Alternative Methods for

Calculating Fair Market Rents

(FMRs) in Rental Markets with

Rapidly Rising Rents

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

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Alternative Methods for Calculating Fair Market Rents (FMRs) in Rental Markets

with Rapidly Rising Rents

Prepared for

U.S Department of Housing and Urban Development

Office of Policy Development and Research

Prepared by

Daniel McMillen

University of Illinois at Chicago

Ruchi Singh

University of Georgia

January 2022

Acknowledgments

The authors would like to thank the U.S. Department of Housing and Urban Development’s Office of Policy Development and Research assistance, especially Adam Bibler, Kurt Usowski, Chalita Brandly, and Marie Lihn, for providing invaluable guidance throughout the study.

Table of Contents

Executive Summary ...................................................................................................................... v

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

1.1 Study Objective ..................................................................................................................... 3

2. Data ............................................................................................................................................ 5

2.1 Axiometrics Data................................................................................................................... 5

2.2 Zillow Data ............................................................................................................................ 5

2.3 House Price Index From the Federal Housing Finance Agency ........................................... 6

3. Methodological Framework ..................................................................................................... 7

3.1 Identifying Markets with Rapidly Rising Rents .................................................................... 7

3.2 Alternative Methods for Calculating FMR ........................................................................... 9

3.3 Predicting Rent Using Axiometrics Data ............................................................................ 13

3.4 Price-to-Rent Ratio Using Zillow Data ............................................................................... 20

3.5 Price-to-Rent Ratio Using the FHFA House Price Index ................................................... 27

3.6 Autoregressive Integrated Moving Average (ARIMA) Models ......................................... 31

4. Conditions Under Which HUD Should Use Alternative Methods ..................................... 32

Appendix A .................................................................................................................................. 33

Appendix B .................................................................................................................................. 34

5. References ................................................................................................................................ 37

iii

List of Exhibits

Exhibit 1.1: Case-Shiller Home Price Index ....................................................................................2

Exhibit 1.2: Zillow Rent Index ........................................................................................................3

Exhibit 3.1: Metro Areas with Rapidly Rising Rents ......................................................................7

Exhibit 3.2: The 60 Metro Areas with Rapidly Rising Rents ..........................................................9

Exhibit 3.3: Regression Results of 5-Year ACS on 5-Year Effective Rent...................................11

Exhibit 3.4: Regression Results of 5-Year ACS on 1-Year Effective Rent...................................12

Exhibit 3.5: Regression Results of Change in 5-Year ACS on Change in Effective Rent ............13

Exhibit 3.6: Comparison of Predicted Rents Using Axiometrics Data to ACS Values .................14

Exhibit 3.7: Predicted Rent Using Axiometrics Data ....................................................................16

Exhibit 3.8: Comparison of Predicted Rents Using CPI Factor for the Year 2018 .......................20

Exhibit 3.9: Comparison of Predicted Rents Using Zillow Data to ACS Values ..........................22

Exhibit 3.10: Predicted Rents Using Zillow Data ..........................................................................23

Exhibit 3.11: Comparison of Predicted Rents Using CPI Factor for the Year 2019 .....................27

Exhibit 3.12: Summary Statistics of Errors for House Values Forecasts ......................................28

Exhibit 3.13: Comparison of Predicted Rent Using the FHFA House Price Index to ACS Values

........................................................................................................................................................29

Exhibit 3.14: Comparison of Predicted Rent Using the FHFA House Price Index to ACS Values

from 2014 and Onwards.................................................................................................................30

Exhibit 3.15: Comparison of Predicted Rent Using the FHFA House Price Index to ACS by Year

........................................................................................................................................................31

Appendix Exhibit A.1: Price to Rent Ratio Using ACS Median Rent and Zillow Home Value

Index ..............................................................................................................................................33

Appendix Exhibit B.1: Crosswalk Between CBSA, FMR Area, and Zillow Region ....................34

iv

Executive Summary

The U.S. Department of Housing and Urban Development (HUD) determines the expected cost of a standard-quality rental housing unit. It sets the “Fair Market Rent” (FMR), which serves as a benchmark for the Housing Choice Voucher and other public programs. HUD calculates the FMR at the 40th percentile of the metropolitan area or nonmetropolitan county rents. Using the FMR as the benchmark, local housing authorities set a local payment standard (PS), usually 90 to 110 percent of FMR.

A key objective when setting the FMR is to maintain an adequate supply of low-income housing, which makes accurate FMR calculations especially important, particularly in markets experiencing rapidly rising rents. Reliable data from sources such as the American Community Survey (ACS) often lag by several years, making accurate FMR estimation more difficult.

Recently, HUD has taken several steps to improve FMR calculations, such as using local and regional trend factors to forecast rent and implementing Small Area Fair Market Rents (SAFMRs) in some metropolitan areas. However, improving the accuracy of FMR calculations for areas witnessing rapid rent increases merits additional research.

This project identifies regions with rapidly rising rents by analyzing the ACS data. Two new methods are proposed for calculating FMR, especially for regions witnessing rapid rent increases. The first method uses rent indices from Axiometrics to update data from ACS. The second method calculates the price-to-rent ratio using the Zillow home value index and the rent data from ACS and then uses that ratio with the Zillow home value index to calculate FMR. In addition, we estimate the rent using the House Price Index (HPI) dataset provided by the Federal Housing Finance Agency (FHFA) instead of using the Zillow data. These methods can be used as additional inputs to determine the FMR.

v

1. Introduction

The U.S. Department of Housing and Urban Development (HUD) annually estimates the Fair Market Rent (FMR) for more than 600 metropolitan areas and about 2,000 nonmetropolitan areas. FMRs are estimates of gross rent and are used as a benchmark for HUD’s assisted housing programs. Accurate measures of the FMR are needed to accomplish HUD’s goal of successfully housing as many families receiving vouchers as possible. An FMR that is too low will severely limit the selection of units and neighborhoods, whereas an FMR that is too high will reduce the number of low-income families whom HUD can serve.

Generally, the FMR is the gross rent (shelter plus utilities) that would need to be paid in an area for a modest (nonluxury) rental unit. The FMR is targeted at the 40th percentile of the distribution of gross rents (CFR 888.113).

Currently, HUD’s FMR calculation is based on three components: 1. A base rent, calculated using the Census Bureau’s 5-year American Community Survey (ACS) data and a recent-mover factor based on 1-year ACS data.

2. An inflation factor, estimated using the Consumer Price Index (CPI), is used to update the ACS to the current level. Local CPIs are used for the 22 metro areas where they are available; otherwise, a regional index is used.

3. A trend factor, used to forecast the rent values for the next fiscal year. In fiscal year 2020, HUD replaced the national trend factor with local and regional trend factors to improve the accuracy of rent calculations.

HUD makes additional adjustments for the number of bedrooms. Moreover, in some metropolitan areas, payment standards are based on Small Area Fair Market Rents (SAFMRs), which are calculated at the ZIP Code level.

The ACS is conducted annually and has replaced the “long-form” data, which were collected once every 10 years during the decennial census. Although the advantage of the ACS is that it allows more current data to be used, the ACS rents still lag behind the timing of the FMR by three years. In contrast to the 10-year cycle of the census, the annual nature of the ACS helps to account for variations in rents over the business cycle, including both booms and busts, although with somewhat delayed timing. For instance, using this methodology, the 2008 Great Recession would not be reflected in the data for at least a year, at which point the economy may have already started to recover. To update the ACS to the current levels, HUD relies on the CPI.

More importantly, different FMR areas are likely to be at different stages of the real estate cycle.

Exhibit 1.1 shows the Case-Shiller Home Price Index for a selected set of large metro areas. The graph clearly indicates substantial heterogeneity in both the timing of the bust and recovery and the magnitude of price changes. This substantial heterogeneity in price is also likely to be reflected in divergences in rent changes across those regions.

1

Exhibit 1.1. Case-Shiller Home Price Index

Case-Shiller Home Price Index

300

January 2000 = 100

250

200

150

100

50 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

USA

Chicago

Cleveland

Los Angeles

San Francisco

Source: Federal Reserve Economic Data (FRED)

2

Exhibit 1.2. Zillow Rent Index

Rent

January 2014 = 100

160

150

140

130

120

110

100

90

14

15

16

17

18

19

20

21

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

Jan-

USA

Chicago

Cleveland

Los Angeles

San Francisco

Source: Zillow

The substantial heterogeneity across the regions indicates a need to use a local trend factor while adjusting the ACS rent values to current levels. HUD uses a regional inflation factor for most areas (except 22 metro areas where local CPI is available, although the top 22 metro areas account for 40 percent of the country’s population). The regional indices ignore local variation, and rents may vary even within an urban area. Using regional trend factors (HUD started using local trend factors in FY 2020) might lead to significant differences between the FMR and actual market rents, especially in regions with rapidly rising rents.

We suggest alternative methods for calculating FMR that might improve its accuracy, especially for regions with rapidly rising rents. We propose two new methods to supplement the current methodology used to calculate FMR. The two methods are as follows: 1. Using Axiometrics data to adjust ACS values.

2. Applying price-to-rent ratio using Zillow data and FHFA’s HPI.

We also reviewed the current method used by HUD to estimate the local trend factors using autoregressive integrated moving average (ARIMA) models. We did not have any additional suggestions to substantially improve the currently used procedure.

1.1 Study Objective

The purpose of this study is to present alternative methods to calculate the FMR in rental markets with rapidly rising rents. More specifically, we will answer the following research questions: What criteria should be used to define a housing market with rapidly rising rents?

3

What criteria should be used to evaluate which alternative methods are better than the current ones?

Under what conditions should HUD implement the alternative method for calculating FMRs, and at what point are the alternative methods no longer needed?

What data that are not currently being used should HUD use to calculate FMRs in housing markets with rapidly rising rents?

Beyond alternative sources of data, what calculation techniques should HUD use when calculating FMRs in markets with rapidly rising rents and more generally?

For metropolitan areas, how do the alternative methods for calculating FMRs change the calculation of metropolitan-area-wide FMRs and SAFMRs?

4

2. Data

The key data we use in this project are the 5-year ACS data for all renters for two-bedroom units.

We also use commercial data sources such as Axiometrics and Zillow to supplement our analysis. Apart from those commercially available datasets, we use the House Price Index (HPI) provided by FHFA and CPI data.

2.1 Axiometrics Data

The Axiometrics data are a survey of rental properties and include data on asking rent, effective rent, occupancy rate, number of units, average size of units, etc. The data are available at the individual property level and include the property’s geographic coordinates, which enables the creation of summary statistics (median, 40th percentile, etc.) for various geographies. The key variable that we analyze is the effective rent, which is the asking rent minus concessions. We use effective rent because it might reflect current rent more accurately as concessions might vary depending on the demand for the apartment units.

We aggregate the data at the Core Based Statistical Area (CBSA) level for our analysis. We construct the effective yearly rent by taking the average of the four quarters. For the rest of the analysis, we use this panel of effective rent data at the CBSA year level.

A disadvantage of the Axiometrics data is that the data track only apartments and student housing. Therefore, understanding the trends in rental data for single-family housing is not possible using this data. Second, several CBSAs have fewer than 30 properties with rent data in every period, which is likely to make the data less accurate for those CBSAs due to the small sample size.

2.2 Zillow Data

The Zillow Home Value Index (ZHVI) is a smoothed, seasonally adjusted measure of typical home value in the 35th to 65th percentiles. It can be used to measure market changes across a given region and housing type. The ZHVI is based on “Zestimates” calculated on more than 100

million new homes, including new homes and homes that have not had any transactions in many years. The Zestimate is based on machine learning models and uses data from various sources, including public data, user-generated data, and data from multiple listing services. We use the ZHVI at the CBSA level. Zillow provides the data at the metropolitan level (using its own definitions of metropolitan areas), and we use a crosswalk to match the metropolitan areas to the CBSA to make the data comparable. We create a yearly estimate of Zillow home value at the CBSA level by taking the average of the monthly value.

We downloaded the Zillow Observed Rent Index (ZORI), a smoothed measure of the typical observed market rent across a given region. Similar to ZHVI, ZORI is a repeat-rent index, and the index is dollar-denominated and calculated by taking the mean of the middle 20 percent (the 40-to-60th percentile) of the asking rent. The index is weighted to reflect the rental housing stock to ensure that the rent index is representative of the market and not just homes currently listed for rent. We did not use ZORI in our analysis but recommend that this rent index be used with ZHVI to determine the trend in the price-to-rent ratio. As discussed later, the price-to-rent ratio should 5

be adjusted if the ratio (computed using Zillow home values and Zillow rent) changes drastically from one year to another.

One of the disadvantages of the Zillow Indexes is that they are a “black box,” and we do not know the exact model being used and the assumptions being made. Additionally, the Zillow data are only available from 2014, providing a limited number of years in which to evaluate the data compared to the ACS.

2.3 House Price Index From the Federal Housing Finance Agency The FHFA index is computed using sales prices and appraisal values for mortgages bought or guaranteed by Fannie Mae and Freddie Mac. 1 The FHFA HPI is a weighted, repeat-sales index, which measures average price changes in repeat sales or refinancings on the same properties.

Those indices are available monthly and quarterly at various levels of geographic aggregation.

The main advantage of this index is its length, as the series data are available starting in 1975.

We use the HPI at the CBSA year level for our analysis.

1 The FHFA index that was downloaded is the All-Transactions Indexes (estimated using sales prices and appraisal data), metropolitan statistical areas and divisions (not seasonally adjusted).

6

3. Methodological Framework

In this section, we discuss the methodological framework that we use to answer the research questions.

3.1 Identifying Markets with Rapidly Rising Rents

Rents have appreciated significantly over the past few years. Rising rents coupled with stagnant incomes have led to an affordability crisis. In this project, we begin by identifying areas that have witnessed a rapid rent increase.

To identify the area with rapidly rising rents, we use 5-year ACS data for 2005 through 2009 to 2014 through 2018 for all renters and focus on the two-bedroom units. We calculate the change in 5-year estimates of the 40th percentile of the CBSA rent and then compute the average increase in rents over our sample period, and sort the data in descending order of rent increase. 2

Then, we select the 60 areas with the highest average rent increase over this period. 3 We use the 5-year ACS data to provide better geographic coverage. However, about 50 percent of those areas also have the highest annual rent increases using the ACS 1-year data. When we use the 1-year ACS data, we find that 33 of the 60 areas selected are among the top 60 areas with the highest average annual rent increase using the 1-year ACS data.

We supplement that analysis with additional data. Some of the areas meet one or more of the following criteria:

Areas that conducted an ad hoc rent survey.

Areas that requested revaluation between FY 2016 and FY 2021.

Areas with payment standards higher than 120 percent at least once between 2002 and 2017.

Areas with low supply elasticity using Saiz’s measure. Saiz (2010) calculates the supply elasticities for metro areas with a population greater than 500,000.

Exhibit 3.1. Metro Areas with Rapidly Rising Rents

CBSA Code

CBSA Name

10540

Albany, OR MSA

11020

Altoona, PA MSA

12420

Austin-Round Rock, TX MSA

13740

Billings, MT MSA

13900

Bismarck, ND MSA

13980

Blacksburg-Christiansburg-Radford, VA MSA

14500

Boulder, CO MSA

2 CBSA definitions are periodically changed by the Office of Management and Budget. Therefore, not all of the CBSAs are comparable over time. The main change was between 2013 and 2014. In our sample of 60 metropolitan areas, the following metro areas had changed: Charleston, WV MSA; Elizabethtown-Fort Knox, KY MSA; Manhattan, KS MSA; and Victoria, TX MSA.

3 For some CBSAs, the data are available for a shorter period, so the average rent increase is computed using the shorter period for which data are available.

7

14740

Bremerton-Silverdale, WA MSA

15540

Burlington-South Burlington, VT MSA

16220

Casper, WY MSA

16620

Charleston, WV MSA

16700

Charleston-North Charleston, SC MSA

17820

Colorado Springs, CO MSA

18700

Corvallis, OR MSA

19060

Cumberland, MD-WV MSA

19740

Denver-Aurora-Lakewood, CO MSA

20220

Dubuque, IA MSA

21060

Elizabethtown-Fort Knox, KY MSA

21340

El Paso, TX MSA

21420

Enid, OK MSA

22020

Fargo, ND-MN MSA

22380

Flagstaff, AZ MSA

22660

Fort Collins, CO MSA

24220

Grand Forks, ND-MN MSA

24420

Grants Pass, OR MSA

24540

Greeley, CO MSA

25420

Harrisburg-Carlisle, PA MSA

25980

Hinesville, GA MSA

26380

Houma-Thibodaux, LA MSA

27860

Jonesboro, AR MSA

28420

Kennewick-Richland, WA MSA

30140

Lebanon, PA MSA

31340

Lynchburg, VA MSA

31740

Manhattan, KS MSA

31860

Mankato-North Mankato, MN MSA

33260

Midland, TX MSA

34060

Morgantown, WV MSA

34900

Napa, CA MSA

35620

New York-Newark-Jersey City, NY-NJ-PA MSA

36220

Odessa, TX MSA

36500

Olympia-Tumwater, WA MSA

38900

Portland-Vancouver-Hillsboro, OR-WA MSA

39660

Rapid City, SD MSA

41420

Salem, OR MSA

41620

Salt Lake City, UT MSA

41700

San Antonio-New Braunfels, TX MSA

41860

San Francisco-Oakland-Hayward, CA MSA

41940

San Jose-Sunnyvale-Santa Clara, CA MSA

42220

Santa Rosa, CA MSA

42660

Seattle-Tacoma-Bellevue, WA MSA

8

44940

Sumter, SC MSA

45540

The Villages, FL MSA

46300

Twin Falls, ID MSA

46520

Urban Honolulu, HI MSA

47020

Victoria, TX MSA

47460

Walla Walla, WA MSA

47900

Washington-Arlington-Alexandria, DC-VA-MD-WV MSA

48300

Wenatchee, WA MSA

48540

Wheeling, WV-OH MSA

48700

Williamsport, PA MSA

These areas are located throughout the country, as can be seen in exhibit 3.2.

Exhibit 3.2. The 60 Metro Areas with Rapidly Rising Rents Source: Arc GIS, NHGIS, Author’s calculations

3.2 Alternative Methods for Calculating FMR

In this section, we present two alternative methods for calculating FMR.

1. Using Axiometrics Data

We find a strong positive correlation between effective rent data in Axiometrics and the 5-year ACS data. However, we find that the percentage change in 5-year ACS data and the percentage change in effective rent using Axiometrics data are very different for some metro areas. In some instances, the change in the effective rents using Axiometrics data is much bigger than the ACS

change. Thus, we propose using the local correlation to predict FMR.

2. Price-to-Rent Ratio

The second method uses the price-to-rent ratio to estimate FMR because (at the margin) a household is likely to be indifferent about whether they obtain housing services through renting or through owning. Thus, in equilibrium, the cost of renting should be equal to the annual cost of owning.

9

Price-to-Rent Ratio Using Zillow Data

We calculate the price-to-rent ratio for each CBSA by dividing the average Zillow home value over 5 years by the 40th percentile of rent from the ACS 5-year file. Then, we use this price-torent ratio with the Zillow home value index to estimate rent.

Price-to-Rent Ratio Using Federal Housing Finance Agency’s House Price Index This method is similar to the second method previously discussed, but instead of using Zillow data, we use other price indices that are readily available: the HPI dataset provided by FHFA.

We first forecast home values using the HPI and then use it with the price-to-rent ratio to estimate rent.

This price-to-rent approach provides a clear advantage because getting reliable house price indices is much easier, but that is not the case for rent indices.

We do not prefer one index over the other and recommend that both be used to obtain a range of FMR estimates.

First, the authors calculate the 5-year moving average of median effective rent using Axiometrics data for each metro area. Next, we run a simple linear regression with the 5-year ACS as the dependent variable, and the results of the analysis are summarized in exhibit 3.3.

10

Exhibit 3.3. Regression Results of 5-Year ACS on 5-Year Effective Rent 5-year ACS

Item

1

2

3

4

5

6

7

8

5-year effective rent

0.6289*** 0.7191*** 1.0961*** 1.2156*** 1.1534*** 1.1328***

-0.0382

0.0183

(0.0124)

(0.1331)

(0.2344)

(0.2650)

(0.2968)

(0.3143)

(0.0568)

(0.0554)

Lag of 5-year effective rent

-0.1022

-1.0927** -1.4467** -1.2600*

-1.3001*

0.1423

0.0361

(0.1423)

(0.4484)

(0.6068)

(0.6881)

(0.7388)

(0.1302)

(0.1259)

Lag 2 of 5-year effective rent

0.6298***

0.8899

0.7422

0.9408

0.1391

0.2100

(0.2418)

(0.6052)

(0.7981)

(0.9227)

(0.1614)

(0.1542)

Lag 3 of 5-year effective rent

-0.0213

-0.1066

-0.0524

-0.0989

-0.2809*

(0.2751)

(0.6773)

(0.9385)

(0.1638)

(0.1606)

Lag 4 of 5-year effective rent

0.1096

-0.4758

-0.2997**

-0.0614

(0.3027)

(0.7991)

(0.1395)

(0.1422)

Lag 5 of 5-year effective rent

0.3969

0.1457**

0.0735

(0.3637)

(0.0636)

(0.0624)

Lag 1 of ACS 5-year

1.0401*** 1.3895***

(0.0132)

(0.0762)

Lag 2 of ACS 5-year

-0.3680***

(0.0791)

Observations

464

409

353

300

251

202

202

202

Adjusted R-Squared

0.8480

0.8528

0.8586

0.8640

0.8692

0.8756

0.9962

0.9966

AIC

5522.5

4863.9

4195.8

3567.1

2986.0

2405.0

1700.8

1681.3

BIC

5530.8

4876.0

4211.3

3585.6

3007.2

2428.1

1727.2

1711.1

ACS = American Community Survey. AIC = Akaike information criterion. BIC = Bayesian information criterion.

* = Significant at 90th percent confidence level. ** = Significant at 90th percent confidence level. *** = Significant at 99th percent confidence level.

11

Exhibit 3.3 indicates a strong positive correlation between the 5-year ACS and the 5-year moving average of effective rent using Axiometrics data. The analysis using the asking rents variable in Axiometrics is similar, with a high correlation between asking rent and effective rent.

We use effective rent for our analysis because forecasts of effective rent are available for some metro areas, which might be helpful in forecasting FMR rents for the next fiscal year.

Next, we analyze the correlation between 5-year ACS and 1-year effective rent, and we again find a high correlation. The regression results are summarized in exhibit 3.4.

Exhibit 3.4. Regression Results of 5-Year ACS on 1-Year Effective Rent 5-year ACS

Item

1

2

Effective rent

0.5411*** 0.2643***

(0.0114)

(0.0590)

Lag of effective rent

0.2963***

(0.0624)

Observations

461

440

Adjusted R-Squared

0.8296

0.8382

AIC

5539.5

5271.3

BIC

5547.8

5283.5

ACS = American Community Survey. AIC = Akaike information criterion. BIC = Bayesian information criterion.

* = Significant at 90th percent confidence level. ** = Significant at 90th percent confidence level. *** = Significant at 99th percent confidence level.

Lastly, we analyze the correlation between change in 5-year ACS and the change in effective rent and lagged values of change in effective rent. The regression results are summarized in exhibit 3.5.

12

Exhibit 3.5. Regression Results of Change in 5-Year ACS on Change in Effective Rent Change in 5-year ACS

Item

1

2

3

4

Change in effective rent

0.0124

0.0069

0.0016

0.0032

(0.0140)

(0.0130)

(0.0123)

(0.0128)

Lag of change in effective rent

0.0412***

0.0485*** 0.0505*** 0.0433***

(0.0143)

(0.0134)

(0.0128)

(0.0141)

Lag 2 of change in effective rent

0.0556***

0.0694*** 0.0756*** 0.0784***

(0.0145)

(0.0137)

(0.0132)

(0.0140)

Lag 3 of change in effective rent

0.1013***

0.0891*** 0.0843*** 0.0888***

(0.0142)

(0.0141)

(0.0134)

(0.0151)

Lag 4 of change in effective rent

0.0739*** 0.0879*** 0.0909***

(0.0149)

(0.0143)

(0.0165)

Lag 5 of change in effective rent

0.0888*** 0.0751*** 0.0682***

(0.0151)

(0.0153)

(0.0167)

Lag 6 of change in effective rent

0.1091*** 0.1044***

(0.0158)

(0.0167)

Lag 7 of change in effective rent

0.0013

-0.0005

(0.0164)

(0.0176)

Lag 8 of change in effective rent

-0.0335*

(0.0187)

Lag 9 of change in effective rent

-0.0254

(0.0166)

Observations

346

314

294

254

Adjusted R-Squared

0.2396

0.4251

0.5253

0.5458

AIC

3019.5

2670.0

2454.6

2128.9

BIC

3038.7

2696.3

2487.7

2167.8

ACS = American Community Survey. AIC = Akaike information criterion. BIC = Bayesian information criterion.

* = Significant at 90th percent confidence level. ** = Significant at 90th percent confidence level. *** = Significant at 99th percent confidence level.

The exhibits indicate an overall high correlation between effective rent data in Axiometrics and the 5-year ACS data. Therefore, Axiometrics data offer potential improvements in FMR

calculation in areas with rapidly rising rents, given that they are available ahead of ACS releases.

3.3 Predicting Rent Using Axiometrics Data

We find a strong positive correlation between effective rent data in Axiometrics and the 5-year ACS data. However, we find that the percentage change in 5-year ACS data and the percentage change in effective rent using Axiometrics data are very different for some metro areas. In some instances, the change in effective rents is much bigger than the ACS change. We propose using the local correlation to predict FMR.

We calculate the 5-year moving average of effective rent using Axiometrics data for each metro area. Next, we calculate the ratio as the 5-year ACS divided by the 5-year moving average of 13

effective rent in 2017. Finally, we predict the rent in 2018 by multiplying this ratio by the 5-year moving average of effective rent in 2018.

To assess the accuracy of this alternative measure, we benchmark it against rents from the ACS

data. We calculate the percentage error using the following formula: (Predicted rent − ACS 5 year rent)

Error =

ACS 5 year rent

∗ 100

Using the steps previously described, when we predict the rent in 2018, we get an error that is summarized in exhibit 3.6.

Exhibit 3.6. Comparison of Predicted Rents Using Axiometrics Data to ACS Values Summary statistics of the error (%)

Minimum

-7.4399

10th percentile

-3.9521

25th percentile

-2.0174

50th percentile

-0.5430

75th percentile

0.6800

90th percentile

2.0964

Maximum

5.4160

Mean

-0.8047

Standard Deviation

2.4234

Observations

56

ACS = American Community Survey.

The number of observations in the previous analysis is 56 because Axiomertics data do not cover all of the 60 areas of rapidly rising rents that we identified. The four CBSAs that Axiometrics does not cover are—

• Dubuque, IA MSA.

• Grants Pass, OR MSA.

• Twin Falls, ID MSA.

• Urban Honolulu, HI MSA.

The minimum and maximum of this error are smaller than 8 percent, so even if we cannot predict the FMR correctly, this small error can easily be corrected by using 90 to 110 percent of the payment standards.

The overall error is small, in the range of -7.5–5.5 percent. A negative error indicates that the ACS rent is higher than the predicted rent, whereas a positive error indicates that the ACS rent is lower than the predicted rent. The median error for the sample is -0.54 percent.

Exhibit 3.7 shows the predicted rent for each of the CBSAs. The variable definitions are as follows:

14

5-year ACS in 2018: 40th percentile of the 5-year ACS rent in 2018.

Effective rent in 2018: Yearly effective rent from Axiometrics in 2018.

5-year effective rent in 2018: 5-year moving average of effective rent.

Ratio in 2017: Ratio of 5-year ACS and 5-year effective rent for 2017.

Predicted rent in 2018: Ratio multiplied by the 5-year effective rent in 2018.

Error (%): Percentage difference between predicted rent and 5-year ACS in 2018.

15

Exhibit 3.7. Predicted Rent Using Axiometrics Data

5-Year

CBSA

5-Year Effective Effective Ratio in Predicted Error

Code

CBSA Name

ACS in

Rent in

Rent in

2018 ($) 2018 ($) Rent in

2017

(%)

2018 ($)

2018 ($)

10540 Albany, OR MSA

857 1,004.25

881.13

0.9946

876.37

2.26

11020 Altoona, PA MSA

713

907.50

911.88

0.7585

691.68

-2.99

12420 Austin-Round Rock, TX MSA

1,184 1,152.75 1,095.10

1.0634 1,164.53

-1.64

13740 Billings, MT MSA

816

970.75

877.10

0.9195

806.53

-1.16

13900 Bismarck, ND MSA

814

991.75

986.25

0.8033

792.21

-2.68

13980 Blacksburg-Christiansburg-Radford, VA MSA

733 1,154.25 1,082.55

0.6838

740.21

0.98

14500 Boulder, CO MSA

1,319 1,597.00 1,445.00

0.9071 1,310.72

-0.63

14740 Bremerton-Silverdale, WA MSA

1,063 1,388.25 1,240.35

0.8613 1,068.27

0.50

15540 Burlington-South Burlington, VT MSA

1,212 1,644.50 1,642.00

0.7090 1,164.10

-3.95

16220 Casper, WY MSA

783

776.25

841.90

0.8984

756.40

-3.40

16620 Charleston, WV MSA

714

746.50

725.60

0.9822

712.68

-0.19

16700 Charleston-North Charleston, SC MSA

978 1,130.00 1,033.75

0.9525

984.62

0.68

17820 Colorado Springs, CO MSA

959 1,049.25

940.45

1.0206

959.79

0.08

16

18700 Corvallis, OR MSA

920 1,117.75

998.40

0.9237

922.20

0.24

19060 Cumberland, MD-WV MSA

644

799.75

789.75

0.7618

601.62

-6.58

19740 Denver-Aurora-Lakewood, CO MSA

1,228 1,468.00 1,339.45

0.9076 1,215.64

-1.01

21060 Elizabethtown-Fort Knox, KY MSA

703

729.00

713.30

0.9445

673.71

-4.17

21340 El Paso, TX MSA

745

737.25

716.70

1.0197

730.80

-1.91

21420 Enid, OK MSA

746

702.25

739.75

0.9334

690.50

-7.44

22020 Fargo, ND-MN MSA

775

767.75

731.60

1.0415

761.98

-1.68

22380 Flagstaff, AZ MSA

1,084 1,372.00 1,253.95

0.8826 1,106.73

2.10

22660 Fort Collins, CO MSA

1,052 1,361.50 1,299.90

0.7824 1,017.04

-3.32

24220 Grand Forks, ND-MN MSA

785

907.50

868.85

0.9002

782.12

-0.37

24540 Greeley, CO MSA

888 1,237.50 1,039.95

0.8816

916.77

3.24

25420 Harrisburg-Carlisle, PA MSA

912

973.25

920.55

0.9971

917.91

0.65

25980 Hinesville, GA MSA

782 1,091.00 1,058.65

0.7342

777.21

-0.61

26380 Houma-Thibodaux, LA MSA

788

867.00

837.65

0.9075

760.19

-3.53

27860 Jonesboro, AR MSA

684

648.00

702.90

0.9637

677.39

-0.97

28420 Kennewick-Richland, WA MSA

867 1,015.00

956.45

0.8884

849.70

-2.00

17

30140 Lebanon, PA MSA

822

954.00

874.40

0.9211

805.44

-2.02

31340 Lynchburg, VA MSA

730

863.25

827.25

0.8781

726.43

-0.49

31740 Manhattan, KS MSA

853

764.00

793.95

1.0593

841.02

-1.41

31860 Mankato-North Mankato, MN MSA

823 1,345.00 1,231.25

0.7046

867.57

5.42

33260 Midland, TX MSA

1,163 1,473.00 1,161.83

1.0224 1,187.81

2.13

34060 Morgantown, WV MSA

781

697.75

679.60

1.1157

758.21

-2.92

34900 Napa, CA MSA

1,492 2,077.00 1,954.70

0.7722 1,509.41

1.17

35620 New York-Newark-Jersey City, NY-NJ-PA

MSA

1,396 2,150.00 2,055.50

0.6723 1,381.97

-1.01

36220 Odessa, TX MSA

1,018 1,329.50 1,108.65

0.9198 1,019.72

0.17

36500 Olympia-Tumwater, WA MSA

1,040 1,214.75 1,043.70

1.0241 1,068.87

2.78

38900 Portland-Vancouver-Hillsboro, OR-WA MSA

1,096 1.349.75 1.218.20

0.8943 1.089.47

-0.60

39660 Rapid City, SD MSA

820

949.00

842.85

0.9795

825.60

0.68

41420 Salem, OR MSA

854 1.003.50

861.50

1.0066

867.22

1.55

41620 Salt Lake City, UT MSA

969 1.132.25 1.008.95

0.9677

976.35

0.76

41700 San Antonio-New Braunfels, TX MSA

949

928.25

860.70

1.1008

947.47

-0.16

41860 San Francisco-Oakland-Hayward, CA MSA

1,709 2.602.00 2.406.20

0.7082 1.703.99

-0.29

18

41940 San Jose-Sunnyvale-Santa Clara, CA MSA

1,948 2.819.75 2.625.85

0.7267 1.908.11

-2.05

42220 Santa Rosa, CA MSA

1,445 2.059.50 1.833.30

0.7994 1.465.48

1.42

42660 Seattle-Tacoma-Bellevue, WA MSA

1,292 1.640.00 1.453.90

0.8857 1.287.76

-0.33

44940 Sumter, SC MSA

690

831.25

726.45

0.9523

691.81

0.26

45540 The Villages, FL MSA

770

975.75

831.02

0.9456

785.83

2.06

47020 Victoria, TX MSA

866

857.25

855.40

0.9596

820.85

-5.21

47460 Walla Walla, WA MSA

833

865.50

875.00

0.9003

787.72

-5.44

47900 Washington-Arlington-Alexandria,

DC-VA-MD-WV MSA

1,532 1,656.38 1,578.93

0.9507 1,501.06

-2.02

48300 Wenatchee, WA MSA

839 1,349.25 1,200.40

0.6895

827.66

-1.35

48540 Wheeling, WV-OH MSA

660

719.75

695.13

0.9530

662.47

0.37

48700 Williamsport, PA MSA

763

913.00

850.75

0.9053

770.18

0.94

19

Next, we compare the errors in predicted rents using Axiometrics data with those in predicted rents using the gross rent Consumer Price Index factor provided by HUD. To predict rents in 2018 using the CPI factor, we multiplied the 40th percentile of ACS 5-year rent in 2017 with the CPI factor in 2017 through 2018. The key objective in all our analyses has been to estimate the 5-year ACS for the next year; hence we again benchmark the predicted rent using the CPI factor against the 40th percentile of ACS 5-year rent in 2018. Thus, we calculate errors using the following formula:

(Predicted rent in 2018 using CPI factor − ACS 5 − year rent in 2018) Error =

ACS 5 − year rent in 2018

∗ 100

Using the steps previously described, we get an error that is summarized in exhibit 3.8. For comparison, we restrict the sample to CBSAs for which we had Axiometrics data.

Exhibit 3.8. Comparison of Predicted Rents Using CPI Factor for 2018

Summary statistics of the error (%)

Minimum

-5.1676

10th percentile

-3.9490

25th percentile

-2.4676

50th percentile

-1.4095

75th percentile

-0.5573

90th percentile

0.1531

Maximum

1.6521

Mean

-1.5404

Standard Deviation

1.5038

Observations

56

CPI = Consumer Price Index.

As shown in exhibit 3.8, for 2018, predicted rents using the CPI factor were marginally lower than the corresponding ACS 5-year rent for most of the sample. The median error using the CPI factor for this sample is -1.41 percent, and the mean is -1.54 percent.

3.4 Price-to-Rent Ratio Using Zillow Data

We calculate the price-to-rent ratio for each CBSA by dividing the average Zillow home value over 5 years by the 40th percentile of rent from the ACS 5-year file (referred to as “Rent” in the following formula). For this analysis, the authors use the Zillow Home Value Index All Homes (SFR, Condo/Co-op) Time Series, Raw, Mid-Tier ($) provided by Zillow. It is a monthly series, and we take the average to calculate the home values at the yearly frequency. Thus, the price-torent ratio is calculated using the following formula:

20

Price − to − rent ratio in the year 2018

Average Zillow value during 2014 − 2018

= 40th percentile of rent in 2018 from the ACS 5 − year file Next, to predict the rent in 2019, we use the following equation: Average Zillow value during 2015 − 2019

Predicted rent in 2019 =

Price − to − rent ratio in the year 2018

To assess the accuracy of this alternative measure, we benchmark it against gross rents from the ACS data. We calculate the percentage error using the following formula: (Predicted rent − Rent)

Error =

Rent

∗ 100

When using the method, we assume that the price-to-rent ratio that we have calculated using the 5-year ACS data and the 5-year moving average of the Zillow home value index does not change much from year to year. If one expects the price-to-rent ratio to change significantly, then adjusting the price-to-rent ratio in that direction might be a good idea. One can compute the price-to-rent ratios by looking at price and rent data from various sources. For instance, one can compute the price-to-rent ratio using Zillow’s value and rent data. An alternative could be to use the HPI available from FHFA or Fannie Mae and use the owners’ equivalent rent of residences (OER), a subcomponent of the shelter component of the Consumer Price Index for All Urban Consumers (CPI-U).

In the method previously discussed, we use the 40th-percentile rents from the ACS 5-year survey. We repeat the analysis using the gross median rent using the 5-year ACS, and the results are summarized in the appendix. As seen in appendix exhibit A.1, the prediction error using the median rent is very similar to those obtained using the 40th percentile. We use the 40th percentile of the rent in our preferred specification because FMR is based on the 40th percentile of the distribution. However, when calculating the price-to-rent ratio, we use the median Zillow value and the 40th percentile of the rent distribution. Ideally, calculating the price-to-rent ratio for the same portion of the distribution would have been better. However, we do not have the 40th percentile of ZHVI.

Next, we use the method previously discussed to estimate rents for 2019. The sample consists of the 60 CBSAs identified as having rapidly rising rents—except for the Victoria, TX MSA—

because Zillow data are missing for a few years.

Using the steps previously described, we calculate the prediction error for rent for 2019, and is summarized in exhibit 3.9.

21

Exhibit 3.9. Comparison of Predicted Rents Using Zillow Data to ACS Values Summary Statistics of the Error (%)

Minimum

-2.7304

10th percentile

-1.3250

25th percentile

0.1518

50th percentile

1.3528

75th percentile

3.0209

90th percentile

4.7082

Maximum

6.9743

Mean

1.6169

Standard deviation

2.1525

Observations

59

When the error calculated in exhibit 3.9 is negative, it indicates that the ACS rent is higher than the predicted rent. For this sample, the error is very small and is in the range of – 2.7 to +7.0

percent. The mean and median are positive, indicating that the predicted rent is higher than the 40th percentile of the ACS rent. Zillow also provides data at the ZIP Code level, which can be used for estimating the SAFMRs using the methodology previously illustrated.

22

Exhibit 3.10. Predicted Rents Using Zillow Data 5-Year Average 5-Price-to-

ACS in Year Zillow

Rent

Predicted

CBSA

2019

Value in

Ratio in

Rent in

Error

Code

CBSA Name

Zillow Region Name

($)

2019 ($)

2018

2019 ($)

(%)

10540 Albany, OR MSA

Albany, OR

892

228,628

242.90

941.24

5.52

11020 Altoona, PA MSA

Altoona, PA

713

110,269

149.88

735.74

3.19

12420 Austin-Round Rock, TX MSA

Austin, TX

1,241

320,234

255.73

1,252.25

0.91

13740 Billings, MT MSA

Billings, MT

834

249,339

299.20

833.35

-0.08

13900 Bismarck, ND MSA

Bismarck, ND

824

268,046

326.06

822.07

-0.23

13980 Blacksburg-Christiansburg, VA MSA

Blacksburg, VA

768

174,999

231.23

756.80

-1.46

14500 Boulder, CO MSA

Boulder, CO

1,418

510,072

359.17

1,420.15

0.15

14740 Bremerton-Silverdale, WA MSA

Bremerton, WA

1,138

326,979

282.89

1,155.87

1.57

15540 Burlington-South Burlington, VT MSA

Burlington, VT

1,236

281,522

224.73

1,252.72

1.35

16220 Casper, WY MSA

Casper, WY

778

208,397

264.49

787.93

1.28

16620 Charleston, WV MSA

Charleston, WV

714

99,037

138.14

716.91

0.41

16700 Charleston-North Charleston, SC MSA

Charleston, SC

1,017

2,48375

241.16

1,029.92

1.27

17820 Colorado Springs, CO MSA

Colorado Springs, CO

1,021

270,377

262.68

1,029.31

0.81

18700 Corvallis, OR MSA

Corvallis, OR

997

329,001

336.26

978.42

-1.86

23

19060 Cumberland, MD-WV MSA

Cumberland, MD

655

91,769

138.75

661.39

0.98

19740 Denver-Aurora-Lakewood, CO MSA

Denver, CO

1,328

394,280

296.73

1,328.74

0.06

20220 Dubuque, IA MSA

Dubuque, IA

751

170,235

224.21

759.26

1.10

21060 Elizabethtown-Fort Knox, KY MSA

Elizabethtown, KY

723

139,365

189.40

735.81

1.77

21340 El Paso, TX MSA

El Paso, TX

756

126,590

166.24

761.49

0.73

21420 Enid, OK MSA

Enid, OK

768

83,472

107.73

774.79

0.88

22020 Fargo, ND-MN MSA

Fargo, ND

800

220,696

275.34

801.55

0.19

22380 Flagstaff, AZ MSA

Flagstaff, AZ

1,170

327,901

288.12

1,138.06

-2.73

22660 Fort Collins, CO MSA

Fort Collins, CO

1,120

369,552

326.65

1,131.35

1.01

24220 Grand Forks, ND-MN MSA

Grand Forks, ND

800

193,311

235.08

822.31

2.79

24420 Grants Pass, OR MSA

Grants Pass, OR

875

259,506

291.39

890.56

1.78

24540 Greeley, CO MSA

Greeley, CO

942

327,706

339.27

965.92

2.54

25420 Harrisburg-Carlisle, PA MSA

Harrisburg, PA

937

177,204

189.27

936.27

-0.08

25980 Hinesville, GA MSA

Hinesville, GA

804

135,556

163.76

827.75

2.95

26380 Houma-Thibodaux, LA MSA

Houma, LA

793

149,715

185.04

809.08

2.03

27860 Jonesboro, AR MSA

Jonesboro, AR

690

117,971

166.92

706.77

2.43

28420 Kennewick-Richland, WA MSA

Kennewick, WA

912

246,120

257.58

955.50

4.77

24

30140 Lebanon, PA MSA

Lebanon, PA

850

173,017

204.86

844.57

-0.64

31340 Lynchburg, VA MSA

Lynchburg, VA

732

165,258

217.82

758.68

3.64

31740 Manhattan, KS MSA

Manhattan, KS

843

185,087

209.25

884.55

4.93

31860 Mankato-North Mankato, MN MSA

Mankato, MN

835

194,911

224.64

867.66

3.91

33260 Midland, TX MSA

Midland, TX

1,201

231,184

189.52

1,219.85

1.57

34060 Morgantown, WV MSA

Morgantown, WV

793

162,401

201.94

804.20

1.41

34900 Napa, CA MSA

Napa, CA

1,605

651,950

414.95

1,571.14

-2.11

New York-Newark-Jersey City, NY-NJ-

35620 PA MSA

New York, NY

1,445

446,149

308.49

1,446.22

0.08

36220 Odessa, TX MSA

Odessa, TX

1,035

158,275

146.06

1,083.61

4.70

36500 Olympia-Tumwater, WA MSA

Olympia, WA

1,077

285,433

254.78

1,120.30

4.02

Portland-Vancouver-Hillsboro, OR-WA

38900 MSA

Portland, OR

1,175

374,163

318.60

1,174.41

-0.05

39660 Rapid City, SD MSA

Rapid City, SD

830

213,192

249.33

855.07

3.02

41420 Salem, OR MSA

Salem, OR

900

252,896

270.08

936.36

4.04

41620 Salt Lake City, UT MSA

Salt Lake City, UT

1,023

319,323

304.85

1,047.48

2.39

41700 San Antonio-New Braunfels, TX MSA

San Antonio, TX

987

186,669

186.16

1,002.76

1.60

25

San Francisco-Oakland-Hayward, CA

41860 MSA

San Francisco, CA

1,827

1,003,347

548.34

1,829.80

0.15

San Jose-Sunnyvale-Santa Clara, CA

41940 MSA

San Jose, CA

2,115

1,065,204

516.60

2,061.97

-2.51

42220 Santa Rosa, CA MSA

Santa Rosa, CA

1,541

605,944

398.49

1,520.58

-1.33

42660 Seattle-Tacoma-Bellevue, WA MSA

Seattle, WA

1,379

447,637

318.69

1,404.63

1.86

44940 Sumter, SC MSA

Sumter, SC

675

115,806

160.64

720.91

6.80

45540 The Villages, FL MSA

The Villages, FL

790

255,149

321.24

794.27

0.54

46300 Twin Falls, ID MSA

Twin Falls, ID

734

17,829

229.03

785.19

6.97

46520 Urban Honolulu, HI MSA

Urban Honolulu, HI

1,591

683,860

426.48

1,603.51

0.79

47020 Victoria, TX MSA

Victoria, TX

899

NA

NA

NA

NA

47460 Walla Walla, WA MSA

Walla Walla, WA

884

237,520

263.51

901.37

1.97

Washington-Arlington-Alexandria, DC-

47900 VA-MD-WV MSA

Washington, DC

1,577

408,016

259.48

1,572.44

-0.29

48300 Wenatchee, WA MSA

Wenatchee, WA

870

303,935

333.64

910.96

4.71

48540 Wheeling, WV-OH MSA

Wheeling, OH

673

89,346

128.32

696.28

3.46

48700 Williamsport, PA MSA

Williamsport, PA

761

146,713

185.86

789.36

3.73

26

Next, we compare the errors in predicted rents using Zillow data with those in predicted rents using the gross rent CPI factor provided by HUD. To predict rents in 2019 using the CPI factor, we multiplied the 40th percentile of ACS 5-year rent in 2018 with the CPI factor in 2018 through 2019. The key objective in all our analyses has been to estimate the 5-year ACS for the next year; hence we again benchmark the predicted rent using the CPI factor against the 40th percentile of ACS 5-year rent in 2019. Thus, we calculate errors using the following formula: (Predicted rent in 2019 using CPI factor − ACS 5 − year rent in 2018) Error =

ACS 5 − year rent in 2018

∗ 100

Using the steps previously described, the error we get is summarized in exhibit 3.11. For comparison, we restrict the sample to CBSAs for which we had Zillow data. As can be seen in exhibit 3.11, the mean error in predicted rents for 2019 using the CPI factor is 0.02 percent when benchmarked against the ACS 5-year rent in 2019, whereas the median error is 0.004 percent.

Exhibit 3.11. Comparison of Predicted Rents Using CPI Factor for the Year 2019

Summary statistics of the error (%)

Minimum

-5.0263

10th percentile

-2.8007

25th percentile

-1.4589

50th percentile

0.0038

75th percentile

1.2619

90th percentile

2.6717

Maximum

5.5849

Mean

0.0211

Standard Deviation

2.1298

Observations

59

CPI = Consumer Price Index.

3.5 Price-to-Rent Ratio Using the FHFA House Price Index In this section, we explore the price-to-rent methodology using another price index that is readily available—namely, the HPI dataset provided by FHFA. In the following analysis, we use the Metropolitan Statistical Areas and Divisions: All Transactions Index (not seasonally adjusted) for this analysis, which is estimated using sales price and appraisal data.

We use this dataset with the ACS 5-year dataset to forecast rents. We perform the following steps:

We begin by forecasting home values.

27

Because we are using the 5-year ACS house value, 4 we first create a 5-year moving average of the HPI. (The 5-year moving average index in 2010 is the average HPI for the period 2006–

2010.)

Next, we calculate the change in this 5-year moving average index as follows: Change in index

(5 − year moving average in year t) − (5 − year moving average in year t − 1)

=

5 − year moving average in year t − 1

Next, we merge it with the ACS 5-year data and forecast value as—

Forecast value in year t = House value in year t-1 + (House value in year t-1 * change in the index in year t)

We calculate the forecast error as—

Forecast value in year 𝑡𝑡 − House value in year 𝑡𝑡

Error in value in year 𝑡𝑡 =

House value in year 𝑡𝑡

∗ 100

The forecast error is summarized in exhibit 3.12.

Exhibit 3.12. Summary Statistics of Errors for House Values Forecasts

Summary statistics of the error (%)

Minimum

-6.9396

10th percentile

-3.1726

25th percentile

-1.7990

50th percentile

-0.5236

75th percentile

0.6617

90th percentile

1.5868

Maximum

6.5750

Mean

-0.6267

Standard Deviation

1.8789

Observations

501

We calculate the price-to-rent ratio as—

Median Value from the ACS 5 − year file

Price − to − rent ratio in the year t = Median Gross Rent from the ACS 5 − year file 4 https://data.census.gov; ACS table ID: B25077

28

Next, to predict rent, we use the following equation:

Forecast value in year t

Predicted rent in year t = Price − to − rent ratio in year t − 1

To assess the accuracy of this alternative measure, we benchmark it against gross rents from the ACS data. We calculate the percentage error using the following formula: (Predicted rent in year 𝑡𝑡 − Gross rent in year 𝑡𝑡)

Error in year 𝑡𝑡 =

Gross rent in year 𝑡𝑡

∗ 100

One of the advantages of using the FHFA HPI for this project is that it allows us to test the accuracy of the rent predictions for a longer period.

We estimate the errors using the steps previously described and are summarized in exhibits 3.13

and 3.14.

Exhibit 3.13. Comparison of Predicted Rent Using the FHFA House Price Index to ACS

Values

Summary statistics of the error (%)

Minimum

-15.0421

10th percentile

-5.8179

25th percentile

-3.3072

50th percentile

-1.0341

75th percentile

1.3355

90th percentile

2.8242

Maximum

8.3926

Mean

-1.2608

Standard Deviation

3.5127

Observations

501

ACS = American Community Survey. FHFA = Federal Housing Finance Agency.

29

Exhibit 3.14. Comparison of Predicted Rent Using the FHFA House Price Index to ACS

Values from 2014 Forward

Summary statistics of the error (%)

Minimum

-7.5760

10th percentile

-2.8913

25th percentile

-1.3538

50th percentile

0.3220

75th percentile

2.1515

90th percentile

3.2103

Maximum

8.3926

Mean

0.3630

Standard Deviation

2.4925

Observations

336

ACS = American Community Survey. FHFA = Federal Housing Finance Agency.

If one looks at the absolute value of median error after 2013, it is lower than the median error for the entire sample. The error distribution for the pre-2014 period reveals large negative errors, which imply that the gross rent is higher than the predicted rent. To analyze the possible reason for this relatively large negative error, we selected two metropolitan areas—San Francisco-Oakland-Fremont, CA Metro Area, and San Jose-Sunnyvale-Santa Clara, CA Metro Area. We found that the price-to-rent ratio for those two metro areas decreased from 2010 through 2014

(for this analysis, we computed the price-to-rent ratio by dividing the ACS 5-year value by the ACS 5-year gross rent). To predict rent, we divide the house price by the price-to-rent ratio; using a larger price-to-rent ratio will result in lower rent. Thus, as discussed earlier, when a large fluctuation occurs in the price-to-rent ratio from one year to another, the ratio can be adjusted to reflect that movement. Exhibit 3.15 summarizes the error for each year.

The sample consists of the 60 CBSAs with rapidly rising rents (see exhibit 3.1) and those in the bulleted list that follows because the HPI for these CBSAs is broken down into separate metropolitan statistical area divisions (MSADs). One can aggregate the MSADs to form the corresponding CBSA by taking a simple average or a population-weighted average. For this analysis, we excluded the following CBSAs to alleviate measurement error concerns when aggregating data across MSADs.

• New York-Newark-Jersey City, NY-NJ-PA Metro Area

• San Francisco-Oakland-Berkeley, CA Metro Area

• Seattle-Tacoma-Bellevue, WA Metro Area

• Washington-Arlington-Alexandria, DC-VA-MD-WV Metro Area FHFA HPI is also available at the ZIP Code level, so it can be used to estimate the SAFMRs using the methodology previously described.

30

Exhibit 3.15. Comparison of Predicted Rent Using the FHFA House Price Index to ACS by Year

Summary statistics of the error (%)

Year Observations

Mean Std. Dev. Minimum Maximum

2011

55

-5.2951 3.1151

-15.0421

-1.0740

2012

55

-4.7587 2.7876

-11.5672

-0.2621

2013

55

-3.6486 2.6425

-10.1195

0.9204

2014

56

-1.9466 2.3158

-7.5760

8.3926

2015

56

0.6455

1.9241

-4.2821

5.1143

2016

56

0.8907

2.5594

-5.2989

6.9322

2017

56

0.3639

2.5773

-5.2919

7.0710

2018

56

0.7147

2.2005

-4.9569

6.6130

2019

56

1.5095

1.8657

-3.3672

5.8224

ACS = American Community Survey. FHFA = Federal Housing Finance Agency. Std. Dev. = standard deviation.

3.6 Autoregressive Integrated Moving Average (ARIMA) Models In addition to proposing those two new methods, we also reviewed the current procedure HUD

uses to calculate the trend factor by using the autoregressive integrated moving average (ARIMA) models. We did not have any additional suggestions to substantially improve the currently used procedure. The only recommendation is that HUD consider using FHFA HPI, Axiometrics, or Zillow data to further localize the inflation factors for areas where CPI is unavailable. Also, FHFA House Price Index/Zillow/Axiometrics data can be an additional input in calculating the trend factors using the ARIMA model.

31

4. Conditions Under Which HUD Should Use

Alternative Methods

HUD should use these new proposed methods to supplement its existing analysis. We recommend that HUD calculates the rent using all three data sources discussed—Axiometrics, Zillow, and FHFA. It is also important to remember that the proposed method using the price-torent ratio assumes that the price-to-rent ratio does not change much in a year. If one expects that the price-to-rent ratio has changed significantly, one will need to adjust the ratio by looking at the contemporaneous price and rent data.

To begin with, HUD should continue using its existing method and do a more careful evaluation of the metropolitan areas for which the rents using the existing method deviate significantly from FMR estimates currently being used by HUD.

Although we have restricted the analysis in this project to areas with rapidly rising rents, we believe these methods can be applied to all areas. One of the constraints in using the proposed methods for all FMR areas will be the availability of the data, as the commercially available data sources will not cover numerous geographic areas. Some of these methods can also be used to estimate SAFMRs because data from Zillow and FHFA HPI are also available at the ZIP Code level.

These methods will also be very useful if, for some reason, the ACS decides not to publish its 1-year estimates, as was the case this year. The Census Bureau is not releasing its 1-year estimates for 2020 because the data collection was affected by the COVID-19 pandemic. Such circumstances will make estimating FMR difficult for HUD. HUD can update the FMR estimate by having alternative methods that do not rely on the release of ACS annual estimates.

Some of the shortcomings of the proposed methods are that the commercial datasets will not be available for all the locations, and the length of the time series of some commercial datasets are relatively short. Thus, HUD must continue to rely on the methodology it currently uses for most regions and use the methods proposed in the current study to supplement its current analysis.

32

Appendix A

In appendix exhibit A.1, we summarize the percentage error when we use the Zillow home value index and the median gross rent from ACS. 5 The errors are very similar to the one obtained using the 40th percentile of the rent distribution.

Appendix Exhibit A.1. Price-to-Rent Ratio Using ACS Median Rent and Zillow Home Value Index

Summary statistics of the error (%)

Minimum

-2.8298

10th percentile

-0.7812

25th percentile

0.4110

50th percentile

1.4483

75th percentile

3.0605

90th percentile

4.7882

Maximum

6.3990

Mean

1.7376

Standard Deviation

2.0399

Observations

59

ACS = American Community Survey.

5 We also predict rent using 1-year gross rent instead of the ACS 5-year survey, but the errors using the 1-year survey data were much higher. Given that the 5-year ACS data are likely to be more representative of the rent distribution in the area, we prefer to use that dataset.

33

Appendix B

Appendix Exhibit B.1. Crosswalk Between CBSA, FMR Area, and Zillow Region CBSA Name

FMR Area Name

Zillow Region Name

Albany, OR MSA

Albany, OR MSA

Albany, OR

Altoona, PA MSA

Altoona, PA MSA

Altoona, PA

Austin-Round Rock, TX MSA

Austin-Round Rock, TX MSA

Austin, TX

Billings, MT MSA

Billings, MT HUD Metro FMR Area

Billings, MT

Bismarck, ND MSA

Bismarck, ND HUD Metro FMR Area

Bismarck, ND

Blacksburg-Christiansburg, VA MSA

Blacksburg-Christiansburg-Radford, VA

Blacksburg, VA

HUD Metro FMR Area

Boulder, CO MSA

Boulder, CO MSA

Boulder, CO

Bremerton-Silverdale, WA MSA

Bremerton-Silverdale, WA MSA

Bremerton, WA

Burlington-South Burlington, VT MSA

Burlington-South Burlington, VT MSA

Burlington, VT

Casper, WY MSA

Casper, WY MSA

Casper, WY

Charleston, WV MSA

Charleston, WV HUD Metro FMR Area

Charleston, WV

Charleston-North Charleston, SC MSA

Charleston-North Charleston, SC MSA

Charleston, SC

Colorado Springs, CO MSA

Colorado Springs, CO HUD Metro FMR

Colorado Springs,

Area

CO

Corvallis, OR MSA

Corvallis, OR MSA

Corvallis, OR

Cumberland, MD-WV MSA

Cumberland, MD-WV MSA

Cumberland, MD

Denver-Aurora-Lakewood, CO MSA

Denver-Aurora-Lakewood, CO MSA

Denver, CO

Dubuque, IA MSA

Dubuque, IA MSA

Dubuque, IA

El Paso, TX MSA

El Paso, TX HUD Metro FMR Area

El Paso, TX

Elizabethtown-Fort Knox, KY MSA

Elizabethtown, KY HUD Metro FMR Area

Elizabethtown, KY

Enid, OK MSA

Enid, OK MSA

Enid, OK

Fargo, ND-MN MSA

Fargo, ND-MN MSA

Fargo, ND

Flagstaff, AZ MSA

Flagstaff, AZ MSA

Flagstaff, AZ

Fort Collins, CO MSA

Fort Collins, CO MSA

Fort Collins, CO

34

Grand Forks, ND-MN MSA

Grand Forks, ND-MN MSA

Grand Forks, ND

Grants Pass, OR MSA

Grants Pass, OR MSA

Grants Pass, OR

Greeley, CO MSA

Greeley, CO MSA

Greeley, CO

Harrisburg-Carlisle, PA MSA

Harrisburg-Carlisle, PA MSA

Harrisburg, PA

Hinesville, GA MSA

Hinesville, GA HUD Metro FMR Area

Hinesville, GA

Houma-Thibodaux, LA MSA

Houma-Thibodaux, LA MSA

Houma, LA

Jonesboro, AR MSA

Jonesboro, AR HUD Metro FMR Area

Jonesboro, AR

Kennewick-Richland, WA MSA

Kennewick-Richland, WA MSA

Kennewick, WA

Lebanon, PA MSA

Lebanon, PA MSA

Lebanon, PA

Lynchburg, VA MSA

Lynchburg, VA MSA

Lynchburg, VA

Manhattan, KS MSA

Manhattan, KS MSA

Manhattan, KS

Mankato-North Mankato, MN MSA

Mankato-North Mankato, MN MSA

Mankato, MN

Midland, TX MSA

Midland, TX HUD Metro FMR Area

Midland, TX

Morgantown, WV MSA

Morgantown, WV MSA

Morgantown, WV

Napa, CA MSA

Napa, CA MSA

Napa, CA

New York-Newark-Jersey City, NY-NJ-PA

New York, NY HUD Metro FMR Area

New York, NY

MSA

New York-Newark-Jersey City, NY-NJ-PA

Jersey City, NJ HUD Metro FMR Area

New York, NY

MSA

New York-Newark-Jersey City, NY-NJ-PA

Newark, NJ HUD Metro FMR Area

New York, NY

MSA

Odessa, TX MSA

Odessa, TX MSA

Odessa, TX

Olympia-Tumwater, WA MSA

Olympia-Tumwater, WA MSA

Olympia, WA

Portland-Vancouver-Hillsboro, OR-WA MSA Portland-Vancouver-Hillsboro, OR-WA Portland, OR

MSA

Rapid City, SD MSA

Rapid City, SD HUD Metro FMR Area

Rapid City, SD

Salem, OR MSA

Salem, OR MSA

Salem, OR

Salt Lake City, UT MSA

Salt Lake City, UT HUD Metro FMR Area

Salt Lake City, UT

San Antonio-New Braunfels, TX MSA

San Antonio-New Braunfels, TX HUD Metro San Antonio, TX

FMR Area

San Francisco-Oakland-Hayward, CA MSA

San Francisco, CA HUD Metro FMR Area

San Francisco, CA

35

San Francisco-Oakland-Hayward, CA MSA

Oakland-Fremont, CA HUD Metro FMR

San Francisco, CA

Area

San Jose-Sunnyvale-Santa Clara, CA MSA

San Jose-Sunnyvale-Santa Clara, CA HUD

San Jose, CA

Metro FMR Area

Santa Rosa, CA MSA

Santa Rosa, CA MSA

Santa Rosa, CA

Seattle-Tacoma-Bellevue, WA MSA

Seattle-Bellevue, WA HUD Metro FMR Area Seattle, WA

Sumter, SC MSA

Sumter, SC MSA

Sumter, SC

The Villages, FL MSA

The Villages, FL MSA

The Villages, FL

Twin Falls, ID MSA

Twin Falls County, ID

Twin Falls, ID

Urban Honolulu, HI MSA

Urban Honolulu, HI MSA

Urban Honolulu, HI

Victoria, TX MSA

Victoria, TX MSA

Victoria, TX

Walla Walla, WA MSA

Walla Walla County, WA HUD Metro FMR Walla Walla, WA

Area

Washington-Arlington-Alexandria, DC-VA-

Washington-Arlington-Alexandria, DC-VA-

Washington, DC

MD-WV MSA

MD HUD Metro FMR Area

Wenatchee, WA MSA

Wenatchee, WA MSA

Wenatchee, WA

Wheeling, WV-OH MSA

Wheeling, WV-OH MSA

Wheeling, OH

Williamsport, PA MSA

Williamsport, PA MSA

Williamsport, PA

FMR = Fair Market Rent. CBSA = Core Based Statistical Area. MSA = Metropolitan Statistical Area.

36

5. References

“Proposals To Update the Fair Market Rent Formula.” 2018.

Saiz, Albert. 2010. “The geographic determinants of housing supply,” The Quarterly Journal of Economics 125.3: 1253–1296.

Steven Manson, Jonathan Schroeder, David Van Riper, Tracy Kugler, and Steven Ruggles.

IPUMS National Historical Geographic Information System: Version 17.0 [dataset].

Minneapolis, MN: IPUMS. 2022. http://doi.org/10.18128/D050.V17.0

37

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

Washington, DC 20410-6000

April 2023

Document Outline

- Alternative Methods for Calculating Fair Market Rents (FMRs) in Rental Markets with Rapidly Rising Rents

- DISCLAIMER

- Acknowledgments

- Table of Contents

- List of Exhibits

- Executive Summary

- 1. Introduction

- 1.1 Study Objective

- 2. Data

- 2.1 Axiometrics Data

- 2.2 Zillow Data

- 2.3 House Price Index From the Federal Housing Finance Agency

- 3. Methodological Framework

- 3.1 Identifying Markets with Rapidly Rising Rents

- 3.2 Alternative Methods for Calculating FMR

- 1. Using Axiometrics Data

- 2. Price-to-Rent Ratio

- Price-to-Rent Ratio Using Zillow Data

- Price-to-Rent Ratio Using Federal Housing Finance Agency’s House Price Index

- 3.3 Predicting Rent Using Axiometrics Data

- 3.4 Price-to-Rent Ratio Using Zillow Data

- 3.5 Price-to-Rent Ratio Using the FHFA House Price Index

- 3.6 Autoregressive Integrated Moving Average (ARIMA) Models

- 4. Conditions Under Which HUD Should Use Alternative Methods

- Appendix A

- Appendix B

- 5. References

Table of Contents

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

DISCLAIMER

Acknowledgments

Table of Contents

List of Exhibits

Executive Summary

1. Introduction

1.1 Study Objective

2. Data

2.1 Axiometrics Data

2.2 Zillow Data

2.3 House Price Index From the Federal Housing Finance Agency

3. Methodological Framework

3.1 Identifying Markets with Rapidly Rising Rents

3.2 Alternative Methods for Calculating FMR

1. Using Axiometrics Data

2. Price-to-Rent Ratio

Price-to-Rent Ratio Using Zillow Data

Price-to-Rent Ratio Using Federal Housing Finance Agency’s House Price Index

3.3 Predicting Rent Using Axiometrics Data

3.4 Price-to-Rent Ratio Using Zillow Data

3.5 Price-to-Rent Ratio Using the FHFA House Price Index

3.6 Autoregressive Integrated Moving Average (ARIMA) Models

4. Conditions Under Which HUD Should Use Alternative Methods

Appendix A

Appendix B

5. References