR

RR

RR

2001Q1 RR

RR

RR

2001Q2 R

RR

R

2001Q3 R

R

R

2001Q4 R

R

R

2002Q1 RR

R

RR

2002Q2 R

RD

R

2002Q3 R

RD

R

2002Q4 RR

RD

RR

2003Q1 RR

RD

RR

2003Q2 RD

D

R

2003Q3 RD

D

RD

2003Q4 D

D

RR

2004Q1 D

RR

RR

2004Q2 D

RR

RR

2004Q3 RD

R

RR

2004Q4 D

R

R

2005Q1 D

RD

RR

2005Q2 RD

RD

R

194

Alternative Methods for Calculating Fair Market Rents

2005Q3 RD

RD

R

2005Q4 D

D

R

2006Q1 RD

D

RD

2006Q2 D

RR

RR

2006Q3 RD

RR

R

2006Q4 RR

RR

RR

2007Q1 RR

RR

RR

2007Q2 R

RR

R

2007Q3 R

RR

R

2007Q4 RR

RR

RR

2008Q1 RR

RR

RR

2008Q2 R

R

R

2008Q3 RR

R

RR

2008Q4 R

R

R

2009Q1 RR

RD

RR

2009Q2 R

RD

R

2009Q3 R

RD

R

2009Q4 RD

RD

RD

2010Q1 RD

D

RD

2010Q2 D

D

D

2010Q3 RD

D

RD

2010Q4 D

RR

D

2011Q1 D

RR

D

2011Q2 RD

RR

RD

2011Q3 RD

R

RD

2011Q4 D

R

D

2012Q1 RD

RR

RD

2012Q2 D

RR

RR

2012Q3 RR

RR

RR

2012Q4 RR

RR

RR

2013Q1 RR

R

RR

2013Q2 R

R

R

2013Q3 RD

R

R

2013Q4 RD

RD

R

2014Q1 RD

RD

RD

2014Q2 D

D

D

2014Q3 D

D

RR

2014Q4 D

RR

RD

2015Q1 RD

RR

RD

2015Q2 D

RD

RR

2015Q3 D

RD

RR

2015Q4 D

RD

RR

2016Q1 RR

D

RR

2016Q2 R

D

R

2016Q3 RR

RR

RR

195

Alternative Methods for Calculating Fair Market Rents

2016Q4 R

RR

R

2017Q1 R

R

R

2017Q2 RD

RD

R

2017Q3 RD

RD

RR

2017Q4 RR

RD

RR

2018Q1 RR

D

R

2018Q2 RR

D

RR

2018Q3 RR

RR

RR

2018Q4 RR

RR

RR

2019Q1 RR

RR

RR

2019Q2 RD

R

R

2019Q3 RD

R

R

2019Q4 RD

R

R

2020Q1 RD

RD

RD

2020Q2 RR

RD

RD

2020Q3 RD

D

D

2020Q4 RD

RD

RD

Miami Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RR

1995Q3 RD

D

RD

1995Q4 D

RR

RR

1996Q1 RR

RR

RR

1996Q2 R

R

R

1996Q3 RD

RD

R

1996Q4 RR

RD

RR

1997Q1 RR

RD

RR

1997Q2 RD

D

R

1997Q3 RD

D

RD

1997Q4 D

RR

D

1998Q1 RD

RR

RD

1998Q2 D

RD

D

1998Q3 D

RD

D

1998Q4 D

RD

RR

1999Q1 RR

D

RR

1999Q2 RD

D

RD

1999Q3 D

RD

D

1999Q4 D

D

D

2000Q1 RD

D

RD

2000Q2 D

RR

RR

2000Q3 RD

RR

RR

196

Alternative Methods for Calculating Fair Market Rents

2000Q4 D

RR

R

2001Q1 RR

R

RR

2001Q2 R

R

R

2001Q3 R

RR

RR

2001Q4 RR

RR

R

2002Q1 RR

RR

RR

2002Q2 R

R

R

2002Q3 R

R

RR

2002Q4 RR

RD

R

2003Q1 RR

RD

RR

2003Q2 RD

RD

R

2003Q3 RD

D

RD

2003Q4 D

D

RR

2004Q1 D

D

R

2004Q2 RD

RR

R

2004Q3 RD

RD

R

2004Q4 D

RD

RR

2005Q1 RR

RD

RR

2005Q2 RD

RD

R

2005Q3 D

RD

RR

2005Q4 D

D

R

2006Q1 D

D

RR

2006Q2 RR

RR

RR

2006Q3 RD

RR

RR

2006Q4 RR

RR

RR

2007Q1 RR

R

RR

2007Q2 R

R

R

2007Q3 RR

R

R

2007Q4 RR

RR

RR

2008Q1 RR

RR

R

2008Q2 RR

RR

RR

2008Q3 R

R

R

2008Q4 R

RD

RR

2009Q1 RR

RD

RR

2009Q2 R

RD

RD

2009Q3 RR

D

RR

2009Q4 RD

D

RD

2010Q1 RD

RR

RD

2010Q2 D

RR

D

2010Q3 RD

R

RD

2010Q4 D

RD

RR

2011Q1 RR

RD

RD

2011Q2 R

D

RR

2011Q3 RD

RR

RD

2011Q4 D

RR

RR

197

Alternative Methods for Calculating Fair Market Rents

2012Q1 RD

RR

RD

2012Q2 RR

R

RR

2012Q3 RR

R

RR

2012Q4 RR

RD

RR

2013Q1 RR

RD

RR

2013Q2 R

RD

R

2013Q3 RD

D

R

2013Q4 D

D

RR

2014Q1 RD

RR

R

2014Q2 D

RR

RD

2014Q3 RD

RR

RD

2014Q4 D

R

RR

2015Q1 RD

R

R

2015Q2 RD

RD

RD

2015Q3 RR

RD

RR

2015Q4 RR

D

R

2016Q1 RR

D

RR

2016Q2 R

RR

R

2016Q3 RR

RR

RR

2016Q4 R

R

R

2017Q1 RD

RD

R

2017Q2 RD

RD

R

2017Q3 RD

RD

RD

2017Q4 D

RD

RR

2018Q1 RR

D

RR

2018Q2 R

D

RR

2018Q3 RD

RR

RD

2018Q4 D

RR

RR

2019Q1 RR

R

RR

2019Q2 RD

R

R

2019Q3 RD

RD

RD

2019Q4 RD

RD

RD

2020Q1 RD

RR

D

2020Q2 D

RD

D

2020Q3 D

RD

RR

2020Q4 RD

RD

RD

Minneapolis Error-

Band-Pass

Income

Correction

1995Q1

D

D

D

1995Q2

RD

RR

RR

1995Q3

D

RR

RR

1995Q4

D

R

RR

198

Alternative Methods for Calculating Fair Market Rents

1996Q1

RD

R

RD

1996Q2

D

R

RR

1996Q3

RD

R

R

1996Q4

D

R

RR

1997Q1

RR

R

RR

1997Q2

RD

RD

RD

1997Q3

RD

RD

RD

1997Q4

RD

RD

RD

1998Q1

RD

RD

RD

1998Q2

D

RD

D

1998Q3

D

D

RR

1998Q4

D

D

RR

1999Q1

RR

D

RR

1999Q2

R

D

R

1999Q3

RR

D

RR

1999Q4

R

RR

R

2000Q1

RD

RR

RD

2000Q2

RR

RR

RR

2000Q3

RR

R

RR

2000Q4

RR

R

RR

2001Q1

RR

R

RR

2001Q2

R

RR

R

2001Q3

R

RR

R

2001Q4

R

RR

R

2002Q1

RR

R

RR

2002Q2

R

R

R

2002Q3

RD

R

R

2002Q4

D

RD

R

2003Q1

RD

RD

RD

2003Q2

D

D

D

2003Q3

RD

D

RD

2003Q4

D

RR

D

2004Q1

RD

RR

RD

2004Q2

D

R

D

2004Q3

RD

RD

RD

2004Q4

D

RD

D

2005Q1

RR

RD

RR

2005Q2

RD

D

RD

2005Q3

RD

D

RD

2005Q4

RD

D

RD

2006Q1

RD

D

RD

2006Q2

D

D

D

2006Q3

D

D

D

2006Q4

D

RR

D

2007Q1

RR

RR

RR

199

Alternative Methods for Calculating Fair Market Rents

2007Q2

RD

RR

R

2007Q3

RD

R

RD

2007Q4

RR

R

RR

2008Q1

RR

R

RR

2008Q2

RR

RR

RR

2008Q3

R

RR

R

2008Q4

R

RR

R

2009Q1

RR

R

RR

2009Q2

R

R

R

2009Q3

RR

RD

RR

2009Q4

R

RD

R

2010Q1

RD

RD

RD

2010Q2

D

D

D

2010Q3

RD

D

RD

2010Q4

D

D

D

2011Q1

RD

D

RD

2011Q2

D

D

D

2011Q3

D

RR

RR

2011Q4

RD

RR

RR

2012Q1

RD

RR

RD

2012Q2

D

R

RR

2012Q3

RD

R

R

2012Q4

RR

RD

RR

2013Q1

RR

RD

RR

2013Q2

R

D

R

2013Q3

RD

RR

RD

2013Q4

D

RR

RR

2014Q1

RD

RR

R

2014Q2

D

R

R

2014Q3

RD

R

RD

2014Q4

RD

RD

RD

2015Q1

RD

RD

RD

2015Q2

D

D

D

2015Q3

RR

D

RR

2015Q4

R

D

R

2016Q1

RR

RD

RR

2016Q2

R

RD

R

2016Q3

RR

D

RR

2016Q4

R

D

R

2017Q1

R

RR

R

2017Q2

RR

RR

R

2017Q3

RD

R

R

2017Q4

RR

RD

RR

2018Q1

RD

RD

R

2018Q2

RR

D

RR

200

Alternative Methods for Calculating Fair Market Rents

2018Q3

R

D

R

2018Q4

RR

RR

RR

2019Q1

RR

RR

RR

2019Q2

R

RR

R

2019Q3

RR

R

RR

2019Q4

RD

RD

R

2020Q1

RD

RD

RD

2020Q2

D

D

RR

2020Q3

D

RD

RR

2020Q4

D

RD

RR

New

Error-

Band-Pass

Income

York

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RR

1995Q3 RD

RD

RD

1995Q4 D

D

RR

1996Q1 RR

D

RR

1996Q2 RD

RR

R

1996Q3 RD

RR

R

1996Q4 D

R

RR

1997Q1 D

R

RR

1997Q2 RD

RD

R

1997Q3 RD

RD

RR

1997Q4 D

D

RR

1998Q1 RD

D

RD

1998Q2 D

RD

D

1998Q3 D

RD

RR

1998Q4 D

RD

RR

1999Q1 RD

RD

RD

1999Q2 RD

D

RD

1999Q3 D

D

D

1999Q4 D

RR

RR

2000Q1 RD

RR

RD

2000Q2 D

RR

D

2000Q3 RR

R

RR

2000Q4 RD

R

R

2001Q1 RR

RD

RR

2001Q2 R

RD

R

2001Q3 RD

D

R

2001Q4 RR

RR

RR

2002Q1 RR

RR

RR

2002Q2 R

R

R

201

Alternative Methods for Calculating Fair Market Rents

2002Q3 R

R

R

2002Q4 RR

RD

RR

2003Q1 RR

RD

R

2003Q2 R

D

R

2003Q3 R

D

R

2003Q4 RD

D

R

2004Q1 RD

RD

R

2004Q2 RR

RD

RR

2004Q3 RD

RD

R

2004Q4 RR

D

R

2005Q1 RR

RR

RR

2005Q2 RD

RR

R

2005Q3 RD

RR

RR

2005Q4 RD

R

R

2006Q1 RD

R

R

2006Q2 D

RR

RR

2006Q3 RD

R

R

2006Q4 RD

RD

RD

2007Q1 RD

RD

RD

2007Q2 D

RD

RR

2007Q3 RR

D

RR

2007Q4 RR

RR

RR

2008Q1 RR

RR

RR

2008Q2 RR

RR

R

2008Q3 RR

RR

RR

2008Q4 R

R

R

2009Q1 RR

R

RR

2009Q2 R

RD

R

2009Q3 RR

RD

RR

2009Q4 R

D

R

2010Q1 RD

D

RD

2010Q2 D

D

RR

2010Q3 RD

RR

RR

2010Q4 D

R

RD

2011Q1 D

RD

D

2011Q2 RR

RD

RR

2011Q3 R

RD

R

2011Q4 RD

D

RD

2012Q1 RD

RR

RD

2012Q2 RR

RR

RR

2012Q3 RR

RR

RR

2012Q4 RR

R

R

2013Q1 RR

R

RR

2013Q2 R

R

R

2013Q3 RD

RR

R

202

Alternative Methods for Calculating Fair Market Rents

2013Q4 D

RR

RR

2014Q1 RD

R

RD

2014Q2 D

RD

RR

2014Q3 RD

RD

RD

2014Q4 D

D

D

2015Q1 RD

RR

RD

2015Q2 D

RR

D

2015Q3 D

RR

RR

2015Q4 RD

R

R

2016Q1 RR

R

RR

2016Q2 RD

RD

RD

2016Q3 D

RD

D

2016Q4 RD

D

D

2017Q1 RD

D

RD

2017Q2 D

RD

D

2017Q3 RD

RD

RD

2017Q4 D

RD

D

2018Q1 RR

RD

RR

2018Q2 RD

D

RD

2018Q3 RD

D

D

2018Q4 D

RR

RR

2019Q1 D

RR

RR

2019Q2 RD

R

R

2019Q3 RD

R

RD

2019Q4 RD

RD

RD

2020Q1 D

RR

D

2020Q2 RD

RD

RD

2020Q3 RD

RD

RD

2020Q4 RD

RD

RD

Philadelphia Error-

Band-Pass

Income

Correction

1995Q1

D

D

D

1995Q2

RD

RR

RD

1995Q3

D

R

RR

1995Q4

D

RD

R

1996Q1

RD

RD

RD

1996Q2

D

RR

D

1996Q3

RR

RR

RR

1996Q4

RD

RR

RD

1997Q1

D

R

RR

1997Q2

RD

R

R

1997Q3

RD

RD

RD

1997Q4

RD

RD

RD

1998Q1

RD

D

RD

203

Alternative Methods for Calculating Fair Market Rents

1998Q2

D

RR

D

1998Q3

RR

RR

RR

1998Q4

RD

R

R

1999Q1

RR

RD

RR

1999Q2

RD

RD

RD

1999Q3

RD

D

RD

1999Q4

RD

D

RD

2000Q1

D

RR

RR

2000Q2

RD

RR

RD

2000Q3

D

RD

RD

2000Q4

D

RD

RR

2001Q1

RR

D

RR

2001Q2

RR

RR

RR

2001Q3

RD

RR

R

2001Q4

RD

R

R

2002Q1

RR

RD

RR

2002Q2

RD

RD

R

2002Q3

RR

RD

RR

2002Q4

R

D

R

2003Q1

RD

RR

R

2003Q2

D

RR

R

2003Q3

RR

RR

RR

2003Q4

R

R

R

2004Q1

RD

RD

RD

2004Q2

D

RD

RR

2004Q3

RR

D

RR

2004Q4

RR

D

RR

2005Q1

R

D

R

2005Q2

RD

RD

RD

2005Q3

D

RD

RR

2005Q4

RR

RD

RR

2006Q1

RR

D

R

2006Q2

R

RR

R

2006Q3

RD

RR

R

2006Q4

RD

RR

R

2007Q1

RD

R

RD

2007Q2

RR

R

RR

2007Q3

RR

R

R

2007Q4

RR

R

RR

2008Q1

R

R

R

2008Q2

RR

R

RR

2008Q3

RR

R

RR

2008Q4

R

RD

R

2009Q1

R

RD

R

2009Q2

RR

RD

R

204

Alternative Methods for Calculating Fair Market Rents

2009Q3

RR

RD

RR

2009Q4

R

RD

R

2010Q1

RD

RD

RD

2010Q2

D

RD

D

2010Q3

RD

D

RD

2010Q4

D

D

D

2011Q1

RR

D

RR

2011Q2

RD

RR

RD

2011Q3

RR

RR

RR

2011Q4

R

RR

R

2012Q1

RD

R

RD

2012Q2

RR

R

RR

2012Q3

RR

R

RR

2012Q4

R

R

R

2013Q1

RR

RR

RR

2013Q2

RD

RR

RD

2013Q3

RR

R

RR

2013Q4

RR

RD

RR

2014Q1

RD

D

RD

2014Q2

D

RR

D

2014Q3

D

RR

D

2014Q4

RD

RR

RR

2015Q1

RD

R

RD

2015Q2

D

R

RD

2015Q3

D

RD

D

2015Q4

RD

RD

RD

2016Q1

D

D

D

2016Q2

D

D

RR

2016Q3

D

D

RD

2016Q4

RR

RR

RR

2017Q1

R

RR

RR

2017Q2

RD

RD

R

2017Q3

RD

RD

RD

2017Q4

D

D

RD

2018Q1

RD

RR

RD

2018Q2

D

RR

RR

2018Q3

RD

R

RD

2018Q4

D

RD

RR

2019Q1

RR

RD

RR

2019Q2

RD

D

R

2019Q3

RR

RR

RR

2019Q4

RD

RR

RD

2020Q1

RD

R

RD

2020Q2

RD

RD

RD

2020Q3

D

RD

D

205

Alternative Methods for Calculating Fair Market Rents

2020Q4

RD

RD

RD

Phoenix Error-

Band-Pass

Income

Correction

2002Q1 RR

RR

RR

2002Q2 R

R

R

2002Q3 R

RD

R

2002Q4 RD

RD

R

2003Q1 RD

RD

RD

2003Q2 RD

RD

RD

2003Q3 RD

RD

RD

2003Q4 RD

D

RD

2004Q1 RD

RD

RD

2004Q2 D

RD

D

2004Q3 D

RD

D

2004Q4 D

RD

D

2005Q1 RD

D

RD

2005Q2 D

D

D

2005Q3 D

D

D

2005Q4 D

RR

D

2006Q1 RD

RR

RD

2006Q2 D

RR

RR

2006Q3 RR

RR

RR

2006Q4 RR

RR

RR

2007Q1 RR

RR

RR

2007Q2 R

RR

R

2007Q3 RR

R

RR

2007Q4 RR

R

RR

2008Q1 RR

R

RR

2008Q2 R

R

R

2008Q3 R

R

R

2008Q4 R

RD

R

2009Q1 RR

RD

RR

2009Q2 R

RD

R

2009Q3 R

RD

RD

2009Q4 RD

RD

RD

2010Q1 RD

RD

RD

2010Q2 D

D

D

2010Q3 D

D

D

2010Q4 D

D

D

2011Q1 RD

D

D

2011Q2 D

RR

D

2011Q3 D

RR

RR

2011Q4 RR

RR

RR

2012Q1 RR

RR

RR

206

Alternative Methods for Calculating Fair Market Rents

2012Q2 R

RR

R

2012Q3 RR

R

RR

2012Q4 RR

R

RR

2013Q1 RR

R

RR

2013Q2 R

R

R

2013Q3 R

RR

R

2013Q4 RD

RR

R

2014Q1 RD

R

R

2014Q2 D

R

R

2014Q3 RD

RD

R

2014Q4 RD

RD

R

2015Q1 RD

RD

RD

2015Q2 D

D

RR

2015Q3 D

D

RR

2015Q4 RR

D

RR

2016Q1 RR

D

RR

2016Q2 R

RD

R

2016Q3 R

RD

R

2016Q4 R

RD

R

2017Q1 RD

D

R

2017Q2 RR

D

RR

2017Q3 RR

RR

RR

2017Q4 RR

RR

RR

2018Q1 RR

RR

RR

2018Q2 R

RR

R

2018Q3 RR

RR

RR

2018Q4 RR

RR

RR

2019Q1 RR

RR

RR

2019Q2 R

RR

R

2019Q3 R

R

R

2019Q4 RD

R

R

2020Q1 RD

RD

R

2020Q2 RD

D

R

2020Q3 RD

RD

RD

2020Q4 RD

RD

RD

San

Error-

Band-Pass

Income

Diego

Correction

1995Q1 D

D

D

1995Q2 RD

RR

RD

1995Q3 RD

R

D

1995Q4 D

R

D

1996Q1 D

RD

D

207

Alternative Methods for Calculating Fair Market Rents

1996Q2 RR

RD

RD

1996Q3 RD

RD

D

1996Q4 RD

RD

D

1997Q1 D

RD

D

1997Q2 RD

D

D

1997Q3 RD

D

D

1997Q4 D

RR

D

1998Q1 RD

RR

RD

1998Q2 D

RR

RR

1998Q3 D

RR

RR

1998Q4 D

R

RR

1999Q1 RR

R

RR

1999Q2 RD

R

R

1999Q3 RD

RD

R

1999Q4 D

RD

R

2000Q1 RD

RD

RD

2000Q2 RR

D

RR

2000Q3 RR

D

RR

2000Q4 RR

RR

RR

2001Q1 RR

RR

RR

2001Q2 R

RR

R

2001Q3 R

R

RR

2001Q4 RR

R

RR

2002Q1 RR

R

RR

2002Q2 R

RR

R

2002Q3 R

RR

R

2002Q4 RR

R

R

2003Q1 R

R

R

2003Q2 RR

RD

R

2003Q3 RD

RD

R

2003Q4 RD

D

R

2004Q1 D

D

R

2004Q2 RD

RD

RR

2004Q3 RD

RD

R

2004Q4 D

RD

R

2005Q1 D

RD

RR

2005Q2 RD

D

R

2005Q3 RD

D

R

2005Q4 RD

D

R

2006Q1 RD

RR

RD

2006Q2 D

RD

RR

2006Q3 RR

RD

RR

2006Q4 RR

D

RR

2007Q1 R

RR

R

2007Q2 RR

RR

RR

208

Alternative Methods for Calculating Fair Market Rents

2007Q3 RR

RR

RR

2007Q4 RR

RR

RR

2008Q1 RR

RR

RR

2008Q2 R

R

R

2008Q3 R

R

R

2008Q4 R

R

R

2009Q1 RR

R

RR

2009Q2 R

RD

R

2009Q3 R

RD

R

2009Q4 RD

RD

RD

2010Q1 RD

RD

RD

2010Q2 D

D

D

2010Q3 RD

D

D

2010Q4 D

D

D

2011Q1 RR

D

D

2011Q2 R

D

RD

2011Q3 RD

RR

D

2011Q4 D

RR

D

2012Q1 RD

RR

RD

2012Q2 D

R

D

2012Q3 RD

R

RR

2012Q4 D

R

RR

2013Q1 RR

R

RR

2013Q2 RD

R

R

2013Q3 RD

RD

RD

2013Q4 D

RD

RD

2014Q1 RD

RD

RD

2014Q2 D

D

D

2014Q3 D

D

D

2014Q4 D

RR

D

2015Q1 RD

RR

RD

2015Q2 D

R

D

2015Q3 D

R

RR

2015Q4 D

RD

RR

2016Q1 D

RD

RR

2016Q2 RD

D

RR

2016Q3 D

RR

RR

2016Q4 RR

RR

RR

2017Q1 RR

RR

RR

2017Q2 RD

RR

R

2017Q3 D

R

R

2017Q4 RR

RR

R

2018Q1 RR

R

RR

2018Q2 RD

R

R

2018Q3 RR

RD

R

209

Alternative Methods for Calculating Fair Market Rents

2018Q4 RR

RD

R

2019Q1 RR

RD

RR

2019Q2 RD

RD

R

2019Q3 RD

D

RD

2019Q4 RD

D

RD

2020Q1 RD

RR

RD

2020Q2 RD

RD

RD

2020Q3 RD

RD

RD

2020Q4 RD

RD

RD

Seattle Error-

Band-Pass

Income

Correction

1998Q1 RR

RD

R

1998Q2 RD

D

RR

1998Q3 D

RR

RR

1998Q4 RR

RR

R

1999Q1 R

RD

RR

1999Q2 RD

RD

R

1999Q3 RD

RD

RD

1999Q4 RR

D

RR

2000Q1 RD

D

RD

2000Q2 RR

RR

RR

2000Q3 RR

RR

RR

2000Q4 RR

RR

RR

2001Q1 R

RR

RR

2001Q2 RR

RR

R

2001Q3 RR

R

RR

2001Q4 RR

R

R

2002Q1 RD

R

R

2002Q2 RD

RD

RD

2002Q3 D

RD

RR

2002Q4 RD

RD

RD

2003Q1 RD

RD

RD

2003Q2 D

D

RD

2003Q3 RD

D

RD

2003Q4 RD

RD

D

2004Q1 D

RD

RD

2004Q2 RD

RD

D

2004Q3 RD

D

D

2004Q4 D

D

D

2005Q1 RD

D

RR

2005Q2 RD

D

R

2005Q3 D

D

RR

210

Alternative Methods for Calculating Fair Market Rents

2005Q4 D

RR

R

2006Q1 RD

RR

RD

2006Q2 D

RR

RR

2006Q3 D

RR

R

2006Q4 RR

RR

RR

2007Q1 RR

RR

R

2007Q2 RR

RR

RR

2007Q3 RR

RR

RR

2007Q4 RR

RR

RR

2008Q1 RR

R

R

2008Q2 RR

R

RR

2008Q3 RR

R

RR

2008Q4 R

R

R

2009Q1 R

RD

RR

2009Q2 RR

RD

R

2009Q3 R

RD

RD

2009Q4 R

RD

RD

2010Q1 RD

RD

RD

2010Q2 D

D

D

2010Q3 RD

D

D

2010Q4 RR

D

D

2011Q1 RR

D

RD

2011Q2 R

RR

RD

2011Q3 RR

RR

RR

2011Q4 RR

RR

RR

2012Q1 R

R

RD

2012Q2 R

R

RR

2012Q3 RD

R

RR

2012Q4 RR

R

RR

2013Q1 RR

R

RR

2013Q2 RD

RR

R

2013Q3 D

RR

RR

2013Q4 RR

R

R

2014Q1 R

R

RD

2014Q2 RD

R

RR

2014Q3 RR

RD

RR

2014Q4 RR

RD

RR

2015Q1 R

RD

R

2015Q2 RD

D

RR

2015Q3 D

D

RR

2015Q4 RR

D

RR

2016Q1 R

RD

RR

2016Q2 RD

RD

R

2016Q3 RR

D

RR

2016Q4 RR

D

R

211

Alternative Methods for Calculating Fair Market Rents

2017Q1 RD

RR

R

2017Q2 RD

RR

RR

2017Q3 RR

RR

RR

2017Q4 RR

R

R

2018Q1 RD

R

R

2018Q2 RD

RD

RR

2018Q3 RR

RD

R

2018Q4 RR

RD

R

2019Q1 RD

D

R

2019Q2 RD

D

RD

2019Q3 RR

RR

RR

2019Q4 R

RR

R

2020Q1 R

RR

RR

2020Q2 R

R

R

2020Q3 RD

RD

RD

2020Q4 RD

RD

RD

San Fran Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RD

1995Q3 RD

RD

RD

1995Q4 D

D

D

1996Q1 RD

D

RD

1996Q2 D

D

RR

1996Q3 RR

D

RR

1996Q4 R

D

R

1997Q1 RR

RR

RR

1997Q2 RD

RR

R

1997Q3 RR

RR

RR

1997Q4 RD

R

R

1998Q1 RD

R

RD

1998Q2 D

RD

RR

1998Q3 RD

RD

R

1998Q4 RR

D

R

1999Q1 RR

D

RR

1999Q2 RD

RD

R

1999Q3 RD

RD

R

1999Q4 RD

RD

R

2000Q1 RD

D

RD

2000Q2 D

D

RR

2000Q3 RR

RR

RR

2000Q4 RR

RR

RR

212

Alternative Methods for Calculating Fair Market Rents

2001Q1 RR

RR

RR

2001Q2 R

R

R

2001Q3 R

R

R

2001Q4 RR

R

R

2002Q1 R

RD

R

2002Q2 RD

RD

RD

2002Q3 RD

D

RR

2002Q4 D

D

RR

2003Q1 RR

D

R

2003Q2 RD

RD

RD

2003Q3 RD

RD

RD

2003Q4 D

D

D

2004Q1 D

D

RD

2004Q2 RD

D

D

2004Q3 RD

D

D

2004Q4 D

RD

D

2005Q1 D

RD

D

2005Q2 RD

RD

RD

2005Q3 D

D

RD

2005Q4 D

D

D

2006Q1 RD

RR

D

2006Q2 D

RR

D

2006Q3 RD

RR

D

2006Q4 RR

RR

RR

2007Q1 RR

RR

RR

2007Q2 R

R

R

2007Q3 R

R

RR

2007Q4 RR

R

RR

2008Q1 RR

R

R

2008Q2 RR

RR

RR

2008Q3 R

RR

RR

2008Q4 R

R

R

2009Q1 RR

R

RR

2009Q2 R

RD

R

2009Q3 R

RD

R

2009Q4 RD

RD

RD

2010Q1 RD

D

RD

2010Q2 D

D

D

2010Q3 RD

D

D

2010Q4 D

D

D

2011Q1 D

RR

D

2011Q2 RR

RR

RR

2011Q3 RD

RR

R

2011Q4 D

RR

R

2012Q1 RD

RR

RD

213

Alternative Methods for Calculating Fair Market Rents

2012Q2 D

RR

RR

2012Q3 RR

R

RR

2012Q4 RR

R

R

2013Q1 RR

R

RR

2013Q2 RD

R

R

2013Q3 RD

RR

R

2013Q4 D

RR

RR

2014Q1 RD

RR

R

2014Q2 RD

RR

RR

2014Q3 D

R

RR

2014Q4 D

R

R

2015Q1 RD

R

RD

2015Q2 D

R

RR

2015Q3 D

RR

RR

2015Q4 RR

RR

RR

2016Q1 RR

RR

R

2016Q2 RR

R

RR

2016Q3 R

R

R

2016Q4 RR

RD

RR

2017Q1 R

RD

R

2017Q2 RD

RD

R

2017Q3 RD

D

RD

2017Q4 RR

RR

RR

2018Q1 R

RR

R

2018Q2 RD

R

R

2018Q3 D

RD

R

2018Q4 RR

RD

RR

2019Q1 RR

RD

RR

2019Q2 RD

D

RD

2019Q3 D

D

D

2019Q4 D

RR

RR

2020Q1 RD

RR

RD

2020Q2 RD

RD

RD

2020Q3 D

RD

D

2020Q4 RD

RD

RD

St. Louis EC

Band-Pass

Income

1995Q1 D

D

D

1995Q2 RD

RR

RR

1995Q3 D

R

RR

1995Q4 RD

R

R

1996Q1 RD

RD

RD

1996Q2 D

RD

RR

214

Alternative Methods for Calculating Fair Market Rents

1996Q3 RR

D

RR

1996Q4 RD

RR

RD

1997Q1 RD

RR

RD

1997Q2 D

RR

RR

1997Q3 RR

RR

RR

1997Q4 RD

R

RD

1998Q1 RD

R

RD

1998Q2 D

RD

D

1998Q3 RR

RD

RR

1998Q4 RD

RD

RD

1999Q1 RR

RD

RD

1999Q2 RD

D

D

1999Q3 RR

D

RR

1999Q4 RD

D

R

2000Q1 RD

RR

RD

2000Q2 D

RR

RR

2000Q3 RD

RR

RD

2000Q4 RR

RR

RR

2001Q1 RR

RR

RR

2001Q2 R

RR

R

2001Q3 RD

R

RD

2001Q4 RR

R

RR

2002Q1 RR

R

RR

2002Q2 R

RD

R

2002Q3 RR

RD

R

2002Q4 R

RD

R

2003Q1 R

D

R

2003Q2 RR

RR

RR

2003Q3 R

RR

R

2003Q4 RR

RR

RR

2004Q1 R

R

RR

2004Q2 R

R

R

2004Q3 RD

RD

R

2004Q4 RR

RD

RR

2005Q1 RR

RD

RR

2005Q2 R

RD

R

2005Q3 RD

D

R

2005Q4 RD

D

RD

2006Q1 RD

RR

RD

2006Q2 D

RR

D

2006Q3 D

RR

RD

2006Q4 D

RR

D

2007Q1 RR

RR

RR

2007Q2 RD

R

R

2007Q3 RD

R

RR

215

Alternative Methods for Calculating Fair Market Rents

2007Q4 D

R

R

2008Q1 RD

R

RD

2008Q2 D

RD

RR

2008Q3 RR

RD

RR

2008Q4 RR

RD

RR

2009Q1 RR

RD

RR

2009Q2 R

RD

R

2009Q3 RR

D

R

2009Q4 R

D

RR

2010Q1 R

D

RR

2010Q2 RR

D

R

2010Q3 R

D

R

2010Q4 RR

RR

RR

2011Q1 R

RR

RR

2011Q2 RD

RR

R

2011Q3 RD

RR

RD

2011Q4 D

R

RR

2012Q1 RD

R

R

2012Q2 RR

R

RR

2012Q3 R

R

R

2012Q4 RR

RD

R

2013Q1 RR

RD

RR

2013Q2 R

RD

R

2013Q3 R

RD

RR

2013Q4 R

RD

R

2014Q1 RD

RD

RD

2014Q2 D

RD

RD

2014Q3 RD

RD

RD

2014Q4 D

D

D

2015Q1 RD

D

RD

2015Q2 D

RR

RR

2015Q3 RR

RR

RR

2015Q4 RD

RR

R

2016Q1 RD

R

RD

2016Q2 D

R

RR

2016Q3 RR

RD

RR

2016Q4 R

RD

R

2017Q1 RR

RD

RR

2017Q2 R

D

R

2017Q3 RD

D

R

2017Q4 RD

RR

R

2018Q1 RD

RR

RR

2018Q2 RR

RR

RR

2018Q3 RD

R

RD

2018Q4 D

R

RR

216

Alternative Methods for Calculating Fair Market Rents

2019Q1 RR

RD

RR

2019Q2 RD

RD

RD

2019Q3 D

D

RR

2019Q4 D

RR

RR

2020Q1 RD

RR

RD

2020Q2 RR

RD

RD

2020Q3 RD

D

D

2020Q4 RD

RD

RD

Tampa Error-

Band-Pass

Income

Correction

1995Q1 D

D

D

1995Q2 RD

RD

RD

1995Q3 D

RD

RR

1995Q4 D

D

RR

1996Q1 RD

D

RD

1996Q2 RR

RD

RR

1996Q3 RD

RD

RR

1996Q4 D

RD

RR

1997Q1 RR

D

RR

1997Q2 R

D

R

1997Q3 RD

RR

R

1997Q4 RD

RR

R

1998Q1 RD

R

R

1998Q2 D

R

RR

1998Q3 RD

RD

RR

1998Q4 D

RD

RR

1999Q1 RR

RD

RR

1999Q2 RD

RD

R

1999Q3 RD

D

R

1999Q4 RD

RR

R

2000Q1 RD

RR

RD

2000Q2 D

RR

RR

2000Q3 D

R

RR

2000Q4 RR

R

RR

2001Q1 RR

RR

RR

2001Q2 RR

RR

RR

2001Q3 RR

RR

RR

2001Q4 RR

RR

RR

2002Q1 RR

R

RR

2002Q2 R

R

R

2002Q3 R

RD

R

2002Q4 R

RD

R

217

Alternative Methods for Calculating Fair Market Rents

2003Q1 RD

RD

RD

2003Q2 D

RD

RR

2003Q3 RD

D

RD

2003Q4 RD

D

RD

2004Q1 RD

D

RD

2004Q2 D

RD

D

2004Q3 RD

RD

D

2004Q4 D

D

RR

2005Q1 RD

D

RD

2005Q2 D

D

RR

2005Q3 D

RR

RR

2005Q4 D

RR

RR

2006Q1 D

RR

R

2006Q2 RR

RR

RR

2006Q3 RR

RR

RR

2006Q4 RR

RR

RR

2007Q1 RR

RR

RR

2007Q2 R

R

R

2007Q3 RR

R

R

2007Q4 R

R

R

2008Q1 R

R

R

2008Q2 RR

RD

RR

2008Q3 RR

RD

R

2008Q4 R

RD

RR

2009Q1 RR

RD

RR

2009Q2 R

RD

R

2009Q3 R

RD

RD

2009Q4 RD

D

RD

2010Q1 RD

D

RD

2010Q2 D

D

D

2010Q3 RD

D

D

2010Q4 D

D

D

2011Q1 RD

D

RD

2011Q2 D

D

D

2011Q3 RD

RR

D

2011Q4 D

RR

RR

2012Q1 RR

RR

RR

2012Q2 RR

R

RR

2012Q3 R

R

RR

2012Q4 RR

R

RR

2013Q1 RR

R

RR

2013Q2 R

RR

R

2013Q3 R

RR

R

2013Q4 R

RR

R

2014Q1 RD

R

R

218

Alternative Methods for Calculating Fair Market Rents

2014Q2 D

R

RR

2014Q3 RR

R

RR

2014Q4 RR

R

RR

2015Q1 R

R

R

2015Q2 RR

RD

RR

2015Q3 RR

RD

RR

2015Q4 RR

RD

RR

2016Q1 RR

RD

RR

2016Q2 R

D

R

2016Q3 RR

D

RR

2016Q4 R

RR

RR

2017Q1 RR

RR

RR

2017Q2 R

R

R

2017Q3 RR

RD

R

2017Q4 R

RD

R

2018Q1 RD

RD

RD

2018Q2 RR

D

RR

2018Q3 RR

D

RR

2018Q4 RR

RR

RR

2019Q1 RR

RR

RR

2019Q2 R

R

R

2019Q3 R

R

R

2019Q4 R

R

R

2020Q1 R

RD

R

2020Q2 RD

D

R

2020Q3 RD

RD

R

2020Q4 RD

RD

R

219

Alternative Methods for Calculating Fair Market Rents

References

Baumeister, Christiane, Lutz Kilian, and Xiaoqing Zhou. 2017. “Are Product Spreads Useful For Forecasting Oil Prices? An Empirical Evaluation Of The Verleger Hypothesis,”

Macroeconomic Dynamics 22 (3): 562–80. doi:10.1017/s1365100516000237.

Baxter, Marianne, and Robert King. 1995. Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series. NBER Working Paper No. 5022. Cambridge, MA: National Bureau of Economic Research. doi:10.3386/w5022.

Christiano, Lawrence, and Terry J. Fitzgerald. 1999. The Band Pass Filter. NBER Working Paper No. 7257. Cambridge, MA: National Bureau of Economic Research.

doi:10.3386/w7257.

Dickey, David A., and Wayne A. Fuller. 1979. “Distribution of the Estimators for Autoregressive Time Series With a Unit Root,” Journal of the American Statistical Association 74 (366a): 427–31. doi:10.2307/2286348.

Johansen, Søren. 1991. “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models,” Econometrica 59 (6): 1551–80.

doi:10.2307/2938278.

Sims, Christopher A. 1980. “Macroeconomics and Reality,” Econometrica 48 (1): 1–48.

doi:10.2307/1912017.

2M Research. 2019. Deriving Local Trend Factors for Fair Market Rent Estimation.

https://www.huduser.gov/portal/sites/default/files/pdf/MDRT-LocalTrendFactor.pdf.

U.S. Census Bureau. 2022. “Census Bureau Releases Experimental 2020 American Community Survey 1-Year Data.” Release Number CB22-CN.08. Washington, DC: U.S. Census Bureau. https://www.census.gov/newsroom/press-releases/2021/experimental-2020-acs-

1-year-data.html.

———. n.d. “2020 ACS 1-Year Experimental Data Release.” https://www.census.gov/programs-

surveys/acs/data/experimental-data.html.

220

U.S. Department of Housing and Urban Development Office of Policy Development and Research

Washington, DC 20410-6000

April 2023

Document Outline

- Fair Market Rents Trend Component Modeling Technical Report

- DISCLAIMER

- Table of Contents

- List of Exhibits

- Executive Summary

- Introduction

- Alternative Calculations to Account for Areas with Rapidly Rising Rents

- Variables

- Dependent Variables

- Additional Variables

- Rent of Primary Residence CPI Model Variables

- Fuel and Utility CPI Model Variables

- CPI Modeling Approach

- Rent of Primary Residence Model

- Utilities and Fuels CPI Component Model

- Rapidly Rising Rent Analysis

- Statistical Approach

- Summary of Results

- Alternative Data Sets and Case Study

- Hypothetical Rent Adjustment Process:

- Conclusions

- Final Considerations and Next Steps

- 2019 Senate Committee on Appropriations Report (S. Rept. 116-109)

- COVID-19 Impact

- Alternative Methodologies

- Implementation

- Possible Areas for Further Study or Review

- Recent Mover Adjustment Factor

- ACS 5-Year Factor and Trend Factor

- Small Area FMRs (SAFMRs)

- Appendix A: Model Estimations and Forecast Evaluations

- Alaska

- Atlanta:

- Baltimore

- Boston:

- Dallas:

- Denver:

- Detroit:

- Honolulu:

- Houston:

- Los Angeles:

- Miami:

- Minneapolis:

- New York/New Jersey:

- Philadelphia:

- Phoenix:

- San Diego:

- Seattle

- San Francisco

- St. Louis

- Tampa

- Washington DC

- Atlanta

- Chicago

- Boston

- Dallas

- Denver

- Detroit

- Honolulu

- Houston

- Miami

- Philadelphia

- New York

- San Francisco

- San Diego

- Phoenix

- Seattle

- Appendix B: Summary of Rapidly Rising Rent Analysis

- Error-Correction Residual (Normalized Scaling)

- Band-Pass Filter 2-8 Year Component (Normalized Scaling)

- Rent-to-Real Income Ratio

- Rent-to-Real Home Price Ratio

- Appendix C: Alternative Data Set Analysis

- Appendix D: Summary of Augmented Dickey-Fuller Tests

- Appendix E: Rapidly Rising Rents Dashboard

- References

Table of Contents

Fair Market Rents Trend Component Modeling Technical Report

DISCLAIMER

Table of Contents

List of Exhibits

Executive Summary

Introduction

Alternative Calculations to Account for Areas with Rapidly Rising Rents

Variables

Dependent Variables

Additional Variables

Rent of Primary Residence CPI Model Variables

Fuel and Utility CPI Model Variables

CPI Modeling Approach

Rent of Primary Residence Model

Utilities and Fuels CPI Component Model

Rapidly Rising Rent Analysis

Statistical Approach

Summary of Results

Alternative Data Sets and Case Study

Hypothetical Rent Adjustment Process:

Conclusions

Final Considerations and Next Steps

2019 Senate Committee on Appropriations Report (S. Rept. 116-109)

COVID-19 Impact

Alternative Methodologies

Implementation

Possible Areas for Further Study or Review

Recent Mover Adjustment Factor

ACS 5-Year Factor and Trend Factor

Small Area FMRs (SAFMRs)

Appendix A: Model Estimations and Forecast Evaluations

Alaska

Atlanta:

Baltimore

Boston:

Dallas:

Denver:

Detroit:

Honolulu:

Houston:

Los Angeles:

Miami:

Minneapolis:

New York/New Jersey:

Philadelphia:

Phoenix:

San Diego:

Seattle

San Francisco

St. Louis

Tampa

Washington DC

Atlanta

Chicago

Boston

Dallas

Denver

Detroit

Honolulu

Houston

Miami

Philadelphia

New York

San Francisco

San Diego

Phoenix

Seattle

Appendix B: Summary of Rapidly Rising Rent Analysis

Error-Correction Residual (Normalized Scaling)

Band-Pass Filter 2-8 Year Component (Normalized Scaling)

Rent-to-Real Income Ratio

Rent-to-Real Home Price Ratio

Appendix C: Alternative Data Set Analysis

Appendix D: Summary of Augmented Dickey-Fuller Tests

Appendix E: Rapidly Rising Rents Dashboard

References