Alternative Fair Market

Rents for Local Housing

Markets

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

DISCLAIMER

The views expressed are those of the authors and should not be attributed to the Urban Institute, its trustees, or its funders. Funders do not determine research findings or the insights and recommendations of Urban experts.

Alternative Fair Market Rents for

Local Housing Markets

Prepared for

U.S. Department of Housing and Urban Development

Office of Policy Development and Research

Prepared by

Daniel Teles

Alyse Oneto

Yipeng Su

Ananya Hariharan

URBAN INSTITUTE

Hiren Nisar

2M RESEARCH

July 2022

Acknowledgments

This report was funded by the U.S. Department of Housing and Urban Development (HUD). The authors are grateful to them and to all our funders, who make it possible for the Urban Institute to advance its mission.

Many people reviewed and contributed to this report. The authors appreciate the feedback and support that Adam Bibler and Marie Lihn, the government technical representatives for this project, and Kurt G. Usowski provided throughout the course of the study. Lydia Lo and Jein Park provided valuable research assistance. The authors would like to thank the technical adviser Dr. Christina Stacy and the reviewers, Dr. A. Bowen Garrett and Alena Stern of Urban, for their support in the design of this work.

Contents

Executive Summary

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Findings

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Alternative Fair Market Rents for Local Housing Markets

1

Background

2

How HUD Forecasts Fair Market Rents

4

Improving FMR Estimates

6

Research Design

8

Data

10

Defining Areas with Rapidly Rising Rents

11

Predicting Areas with Rapidly Rising Rents

11

Estimating Rent Time Series Models with Local Data

14

Creating Alternative FMR Calculations

18

Assessing Alternative FMR Calculations

21

Limitations

22

Findings

23

Defining Areas with Rapidly Rising Rents

24

Predicting Areas with Rapidly Rising Rents

26

Estimating Rent Time Series Models with Local Data

30

Assessing Alternative FMR Calculations

35

Implications for Policy and Future Research

43

Conclusion

46

Appendix A. Exploring Alternative Definitions of Rapidly Rising Rents

46

Appendix B. Supplemental Exhibits

50

Predicting Areas with Rapidly Rising Rents

50

Estimating Rent Time Series Models with Local Data

51

Assessing Alternative FMR Performance

82

References

91

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CON TENTS

List of Exhibits

Exhibit 1. Fair Market Rent Calculations Process

4

Exhibit 2. Datasets by Source and Use

10

Exhibit 3. ARIMA Model Identification for the Seattle-Tacoma-Bellevue, Washington, Metropolitan

Area and Midwest Region (Size Class B/C)

17

Exhibit 4. Correlation Between the Predictor Variables

18

Exhibit 5. Construction of County-Level Dataset

19

Exhibit 6. Number of Years in Which Counties Saw Rapidly Rising Rents, 2009–2010 to 2018–2019

24

Exhibit 7. Number of Years in Which the Majority of Households in Metropolitan and State

Nonmetropolitan Areas Saw Rapidly Rising Rents, 2009–2010 to 2018–2019

26

Exhibit 8. Boolean Model Accuracy with Vacancy Rate

27

Exhibit 9. Predicting the Likelihood of Having Rapidly Rising Rents

29

Exhibit 10. Performance of Logit Model Predicting Areas with Rapidly Rising Rents, 2009–2010 to

2015–2016

30

Exhibit 11. Root Mean Squared Error for ARIMA and ARIMAX Models Comparison, Seattle-Tacoma-

Bellevue, Washington, Metropolitan Area and Midwest Region (Size Class B/C)

31

Exhibit 12. Summary of ARIMA and ARIMAX Model Performance

32

Exhibit 13. Coefficients for Select Predictors Using the ARIMAX Model for 2005–2018, Seattle-

Tacoma-Bellevue, Washington, Metropolitan Area and Midwest Region

33

Exhibit 14. Coefficients for Expanded ARIMAX Model for 2005–2018, Seattle-Tacoma-Bellevue,

Washington, Metropolitan Area and Midwest Region (Size Class B/C)

34

Exhibit 15. Significant Predictor Variables and Select Predictors for ARIMAX Model, 2005–2018 35

Exhibit 16. Goodness of Fit Measures at the County Level (RMSE in Nominal Dollars)

36

Exhibit 17. Ratio of Actual Gross Rent to FMRs for HUD FMRs and Alternatives by Year

38

Exhibit 18. Performance of HUD FMRs and Alternatives in Counties with High or Rapidly Rising

Rents, 2018

40

Exhibit 19. Performance of HUD’s FMRs and Alternatives in Metropolitan and Nonmetropolitan

Counties, 2018

41

Exhibit 20. Performance of HUD’s FMRs and Alternatives in Counties with SAFMRs, 2018

43

Exhibit 21. Number of Years Counties Saw More than a 10 Percent Increase in Rents, 2009–2010 to

2015–2016

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LIS T OF EXH IB ITS

v

Exhibit 22. Number of Years Counties Saw More than a 5 Percent Increase in Rents, 2009–2010 to

2015–2016

48

Exhibit 23. Number of Years Counties Saw More than an 8 Percent Increase in Rents, 2009–2010 to

2015–2016

48

Exhibit 24. Counties Where 2009 Rents Were in the Top 20th Percentile Nationally

49

Exhibit 25. Predictors of Rapidly Rising Rents and Counties with Rapidly Rising Rents, 2009–2016 50

Exhibit 26. Correlation Between Indicator for Rapidly Rising Rents and Predictor Variables (2009–

2016)

50

Exhibit 27. Preferred ARIMA Model Specification by Area

51

Exhibit 28. Summary Statistics for Predictor Variables for the ARIMAX Model

52

Exhibit 29. Correlation of Predictor Variables for the ARIMAX Model

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Exhibit 30. Time Series Model Performance

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Exhibit 31. Coefficients for ARIMAX with Selected Predictor, 2005–2018

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Exhibit 32. Coefficients for the Expanded ARIMAX Model, 2005–2018

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Exhibit 33. Gross Rent CPI Validation and Forecast for Seattle-Tacoma-Bellevue, Washington, Using

ARIMAX with Selected Predictors, 2005–2016

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Exhibit 34. Gross Rent CPI Validation and Forecast for San Francisco-Oakland-Hayward, California,

Using ARIMAX Model with Selected Predictors, 2005–2016

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Exhibit 35. Gross Rent CPI Validation and Forecast for Los Angeles-Long Beach-Anaheim, California,

Using ARIMAX Model with Selected Predictors, 2005–2016

67

Exhibit 36. Gross Rent CPI Validation and Forecast for Dallas-Fort Worth-Arlington, Texas, Using

ARIMAX Model with Selected Predictors, 2005–2016

68

Exhibit 37. Gross Rent CPI Validation and Forecast for Baltimore-Columbia-Towson, Maryland, Using

ARIMAX Model with Selected Predictors, 2005–2016

69

Exhibit 38. Gross Rent CPI Validation and Forecast for Atlanta-Sandy Springs-Roswell, Georgia,

Using ARIMAX Model with Selected Predictors, 2005–2016

70

Exhibit 39. Gross Rent CPI Validation and Forecast for Miami-Fort Lauderdale-West Palm Beach,

Florida, Using ARIMAX with Selected Predictors, 2005–2016

71

Exhibit 40. Gross Rent CPI Validation and Forecast for Washington-Arlington-Alexandria, DC-

Virginia-Maryland-West Virginia, Using ARIMAX Model with Selected Predictors, 2005—2016 72

Exhibit 41. Gross Rent CPI Validation and Forecast for Detroit-Warren-Dearborn, Michigan, Using

ARIMAX Model with Selected Predictors, 2005–2016

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Exhibit 42. Gross Rent CPI Validation and Forecast for Chicago-Naperville-Elgin, Illinois-Indiana-

Wisconsin, Using ARIMAX Model with Selected Predictors, 2005–2016

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LIS T OF EXH IB ITS

Exhibit 43. Gross Rent CPI Validation and Forecast for Philadelphia-Camden-Wilmington,

Pennsylvania-New Jersey-Delaware-Maryland Metro Area, Using ARIMAX Model with Selected

Predictors, 2005–2016

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Exhibit 44. Gross Rent CPI Validation and Forecast for New York-Newark-Jersey City, New York-

New Jersey-Pennsylvania, Using ARIMAX Model with Selected Predictors, 2005–2016

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Exhibit 45. Gross Rent CPI Validation and Forecast for Boston-Cambridge-Newton, Massachusetts-

New Hampshire, Using ARIMAX Model with Selected Predictors, 2005–2016

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Exhibit 46. Gross Rent CPI Validation and Forecast for Midwest Region (Size Class B/C) Using

ARIMAX Model with Selected Predictors, 2005–2016

78

Exhibit 47. Gross Rent CPI Validation and Forecast for the Northeast Region (Size Class B/C) Using

ARIMAX Model with Selected Predictors, 2005–2016

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Exhibit 48. Gross Rent CPI Validation and Forecast for the Southern Region (Size Class B/C) Using

ARIMAX Model with Selected Predictors, 2005–2016

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Exhibit 49. Gross Rent CPI Validation and Forecast for the Western Region (Size Class B/C) Using

ARIMAX Model with Selected Predictors, 2005–2016

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Exhibit 50. Performance of HUD FMRs and Alternatives, 2017

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Exhibit 51. Performance of HUD FMRs and Alternatives, 2018

84

Exhibit 52. Performance of HUD FMRs and Alternatives, 2019

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Exhibit 53. Performance of HUD FMRs and Alternatives, 2020

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Exhibit 54. Alternative Calculations of Root Mean Squared Error, 2017

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Exhibit 55. Alternative Calculations of Root Mean Squared Error, 2018

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LIS T OF EXH IB ITS

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Executive Summary

Every year, HUD estimates Fair Market Rents (FMRs), which are used to determine payment standards and rental assistance levels for housing programs. Accurate FMRs play a critical role in whether voucher households can secure safe, decent, and affordable housing through the private market. If HUD inaccurately calculates FMR

estimates and FMRs do not keep pace with rising rents, families may face limited housing options, have to devote a large portion of their income to housing costs, or fail to find a decent unit to lease with a voucher. Therefore, accurately estimating FMRs is vital to ensuring that renters with vouchers can maintain access to stable and decent housing. In places where rents rise more rapidly than FMR estimates, the negative implications of low or inaccurate FMRs may be even more severe.

This research examined avenues for identifying areas with rapidly rising rents and providing viable approaches to improving HUD’s FMR calculations. We explored models that leverage local data to forecast whether a county will likely see rapidly rising rents in the future. We also used local data to improve the predictive ability of time series models, building on prior work and HUD’s current methods. In our analysis, we found that incorporating timely data on vacancies, housing starts, population growth, unemployment, home values, and interest rates can improve models’ performance in forecasting rents at the metropolitan and regional levels. We then applied these models to county-level data and calculated six sets of alternative FMRs. When compared with historical data, the alternative FMR estimates tended to outperform HUD–produced FMRs from the same period.

Findings

One overarching question drove our research: what method should HUD use to calculate FMRs in markets with rapidly rising rents so that families using housing choice vouchers (HCVs) can find and lease suitable housing? Although the agency’s current estimation approach accounts for regional, metro-level, and national trend factors, our research examined whether incorporating timely county-level data can improve FMR estimates in markets with rapidly rising rents. We found the following:



Between 2009 (2009–2010) and 2019 (2018–2019), an average of 19.5 percent of counties saw rapidly rising rents from the previous year. These counties are located across the country but are concentrated in the West—particularly in Montana, North Dakota, Alaska, and

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EXECUTIVE S UM MAR Y

Colorado—with fewer counties in the industrial Midwest. We also captured rising rents in urban areas along the Pacific Coast.



We explored models using local area unemployment rates, vacancy rates, the share of building permits per 1,000 housing units, and growth in the number of housing units to predict which counties will experience rapidly rising rents before rental data become available. Our models showed relationships between vacancy rates and unemployment and the likelihood of rapidly rising rents. However, in a validation sample, the models could not accurately predict which counties had rapidly rising rents.



We found that an Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) model that incorporates data on vacancies, building permits, housing unit growth, unemployment, home values, and mortgage interest rates tends to provide better predictions of future changes in gross rent levels across metropolitan areas or for regional aggregates of midsize cities than a pure time series Autoregressive Integrated Moving Average (ARIMA) model.



We saw promising results when we applied six alternative models to county-level data to generate FMRs and assessed their performance. We calculated six sets of alternative FMRs for U.S. counties that use local data to create unique forecasts for each. We designed these alternatives to maximize the accuracy of forecasts by county and did not include adjustments to increase FMRs above statewide minimums or 90 percent of the previous year’s FMR.

Looking across counties in 2018, five of the six alternative models were more accurate than HUD’s FMRs according to root mean squared error. However, when FMRs were more than 10

percent off from actual rents, HUD more frequently set FMRs too high, whereas our models more frequently forecasted FMRs that were too low. Relative to HUD’s FMRs, the six sets of alternative FMRs performed similarly in counties with rapidly rising rents.

The importance of accurate FMRs cannot be overstated. FMRs that fail to keep up with rising rents can limit housing choice, hinder the ability of new voucher holders to find eligible rental units, and increase housing instability. Our research shows that rents have risen rapidly in many U.S. counties; however, it is difficult to forecast which counties will have rapidly rising rents in any given year. In addition, the county-level FMRs we developed performed relatively well compared with HUD’s FMRs, including the 2020 FMRs that calculated local and regional trend factors. Taken together, the best path to improve FMR calculations in areas with rapidly rising rents appears to be improving FMR

calculations overall. HUD could take steps to improve FMR calculations by using county-level local data, as we did, although further refinements to our methods are needed.

EXECUTIVE S UM MAR Y

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As an alternative, HUD could incorporate local data and generate more local trend factors while staying within the basic framework of its current FMR calculation process. Our research shows that using more precise local data and focusing on smaller geographies could improve FMR calculations. In addition, HUD’s shift toward using Small Area Fair Market Rents (SAFMRs) makes such local data even more important. Many of the datasets used in this study, for example, provide county-level but not ZIP Code–level information. As housing searches, job searches, and permitting continue to move online, new types of data collection could help develop more accurate FMR calculations in the near future.

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Alternative Fair Market Rents for

Local Housing Markets

Every year, HUD estimates Fair Market Rents (FMRs), which determine payment standards and rent levels for housing programs. Accurate FMRs play a critical role in whether voucher households can secure safe, decent, and affordable housing through the private market. If HUD calculates FMR

estimates inaccurately and they do not keep pace with rising rents, families may face limited housing options, need to devote a large portion of their income to housing costs, or fail to find a decent unit to lease with a voucher. Therefore, accurately estimating FMRs is vital to ensuring that renters with vouchers can maintain access to stable and decent housing. In places where rent increases outpace FMR estimates, the negative implications of low or inaccurate FMRs may be even more severe.

Our research explored avenues for identifying areas with rapidly rising rents and providing viable approaches to improving HUD’s FMR calculations. We began our analysis by defining a market with rapidly rising rents as any county with a 10 percent year-over-year increase in rents or any high-cost county (in the top quintile) with a 5 percent year-over-year increase in rents. We show that this definition picks up both high-cost urban areas with steady high-dollar rent increases and more affordable rural areas that saw rapid spikes in rents over the study period. We explored models that could leverage local data to forecast whether a county would likely see rapidly rising rents in the future. Our models, however, have limited predictive capabilities.

To improve the predictive ability of time series models, we incorporated timely data on vacancies, housing starts, population growth, unemployment, home values, and interest rates and found that these data can improve the performance of models that forecast rents at the metropolitan and regional levels. We then applied these models to county-level data and calculated six sets of alternative FMRs; these alternative FMR estimates show promise and tend to outperform the HUD–

produced FMRs over the same period.

In this report, we provide background on how HUD calculates FMRs and present additional research on the process for calculating FMRs. We then detail the methods and data used in this study. Finally, we share findings from the main components of the study and conclude with a brief overview of the implications of this report for policy and future research.

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Background

Congress created the Housing Choice Voucher (HCV) program (formerly known as Section 8) as part of the Housing and Community Development Act of 1974. For the first time, this legislation allowed HUD to provide assistance to households with low incomes to rent from private landlords, thus expanding the volume of housing units available to elderly renters and renters with low incomes or disabilities.

Under the federal HCV program, households identify a rental unit to live in; if the landlord accepts their rental application, they can use their voucher to pay all or a portion of their rent (HUD, 1999).

Rental units participating in the program need approval from the local public housing agency. Before receiving approval to use a voucher on a housing unit, the public housing agency inspects the housing unit to verify that it conforms to health and safety standards. The local public housing agency also determines the level of rent support on the basis of the area’s FMR, cost of the rental unit, household size, and household income. If a renter chooses a rental unit that exceeds the calculated value of the HCV, the renter pays the difference.

To support the HCV program, HUD must produce FMR estimates to cover the entire country. FMRs approximate the market rate of decent, affordable housing and are calculated at the 40th percentile of the local distribution of rental units occupied by recent movers. Public housing agencies use FMRs to determine payment standards for the HCV program and rent levels—such as initial rents and rent ceilings—for many other housing programs, including public housing, Section 8 project-based rental assistance, the Moderate Rehabilitation Single Room Occupancy program, HOME Investment Partnerships, and Emergency Solutions Grants (HUD, n.d.). Agencies also use FMRs to determine award amounts for Continuum of Care grantees and rent limits for Continuum of Care funds (HUD, n.d.). See exhibit 1 for more on the value of effective housing affordability programs.

The official definition of FMRs has changed since 1974. HUD originally set FMRs at the 50th percentile of area rents until 1984, when it changed to the 45th percentile. FMRs remained at the 45th percentile until 1995, when this threshold changed to the 40th percentile. In 2000, HUD began setting FMRs at the 50th percentile in areas where households needed higher FMRs to find and lease decent, affordable units. The agency phased out the use of 50th percentile FMRs between 2017 and 2020. During this period, it calculated FMRs for HUD Metropolitan FMR Areas (HMFAs)—a HUD-designated geography that largely maps onto U.S. Office of Management and Budget-designated counties and metropolitan statistical areas. HUD also divides some metropolitan statistical areas into smaller HMFAs, such as the Dallas/Fort Worth HMFAs and San Francisco/Oakland HMFAs.

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Exhibit 1. Value of Effective Housing Affordability Programs Research documents the effects of housing instability—which we define as living with rent burden, living in poor-quality housing, 1 being behind on rent, making frequent moves, being evicted, or experiencing homelessness—on families and children, which can negate or greatly diminish the benefits of HCVs. Inaccurate FMR calculations can exacerbate these issues.

Further, housing instability affects all aspects of people’s lives, including long-term financial stability, health and health care insecurity, and food insecurity.



Long-term financial stability. Housing instability in the form of high-cost burdens and evictions can lead to a self-perpetuating poverty cycle because affected individuals have a harder time retaining a job and making positive long-term financial savings and investments (Desmond and Gershenson, 2016; Verma and Hendra, 2003). In addition, an initial shock to housing instability can begin a cycle of worsening housing instability (Collinson and Reed, 2018; Harrison et al., 2021; Robinson and Steil, 2020).



Health and health care. Responding to the immediate pressures of housing instability can crowd out proactive healthy behavior. Housing instability is associated with the lack of a primary care doctor or health insurance, postponement of needed or preventative medical care and medications, an increase in emergency department use, and an increase in hospitalization (Hatef et al., 2019; Kushel et al., 2005; Reid, Vittinghoff, and Kushel, 2008).



Food insecurity. Several studies document the tradeoff between housing and food, finding that housing and food insecurity are deeply interlinked (Kirkpatrick and Tarasuk, 2011; Meyers et al., 2005; Mueller and Tighe, 2007). These harms can become self-reinforcing.

In recent years, HUD began calculating FMRs for individual ZIP Codes in response to calls for more granularity within HMFAs with high variations in rent. These localized FMRs, called Small Area Fair Market Rents (SAFMRs), mostly exist in areas where a single FMR for the entire HMFA would not accurately capture the area’s diverse rent costs, especially in high-opportunity neighborhoods. In practice, these areas also tend to be HMFAs with high concentrations of voucher holders. Currently, HUD mandates the use of SAFMRs for some metropolitan areas.

(Federal Register, 2016b).

1 Poor quality is defined here as a combination of two elements: (1) housing deterioration (for example, peeling paint and holes in floor), and (2) housing disarray (for example, dark, crowded, and noisy) (Suglia, Duarte, and Sandel, 2011).

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How HUD Forecasts Fair Market Rents

To calculate FMRs, HUD approximates the 40th percentile gross rent—contract rent plus utilities—

paid by people who recently moved into standard-quality units within the FMR area (HUD, 2018). This process involves three steps, as shown in exhibit 2.

Exhibit 1. Fair Market Rent Calculations Process

ACS = American Community Survey. BLS = Bureau of Labor Statistics. CPI = Consumer Price Index. FY = fiscal year.

Note: All years refer to calendar year unless otherwise noted.

Source: HUD Fair Market Rents Introductory Overview PowerPoint slides For each FMR area, HUD calculates a local gross rent basis using special American Community Survey (ACS) tabulations from the U.S. Census Bureau. 2 HUD starts with a 5-year ACS tabulation of 40th percentile estimates of gross rents paid by all renters and adjusts it using a recent mover adjustment.

The recent mover adjustment is calculated by dividing the 1-year, 40th percentile, recent mover ACS

tabulation for the smallest available geography by the 5-year, 40th percentile, all-renters tabulation for the corresponding geography. For small areas, HUD applies the recent mover adjustment at a higher level of geography than the gross rent basis. 3 HUD calculates the gross rent basis using the 2 If public housing agencies supply HUD with local survey data that are more recent than American Community Survey data, we used the local survey data to create the gross rent basis.

3 For example, the gross rent basis for a nonmetropolitan county FMR in 2021 could be calculated as the 2014-to-2018 5-year estimate of the 40th percentile of gross rents paid for all renters in the county, times the 2018 1-year estimate of the 40th percentile of recent movers across nonmetropolitan areas in the state, divided by the 2014-to-2018 5-year estimate of the 40th percentile of all renters across nonmetropolitan areas in the state.

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most recent data available from the ACS. For example, for 2020 FMRs—which are calculated in 2019—

the gross rent basis approximated rent levels in 2017.

The gross rent basis is then adjusted to account for inflation over the past year using an inflation factor. The inflation factor is calculated as a weighted average of two Consumer Price Index (CPI) series: rent of primary residence and housing fuels and utilities. CPI data are available for the four census regions (Northeast, Midwest, South, and West) by metropolitan area size, the 21 largest metropolitan areas, urban Alaska, and urban Hawaii. We refer to these regions as CPI geographies.

HUD derives weights to account for the share of gross rent (comprising contract rent and utilities) and the share of renters with utilities included in their contract rent within each CPI geography.

Finally, HUD accounts for expected growth in rent prices between the previous calendar year and the forthcoming fiscal year using a trend factor. The agency currently estimates gross rent trend factors for CPI geographies. For each metro area and region, HUD estimates the trend factor using Autoregressive Integrated Moving Average (ARIMA) or Autoregressive Integrated Moving Average with Exogenous Variables (ARIMAX) models that forecast changes in the rents of primary residences and housing fuels and utilities CPI series (Federal Register, 2019).

HUD policy also includes two rules that set floors for FMRs. First, HUD sets a state minimum FMR

based on the population-weighted median of unadjusted nonmetropolitan FMRs in each state.

Second, the agency sets a floor for the FMR in each area at 90 percent of the prior fiscal year’s FMR.

RECENT IMPROVEMENTS IN FMR CALCULATIONS

HUD has updated its method of calculating FMRs over time. The first two steps of the current process (exhibit 1), with slight adjustments, have been in place since fiscal year 2012, as that was the first year for which 5-year ACS data were available. Before the FY 2020 FMRs, HUD used a national trend factor to account for expected growth in rent prices. Before the FY 2016 FMRs, the national trend factor was the average annual rent growth over the past five years. Between FY 2017 and FY 2019, HUD used a time series model to forecast a national trend factor. For the FY 2020 FMRs, HUD asked its multidisciplinary research team4 to explore approaches to deriving more localized trend factors.

4 From HUD (2015), “PD&R developed the Multidisciplinary Research Team (MDRT) vehicle to manage a team of qualified researchers. Researchers are selected for their expertise to produce an array of high quality, short-turnaround research. MDRT researchers use a variety of HUD and external data sources to answer research questions relating to HUD’s priority policies and strategic goals.”

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In the report “Deriving Local Trend Factors for Fair Market Rent Estimation , ” HUD’s multidisciplinary research team explored approaches to incorporate local market conditions into FMR calculations, starting with HUD’s existing methodology, followed by methods using alternate data sources and empirical strategies (2M Research, 2019). HUD used autoregressive integrated moving average models with exogenous variables (ARIMAX models) to estimate different trend factors for local metropolitan areas with more than 2.5 million people and aggregates for each in the same census region.

To estimate local rent and utilities (the two components of the gross rent index), the research team used three potential ARIMAX models:

1. A univariate time series model without exogenous variables.

2. A multivariate model with national exogenous variables.

3. A multivariate model with local exogenous variables to estimate the local rent and utilities.

Comparing the forecast errors for all three models for each geographic region using the root mean squared error (RMSE), the study found that the multivariate model with national exogenous variables provided the most accurate forecast for rent, and the univariate time series model without exogenous variables provided the most accurate forecast for the utilities series (2M Research, 2019).

Following the release of the 2019 report, HUD announced its plan to update the FMR estimation process to include local and regional trend factors (Federal Register, 2019).

Improving FMR Estimates

FMR estimation is complicated by the lack of rental data that are high quality, comprehensive, local, and timely. ACS estimates of gross rents are high quality, have broad geographic coverage, and include all types of rental units (HUD, 2018). However, 5-year estimates suffer from significant lag, and 1-year ACS estimates are not available for communities with smaller populations. By contrast, rent data collected by the Bureau of Labor Statistics (BLS) are more current and released more regularly, but they are available only for large metropolitan areas and regional aggregates of smaller cities.

Other sources of rent data are private or proprietary or oversample multifamily rental units (Feldman and MacDonald, 2019). Proprietary rent datasets such as CoStar, Reonomy, or Zillow may contain more up-to-date information than publicly available data. However, they often oversample multi-unit developments and undersample single-family rentals and rentals that are not professionally managed.

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Therefore, these sources may not be comprehensive enough to incorporate into FMR calculations and may be biased toward higher rent prices (Feldman and MacDonald, 2019). Data aggregated from rental listing websites are also timely but include only asking prices and not final contracted rents (Boeing, Wegmann, and Jiao, 2020). If HUD were to use proprietary rent data, which often come from surveys of renters and landlords, they may have access to more contemporary information, which would, in turn, allow them to produce more timely and accurate rent estimates—provided biases in the data could be addressed.

Even without better rental data, there are at least two possible avenues to improve FMR calculations and estimates’ usefulness. First, HUD could consider developing FMRs for smaller geographies. HUD

already calculates SAFMRs at a more granular level (the ZIP Code tabulation area level) within some HMFAs, but apart from the geography for the gross rent basis, FMR and SAFMR calculations are otherwise identical (Federal Register, 2016a). Therefore, if gross rent inflation or trend factors change unevenly within a metropolitan area or region, SAFMRs within that area or region would not reflect relative intra-metro and intra-region changes in gross rent inflation or trend factors; consequently, the accuracy of SAFMRs would decrease. Inaccurate FMRs and SAFMRs that arise from intra-regional variations in rent inflation adversely affect renters with HCVs because accurate projections of annual changes in gross rent help HCV users find or stay in housing.

Second, HUD could improve its forecasts by using timelier data and including factors that are more closely tied to local predictors of rent changes. In a basic supply and demand model, rents increase when the demand for rental units is higher than the number of units available and fall if more units are available than prospective renter households. This study explores the use of timely, public-use data on factors that previous research suggests may correlate with rent changes: vacancies, employment, population growth, and residential construction.



Vacancies. One way to determine whether the demand or supply of rental units is greater at current prices is by examining vacancy rates, which indicate whether or not the housing market is at equilibrium; declining vacancy rates, for example, are a sign that demand is growing more quickly than supply. Research shows a link between vacancy rates and rent changes, with much of it focusing on the so-called natural vacancy rate (Hagen and Hansen, 2010; Rosen and Smith, 1983; Smith, 1974). Conceptually, the natural vacancy rate is the level of vacancies in a housing market with neither excess supply nor excess demand. Vacancy rates below the natural rate indicate excess demand and are predictive of increases in future rents (Hagen and Hansen, 2010; Rosen and Smith, 1983; Smith, 1974). HUD’s aggregated U.S.

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Postal Service administrative data on address vacancies provide quarterly data on vacancies for a variety of geographies.



Employment. The unemployment rate serves as a proxy for local economic conditions that affect demand. Statistics on income might align better with demand, but BLS local area unemployment statistics data are timelier than data on income at the county level. In addition, other studies have shown that rent is associated with the national employment rate (2M

Research, 2019).



Population growth. Analyses of long-run demographic changes show how population growth and household formation affect housing demand. The growth in the number of households in a county also implies an increase in demand for housing (Mankiw and Weil, 1989). All else constant, population increases have been shown to lead to higher rents (Saiz, 2003).



Residential construction . Increased construction and maintenance may lead to higher rents.

Home values and rents rise more steeply in markets that are constrained by geographic features such as a coastline (Saiz, 2010), and research has consistently shown that home values and rents rise because of regulatory constraints on housing supply (Glaeser, Gyourko, and Saks, 2005; Glaeser and Ward, 2009; Quigley and Raphael, 2005). The number of new building permits could serve as a leading indicator of future housing supply and current tightness in the housing market. Alternatively, construction could look forward—a rise in the number of building permits, for example, could indicate growing housing demand and the expectation of higher home values and rents. The Census Bureau’s Building Permits Survey provides data on the number of new housing units authorized by building permits at the county level. We combine these data with address counts from the aggregated U.S. Postal Service dataset to calculate a housing start rate.

Research Design

One overarching question drove our research: what method should HUD use to calculate FMRs in markets with rapidly rising rents so families using HCVs can find and lease suitable housing?

Although HUD’s current estimation approach accounts for regional, metropolitan-area, and national trend factors, our research examines whether incorporating timely county-level data can improve the estimation of FMRs in markets with rapidly rising rents. Our research design includes five analytical components:



Defining areas with rapidly rising rents.

8

ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS



Predicting areas with rapidly rising rents.



Estimating time series models with local data.



Creating alternative FMR calculations.



Assessing the alternative FMR calculations.

We began our analysis by defining and identifying areas with rapidly rising rents. Although it is important to have accurate FMR calculations in all areas, policymakers have expressed specific concern about the ability of current methodologies to accurately forecast market rents in areas where rents are rising more quickly relative to the rest of the country. 5 In the absence of an official definition of what defines an area with rapidly rising rents, we proposed a county-level rubric.

We explored models that can forecast which counties are experiencing rapidly rising rents before rental data become available. The models use predictors that we hypothesized are leading indicators of housing supply and demand, available at the county level: vacancy rate, number of building permits, unemployment rate, and changes in the number of housing units.

We then developed alternative methods for calculating FMRs by fitting time series models to quarterly CPI regional and metropolitan area rent data and introduced vacancy rate, number of building permits, unemployment rate, and changes in the number of housing units as potential predictors. To improve model performance, we also explored adding mortgage interest rates and regional measures of home values as predictors in the time series models.

Finally, we used the models developed using regional and metropolitan-area rent data for county-level data to create a set of county-specific FMR alternatives. We examined the performance of each of these six alternative FMRs by comparing them with county-level rent data from 2017 to 2020. We also assessed the performance of HUD’s FMRs over the same period and compared the performance of our alternative FMRs with that of HUD’s FMRs.

In the remainder of this section, we describe the data sources and methods used in each component.

5 House Report 116-106. “Transportation, Housing and Urban Development, and Related Agencies Appropriations Act, 2020,” House Appropriations Committee.

https://appropriations.house.gov/sites/democrats.appropriations.house.gov/files/HR%201865%20-

%20Division%20H%20-%20THUD%20SOM%20FY20.pdf.

ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

9

Data

Our analysis draws from various publicly available datasets and HUD–provided datasets that shed light on the supply of and demand for rental units and allow us to validate our analysis. These datasets and their use in our analyses are described in exhibit 3.

Exhibit 2. Datasets by Source and Use

Dataset (Provider)

Data of Interest

Analysis and Use

Years

Geography

Aggregated U.S.

Vacancy rates as a

Predicting areas with 2006–2019

Counties,

Postal Service

predictor of housing

rapidly rising rents

aggregated to

administrative data

market

Predictor variable for

CPI geographies and

on address

disequilibrium

trend factors

FMR areas

vacancies (HUD)

American

40th percentile gross Primary source of

2009–2013

FMR areas,

Community Survey

rent, 40th percentile rent measurements

to 2015–

counties,

(Census Bureau)

gross rent of recent

2019 5-year

metropolitan statistical

special extract for

movers

averages;

areas,

HUD

2011–2019

state nonmetro areas

1-year

estimates

Building permits

Number of permits

Predicting areas with 2006–2019

Counties,

survey (Census

rapidly rising rents;

aggregated to

Bureau)

predictor variable for

CPI geographies, FMR

trend factors

areas, and

metropolitan statistical

areas

Population

Number of housing

Standardized

1997–2019

CPI geographies,

Estimates Program

units

number of housing

FMR areas,

(Census Bureau)

units; predicting

metropolitan statistical

areas with rapidly

areas,

rising rents

counties

Fair Market Rents

FMRs

Assessment of

2017–2020

FMR areas

(HUD public-use

alternate FMRs

data)

Consumer Price

Rent of primary

Estimation of trend

1997–2020

CPI geographies

Indices (Bureau of

residence CPI;

factors

Labor Statistics)

housing fuels and

utilities CPI; energy

CPI, electricity CPI

House Price Index

HPI

Local input to trend

1997–2019

CPI geographies

(Federal Housing

factors

Finance Agency)

30-year fixed

Mortgage interest

National input to

1997–2019

National

mortgage interest

rates

trend factors

rates (Federal

Reserve)

Local area

Unemployment rate

Predicting areas with 1997–2019

Counties,

unemployment

rapidly rising rents;

aggregated to CPI

statistics (Bureau of

predictor variable for

geographies, FMR

Labor Statistics)

trend factors

areas, and

metropolitan statistical

areas

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ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

Dataset (Provider)

Data of Interest

Analysis and Use

Years

Geography

Zillow observed

Zillow observed rent Assessing alternative 2014–2020

Metro (analogous to

rent index (Zillow)

index

FMRs

metropolitan statistical

area), ZIP Code

(analogous to ZIP

Code tabulation area)

HUD-provided

CPI weights used in

Creating gross rent

2020 (held

CPI geographies

dataset

FMR calculations

CPI series

constant for

all years)

CPI = Consumer Price Index. FMR = Fair Market Rent. HPI = House Price Index.

Defining Areas with Rapidly Rising Rents

We began our analyses by defining and identifying counties with rapidly rising rents. To start, we calculated county-level recent mover–adjusted rents for 2008 to 2018. We used HUD’s 40th percentile county-level ACS rent estimates and applied the recent mover adjustment at the smallest available level of geography. We then calculated year-over-year changes in rents from 2009 to 2019.

We explored multiple definitions of counties with rapidly rising rents and determined that a two-tiered definition best accounted for both large percentage point changes in rents and impactful increases in rents in high-cost areas.

Our preferred definition for counties experiencing rapidly rising rents includes—



Counties with rents in the top 20th percentile nationally that experience a rent increase of greater than 5 percent.



Counties with rents in the bottom 80th percentile nationally that experience a rent increase of greater than 10 percent.

We provide additional information on the analysis that led to this definition in appendix A.

Predicting Areas with Rapidly Rising Rents

We developed models to predict areas with rapidly rising rents using the following data:



Annual estimated housing unit counts, by county, from the Census Bureau’s Population Estimates Program.

ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

1 1



Aggregate vacancy and address data from HUD’s aggregated U.S. Postal Service administrative data on address vacancies, updated quarterly. 6



Data on the number of new housing units authorized annually through building permits from the Census Bureau’s Building Permits Survey, by county.



Unemployment data at the county level from BLS local area unemployment statistics.

We then calculate the housing growth rate, the rate of new housing starts, and vacancy rates with the following formulas:

number of housing units − prior year number of units

𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝐻𝐻𝑔𝑔𝐻𝐻𝑔𝑔𝑔𝑔ℎ 𝑔𝑔𝑟𝑟𝑔𝑔𝑟𝑟 = 100 ×

prior year number of units

the number of housing starts

𝑅𝑅𝑟𝑟𝑔𝑔𝑟𝑟 𝐻𝐻𝑜𝑜 𝐻𝐻𝑟𝑟𝑔𝑔 ℎ𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻𝐻 𝐻𝐻𝑔𝑔𝑟𝑟𝑔𝑔𝑔𝑔𝐻𝐻 = 1000 ×

the number of households

the number of vacant residential units

𝑉𝑉𝑟𝑟𝑉𝑉𝑟𝑟𝐻𝐻𝑉𝑉𝑉𝑉 𝑔𝑔𝑟𝑟𝑔𝑔𝑟𝑟 = 100 ×

the sum of vacant and occupied residential units

To account for lags in data availability, our analysis attempts to forecast whether a county will have rapidly rising rents (between year t and year t+1) using the unemployment rate, vacancy rate, and housing growth rate for the prior year (t−1) and the rate of housing starts two years prior (t−2).

Our final dataset is a repeated cross-section of counties from 2009 to 2016, with data from previous years used to calculate housing growth rates, identify counties with rapidly rising rents, and measure lags of predictor variables. 7

6 The U.S. Postal Service vacancy data from HUD include three categories for each address: vacant, occupied, and

“no stat.” No stat addresses include rural route addresses that are vacant for 90 days or longer, addresses for businesses or homes under construction that are not yet occupied, and addresses in urban areas identified by a carrier as not likely to be active for some time. Because no stat addresses could signal that housing supply is rising (in the case of new construction) or falling (in the case of units being removed from the market), we exclude them from this analysis.

7 We chose to end the analysis in 2016 so that we could use predictions about which counties had rapidly rising rents to create alternative FMR calculations. However, because the predictive models performed poorly, we elected not to use the predictions.

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METHODOLOGY

To evaluate the out-of-sample performance of our models, we randomly divide the counties such that 70 percent of counties are in an estimation sample and 30 percent are in a validation sample. Next, we developed two types of models using the estimation sample and evaluated the models’ predictive ability using the validation sample.

The first type of model is a Boolean function that would identify any county with statistics above or below some threshold as likely to have rapidly rising rents. (For example, is there a vacancy rate below which counties are more likely to have rapidly rising rents?) These models take the following form: 𝐸𝐸[𝑅𝑅𝑖𝑖 ] = 1 if 𝑣𝑣𝑖𝑖 < 𝑉𝑉∗ OR

𝐸𝐸[𝑅𝑅𝑖𝑖 ] = 1 if 𝑣𝑣𝑖𝑖 < 𝑉𝑉∗, 𝑟𝑟𝑖𝑖 < 𝐸𝐸∗, 𝐻𝐻𝑖𝑖 < 𝑆𝑆∗, and 𝐻𝐻𝑖𝑖 < 𝐺𝐺∗

where 𝑅𝑅𝑖𝑖 is equal to 1 for rapidly rising counties, the local vacancy rate is 𝑣𝑣𝑖𝑖, the local unemployment rate is 𝑟𝑟𝑖𝑖, the local housing start rate is 𝐻𝐻𝑖𝑖, and the housing growth rate is 𝐻𝐻𝑖𝑖. The goal of these Boolean models is to determine if there are simple rules that might help forecast which counties are likely to see rapidly rising rents.

We calculated whether the models correctly identified each county using 100 values of 𝑉𝑉, 𝐸𝐸, 𝑆𝑆, and 𝐺𝐺

individually, as in the second equation. We then selected the parameters 𝑉𝑉∗, 𝐸𝐸∗, 𝑆𝑆∗ and 𝐺𝐺∗ (from the 100 tested values) that maximized the share of counties that the model correctly identified. Next, we estimated whether the model correctly identified each county using every potential combination from 10 values each of 𝑉𝑉, 𝐸𝐸, 𝑆𝑆, and 𝐺𝐺 in the third equation—producing 10,000 estimates—and again identified the parameters that maximized the share of correctly identified counties.

The second type of model is a logit model, which takes the following form: 𝑃𝑃(𝑅𝑅

log

𝑖𝑖 = 1)

1 − 𝑃𝑃(𝑅𝑅𝑖𝑖 = 1) = 𝛽𝛽0 + 𝛽𝛽1𝑣𝑣𝑖𝑖 + 𝛽𝛽2𝑟𝑟𝑖𝑖 + 𝛽𝛽3𝐻𝐻𝑖𝑖 + 𝛽𝛽4𝐻𝐻𝑖𝑖

where 𝛽𝛽0, 𝛽𝛽1, 𝛽𝛽2, 𝛽𝛽3, and 𝛽𝛽4 are estimated coefficients representing the relationship between the predictor variables and the log of the likelihood that a county has rapidly rising rents. We also ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

1 3

estimated an expanded logit model with inverse measures of vacancy rates, unemployment, housing start rate, and housing growth rate. 8

For each model, we calculate an F-score using the validation sample. In the validation sample, we categorize each county-year combination in the validation set as either—



A true positive (correctly identified as a place with rapidly rising rents).



A true negative (correctly identified as a place without rapidly rising rents).



A false positive (predicted to have rapidly rising rents but did not).



A false negative (predicted not to have rapidly rising rents but did).

Next, we calculate the number of counties that appear in each of these four categories along with accuracy, recall, precision, and the F-score, as follows:



Accuracy is the percentage of the total that is either a true positive or a true negative.



Recall is the percentage of places with rapidly rising rents that were correctly identified (true positives divided by the sum of true positives and false negatives).



Precision is calculated as true positives divided by the sum of true positives and false positives.



F-score is the harmonic mean of recall and precision.

Estimating Rent Time Series Models with Local Data

We modeled gross rent series9 for the large metropolitan areas that BLS identifies as primary sampling units (PSUs) and all the regional series comprising urban areas with fewer than 2.5 million people (classified as size class B/C by the BLS) in each census region using new predictor variables. We examined predictors that are available at the county level but also included some variables at larger 8 Hagen and Hansen (2010) show that there are benefits to using both vacancy rate and inverse vacancy rate in modeling changes in rents because the relationship between vacancy and changes in rents is nonlinear. They estimate a negative coefficient on vacancy rate and a positive coefficient on inverse vacancy rate.

9 Because we estimate the ARIMAX model with the same sets of predictor variables used for the ARIMA model for rent of primary residence CPI and the fuels and utilities CPI, we create a combined gross rent CPI series with HUD gross rent component shares weight.

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geographies as indicators for overall economic conditions and housing prices that would affect rent levels and affordability. In sum, we included the following:



Annual estimated housing unit counts at the county level and aggregated to PSU and census region from the Census Bureau’s Population Estimates Program.



Aggregate vacancy and address data from HUD’s aggregated U.S. Postal Service administrative data on address vacancies, by tract and aggregated to PSU and census region.



Data on the number of new housing units authorized annually through building permits, by county and aggregated to PSU from the Census Bureau Building Permits Survey.



Unemployment data, by PSU and census region from BLS local area unemployment statistics.



30-year national fixed mortgage interest rate from the Federal Reserve.



House Price Index, by PSU and census region, from the Federal Housing Finance Agency.

For vacancy rate, mortgage interest rate, and unemployment rate, we used a 1-year lag to account for the time it takes for the rental market to respond to changes in these predictor levels. For building permits per 1,000 housing units, we used a 2-year lag; for House Price Index and housing stock, we calculated the percentage change in the 1-year lag and 2-year lag values.

For the ARIMA models, the datasets included quarterly rent and utilities data from 1997 to 2019, aggregated into our composite gross rent CPI. For the ARIMAX models, we also used 2005 to 2018

quarterly data, for which 2005 is the earliest year of vacancy data available. For data that are only available on a yearly basis, we used linear interpolation to impute quarterly data; we assume the same numeric change for each of the four quarters in each year.

METHODOLOGY

We first identified the best-fitting ARIMA model for each metropolitan area or region. Suppose 𝑌𝑌𝑡𝑡 is the variable of interest (gross rent CPI) and let 𝑦𝑦𝑡𝑡 be the d th differential of gross rent CPI. We want to fit an ARIMA ( p, d, q) model, with the forecasting equation given by where i = 1 to p, j = 1 to q.

ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

1 5

The ARIMA model helped produce forecasts based on prior values in the time series (AR terms) and the errors made by previous predictions (MA terms). These models rapidly adjusted for sudden changes in trends, resulting in increased forecast accuracy.

We used the Dickey-Fuller Generalized Least Squares (DF-GLS) test to examine the stationarity of the gross rent CPI series, assess whether the ARIMA assumptions are met, and determine the degree of integration “d” in the model specification. Our test output revealed that gross rent CPI in all geographies achieved stationarity after first differencing.

To select the AR and MA terms in the model, we conducted repeated test models with different specifications and used the Schwarz Bayesian Information Criterion (SBC)—which penalizes additional model parameters to avoid overfitting—to select our best model. Lower SBC is preferable because it indicates the optimum tradeoff between the number of explanatory variables and better fit. Exhibit 4

shows the selection process for the Seattle-Tacoma-Bellevue, Washington, metropolitan area and the class size B/C series in the Midwest region. We present the results for the rest of the geographies in exhibit 28 in appendix B. We applied the autocorrelation function (ACF) and partial autocorrelation function (PACF) to confirm the stationarity of the series if the model residuals are white noise and not correlated.

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Exhibit 3. ARIMA Model Identification for the Seattle-Tacoma-Bellevue, Washington, Metropolitan Area and Midwest Region (Size Class B/C)

Level of

Moving

Autoregressive

Integration

Average

Schwarz Bayesian Information

Area

Terms (p)

(d)

Terms (q)

Criterion

Seattle-Tacoma-

Bellevue, WA

0

1

1

352.35

Seattle-Tacoma-

Bellevue, WA

0

1

2

355.45

Seattle-Tacoma-

Bellevue, WA

1

1

0

345.13

Seattle-Tacoma-

Bellevue, WA

1

1

1

343.05

Seattle-Tacoma-

Bellevue, WA

1

1

2

347.21

Seattle-Tacoma-

Bellevue, WA

2

1

0

347.62

Seattle-Tacoma-

Bellevue, WA

2

1

1

347.42

Midwest (Size Class

B/C)

0

1

1

264.10

Midwest (Size Class

B/C)

0

1

2

265.99

Midwest (Size Class

B/C)

1

1

0

265.52

Midwest (Size Class

B/C)

1

1

1

262.96

Midwest (Size Class

B/C)

1

1

2

267.36

Midwest (Size Class

B/C)

2

1

0

269.26

Midwest (Size Class

B/C)

2

1

1

255.06

Source: Urban Institute analysis of Bureau of Labor Statistics CPI data Once we identified the best fitting ARIMA model, we added local and national predictors, 𝑋𝑋, to the model (for example, local vacancy rate and national mortgage interest rate) using an ARIMAX model defined as

where i = 1 to p, j= 1 to q, and k = 1 to b (number of lags of the exogenous predictors, 𝑋𝑋).

With several predictors, we risked issues with multicollinearity between predictors that bias the estimation of coefficients. We examined the correlation between the predictor variables to avoid ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

1 7

multicollinearity that could bias the model results, and exhibit 5 demonstrates the correlation matrix of the predictors.

House Price Index and vacancy rate are the most closely correlated predictor variables at −0.66 and significant at 0.01 significance level, followed by mortgage rate and House Price Index at −0.57 at 0.01 significance level (exhibit 5). For our select predictors ARIMAX model, we included the three least-correlated variables: House Price Index, unemployment rate, and building permits per 1,000

housing units. Building permits per 1,000 housing units incorporates a measure of housing stock and mortgage interest rate as a national-level predictor and does not vary by area. For the expanded ARIMAX model, we include all the predictor variables in the model.

Exhibit 4. Correlation Between the Predictor Variables

Building Permits

Unemployment per 1,000 Housing

Housing

Vacancy

Mortgage

Rate

Units

Units

Mortgage interest rate

0.12***

Unemployment rate

0.31***

−0.35***

Building permits per 1,000

−0.24***

0.20***

−0.33***

housing units

Housing units

−0.18***

−0.06**

0.12***

0.45***

House Price Index

−0.66***

−0.57***

−0.03

0.06*

0.13***

* Significance level of 0.05.

** Significance level of 0.01.

*** Significance level of 0.001.

Sources: Urban Institute analysis of Bureau of Labor Statistics CPI and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau Building Permits Survey and Population Estimates Program data; Federal Housing Finance Agency House Price Index data; Federal Reserve mortgage interest rate data

Creating Alternative FMR Calculations

We calculated alternative FMRs by applying the coefficients from the ARIMA and ARIMAX models to quarterly county-level data. To create this dataset, we took the annual 40th percentile gross rent series that we constructed to define and predict areas with rapidly rising rents and expanded it to

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quarterly data, fitting a cubic spline to the natural log of annual gross rent (exhibit 6). 10 We followed the same procedure for the estimated number of housing units and unemployment rate. We also included quarterly county-level vacancy data, the metro/regional HPI, and the national mortgage interest rate. Just as when we defined and predicted areas with rapidly rising rents, we excluded counties in the six New England states because New England HMFAs do not align with counties.

For each year from 2017 to 2020, we created a dataset that includes only data that would have been able to forecast the FMR for that fiscal year. For example, while producing alternative FMRs for FY

2018, we use an ACS–derived gross rent series that runs from 2005 through 2015, BLS CPI data that run through 2016, and local area unemployment data that run through 2017.

Exhibit 5. Construction of County-Level Dataset

Data

Geography

Adjustments

Timeframe

Models

ARIMA, select

predictors

Gross rent series

County

Quarterly imputed from

annual calculations

Quarterly change

ARIMAX, and

expanded

ARIMAX

Vacancy rates

County

None

1-year lagged

Expanded

ARIMAX

Select predictors

Building permits per

ARIMAX and

1,000 housing units

County

Quarterly imputed from

annual calculations

2-year lagged

expanded

ARIMAX

Percentage change Select predictors

House Price Index

Metro/Region None

between 1-year

ARIMAX and

lagged and 2-year

expanded

lagged

ARIMAX

Mortgage interest

rates

National

None

1-year lagged

Expanded

ARIMAX

Quarterly unemployment

Select predictors

Unemployment rate

County

rates imputed from

1-year lagged

ARIMAX and

annual BLS estimates

expanded

ARIMAX

Change in housing

Quarterly count of

Percentage change Expanded

units

County

housing units imputed

between 1-year and ARIMAX

from annual estimates

2-year lagged

10 We converted annual data to quarterly data using the expand procedure in Statistical Analysis System (SAS).

Linear interpolation, which was used for predictor variables to estimate the local rent time series, produced unrealistic results at the county level.

ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

1 9

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. BLS = Bureau of Labor Statistics.

Source: Urban Institute analysis of Bureau of Labor Statistics CPI and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau Building Permits Survey and Population Estimates Program data; Federal Housing Finance Agency House Price Index data; Federal Reserve mortgage interest rate data

MODELING

We explored three models: the ARIMA model, the select predictors ARIMAX model, and the expanded ARIMAX model. We separately estimated each model using CPI series that end in 2015, 2016, 2017, and 2018. We then applied these models to the county-level data as follows.

First, we assigned each county (in each year) to a set of models. If counties are within a metropolitan area that has a BLS rent series, they are assigned to models estimated for their metro area. Otherwise, counties are assigned to models for their census region. Within metropolitan areas and regions, we assigned the model based on the most recent data that would be available. For the FY 2017 FMRs, we applied the ARIMA and ARIMAX models calculated using CPI data through 2015 to county-level rent data from the ACS that runs through 2014. We calculated alternative FY 2018 FMRs using rent data through 2015 and models fit CPI data through 2016; FY 2019 FMRs using rent data through 2016 and models fit CPI data through 2017; and FY 2020 FMRs using rent data through 2017 and models fit CPI data through 2018.

We used two techniques for implementing the regional models to forecast gross rent series. The techniques differ in how they account for rent changes over the previous year. Method A uses county-level forecasts, and Method B uses regional and metro-level inflation data. By comparing the two methods, we can see if local forecasting can outperform regional and metro-level inflation adjustments. The two techniques are implemented as follows:



Method A.

1. Because the d term in all the ARIMA and ARIMAX models is 1, we took the first difference of the county gross rent series, creating series of quarterly changes in rents.

2. We applied the ARIMA and ARIMAX models to the first-differenced gross rent series and accompanying predictor variables to create forecasted first differences.

3. We calculated predicted rent levels based on the forecasted first differences. For FY

2018, we calculated out 11 quarters, or through the third quarter of 2018.

4. We calculated alternative FMRs as the average across the four quarters of that fiscal year.

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ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS



Method B. This technique takes advantage of available metro-level and regional CPI data.

1. We estimated four additional quarters of gross rents by 1 year using the regional or metropolitan area CPI data. For example, for FY 2018 FMRs, we estimated calendar year 2016 gross rents using CPI data.

2. We took the first difference of the county gross rent series, creating series of quarterly changes in rents.

3. We applied the ARIMA and ARIMAX models to the first-differenced gross rent series and accompanying predictor variables to create forecasted first differences.

4. We calculated predicted rent levels based on the forecasted first differences. For FY

2018, we calculated out seven quarters, or through the third quarter of 2018.

5. We calculated alternative FMRs as the average across the four quarters of that fiscal year.

From these two methods and the three models, we estimated six sets of alternative FMRs each year.

To assess the accuracy of our methods, we did not adjust our alternative FMRs based on a state minimum, nor did we adjust FMRs to ensure that they did not fall below 90 percent of the previous year’s FMR.

Assessing Alternative FMR Calculations

To assess the performance of our alternative FMRs, we compared the six alternative FMR values and HUD’s FMR values with the actual 40th percentile gross rent to examine whether any of our alternative FMRs outperformed HUD’s FMRs.

To evaluate our results, we compiled the following data by fiscal year:



40th percentile gross rents in 2017 and 2018, calculated retrospectively from HUD’s ACS

extracts



40th percentile gross rents, for a subset of counties, constructed by adjusting the 2018 gross rents by the change in rent prices from Zillow’s ZIP Code–level observed rent index (ZORI) for 2019 and 2020.

At the time of the analysis, county-level ACS data for 2019 and 2020 were not available. To calculate goodness of fit in 2019 and 2020, we used ZORI and a ZIP Code-to-county crosswalk from Geocorr to ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

2 1

adjust the gross rent series for inflation. Because ZORI is only available for certain ZIP Codes, our sample size for comparison in 2019 and 2020 is much smaller than in 2017 and 2018.

METHODOLOGY

To evaluate the predictive power of the proposed methods, we calculated the RMSE for each of the six sets of alternative FMRs in each year and overall. 11 For each year of the analysis, we also calculated the share of counties for which the actual 40th percentile gross rent fell below 90 percent of the alternative FMR, between 90 and 110 percent of the alternative FMR, or above 110 percent of the alternative FMR.

These metrics allowed us to see whether FMRs tend to be too high or too low. We selected the 90 and 110 percent thresholds because public housing agencies have the option to set payment standards between 90 and 110 percent of FMRs without special approval from HUD and because HUD used similar metrics in its 2018 report.

We explored performance across all counties in 2017 and 2018 and across a subset of counties (for which Zillow data are available) in 2019 and 2020 against these metrics. We then conducted further subgroup analyses to assess the alternative FMRs’ performance among metropolitan and nonmetropolitan counties, in counties with high or rapidly rising rents, and in counties for which SAFMRs are calculated.

Limitations

Several limitations of the study design may influence the research findings, including how we defined and predicted areas with rapidly rising rents and how we assessed our alternative FMR calculations.

We detail major limitations and how they affect our evaluation below.

Data availability. FMR calculations and the analysis described above are limited by data availability.

Most of our analyses focused on housing markets defined at the county level. This offers the potential for more granularity than current FMR calculation methods, but counties vary greatly in both geographic size and population. Ideally, we would have examined smaller areas, such as ZIP Codes or census tracts. At these lower levels, however, the best available data likely come from ACS 5-year 11 The RMSE is the square root of the sum of squared differences between the alternative FMR (or HUD’s official FMR) and the 40th percentile gross rent calculated retrospectively.

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estimates, meaning we could not take advantage of timelier data from the BLS’s local area unemployment statistics or the Census Bureau’s Population Estimates Program and Building Permits Survey.

Limitations of available datasets. The timely, county-level datasets we used each have their limitations.

Notably, the BLS Local Area Unemployment Statistics are modeled—meaning they include modeling error—and the Census Bureau’s Building Permits Survey data are affected by nonresponse bias and imputation error. In addition, each of our predictor variables had some gaps in geographic coverage.

As a result, the alternative FMRs that we generate with ARIMAX models exclude some counties.

Streamlining decisions. We also made several decisions to streamline our analysis that introduced potential study limitations. First, we focused on two-bedroom FMRs. If rent changes for larger or smaller units deviated significantly over time, our analysis misses this nuance. Second, we excluded New England counties and Puerto Rico’s municipios from our analysis of counties with rapidly rising rents and our alternative FMR calculations. Although there is no obvious reason that the analysis would have substantively different findings if these places were included, we cannot say this with certainty. Third, our alternative FMRs deviated from HUD’s in various ways, and we did not systematically examine the influence of each decision on the differences between our estimates and those from HUD. We developed our time series models to predict composite gross rent CPI instead of following the current FMR methodology of estimating separate models for rent CPI and utility CPI.

We introduced new predictor variables to the ARIMAX models and applied the coefficients from regional and metropolitan-area models to county-level data. In addition, we did not adjust FMRs based on the state minimum or the previous year’s FMR. Any of these differences could be responsible for the differences between our alternative FMRs and HUD’s FMRs. HUD also changed its FMR

methodology during our study period, and we did not examine how HUD’s current methods would have performed over the earlier period.

Findings

As we described in the previous section, we designed this study to develop insights that may help HUD improve FMR calculations, particularly in areas with rapidly rising rents. In this section, we discuss the geographic distribution of the counties we defined as having rapidly rising rents. We then present the results of our attempts to develop models that predict areas with rapidly rising rents using data from 2009 to 2016. Next, we describe the models that we estimated to fit gross rent price data ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

2 3

at the regional and metropolitan-area levels. Finally, we assess the performance of alternative, county-level FMRs relative to actual rent levels and the FMRs used between 2017 and 2020.

Defining Areas with Rapidly Rising Rents

Using the definition proposed in the Research Design section of this report, we found that an average of 19.5 percent of counties had rapidly rising rents between 2009 (2009–2010) and 2019 (2018–

2019). Exhibit 7 illustrates the counties that saw rapidly rising rents during this period and the number of years during which the county experienced rapidly rising rents. These counties are more heavily concentrated in Western states, including Montana, North Dakota, Alaska, and Colorado, and are less concentrated in the industrial Midwest. Exhibit 2 also captures rising rents in urban areas along the Pacific Coast, which could pose a concern for policymakers and local public housing agencies.

Exhibit 6. Number of Years in Which Counties Saw Rapidly Rising Rents, 2009–2010 to 2018–2019

Note: We define a county as having rapidly rising rents if (1) the county has rents in the top 20th percentile nationally and experiences a rent increase of greater than 5 percent, or (2) the county has rents in the bottom 80th percentile nationally and experiences a rent increase of greater than 10 percent.

Source: Urban Institute analysis of HUD American Community Survey extracts of gross rents from 2009 to 2019

Although our research focuses on rent changes at the county level, HUD’s current methodology estimates rents for FMR areas that generally align with metropolitan areas, small areas (such as ZIP

Codes) within metropolitan areas, and nonmetropolitan counties. For comparison, exhibit 8 identifies

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metropolitan and state nonmetropolitan areas in which more than one-half of households live in counties with rapidly rising rents under our preferred definition. The map shows rapidly rising rents for more than 1 year within metropolitan areas in Alaska, Hawaii, North Dakota, and the Pacific Coast.

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Exhibit 7. Number of Years in Which the Majority of Households in Metropolitan and State Nonmetropolitan Areas Saw Rapidly Rising Rents, 2009–2010 to 2018–2019

Notes: We define a county as having rapidly rising rents if (1) the county has rents in the top 20th percentile nationally and experiences a rent increase of greater than 5 percent, or (2) the county has rents in the bottom 80th percentile nationally and experiences a rent increase of greater than 10 percent. Metro and state nonmetropolitan areas are designated as having rapidly rising rents if more than 50 percent of households in the area live in counties with rapidly rising rents.

Source: Urban Institute analysis of HUD American Community Survey extracts of gross rents from 2009 to 2019

Predicting Areas with Rapidly Rising Rents

We explored two sets of models that could be used to predict which counties are experiencing rapidly rising rents before rental data become available. The first is Boolean models, which set thresholds above or below which we predict counties will have rapidly rising rents. The second is logit models, which estimate the likelihood function. Both models used predictors that we hypothesize are leading indicators of housing supply and demand available at the county level: vacancy rates, number of building permits, unemployment rate, and changes in the number of households. Throughout the analysis period (2009 to 2016), 18.8 percent of counties experienced rapidly rising rents. Additional descriptive statistics appear in appendix B.

BOOLEAN MODELING RESULTS

For each of the predictors examined, we identified cut-off thresholds 𝑉𝑉∗, 𝐸𝐸∗, 𝑆𝑆∗, and 𝐺𝐺∗ that maximized the accuracy of our prediction as to which counties had rapidly rising rents. We found that accuracy is maximized when our models predicted that few or no counties would have rapidly rising rents.

Exhibit 9 displays the results of the Boolean model using only vacancy rate as a predictor and varying the threshold 𝑉𝑉, below which we forecast that counties will have rapidly rising rents. The top panel

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shows the percentage of counties with vacancy rates below a given threshold. As the vacancy rate threshold 𝑉𝑉 increases, the fraction of counties below 𝑉𝑉—the counties we would predict to have rapidly rising rents—falls. The bottom panel shows the accuracy of the Boolean model. We see that efficiency is maximized at = 0, the point at which the fraction of counties predicted to have rapidly rising rents falls to zero. The dashed line in the lower panel represents the accuracy of a null hypothesis that no counties have rapidly rising rents. Put more simply, if we predict that no counties have rapidly rising rents, we are correct 81 percent of the time—and no Boolean model using only vacancy rate improves on this level of accuracy.

The same pattern holds for unemployment, rate of housing starts, and housing growth rate when each is modeled on its own. In a combined model, we found that some combinations of 𝑉𝑉∗, 𝐸𝐸∗, 𝑆𝑆∗ and 𝐺𝐺∗ led to accuracy rates marginally higher than a null assumption that no counties have rapidly rising rents.

However, these combinations are all edge cases predicting that fewer than 10 of 14,081 county-by-year observations are instances of rapidly rising rents, and none of these combinations increased accuracy by as much as one-tenth of 1 percent beyond the null assumption that no place has rapidly rising rents.

Exhibit 8. Boolean Model Accuracy with Vacancy Rate

Accuracy (Percentage of Observations Correctly Predicted)

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Vacancy Rate

Notes: The top panel shows the percentage of counties with vacancy rates below a given threshold. The bottom panel shows the accuracy of the Boolean model, which predicts that counties below a certain vacancy rate have rapidly rising rents and counties above that vacancy rate do not have rapidly rising rents.

Sources: Urban Institute analysis of BLS unemployment statistics; HUD FMR program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

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LOGIT MODELING RESULTS

Next, we examined whether we could use logit models to predict whether counties experience rapidly rising rents. To accommodate the two-part definition of rapidly rising rents, we estimated logit models separately for places in the top 20th percentile of rents, the bottom 80th percentile of rents, and all together, all based on 40th percentile recent-mover–adjusted rents in 2009. Because counties with smaller populations tend to have larger margins of error around estimates of rent and the unemployment rate, we also estimated the model using a subset of counties with at least 20,000

households. For ease of interpreting analysis findings, we calculated odds ratios for each logit model.

Odds ratios show how each predictor affects the likelihood of having rapidly rising rents. An odds ratio of 0.9 means that an increase in the predictor of 1 reduces the odds of having rapidly rising rents by 10 percent, and an odds ratio of 1.1 means that an increase in the predictor of 1 increases the odds of having rapidly rising rents by 10 percent.

The 95 percent confidence intervals for the odds ratios appear in exhibit 10, and the low and high columns show each side of the confidence interval. If the low end falls above 1, we have 95 percent confidence in a positive relationship; if the high end falls above 1, we have 95 percent confidence that the relationship is positive.

Some evidence indicates that higher vacancy rates are associated with a decreased likelihood of having rapidly rising rents. The estimated odds ratio for all counties implies that a 1 percentage point increase in vacancy rate decreases the likelihood of having rapidly rising rents by between 1 and 4

percent. Places with higher unemployment rates also appear less likely to have rapidly rising rents. The 95 percent confidence intervals for the variables that appear only in the expanded model span 1.000, which indicates that we cannot identify whether the relationship is positive or negative.

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Exhibit 9. Predicting the Likelihood of Having Rapidly Rising Rents Logit Model Results (95 Percent Confidence Odds Ratios), 2009–2010 to 2015–2016

Rent in Top

Rent in Bottom

At Least 20K

All Counties

20%

80%

Households

Low

High

Low

High

Low

High

Low

High

Base model

Vacancy rate

0.957 0.987 0.931

1.003

0.986

1.022

0.898 0.958

Housing start rate

1.008 1.034 0.982

1.022

0.998

1.031

0.991 1.027

Unemployment rate

0.971 1.001 0.944

0.997

0.963

1.000

0.956 1.003

Growth rate

0.989 1.168 0.859

1.113

0.944

1.101

0.949 1.214

Observations

14,081

3,063

11,018

5,770

Expanded model

Vacancy rate

0.955 0.986 0.926

1.000

0.985

1.022

0.892 0.953

Inverse vacancy rate

0.997 1.001 0.996

1.002

0.997

1.002

0.994 1.001

Housing start rate

1.006 1.034 0.982

1.023

0.999

1.035

0.991 1.028

Inverse housing start rate

0.958 1.017 0.959

1.046

0.979

1.048

0.959 1.038

Unemployment rate

0.977 1.036 0.911

1.012

1.018

1.094

0.905 1.001

Inverse unemployment

rate

0.748 9.846 0.031

8.685

7.241

145.1

0.013 2.594

Housing growth rate

0.983 1.161 0.861

1.118

0.929

1.081

0.956 1.225

Inverse housing growth

rate

0.999 1.002 0.997

1.005

0.999

1.002

0.999 1.004

Observations

13,865

3,054

10,811

5,756

Notes: Top 20 percent and bottom 80 percent are based on 40th percentile recent-mover–adjusted rents in 2009.

Relationships that are nonzero with 95 percent confidence are in bold.

Sources: Urban Institute analysis of BLS unemployment statistics; HUD FMR program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data Exhibit 11 displays forecast validation statistics for the logit models. We compared the logit model with a null assumption that no county has rapidly rising rents. Because we identified 19 percent of our county-by-year observations as having rapidly rising rents and 81 percent as not having rapidly rising rents, the null assumption that no county has rapidly rising rents has an accuracy rate of 81 percent.

Because the null never correctly identifies counties with rapidly rising rents, its recall—the percentage of places with rapidly rising rents that were correctly identified—is zero. Precision and F-score are undefined for the null hypothesis; because the null never predicts that rents are rising, there are no true or false positives (only true and false negatives). Neither logit model was more accurate than the null across all counties or for any of the three county subsets we examined. Recall was greater than zero for both models using any set of counties, but neither model correctly identified even one in four counties with rapidly rising rents across all counties.

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Exhibit 10. Performance of Logit Model Predicting Areas with Rapidly Rising Rents, 2009–2010 to 2015–2016

Null

Base Model

Expanded Model

Rent

Rent

in

Rent in

in

Rent in

All

Top

Bottom At Least 20K

All

Top

Bottom At Least 20K

Counties

20%

80%

Households

Counties

20%

80%

Households

True

positives

0

293

176

143

201

293

177

128

203

False

positives

0

940

292

639

473

920

282

610

466

True

negatives

5,251

4,311

654

3,666

1,481

4,264

663

3,629

1,479

False

negatives

1,199

906

299

581

443

894

296

586

440

Accuracy

0.814

0.714

0.584

0.757

0.647

0.715

0.592

0.759

0.650

Recall

0.000

0.244

0.371

0.198

0.312

0.247

0.374

0.179

0.316

Precision

n/a

0.238

0.376

0.183

0.298

0.242

0.386

0.173

0.303

F-Score

n/a

0.241

0.373

0.190

0.305

0.244

0.380

0.176

0.309

Note: Top 20 percent and bottom 80 percent are based on 40th percentile recent-mover–adjusted rents in 2009.

Sources: Urban Institute analysis of BLS unemployment statistics; HUD FMR program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data Estimating Rent Time Series Models with Local Data

Our next section of analysis focuses on predicting gross rent CPI with additional predictor variables.

To evaluate whether the additional predictor variables improve the fitness of the time series model, we calculated the RMSE to compare forecast errors for the ARIMA, select predictors ARIMAX, and expanded ARIMAX models. This reveals how well the selected model predicts compared with the actual gross CPI for the forecast periods we chose.

Specifically, we estimated each model specification over four overlapping sample periods: 2005 to 2015, 2005 to 2016, 2005 to 2017, and 2005 to 2018. Next, we calculated the predicted gross rent CPI over the following seven quarters and calculated RMSE, mimicking models used to forecast FMRs in FY 2017, FY 2018, FY 2019, and FY 2020, respectively.

We found mixed results in improvements to the ARIMA model. In general, the ARIMAX models had lower RMSE and performed better than the ARIMA model, but this is not always the case. As demonstrated in exhibit 12, for example, the ARIMA model performed best for the Seattle-Tacoma-Bellevue, Washington, metropolitan area during the 2005–2018 estimate period, and the ARIMAX

model performed better for the other periods. Exhibit 13 shows the number of times each model performed the best for Seattle and the Midwest. Statistics describing the model performance for all

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other PSUs can be found in exhibit 31 in appendix B. Overall, the expanded ARIMAX model performed the best nationally more than one-half of the time (53 percent), followed by the ARIMAX

model with selected predictors (34 percent); this is intuitive because we introduced additional predictor variables that capture trends in rent CPI and, therefore, reduce RMSE. The ARIMA model only performed better than the ARIMAX model in 13 percent of the models we estimated.

Exhibit 11. Root Mean Squared Error for ARIMA and ARIMAX Models Comparison, Seattle-Tacoma-Bellevue, Washington, Metropolitan Area and Midwest Region (Size Class B/C)

FMR Prediction

Estimate Time

RMSE for

RMSE for Select RMSE for Expanded

Year

Period

ARIMA

Predictors

ARIMAX

ARIMAX

Seattle-Tacoma-Bellevue, WA

FY 2020

2005–2018

1.799

2.059

2.300

FY 2019

2005–2017

2.098

1.924

2.324

FY 2018

2005–2016

1.861

1.804

1.017

FY 2017

2005–2015

2.064

1.682

1.417

Midwest (Size Class B/C)

FY 2020

2005–2018

0.588

0.554

0.479

FY 2019

2005–2017

0.618

0.552

0.588

FY 2018

2005–2016

0.773

0.685

0.720

FY 2017

2005–2015

1.075

1.043

1.080

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. FY = fiscal year. RMSE = root mean squared error.

Notes: Size Class B/C consists of urban areas with a population of 2.5 million or fewer. Results for all regions appear in exhibit 32.

Source: Urban Institute analysis of HUD FMR program data and BLS Consumer Price Index data

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Exhibit 12. Summary of ARIMA and ARIMAX Model Performance

Select Predictors

Expanded

Area

ARIMA

ARIMAX

ARIMAX

Northeast (Size Class B/C)

3

0

1

Midwest (Size Class B/C)

0

3

1

South (Size Class B/C)

0

2

2

West (Size Class B/C)

0

1

3

Boston-Cambridge-Newton, MA-NH

1

1

2

New York-Newark-Jersey City, NY-

NJ-PA

1

1

2

Philadelphia-Camden-Wilmington,

PA-NJ-DE-MD

1

0

3

Chicago-Naperville-Elgin, IL-IN-WI

0

2

2

Detroit-Warren-Dearborn, MI

0

3

1

Washington-Arlington-Alexandria,

DC-VA-MD-WV

1

1

2

Miami-Fort Lauderdale-West Palm

Beach, FL

0

2

2

Atlanta-Sandy Springs-Roswell, GA

0

2

2

Baltimore-Columbia-Towson, MD

0

1

3

Dallas-Fort Worth-Arlington, TX

0

2

2

Los Angeles-Long Beach-Anaheim,

CA

0

0

4

San Francisco-Oakland-Hayward, CA

1

1

2

Seattle-Tacoma-Bellevue, WA

1

1

2

Total

9

23

36

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables.

Note: Size Class B/C consists of urban areas with a population of 2.5 million or fewer.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index data; Federal Reserve mortgage interest rate data

We found that no single predictor variable performs the best as a predictor for change in gross rent CPI across all geographies. Exhibits 14 and 15 present the coefficients and standard deviations for the predictor variables in the ARIMAX models for the Seattle metropolitan area and the Midwest region.

In Seattle, for the select predictors used in the ARIMAX model (House Price Index, unemployment rate, and building permits per 1,000 housing units), the number of building permits and the House Price Index are statistically significant. The negative coefficient for building permits per 1,000 housing units indicates that an increase in building permits predicts a smaller increase in gross rent in the

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future, although the magnitude and significance vary in other locations. Conversely, House Price Index is significant and positive for the Seattle-Tacoma-Bellevue analysis, indicating that as the House Price Index increases, larger gross rent increases follow; as with the building permits coefficient, the magnitude and significance vary for other locations. In contrast, we find much smaller coefficients on relationships between predictor variables and the gross rent series for the Midwest (size class B/C).

Exhibit 13. Coefficients for Select Predictors Using the ARIMAX Model for 2005–2018, Seattle-Tacoma-Bellevue, Washington, Metropolitan Area and Midwest Region

Predictor

Coefficient

Standard Error

Seattle-Tacoma-Bellevue, WA

Building permits per 1,000 housing

units*

-0.433*

0.173

House Price Index*

0.172**

0.051

Unemployment rate

-0.006

0.004

Midwest (Size Class B/C)

Building permits per 1,000 housing

units

0.015

0.178

House Price Index

0.063

0.108

Unemployment rate

0.000

0.002

* Significance level of 0.05.

** Significance level of 0.01.

*** Significance level of 0.001.

Notes: Size Class B/C consists of urban areas with a population of 2.5 million or fewer. Results for all regions appear in exhibit 32.

Sources: Urban Institute analysis of Bureau of Labor Statistics unemployment statistics, U.S. Department of Housing and Urban Development FMR program data, Census Bureau Building Permits Survey data, and Federal Housing Finance Agency House Price Index.

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Exhibit 14. Coefficients for Expanded ARIMAX Model for 2005–2018, Seattle-Tacoma-Bellevue, Washington, Metropolitan Area and Midwest Region (Size Class B/C)

Predictor

Coefficient

Standard

Error

Seattle-Tacoma-Bellevue, WA

Permits per 1,000 housing units

-0.296

1.317

House Price Index**

0.207

0.082

Unemployment rate

-0.002

0.005

Mortgage interest rate

-0.004

0.008

Vacancy rate

-0.148

1.435

Housing growth rate

0.464

13.56

Midwest (Size Class B/C)

Permits per 1,000 housing units

-0.049

1.541

House Price Index

0.012

0.147

Unemployment rate

-0.001

0.003

Mortgage interest rate

0.000

0.006

Vacancy rate

0.07

0.823

Housing growth rate

0.511

16.547

* Significance level of 0.05.

** Significance level of 0.01.

*** Significance level of 0.001.

Note: Size Class B/C consists of urban areas with a population of 2.5 million or fewer. Results for all regions appear in exhibit 33.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics CPI and unemployment statistics; U.S.

Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index data; Federal Reserve mortgage interest rate data In exhibit 16, we summarize the frequency of significance of the predictor variables for the select predictors ARIMAX model for 2005–2018. House Price Index appears to be the predictor that is most often significant, although the direction of coefficient may vary by region. Detailed coefficient and standard error values for each PSU and size class B/C series for each region can be found in exhibits 32 and 33 in appendix B. We do not show counts of significance for the expanded ARIMAX model

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because the predictors are correlated, so statistical significance does not necessarily identify the most important predictors in the expanded ARIMAX model.

Exhibit 15. Significant Predictor Variables and Select Predictors for ARIMAX Model, 2005–2018

Building

Permits per

1,000 Housing

House Price

Item

Unemployment Rate

Units

Index

Select predictors ARIMAX

model

0

2

8

ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables.

Notes: Significance test is based on a significance level of 0.05. See exhibit 32 for complete results.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics CPI and unemployment statistics; U.S.

Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data Assessing Alternative FMR Calculations

To assess the performance of our alternative FMR estimates, we compared estimates calculated from the six alternative models and HUD–calculated FMRs with the actual 40th percentile gross rent.

USING THE RMSE AS AN ASSESSMENT STRATEGY

Although the ARIMAX models tend to better fit the metropolitan and regional gross rent CPI series (exhibit 13), the ARIMA model better predicted county gross rents while using RMSE. Exhibit 17

displays the RMSE for estimates from the six alternative FMR models and the HUD FMRs between 2017 and 2020. We calculated RMSE in terms of nominal dollars and with each county weighted equally. Alternative formulations of RMSE with errors calculated as a percentage of actual rent and weighted by the number of housing units in each county appear in exhibits 55 and 56. For each of the ARIMA and ARIMAX models, alternative A shows the results when we apply the model directly to the county gross rent series and forecast 11 quarters forward to estimate FMRs. Alternative B shows the results when we use regional and metropolitan-area CPI data to forecast gross rent for four quarters and then use the ARIMA and ARIMAX models to forecast the next seven quarters.

Based on RMSE, version A of the ARIMA model performed best in 2017 and 2018 (exhibit 17). The A version of the select predictors ARIMAX model provided the best fit for the data in 2019 and 2020, but our calculated gross rents in those years include less than 10 percent of all counties and include only four nonmetropolitan counties. Forecasting directly from the county gross rents (rows marked ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

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“A” in exhibit 17) tended to provide a better fit than forecasting after using 1 year of metropolitan area or regional inflation adjustments. However, version B using the select predictors ARIMAX model performed better in 2017 and 2018. Results are similar when we calculate RMSE using errors measured as a percentage of actual rents. Weighting by the number of housing units, version B using the select predictors ARIMAX model performs best in 2017 and 2018, and the expanded ARIMAX

model performs worse (exhibits 55 and 55).

Exhibit 16. Goodness of Fit Measures at the County Level (RMSE in Nominal Dollars)

HUD FMRs and Alternatives by Year

FMR Definition

2017

2018

2019

2020

HUD FMR

111

109

184

188

ARIMA (A)

84

90

143

131

ARIMA (B)

85

90

148

136

Select predictors ARIMAX (A)

125

113

118

113

Select predictors ARIMAX (B)

113

107

118

114

Expanded ARIMAX (A)

91

95

150

137

Expanded ARIMAX (B)

94

101

160

143

Observations (counties)

2,634

2,613

218

218

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors calculated between HUD’s two-bedroom FMR or proposed alternatives and actual 40th percentile gross rents for two-bedroom units. For 2019 and 2020, we adjusted the 2018 gross rents to 2019 and 2020 levels using ZIP Code-level ZORI estimates from Zillow. Because ZORI estimates are available for select ZIP Codes, the sample size is smaller in 2019 and 2020.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics CPI and unemployment statistics; U.S.

Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data We expect that HUD FMRs will have larger RMSEs compared with county gross rents than our alternatives for three reasons: first, many FMRs are developed for multicounty HMFAs; second, HUD

used national trend factors in 2017, 2018, and 2019 to calculate FMRs in those fiscal years; and third, HUD adjusts FMRs based on the state minimum and previous year’s FMR floors but we did not. For

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each year in the study period, FMRs calculated from the ARIMA model and the expanded ARIMAX

model better fit the data than HUD’s FMRs. The select predictors model, however, did not universally outperform HUD’s FMRs in terms of minimizing relative RMSE. In 2017, neither technique using the select predictors ARIMAX model had a lower RMSE than HUD’s FMRs, and in 2018, only version “B”

of the select predictors ARIMAX model had a lower RMSE than HUD’s FMRs. Notably, all our alternatives performed better than HUD’s FMRs in 2020, when HUD began using local trend factors at the metropolitan and regional levels.

USING TRUE VALUE WITHIN 10 PERCENT RANGE AS AN ASSESSMENT STRATEGY

To more practically evaluate how well our alternative models perform, we also examined whether actual 40th percentile gross rents were within 10 percent of our alternative FMRs, less than 90

percent of our alternative FMRs, or more than 110 percent of our alternative FMRs (exhibit 18). If actual rents are lower than FMRs, public housing agencies and some households with HCVs may be able to lease more expensive units than the program was designed to subsidize, leading to higher costs per assisted household and, potentially, fewer households served. If actual rents are higher than FMRs, however, households with HCVs may have difficulty finding decent-quality rental units. We considered this latter issue to be of greater concern than the former. All else equal, we considered FMRs that overestimate rent (producing instances in which actual rent is less than 90 percent of the FMR) preferable to FMRs that underestimate rent (producing instances in which actual rent is greater than 110 percent of the FMR). HUD’s use of a state minimum and floor set at 90 percent of the previous year’s FMR helps minimize instances in which FMRs might be too low. Because we did not replicate this policy, we expect that actual rents will be more than 110 percent of HUD’s FMRs less frequently than our alternatives.

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Exhibit 17. Ratio of Actual Gross Rent to FMRs for HUD FMRs and Alternatives by Year

40th Percentile Gross Rents

Less than 90%

90– 110%

Greater than 110%

Item

of FMR

of FMR

of FMR

Observations

2017

2,634

HUD FMR

35%

60%

5%

ARIMA (A)

7%

70%

23%

ARIMA (B)

6%

68%

26%

Select predictors ARIMAX (A)

57%

36%

7%

Select predictors ARIMAX (B)

43%

49%

8%

Expanded ARIMAX (A)

10%

66%

24%

Expanded ARIMAX (B)

9%

64%

27%

2018

2,613

HUD FMR

32%

62%

6%

ARIMA (A)

5%

68%

27%

ARIMA (B)

5%

67%

28%

Select predictors ARIMAX (A)

45%

47%

8%

Select predictors ARIMAX (B)

35%

55%

10%

Expanded ARIMAX (A)

6%

66%

28%

Expanded ARIMAX (B)

7%

63%

30%

2019

218

HUD FMR

21%

56%

23%

ARIMA (A)

3%

56%

41%

ARIMA (B)

3%

54%

43%

Select predictors ARIMAX (A)

12%

76%

12%

Select predictors ARIMAX (B)

14%

74%

12%

Expanded ARIMAX (A)

3%

53%

44%

Expanded ARIMAX (B)

3%

51%

46%

2020

218

HUD FMR

19%

55%

26%

ARIMA (A)

3%

59%

38%

ARIMA (B)

3%

56%

41%

Select predictors ARIMAX (A)

12%

80%

8%

Select predictors ARIMAX (B)

12%

80%

8%

Expanded ARIMAX (A)

3%

59%

38%

Expanded ARIMAX (B)

3%

56%

41%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent.

Notes: Exhibit displays percentage of counties for which the actual 40th percentile gross rent (calculated using ACS data) is less than 90 percent of, between 90 and 110 percent of, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year. For 2019 and 2020, we adjusted the 2018

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gross rents to 2019 and 2020 levels using ZIP Code-level ZORI estimates from Zillow. Because ZORI estimates are available for select ZIP Codes, the sample size is smaller in 2019 and 2020.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics CPI and unemployment statistics; HUD FMR program data and U.S.

Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

The ARIMA model produced FMRs that were closest to actual rents most frequently, using data from 2017 and 2018. Actual rents were within 10 percent of the ARIMA model FMRs 70 and 68 percent of the time in 2017 and 68 and 67 percent of the time in 2018. The expanded ARIMAX model performed similarly on this metric. However, the ARIMA and expanded ARIMAX models were more likely to underestimate actual rents than either the selected predictors ARIMAX model or HUD’s FMRs. In 2018, the ARIMA model created FMRs that were too low in 27 and 28 percent of counties, and the expanded ARIMAX model created FMRs that were too low in 28 and 30 percent of counties. Of our alternative FMRs, the two generated from the select predictors ARIMAX model were least likely to undershoot the actual gross rent. In 2017, only 7 and 8 percent of counties had actual rents greater than 110 percent of these predicted FMRs, and in 2018, only 8 and 10 percent of counties had actual rents greater than 110 percent of the predicted FMRs.

In 2017 and 2018, HUD’s FMRs were rarely lower than any of our alternative estimates—in 2017 and 2018, the actual 40th percentile gross rent was more than 110 percent of HUD’s FMR in only 5 and 6

percent of counties. In 2017 and 2018, 90 to 110 percent of HUD’s FMRs covered the actual 40th percentile rent level more frequently than the alternatives based on the select predictors ARIMAX

model but less frequently than the alternatives based on either the ARIMA or expanded ARIMAX

models.

For the 218 counties for which we calculated actual rents for 2019 and 2020, the select predictors ARIMAX model performed better than HUD’s FMRs and alternative FMRs based on the ARIMA and expanded ARIMAX models. In 2019, actual rents were within 10 percent of the FMRs produced by the select predictors ARIMAX model 74 and 76 percent of the time. In 2020, actual rents were within 10 percent of the FMRs from the select predictors ARIMAX model 80 percent of the time. Finally, the select predictors ARIMAX model produced FMRs that were too low only 12 percent of the time in 2019 and only 8 percent in 2020.

SUBGROUP ANALYSIS

In this section, we examine how well the models performed based on calculations using data from different types of counties. We focus here on FY 2018, the most recent year for which we have broad ALTER NATIVE FAIR M AR KET R EN TS FOR LOCAL H OUS IN G M AR KETS

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coverage on alternative FMRs generated without using metropolitan area or regional inflation adjustments (version A). Results for other years are presented in appendix B.

We first look at counties within the top 20th percentile of rents in 2009 and those identified as having rapidly rising rents in 2018 (exhibit 19). With respect to RMSE, all the models perform similarly well in counties with higher rents compared with HUD’s FMRs. Examining the distribution, however, we see that the expanded ARIMAX and ARIMA models tend to underestimate rent levels.

We find similar results in counties with rapidly rising rents. The ARIMA and expanded ARIMAX models have a lower RMSE among counties with rapidly rising rents, but they are more likely than HUD’s previous methodology to produce FMRs lower than the actual 40th percentile gross rent.

Exhibit 18. Performance of HUD FMRs and Alternatives in Counties with High or Rapidly Rising Rents, 2018

RMSE

40th Percentile Gross Rents

Greater

(dollars)

Less than 90%

90–110% than 110%

Item

of FMR

of FMR

of FMR

Observations

Counties with higher rents (top 20th percentile)

529

HUD FMR

153

19%

63%

18%

ARIMA (A)

143

4%

57%

39%

Select predictors ARIMAX (A)

143

19%

63%

18%

Expanded ARIMAX (A)

151

4%

55%

41%

Counties with rapidly rising rents

593

HUD FMR

124

39%

55%

6%

ARIMA (A)

92

10%

67%

23%

Select predictors ARIMAX (A)

126

47%

46%

7%

Expanded ARIMAX (A)

94

9%

67%

24%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error.

Notes: Exhibit displays root mean squared prediction errors and percentage of counties for which the actual 40th percentile gross rent (calculated using American Community Survey data) is less than 90 percent, between 90 and 110 percent, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year. Categories are not mutually exclusive—some counties appear in both groups.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics CPI and unemployment statistics; HUD FMR program data and U.S.

Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

Exhibit 20 shows results for counties broken down by metropolitan and nonmetropolitan status in 2018. HUD’s FMRs, which are calculated directly for nonmetropolitan counties, perform better by RMSE among nonmetropolitan counties than they do in metropolitan areas, where a single FMR may

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be used for a multicounty HMFA. Our alternative FMRs also perform well among nonmetropolitan counties, whether evaluated based on RMSE or distribution of the actual 40th percentile rents relative to HUD–estimated FMRs.

Comparing alternatives, the ARIMA model has the lowest RMSE and is most frequently within 10

percent of the actual gross rent level in both metropolitan and nonmetropolitan counties, but it is also most likely to set FMRs too low so that the true 40th percentile of rents is more than 110 percent of FMRs. In nonmetropolitan areas, the select predictors ARIMAX model leads to FMRs that tend to be too high; the 40th percentile of gross rent was less than 90 percent of the alternative FMR in 59

percent of counties.

Exhibit 19. Performance of HUD’s FMRs and Alternatives in Metropolitan and Nonmetropolitan Counties, 2018

40th Percentile Gross Rents

RMSE

Less than 90%

90–110% Greater than 110%

Item

(dollars)

of FMR

of FMR

of FMR

Observations

Counties in metropolitan areas

1,035

HUD FMR

138

30%

60%

10%

ARIMA (A)

116

4%

62%

34%

Select predictors ARIMAX

(A)

125

34%

55%

11%

Expanded ARIMAX (A)

122

5%

60%

35%

Counties in nonmetropolitan areas

1,578

HUD FMR

84

33%

64%

3%

ARIMA (A)

68

6%

72%

22%

Select predictors ARIMAX

(A)

105

53%

41%

6%

Expanded ARIMAX (A)

72

7%

70%

23%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error.

Note: Exhibit displays root mean squared prediction errors and percentage of counties for which the actual 40th percentile gross rent (calculated using American Community Survey data) is less than 90 percent, between 90 and 110 percent, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics CPI and unemployment statistics; HUD FMR program data and U.S.

Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

Finally, we examine the performance of our alternative FMRs in 139 counties in metropolitan areas that calculate SAFMRs (exhibit 21). In these counties, the selected predictors ARIMAX model has the lowest RMSE; the actual 40th percentile of rents was within 10 percent of the predicted FMR 72

percent of the time; and the actual 40th percentile was more than 110 percent of the predicted FMR

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12 percent of the time. However, in 2017, the ARIMA model had a lower RMSE, but FMRs from the select predictors ARIMAX model performed better according to the distributional metrics (appendix B).

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Exhibit 20. Performance of HUD’s FMRs and Alternatives in Counties with SAFMRs, 2018

40th Percentile Gross Rents

RMSE

Less than

90–110%

Greater than

Item

(dollars)

90% of FMR

of FMR

110% of FMR

Observations

Counties with SAFMRs

139

HUD FMR

226

38%

45%

17%

ARIMA (A)

165

5%

59%

36%

Select predictors ARIMAX (A)

158

16%

72%

12%

Expanded ARIMAX (A)

179

6%

58%

36%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error. SAFMR = Small Area Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors and percentage of counties for which the actual 40th percentile gross rent (calculated using American Community Survey data) is less than 90 percent, between 90 and 110 percent, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics CPI and unemployment statistics; HUD FMR program data and U.S.

Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

Implications for Policy and Future Research

The research presented in this report aims to help HUD determine the best method for calculating FMRs in markets with rapidly rising rents. We began our work by defining markets with rapidly rising rents, which we apply to U.S. counties. We recommend a two-tiered definition: rents are rapidly rising if gross rents fall in the top 20 percent nationally and rise 5 percent year over year, or if rents are not in the top 20 percent nationally but increase 10 percent year over year. This definition captures rural or lower-cost areas that see sharp increases in rents in percentage terms and higher-cost areas that see moderate increases in rent in percentage terms that are large in terms of the dollar amount for renters.

Next, we developed predictive models to forecast counties likely to have rapidly rising rents, using local data that are available more quickly than rental data. We focused on local area unemployment rates, vacancy rates, the number of building permits per 1,000 housing units, and growth in the number of housing units. Our models showed that places with higher vacancy and unemployment rates were less likely to have rapidly rising rents. However, the models could not accurately predict which counties had rapidly rising rents in a validation sample.

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Our predictive models used simple approaches that produced results that are relatively easy to interpret. We explored a Boolean model that sought to find thresholds and a logit model that assumed that predictors were independently associated with the probability of rapidly rising rents.

Unfortunately, these approaches failed to make accurate predictions, leaving several avenues open for future work in forecasting areas with rapidly rising rents. Future work could examine—



The functional form of the predictive models and the potential interactions between the predictor variables.



Interactions between predictor variables or incorporating thresholds into logit, probit, or linear probability models.



More complex classification schemes, such as Bayesian models, random forests, or other machine learning algorithms that might prove effective at identifying areas with rapidly rising rents.



A prediction process built on the ARIMA and ARIMAX models that have proven relatively effective at forecasting rent levels.

We also estimated time series models with local data, using ARIMA and ARIMAX models based on BLS

rent and utilities prices (aggregated into a gross rent series). We show that an ARIMAX model that incorporates data on vacancies, building permits, population growth, unemployment, home values, and mortgage interest rates tends to provide better predictions of future changes in gross rent levels across metropolitan areas than a pure time series ARIMA model. Adding these predictors to the ARIMAX models could improve the estimation of local trend factors at the county level, even while staying within the basic framework of HUD’s current FMR calculation process.

Future research should explore refinements to our ARIMA and ARIMAX models. We used lags of predictor variables to account for the timeliness of data releases and educated guesses about long-term relationships between those predictors and the rental market. But the ideal number of lags may depend on each geography’s preexisting conditions and unique trends in those factors. Future research could further refine the models designed to predict areas with rapidly rising rents and the ARIMAX models by identifying the number of lags needed to maximize the predictive capability of each predictor variable.

In our analysis, we applied the coefficients from regional and metropolitan-area ARIMA and ARIMAX

models to county-level data to generate six alternative FMRs and assess their performance. We designed our alternative FMRs to maximize accuracy at the county level and did not include

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adjustments that HUD makes to maintain FMRs above statewide and previous-year floors. The results were promising. Looking across counties in 2017, four of our FMRs more accurately predicted the true 40th percentile rent (had a smaller RMSE) than HUD’s FMRs. In 2018, five of our alternatives had lower county-level RMSEs than HUD’s FMRs, and in 2019 and 2020, all six sets of alternative FMRs had lower RMSEs than HUD’s FMRs. These results generally held both in metropolitan areas and nonmetropolitan areas. Looking only at counties with rapidly rising rents, we found that our six sets of FMRs performed similarly, relative to HUD FMRs and to each other, as they had across the full sample of counties.

Our research suggests that we can predict FMRs at a local level by predicting changes in rent locally rather than applying regional inflation and trend factors. We can apply a similar process to ZIP Codes to calculate SAFMRs. Although many predictor variables are not available at the ZIP Code level, the ARIMA model could be applied to an imputed ZIP Code-level gross rent series. Future work could examine estimating county- or even ZIP Code–specific ARIMA and ARIMAX models.

We also found that although the local predictors tended to improve the fit of time series models of gross rent, the ARIMAX-based FMRs did not always outperform the ARIMA-based models when applied to the county data. Further research could examine additional predictors, new combinations of predictors, and more systematic testing of the predictive capacity of each.

In addition, as discussed in the limitations section, our research made several simplifications—notably, excluding New England and Puerto Rico and focusing only on two-bedroom FMRs—that could be explored individually. Our alternative FMRs differed from HUD’s FMRs in several ways: introducing new predictor variables, using a single gross rent series rather than separate utility and rent series, applying the model rather than the implied trend factor to local data, and using county-level FMRs.

Future research could also explore how each difference affects FMR calculations and which differences have the largest impact.

Finally, it is important to note that during our study period, we see no evidence that HUD

systematically set FMRs too low. Rather, in 2017 and 2018, HUD rarely set the two-bedroom FMRs much lower than actual rents. In 2017, actual rents were more than 10 percent higher than the FMR in only 5 percent of counties, and in 2018, actual rents were more than 10 percent higher than the FMR

in only 6 percent of counties. FMRs appear to have been too low more frequently in 2019 and 2020, but we were only able to examine a smaller set of counties in those years.

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Conclusion

The importance of accurate FMRs cannot be overstated. FMRs that fail to keep up with rising rents can limit housing choice, hinder the ability of new entrants into the voucher program to find eligible rental units, and increase housing instability. Our research shows that rents have risen rapidly in many U.S. counties; however, it is difficult to forecast which counties will have rapidly rising rents in any given year. In addition, the county-level FMRs that we developed performed relatively well compared with HUD’s FMRs, including the 2020 FMRs that calculated local and regional trend factors. Taken together, the best path to improve FMR calculations in areas with rapidly rising rents appears to be improving FMR calculations overall. HUD could take steps to improve FMR calculations by calculating FMRs at the county level using local data, as we did, although further refinements to our methods are needed. Alternatively, HUD could incorporate local data and generate more local trend factors while staying within the basic framework of its current FMR calculation process.

Our research also shows that using more precise local data and focusing on smaller geographies could improve FMR calculations. HUD’s shift toward increased use of SAFMRs makes such local data even more important. Many of the datasets we used in this study, for example, are available at the county level but not the ZIP Code level. As housing searches, job searches, and permitting continue to shift online, more data collection could help develop more accurate FMR calculations in the near future.

Appendix A. Exploring Alternative

Definitions of Rapidly Rising Rents

In this appendix, we identify areas of the country experiencing rapidly rising rents, which we define as increases in rent that drive renters to seek alternative housing. We originally envisioned this designation as including any U.S. county where rent values increased by more than 10 percent in a single year. The 10 percent threshold aligns with previous research that examined Fair Market Rent (FMR) areas with rents between 90 and 110 percent of the FMR (HUD, 2018). However, a preliminary analysis showed that a 10 percent threshold would only classify between 5 and 15 percent of all U.S.

counties as having rapidly rising rents each year. Moreover, the 10 percent threshold did not include many of the most populous and expensive cities, where rising rents pose a major policy concern.

Exhibit 22 displays the number of times (maximum of six) each county experienced rents that rose by more than 10 percent between 2009–2010 and 2015–2016. Counties experiencing rapidly rising rents by this definition appear concentrated along a region extending south from North Dakota and

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Montana to west Texas and some counties in the Southeast. This definition finds fewer coastal, highly populated, and high-cost counties with rapidly rising rents. Our researchers were concerned about missing high-cost areas in which a rent increase of less than 10 percent may still represent a significant cost increase in dollars. For example, although we might expect Los Angeles County to experience rapidly rising rents—when the 40th percentile rent for a two-bedroom rose by more than $100 between 2015 and 2016—this definition would omit the county.

Exhibit 21. Number of Years Counties Saw More than a 10 Percent Increase in Rents, 2009–2010 to 2015–2016

Source: Urban Institute analysis of HUD American Community Survey extracts of gross rents from 2009 to 2016

We next explored lower thresholds of 5 and 8 percent for rapidly rising rents. The 5 percent threshold (exhibit 23) would designate almost every county in the United States as having experienced rapidly rising rents at least once during the study period, which means that the standard is too sensitive to positive changes in rent. We expect some changes in rent year to year—for example, inflation drives the absolute cost of rent upward. However, this study intends to identify counties where renters are priced out of their housing, not just counties where rents are rising.

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Exhibit 22. Number of Years Counties Saw More than a 5 Percent Increase in Rents, 2009–2010 to 2015–2016

Source: Urban Institute analysis of HUD American Community Survey extracts of gross rents from 2009 to 2016

Similarly, the 8 percent threshold (exhibit 24) picks up about one-half of U.S. counties but drops off known high-cost counties with tight rental markets, such as areas around Silicon Valley, New York City, and southern Florida.

Exhibit 23. Number of Years Counties Saw More than an 8 Percent Increase in Rents, 2009–2010 to 2015–2016

Source: Urban Institute analysis of HUD American Community Survey extracts of gross rents from 2009 to 2016

To ensure that our final definition of rapidly rising rents accounted for high-cost areas where larger dollar-delineated increases in rent still fall below the 10 percent and 8 percent thresholds, we

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examined a graduated definition wherein counties with rents in the top 20th percentile nationally that experience a rent increase of greater than 5 percent and counties with rents in the bottom 80th percentile nationally that experience a rent increase of greater than 10 percent are considered rapidly rising. Exhibit 25 identifies counties in the top 20th percentile of rents in 2009. As expected, these areas are concentrated in California, the Northeast Corridor, Florida, Alaska, and Hawaii. We determined that the two-tiered definition best identified places where rents are rising either in dollars or as a percentage of previous rent levels. This preferred definition appears in exhibit 7 of this report.

Exhibit 24. Counties Where 2009 Rents Were in the Top 20th Percentile Nationally Source: Urban Institute analysis of HUD ACS extracts of gross rents from 2009 to 2016

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Appendix B. Supplemental Exhibits

This appendix contains exhibits that describe the data we used to predict rapidly rising rents and estimate rent time series models. It supplements the sections on analyses A and B from this report.

Predicting Areas with Rapidly Rising Rents

Exhibit 25. Predictors of Rapidly Rising Rents and Counties with Rapidly Rising Rents, 2009–2016

Summary Statistics

Standard Deviation

Observations

Item

Mean (percent)

(percent)

(counties x years)

Housing growth rate

0.40

1.80

25,142

Vacancy rate

3.89

3.08

23,250

Housing starts per 1,000 units

4.27

4.86

22,270

Unemployment rate

7.48

3.04

25,124

County has rapidly rising rents

18.8

39.0

24,504

Sources: Urban Institute analysis of Bureau of Labor Statistics unemployment statistics; HUD FMR program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

Exhibit 26. Correlation Between Indicator for Rapidly Rising Rents and Predictor Variables (2009–2016)

Rapidly Rising

Housing Growth

Vacancy

Housing Starts

Item

County

Rate

Rate

per 1,000 Units

Housing growth rate

0.06

(24,492)

Vacancy rate

-0.05

-0.14

(22,680)

(23,238)

Housing starts per

0.06

0.72

-0.18

1,000 units

(21,707)

(22,268)

(21,056)

-0.03

-0.13

0.13

-0.17

Unemployment rate

(24,494)

(25,106)

(23,238)

(22,267)

Sources: Urban Institute analysis of Bureau of Labor Statistics unemployment statistics; HUD FMR program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

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Estimating Rent Time Series Models with Local Data Exhibit 27. Preferred ARIMA Model Specification by Area

Geographic

Area

Code

p

d

q

SBC

Atlanta-Sandy Springs-Roswell,

GA

S35C

2

1

0

456.3099

Baltimore-Columbia-Towson,

MD

S35E

0

1

1

389.0183

Boston-Cambridge-Newton,

MA-NH

S11A

0

1

1

373.2472

Chicago-Naperville-Elgin, IL-IN-

WI

S23A

0

1

1

328.7474

Dallas-Fort Worth-Arlington, TX

S37A

0

1

1

344.9239

Detroit-Warren-Dearborn, MI

S23B

0

1

1

322.7242

Los Angeles-Long Beach-

Anaheim, CA

S49A

1

1

1

245.7559

Miami-Fort Lauderdale-West

Palm Beach, FL

S35B

1

1

1

286.5353

New York-Newark-Jersey City,

NY-NJ-PA

S12A

1

1

0

261.5284

Philadelphia-Camden-

Wilmington, PA-NJ-DE-MD

S12B

0

1

1

293.1719

San Francisco-Oakland-

Hayward, CA

S49B

1

1

0

304.0293

Seattle-Tacoma-Bellevue, WA

S49D

1

1

1

343.0479

Washington-Arlington-

Alexandria, DC-VA-MD-WV

S35A

1

1

0

299.1943

Midwest (Size Class B/C)

N200

2

1

1

256.8544

Northeast (Size Class B/C)

N100

0

1

1

221.9262

South (Size Class B/C)

N300

0

1

1

215.8605

West (Size Class B/C)

N400

2

1

0

214.4220

SBC = Schwarz Bayesian Information Criterion.

Note: The following models failed to converge during the maximum likelihood estimated and were not considered: Atlanta-Sandy Springs-Roswell, GA 2,1,2; Boston-Cambridge-Newton, MA-NH 2,1,1; Baltimore-Columbia-Towson, MD 2,1,2; Miami-Fort Lauderdale-West Palm Beach, FL 2,1,2; New York-Newark-Jersey City, NY-NJ-PA 0,1,2; Philadelphia-Camden-Wilmington, PA-NJ-DE-MD 1,1,2; and Washington-Arlington-Alexandria, DC-VA-MD-WV 0,1,1 and 0,1,2; West region 2,1,1 only converged for some years in the ARIMAX model, so we updated to 2,1,0 because the SBC is very close (214.422) to the SBC for 2,1,1

(214.302).

Sources: Urban Institute analysis of Bureau of Labor Statistics Consumer Price Index; HUD FMR program data N OTES

5 1

Exhibit 28. Summary Statistics for Predictor Variables for the ARIMAX Model

Standard

Variable

Mean

Deviation

Minimum

Maximum

Vacancy rate

0.027

0.013

0.006

0.076

Housing units

4058911

6709509

128250

38208553

Building permits

37242

65109

99

583518

Unemployment rate

5.639

2.290

2.000

22.567

House Price Index

217.33

89.24

84.88

605.82

Mortgage rate

5.30

1.42

2.76

8.32

Sources: Urban Institute analysis of Bureau of Labor Statistics unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data Exhibit 29. Correlation of Predictor Variables for the ARIMAX Model

Building

Vacancy

Permits per

Housing

Rate

Mortgage

Unemployment

Rate

1,000

Stock

Item

Housing Units

Vacancy rate

1.00

Mortgage

0.12***

1.00

Unemployment

0.31***

-0.35***

1.00

rate

Building permits per

-0.27***

0.20***

-0.34***

1.00

1,000 housing units

Housing stock

-0.19***

-0.06**

0.12***

0.47***

1.00

* Significance level of 0.05.

** Significance level of 0.01.

*** Significance level of 0.001.

Sources: Urban Institute analysis of Bureau of Labor Statistics unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

5 2

N OTES

Exhibit 30. Time Series Model Performance

Area

Time Period

ARIMA

ARIMAX, Selected

ARIMAX, Expanded

Northeast (Size

Class B/C)

2005–2018

0.4612

0.4537

0.4124

Northeast (Size

Class B/C)

2005–2017

0.6936

0.7380

0.7748

Northeast (Size

Class B/C)

2005–2016

0.9094

0.9103

0.9408

Northeast (Size

Class B/C)

2005–2015

0.9803

1.0004

1.0286

Midwest (Size Class

B/C)

2005–2018

0.5885

0.5541

0.4795

Midwest (Size Class

B/C)

2005–2017

0.6180

0.5520

0.5883

Midwest (Size Class

B/C)

2005–2016

0.7733

0.6849

0.7203

Midwest (Size Class

B/C)

2005–2015

1.0746

1.0433

1.0804

South (Size Class

B/C)

2005–2018

0.4793

0.4263

0.3941

South (Size Class

B/C)

2005–2017

0.4934

0.4715

0.4312

South (Size Class

B/C)

2005–2016

0.8391

0.7427

0.8137

South (Size Class

B/C)

2005–2015

0.9359

0.8667

0.9115

West (Size Class

B/C)

2005–2018

0.9545

0.6379

0.3446

West (Size Class

B/C)

2005–2017

1.0980

0.7838

0.5184

West (Size Class

B/C)

2005–2016

0.7866

0.6017

0.4856

West (Size Class

B/C)

2005–2015

0.7143

0.5152

0.5441

Boston-Cambridge-

Newton, MA-NH

2005–2018

2.3692

2.5680

2.7837

Boston-Cambridge-

Newton, MA-NH

2005–2017

2.8881

2.9493

2.5398

Boston-Cambridge-

Newton, MA-NH

2005–2016

3.4299

3.2090

1.2153

Boston-Cambridge-

Newton, MA-NH

2005–2015

1.1490

0.9139

2.5486

New York-Newark-

Jersey City, NY-NJ-

PA

2005–2018

1.1568

1.0628

0.9534

New York-Newark-

Jersey City, NY-NJ-

PA

2005–2017

0.9651

0.9629

1.0173

New York-Newark-

Jersey City, NY-NJ-

PA

2005–2016

0.7842

0.9406

0.6355

New York-Newark-

Jersey City, NY-NJ-

PA

2005–2015

0.6139

0.6358

0.6770

N OTES

5 3

Area

Time Period

ARIMA

ARIMAX, Selected

ARIMAX, Expanded

Philadelphia-

Camden-

Wilmington, PA-

NJ-DE-MD

2005–2018

1.0918

1.0826

1.0249

Philadelphia-

Camden-

Wilmington, PA-

NJ-DE-MD

2005–2017

0.9815

0.9391

0.7373

Philadelphia-

Camden-

Wilmington, PA-

NJ-DE-MD

2005–2016

0.8095

0.7961

0.6806

Philadelphia-

Camden-

Wilmington, PA-

NJ-DE-MD

2005–2015

0.6352

0.6396

0.7634

Chicago-Naperville-

Elgin, IL-IN-WI

2005–2018

0.8744

0.8743

1.1023

Chicago-Naperville-

Elgin, IL-IN-WI

2005–2017

1.1765

1.1371

1.0998

Chicago-Naperville-

Elgin, IL-IN-WI

2005–2016

0.9684

0.8842

0.7786

Chicago-Naperville-

Elgin, IL-IN-WI

2005–2015

0.5974

0.5777

0.9772

Detroit-Warren-

Dearborn, MI

2005–2018

1.4253

1.2686

1.3662

Detroit-Warren-

Dearborn, MI

2005–2017

1.1480

0.8930

0.9373

Detroit-Warren-

Dearborn, MI

2005–2016

0.8134

0.5716

0.6480

Detroit-Warren-

Dearborn, MI

2005–2015

0.8749

0.7460

0.6921

Washington-

Arlington-

Alexandria, DC-VA-

MD-WV

2005–2018

1.0594

1.0332

1.0576

Washington-

Arlington-

Alexandria, DC-VA-

MD-WV

2005–2017

1.5264

1.6118

1.3712

Washington-

Arlington-

Alexandria, DC-VA-

MD-WV

2005–2016

1.4640

1.5420

0.6203

Washington-

Arlington-

Alexandria, DC-VA-

MD-WV

2005–2015

0.7643

0.9622

1.4950

Miami-Fort

Lauderdale-West

Palm Beach, FL

2005–2018

2.1331

2.0704

1.9103

Miami-Fort

Lauderdale-West

Palm Beach, FL

2005–2017

1.9146

1.8169

1.9334

5 4

N OTES

Area

Time Period

ARIMA

ARIMAX, Selected

ARIMAX, Expanded

Miami-Fort

Lauderdale-West

Palm Beach, FL

2005–2016

0.9807

0.8907

0.8356

Miami-Fort

Lauderdale-West

Palm Beach, FL

2005–2015

1.3858

0.8764

0.9910

Atlanta-Sandy

Springs-Roswell,

GA

2005–2018

2.8459

2.5256

2.6581

Atlanta-Sandy

Springs-Roswell,

GA

2005–2017

3.5624

2.5187

2.8014

Atlanta-Sandy

Springs-Roswell,

GA

2005–2016

5.0632

4.1900

3.6340

Atlanta-Sandy

Springs-Roswell,

GA

2005–2015

4.7300

3.8223

3.6732

Baltimore-

Columbia-Towson,

MD

2005–2018

2.4664

2.3244

2.2723

Baltimore-

Columbia-Towson,

MD

2005–2017

3.0461

2.8998

1.9417

Baltimore-

Columbia-Towson,

MD

2005–2016

4.0981

4.0842

3.2566

Baltimore-

Columbia-Towson,

MD

2005–2015

3.1826

3.1526

3.7167

Dallas-Fort Worth-

Arlington, TX

2005–2018

1.2348

0.9822

1.0809

Dallas-Fort Worth-

Arlington, TX

2005–2017

2.0476

1.7321

1.1061

Dallas-Fort Worth-

Arlington, TX

2005–2016

2.6743

1.8452

1.3216

Dallas-Fort Worth-

Arlington, TX

2005–2015

2.3954

1.2631

1.3339

Los Angeles-Long

Beach-Anaheim,

CA

2005–2018

1.4437

1.2717

1.0798

Los Angeles-Long

Beach-Anaheim,

CA

2005–2017

1.2790

1.0193

0.7637

Los Angeles-Long

Beach-Anaheim,

CA

2005–2016

0.5525

0.4779

0.4018

Los Angeles-Long

Beach-Anaheim,

CA

2005–2015

1.1340

1.0122

0.6322

San Francisco-

Oakland-Hayward,

CA

2005–2018

3.7575

3.7399

3.6236

N OTES

5 5

Area

Time Period

ARIMA

ARIMAX, Selected

ARIMAX, Expanded

San Francisco-

Oakland-Hayward,

CA

2005–2017

1.7655

2.0420

2.4209

San Francisco-

Oakland-Hayward,

CA

2005–2016

1.9465

1.9410

0.8633

San Francisco-

Oakland-Hayward,

CA

2005–2015

1.4152

0.7045

2.0023

Seattle-Tacoma-

Bellevue, WA

2005–2018

1.7994

2.0593

2.3000

Seattle-Tacoma-

Bellevue, WA

2005–2017

2.0977

1.9241

2.3245

Seattle-Tacoma-

Bellevue, WA

2005–2016

1.8613

1.8041

1.0168

Seattle-Tacoma-

Bellevue, WA

2005–2015

2.0640

1.6821

1.4167

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables.

Note: We calculated root mean squared error for forecasts 2 years out based on the specified period.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

5 6

N OTES

Exhibit 31. Coefficients for ARIMAX with Selected Predictor, 2005–2018

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Seattle-Tacoma-

Bellevue, WA

Permits per 1,000 housing units*

-0.433

0.173

Yes

Seattle-Tacoma-

Bellevue, WA

House Price Index**

0.172

0.051

Yes

Seattle-Tacoma-

Bellevue, WA

Unemployment rate

-0.006

0.004

New York-Newark-

Jersey City, NY-NJ-

PA

Permits per 1,000 housing units

0.077

0.109

New York-Newark-

Jersey City, NY-NJ-

PA

House Price Index**

0.089

0.034

Yes

New York-Newark-

Jersey City, NY-NJ-

PA

Unemployment rate

0.001

0.001

Boston-Cambridge-

Newton, MA-NH

Permits per 1,000 housing units

-0.175

0.390

Boston-Cambridge-

Newton, MA-NH

House Price Index**

0.125

0.106

Boston-Cambridge-

Newton, MA-NH

Unemployment rate

-0.003

0.005

Philadelphia-

Camden-Wilmington,

PA-NJ-DE-MD

Permits per 1,000 housing units

-0.093

0.180

Philadelphia-

Camden-Wilmington,

PA-NJ-DE-MD

House Price Index**

0.132

0.054

Yes

Philadelphia-

Camden-Wilmington,

PA-NJ-DE-MD

Unemployment rate

0.001

0.001

Chicago-Naperville-

Elgin, IL-IN-WI

Permits per 1,000 housing units

-0.057

0.070

Chicago-Naperville-

Elgin, IL-IN-WI

House Price Index

0.088

0.060

Chicago-Naperville-

Elgin, IL-IN-WI

Unemployment rate

0.000

0.001

Detroit-Warren-

Dearborn, MI

Permits per 1,000 housing units

-0.015

0.065

Detroit-Warren-

Dearborn, MI

House Price Index

0.054

0.030

Detroit-Warren-

Dearborn, MI

Unemployment rate

-0.001

0.001

Baltimore-Columbia-

Towson, MD

Permits per 1,000 housing units

0.409

0.466

Baltimore-Columbia-

Towson, MD

Housing price index

0.007

0.094

Baltimore-Columbia-

Towson, MD

Unemployment rate

0.002

0.003

Miami-Fort

Lauderdale-West

Palm Beach, FL

Permits per 1,000 housing units

0.009

0.054

N OTES

5 7

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Miami-Fort

Lauderdale-West

Palm Beach, FL

House Price Index***

0.100

0.019

Yes

Miami-Fort

Lauderdale-West

Palm Beach, FL

Unemployment rate

0.000

0.001

Los Angeles-Long

Beach-Anaheim, CA

Permits per 1,000 housing units

-0.068

0.272

Los Angeles-Long

Beach-Anaheim, CA

House Price Index**

0.070

0.025

Yes

Los Angeles-Long

Beach-Anaheim, CA

Unemployment rate

-0.002

0.002

San Francisco-

Oakland-Hayward,

CA

Permits per 1,000 housing units

-1.272

0.221

Yes

San Francisco-

Oakland-Hayward,

CA

House Price Index***

0.097

0.026

Yes

San Francisco-

Oakland-Hayward,

CA

Unemployment rate

-0.012

0.002

Dallas-Fort Worth-

Arlington, TX

Permits per 1,000 housing units

-0.055

0.076

Dallas-Fort Worth-

Arlington, TX

House Price Index

0.163

0.118

Dallas-Fort Worth-

Arlington, TX

Unemployment rate

-0.002

0.004

Atlanta-Sandy

Springs-Roswell, GA

Permits per 1,000 housing units

-0.041

0.033

Atlanta-Sandy

Springs-Roswell, GA

House Price Index*

0.163

0.077

Yes

Atlanta-Sandy

Springs-Roswell, GA

Unemployment rate

-0.001

0.003

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

Permits per 1,000 housing units

-0.036

0.128

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

House Price Index

0.032

0.036

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

Unemployment rate

-0.002

0.003

Northeast (Size Class

B/C)

Permits per 1,000 housing units

0.027

0.267

Northeast (Size Class

B/C)

House Price Index

0.018

0.104

Northeast (Size Class

B/C)

Unemployment rate

0.000

0.002

Midwest (Size Class

B/C)

Permits per 1,000 housing units

0.015

0.178

Midwest (Size Class

B/C)

House Price Index

0.063

0.108

5 8

N OTES

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Midwest (Size Class

B/C)

Unemployment rate

0.000

0.002

South (Size Class

B/C)

Permits per 1,000 housing units

0.023

0.078

South (Size Class

B/C)

Housing price index

0.104

0.062

South (Size Class

B/C)

Unemployment rate

0.001

0.002

West (Size Class B/C) Permits per 1,000 housing units

-0.066

0.105

West (Size Class B/C) House Price Index**

0.028

0.039

Yes

West (Size Class B/C) Unemployment rate

-0.002

0.002

* Significance level of 0.05.

** Significance level of 0.01.

*** Significance level of 0.001.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data.

N OTES

5 9

Exhibit 32. Coefficients for the Expanded ARIMAX Model, 2005–2018

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Seattle-Tacoma-

Bellevue, WA

Unemployment rate

-0.002

0.005

Seattle-Tacoma-

Bellevue, WA

House Price Index**

0.207

0.082

Yes

Seattle-Tacoma-

Building permits per 1,000

Bellevue, WA

households

-0.296

1.317

Seattle-Tacoma-

Bellevue, WA

Mortgage interest rate

-0.004

0.008

Seattle-Tacoma-

Bellevue, WA

Vacancy rate

-0.148

1.435

Seattle-Tacoma-

Bellevue, WA

Housing unit growth

0.464

13.560

New York-Newark-

Jersey City, NY-NJ-

PA

Unemployment rate

-0.002

0.002

New York-Newark-

Jersey City, NY-NJ-

PA

House Price Index

0.031

0.057

New York-Newark-

Jersey City, NY-NJ-

Building permits per 1,000

PA

households

0.036

0.120

New York-Newark-

Jersey City, NY-NJ-

PA

Mortgage interest rate

-0.003

0.004

New York-Newark-

Jersey City, NY-NJ-

PA

Vacancy rate

2.330

1.218

New York-Newark-

Jersey City, NY-NJ-

PA

Housing unit growth

0.916

2.031

Boston-Cambridge-

Newton, MA-NH

Unemployment rate

0.001

0.006

Boston-Cambridge-

Newton, MA-NH

House Price Index

-0.005

0.257

Boston-Cambridge-

Building permits per 1,000

Newton, MA-NH

households

-0.116

1.102

Boston-Cambridge-

Newton, MA-NH

Mortgage interest rate

-0.013

0.010

Boston-Cambridge-

Newton, MA-NH

Vacancy rate

-0.030

1.956

Boston-Cambridge-

Newton, MA-NH

Housing unit growth

5.876

9.214

Philadelphia-Camden-

Wilmington, PA-NJ-

DE-MD

Unemployment rate

0.003

0.002

Philadelphia-Camden-

Wilmington, PA-NJ-

DE-MD

House Price Index**

0.284

0.087

Yes

6 0

N OTES

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Philadelphia-Camden-

Wilmington, PA-NJ-

Building permits per 1,000

DE-MD

households

-0.532

0.894

Philadelphia-Camden-

Wilmington, PA-NJ-

DE-MD

Mortgage interest rate

0.004

0.004

Philadelphia-Camden-

Wilmington, PA-NJ-

DE-MD

Vacancy rate

-0.108

0.513

Philadelphia-Camden-

Wilmington, PA-NJ-

DE-MD

Housing unit growth

2.051

9.255

Chicago-Naperville-

Elgin, IL-IN-WI

Unemployment rate

0.003

0.002

Chicago-Naperville-

Elgin, IL-IN-WI

House Price Index

0.053

0.075

Chicago-Naperville-

Building permits per 1,000

Elgin, IL-IN-WI

households

0.355

3.255

Chicago-Naperville-

Elgin, IL-IN-WI

Mortgage interest rate

-0.013

0.007

Chicago-Naperville-

Elgin, IL-IN-WI

Vacancy rate

-0.085

0.823

Chicago-Naperville-

Elgin, IL-IN-WI

Housing unit growth

0.134

31.986

Detroit-Warren-

Dearborn, MI

Unemployment rate

-0.001

0.001

Detroit-Warren-

Dearborn, MI

House Price Index

0.012

0.062

Detroit-Warren-

Building permits per 1,000

Dearborn, MI

households

-0.041

0.450

Detroit-Warren-

Dearborn, MI

Mortgage interest rate

-0.004

0.004

Detroit-Warren-

Dearborn, MI

Vacancy rate

-0.155

0.662

Detroit-Warren-

Dearborn, MI

Housing unit growth

0.199

3.362

Baltimore-Columbia-

Towson, MD

Unemployment rate

0.005

0.003

Baltimore-Columbia-

Towson, MD

House Price Index

0.002

0.116

Baltimore-Columbia-

Building permits per 1,000

Towson, MD

households

1.366

0.893

Baltimore-Columbia-

Towson, MD

Mortgage interest rate

0.017

0.009

Baltimore-Columbia-

Towson, MD

Vacancy rate

2.206

2.328

Baltimore-Columbia-

Towson, MD

Housing unit growth

-7.916

7.685

Miami-Fort

Lauderdale-West

Palm Beach, FL

Unemployment rate

0.002

0.002

N OTES

6 1

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Miami-Fort

Lauderdale-West

Palm Beach, FL

House Price Index

0.053

0.038

Miami-Fort

Lauderdale-West

Building permits per 1,000

Palm Beach, FL

households

0.185

0.649

Miami-Fort

Lauderdale-West

Palm Beach, FL

Mortgage interest rate

-0.009

0.006

Miami-Fort

Lauderdale-West

Palm Beach, FL

Vacancy rate

0.043

0.491

Miami-Fort

Lauderdale-West

Palm Beach, FL

Housing unit growth

0.670

5.793

Los Angeles-Long

Beach-Anaheim, CA

Unemployment rate

0.001

0.003

Los Angeles-Long

Beach-Anaheim, CA

House Price Index***

0.087

0.023

Yes

Los Angeles-Long

Building permits per 1,000

Beach-Anaheim, CA

households

-0.065

0.395

Los Angeles-Long

Beach-Anaheim, CA

Mortgage interest rate

-0.002

0.003

Los Angeles-Long

Beach-Anaheim, CA

Vacancy rate

-2.397

1.337

Los Angeles-Long

Beach-Anaheim, CA

Housing unit growth

1.949

5.613

San Francisco-

Oakland-Hayward,

CA

Unemployment rate

-0.008

0.004

San Francisco-

Oakland-Hayward,

CA

House Price Index***

0.153

0.040

Yes

San Francisco-

Oakland-Hayward,

Building permits per 1,000

CA

households

-0.937

0.486

San Francisco-

Oakland-Hayward,

CA

Mortgage interest rate

0.005

0.007

San Francisco-

Oakland-Hayward,

CA

Vacancy rate

-0.676

1.406

San Francisco-

Oakland-Hayward,

CA

Housing unit growth

-0.970

4.917

Dallas-Fort Worth-

Arlington, TX

Unemployment rate

-0.001

0.004

Dallas-Fort Worth-

Arlington, TX

House Price Index

0.143

0.139

Dallas-Fort Worth-

Building permits per 1,000

Arlington, TX

households**

1.279

0.492

Yes

Dallas-Fort Worth-

Arlington, TX

Mortgage interest rate

0.004

0.007

6 2

N OTES

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Dallas-Fort Worth-

Arlington, TX

Vacancy rate

1.481

0.890

Dallas-Fort Worth-

Arlington, TX

Housing unit growth

-13.193

4.781

Atlanta-Sandy

Springs-Roswell, GA

Unemployment rate

-0.003

0.005

Atlanta-Sandy

Springs-Roswell, GA

House Price Index

0.096

0.090

Atlanta-Sandy

Building permits per 1,000

Springs-Roswell, GA

households

0.084

1.218

Atlanta-Sandy

Springs-Roswell, GA

Mortgage interest rate

-0.016

0.010

Atlanta-Sandy

Springs-Roswell, GA

Vacancy rate

1.295

0.969

Atlanta-Sandy

Springs-Roswell, GA

Housing unit growth

-0.013

12.587

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

Unemployment rate

-0.010

0.003

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

House Price Index***

0.130

0.035

Yes

Washington-

Arlington-Alexandria,

Building permits per 1,000

DC-VA-MD-WV

households

-0.246

0.244

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

Mortgage interest rate

0.008

0.004

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

Vacancy rate

1.810

0.972

Washington-

Arlington-Alexandria,

DC-VA-MD-WV

Housing unit growth

-2.890

1.839

Northeast (Size Class

B/C)

Unemployment rate

0.001

0.003

Northeast (Size Class

B/C)

Housing price index

0.057

0.138

Northeast (Size Class

Building permits per 1,000

B/C)

households

-0.095

2.098

Northeast (Size Class

B/C)

Mortgage interest rate

0.002

0.005

Northeast (Size Class

B/C)

Vacancy rate

-0.313

0.827

Northeast (Size Class

B/C)

Housing unit growth

0.504

21.946

Midwest (Size Class

B/C)

Unemployment rate

-0.001

0.003

Midwest (Size Class

B/C)

House Price Index

0.012

0.147

Midwest (Size Class

Building permits per 1,000

B/C)

households

-0.049

1.541

N OTES

6 3

Statistically

Standard

Significant

Area

Predictor

Coefficient

Deviation

(nonzero)

Midwest (Size Class

B/C)

Mortgage interest rate

0.000

0.006

Midwest (Size Class

B/C)

Vacancy rate

0.070

0.823

Midwest (Size Class

B/C)

Housing unit growth

0.511

16.547

South (Size Class B/C) Unemployment rate

0.000

0.002

South (Size Class B/C) House Price Index

0.088

0.093

Building permits per 1,000

South (Size Class B/C) households

0.003

1.258

South (Size Class B/C) Mortgage interest rate

0.000

0.005

South (Size Class B/C) Vacancy rate

0.586

0.684

South (Size Class B/C) Housing unit growth

-0.003

9.852

West (Size Class B/C) Unemployment rate

-0.001

0.002

West (Size Class B/C) House Price Index**

0.062

0.023

Yes

Building permits per 1,000

West (Size Class B/C) households

-0.100

0.401

West (Size Class B/C) Mortgage interest rate

0.004

0.004

West (Size Class B/C) Vacancy rate

-0.437

0.464

West (Size Class B/C) Housing unit growth

-0.003

2.717

**Significance level of 0.05.

** Significance level of 0.01.

*** Significance level of 0.001.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

6 4

N OTES

Exhibit 33. Gross Rent CPI Validation and Forecast for Seattle-Tacoma-Bellevue, Washington, Using ARIMAX

with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

400

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

6 5

Exhibit 34. Gross Rent CPI Validation and Forecast for San Francisco-Oakland-Hayward, California, Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

400

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

6 6

N OTES

Exhibit 35. Gross Rent CPI Validation and Forecast for Los Angeles-Long Beach-Anaheim, California, Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

400

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

6 7

Exhibit 36. Gross Rent CPI Validation and Forecast for Dallas-Fort Worth-Arlington, Texas, Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

6 8

N OTES

Exhibit 37. Gross Rent CPI Validation and Forecast for Baltimore-Columbia-Towson, Maryland, Using ARIMAX

Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

400

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

6 9

Exhibit 38. Gross Rent CPI Validation and Forecast for Atlanta-Sandy Springs-Roswell, Georgia, Using ARIMAX

Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

7 0

N OTES

Exhibit 39. Gross Rent CPI Validation and Forecast for Miami-Fort Lauderdale-West Palm Beach, Florida, Using ARIMAX with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

7 1

Exhibit 40. Gross Rent CPI Validation and Forecast for Washington-Arlington-Alexandria, DC-Virginia-Maryland-West Virginia, Using ARIMAX Model with Selected Predictors, 2005—2016

RentCPI

Forecast_CPI

400

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

7 2

N OTES

Exhibit 41. Gross Rent CPI Validation and Forecast for Detroit-Warren-Dearborn, Michigan, Using ARIMAX

Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

7 3

Exhibit 42. Gross Rent CPI Validation and Forecast for Chicago-Naperville-Elgin, Illinois-Indiana-Wisconsin, Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

7 4

N OTES

Exhibit 43. Gross Rent CPI Validation and Forecast for Philadelphia-Camden-Wilmington, Pennsylvania-New Jersey-Delaware-Maryland Metro Area, Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

7 5

Exhibit 44. Gross Rent CPI Validation and Forecast for New York-Newark-Jersey City, New York-New Jersey-Pennsylvania, Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

400

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

7 6

N OTES

Exhibit 45. Gross Rent CPI Validation and Forecast for Boston-Cambridge-Newton, Massachusetts-New Hampshire, Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

400

350

300

250

200

150

100

50

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

7 7

Exhibit 46. Gross Rent CPI Validation and Forecast for Midwest Region (Size Class B/C) Using ARIMAX Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

200

180

160

140

120

100

80

60

40

20

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

7 8

N OTES

Exhibit 47. Gross Rent CPI Validation and Forecast for the Northeast Region (Size Class B/C) Using ARIMAX

Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

180

160

140

120

100

80

60

40

20

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

7 9

Exhibit 48. Gross Rent CPI Validation and Forecast for the Southern Region (Size Class B/C) Using ARIMAX

Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

200

180

160

140

120

100

80

60

40

20

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

8 0

N OTES

Exhibit 49. Gross Rent CPI Validation and Forecast for the Western Region (Size Class B/C) Using ARIMAX

Model with Selected Predictors, 2005–2016

RentCPI

Forecast_CPI

200

180

160

140

120

100

80

60

40

20

0Jan-04

Oct-06

Jul-09

Apr-12

Dec-14

Sep-17

Jun-20

CPI = Consumer Price Index.

Sources: Urban Institute analysis of HUD FMR program data; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data; Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest rate data

N OTES

8 1

Assessing Alternative FMR Performance

Exhibit 50. Performance of HUD FMRs and Alternatives, 2017

Percentage of Counties in Which 40th

Percentile Gross Rents Are

Greater than

RMSE

Less than

90–110% of

110% of

Item

(dollars)

90% of FMR

FMR

FMR

Observations

All counties

2,634

HUD FMR

111

35%

60%

5%

ARIMA (A)

84

7%

70%

23%

ARIMA (B)

85

6%

68%

26%

Select ARIMAX (A)

125

57%

36%

7%

Select ARIMAX (B)

113

43%

49%

8%

Expanded ARIMAX (A)

91

10%

66%

24%

Expanded ARIMAX (B)

94

9%

64%

27%

Counties with higher rents (top 20th percentile)

529

HUD FMR

151

21%

66%

13%

ARIMA (A)

129

4%

64%

32%

ARIMA (B)

130

4%

61%

35%

Select ARIMAX (A)

136

23%

62%

15%

Select ARIMAX (B)

132

21%

63%

16%

Expanded ARIMAX (A)

138

4%

62%

34%

Expanded ARIMAX (B)

144

4%

59%

37%

Counties with rapidly rising rents

597

HUD FMR

140

47%

49%

4%

ARIMA (A)

100

14%

61%

25%

ARIMA (B)

101

12%

60%

28%

Select ARIMAX (A)

140

52%

38%

10%

Select ARIMAX (B)

134

46%

43%

11%

Expanded ARIMAX (A)

107

14%

58%

28%

Expanded ARIMAX (B)

113

13%

56%

31%

Counties in metropolitan areas

1,038

HUD FMR

140

33%

59%

8%

ARIMA (A)

105

7%

66%

27%

ARIMA (B)

106

6%

64%

30%

Select ARIMAX (A)

128

42%

50%

8%

Select ARIMAX (B)

120

34%

57%

9%

Expanded ARIMAX (A)

110

7%

65%

28%

Expanded ARIMAX (B)

114

6%

63%

31%

Counties in nonmetropolitan areas

1,596

8 2

N OTES

HUD FMR

87

37%

60%

3%

ARIMA (A)

68

8%

72%

20%

ARIMA (B)

69

8%

70%

22%

Select ARIMAX (A)

123

67%

27%

6%

Select ARIMAX (B)

108

48%

45%

7%

Expanded ARIMAX (A)

76

12%

67%

21%

Expanded ARIMAX (B)

78

11%

65%

24%

Counties with SAFMRs

139

HUD FMR

225

41%

46%

13%

ARIMA (A)

128

3%

65%

32%

ARIMA (B)

129

3%

63%

34%

Select ARIMAX (A)

135

26%

66%

8%

Select ARIMAX (B)

127

28%

65%

7%

Expanded ARIMAX (A)

144

5%

65%

30%

Expanded ARIMAX (B)

151

4%

63%

33%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error. SAFMR = Small Area Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors and percentage of counties for which the actual 40th percentile gross rent (calculated using American Community Survey data) is less than 90 percent, between 90 and 110 percent, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year. Categories are not mutually exclusive.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; HUD FMR

program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

N OTES

8 3

Exhibit 51. Performance of HUD FMRs and Alternatives, 2018

Percentage of Counties in which 40th

Percentile Gross Rents Are

Greater than

RMSE

Less than

90–110% of

110% of

Item

(dollars)

90% of FMR

FMR

FMR

Observations

All counties

2,613

HUD FMR

109

32%

62%

6%

ARIMA (A)

90

5%

68%

27%

ARIMA (B)

90

5%

67%

28%

Select ARIMAX (A)

113

45%

47%

8%

Select ARIMAX (B)

107

35%

55%

10%

Expanded ARIMAX (A)

95

6%

66%

28%

Expanded ARIMAX (B)

101

7%

63%

30%

Counties with higher rents (top 20th percentile)

529

HUD FMR

153

19%

63%

18%

ARIMA (A)

143

4%

57%

39%

ARIMA (B)

144

4%

56%

40%

Select ARIMAX (A)

143

19%

63%

18%

Select ARIMAX (B)

139

19%

60%

21%

Expanded ARIMAX (A)

151

4%

55%

41%

Expanded ARIMAX (B)

165

4%

51%

45%

Counties with rapidly rising rents

593

HUD FMR

124

39%

55%

6%

ARIMA (A)

92

10%

67%

23%

ARIMA (B)

90.4

9%

68%

23%

Select ARIMAX (A)

126

47%

46%

7%

Select ARIMAX (B)

120

41%

51%

8%

Expanded ARIMAX (A)

94

9%

67%

24%

Expanded ARIMAX (B)

99

10%

63%

27%

Counties in metropolitan areas

1,035

HUD FMR

138

30%

60%

10%

ARIMA (A)

116

4%

62%

34%

ARIMA (B)

116

4%

61%

35%

Select ARIMAX (A)

125

34%

55%

11%

Select ARIMAX (B)

119

27%

60%

13%

Expanded ARIMAX (A)

122

5%

60%

35%

Expanded ARIMAX (B)

130

4%

58%

38%

Counties in nonmetropolitan areas

1,578

HUD FMR

84

33%

64%

3%

ARIMA (A)

68

6%

72%

22%

8 4

N OTES

ARIMA (B)

68

6%

71%

23%

Select ARIMAX (A)

105

53%

41%

6%

Select ARIMAX (B)

97

39%

53%

8%

Expanded ARIMAX (A)

72

7%

70%

23%

Expanded ARIMAX (B)

75

7%

67%

26%

Counties with SAFMRs

139

HUD FMR

226

38%

45%

17%

ARIMA (A)

165

5%

59%

36%

ARIMA (B)

169

4%

60%

36%

Select ARIMAX (A)

158

16%

72%

12%

Select ARIMAX (B)

149

20%

68%

12%

Expanded ARIMAX (A)

179

6%

58%

36%

Expanded ARIMAX (B)

194

6%

57%

37%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error. SAFMR = Small Area Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors and percentage of counties for which the actual 40th percentile gross rent (calculated using American Community Survey data) is less than 90 percent, between 90 and 110 percent, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year. Categories are not mutually exclusive.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; HUD FMR

program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

N OTES

8 5

Exhibit 52. Performance of HUD FMRs and Alternatives, 2019

Percentage of Counties in which 40th

Percentile Gross Rents Are

Greater than

RMSE

Less than

90–110% of

110% of

Item

(dollars)

90% of FMR

FMR

FMR

Observations

All counties

218

HUD FMR

184

21%

56%

23%

ARIMA (A)

143

3%

56%

41%

ARIMA (B)

148

3%

54%

43%

Select ARIMAX (A)

118

12%

76%

12%

Select ARIMAX (B)

118

14%

74%

12%

Expanded ARIMAX (A)

150

3%

53%

44%

Expanded ARIMAX (B)

160

3%

51%

46%

Counties in metropolitan areas

214

HUD FMR

186

21%

55%

24%

ARIMA (A)

144

4%

55%

41%

ARIMA (B)

148

4%

53%

43%

Select ARIMAX (A)

118

12%

76%

12%

Select ARIMAX (B)

119

13%

74%

13%

Expanded ARIMAX (A)

151

4%

53%

43%

Expanded ARIMAX (B)

161

3%

51%

46%

Counties with SAFMRs

101

HUD FMR

213

26%

49%

25%

ARIMA (A)

151

3%

56%

41%

ARIMA (B)

157

2%

53%

45%

Select ARIMAX (A)

126

13%

77%

10%

Select ARIMAX (B)

127

14%

75%

11%

Expanded ARIMAX (A)

163

4%

51%

45%

Expanded ARIMAX (B)

178

2%

50%

48%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error. SAFMR = Small Area Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors and percentage of counties for which the actual 40th percentile gross rent (calculated using American Community Survey data) is less than 90 percent, between 90 and 110 percent, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year. Categories are not mutually exclusive.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; HUD FMR

program data and U.S. Postal Service vacancy data; and Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

8 6

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Exhibit 53. Performance of HUD FMRs and Alternatives, 2020

Percentage of Counties in which 40th

Percentile Gross Rents Are

Greater than

RMSE

Less than

90–110% of

110% of

Item

(dollars)

90% of FMR

FMR

FMR

Observations

All counties

218

HUD FMR

188

19%

55%

26%

ARIMA (A)

131

3%

59%

38%

ARIMA (B)

136

3%

56%

41%

Select ARIMAX (A)

113

12%

80%

8%

Select ARIMAX (B)

114

12%

80%

8%

Expanded ARIMAX (A)

137

3%

59%

38%

Expanded ARIMAX (B)

143

3%

56%

41%

Counties in metropolitan areas

214

HUD FMR

189

19%

55%

26%

ARIMA (A)

132

4%

59%

37%

ARIMA (B)

136

3%

57%

40%

Select ARIMAX (A)

113

12%

80%

8%

Select ARIMAX (B)

115

13%

79%

8%

Expanded ARIMAX (A)

137

3%

60%

37%

Expanded ARIMAX (B)

143

4%

56%

40%

Counties with SAFMRs

101

HUD FMR

218

27%

50%

23%

ARIMA (A)

132

4%

59%

37%

ARIMA (B)

138

4%

55%

41%

Select ARIMAX (A)

116

12%

80%

8%

Select ARIMAX (B)

118

12%

80%

8%

Expanded ARIMAX (A)

139

5%

58%

37%

Expanded ARIMAX (B)

149

5%

52%

43%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error. SAFMR = Small Area Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors and percentage of counties for which the actual 40th percentile gross rent (calculated using American Community Survey data) is less than 90 percent, between 90 and 110 percent, or greater than 110 percent of HUD’s two-bedroom FMR or proposed alternatives. Alternative FMRs are the average of the four quarters of the fiscal year. Categories are not mutually exclusive.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; HUD FMR

program data and U.S. Postal Service vacancy data; and Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

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8 7

Exhibit 54. Alternative Calculations of Root Mean Squared Error, 2017

Population-Weighted

RMSE

RMSE

Item

(dollars)

(percent)

(dollars)

(percent)

Observations

All counties

2,634

HUD FMR

111

16.4%

152

11.3%

ARIMA (A)

84

10.7%

118

9.6%

ARIMA (B)

85

10.8%

122

9.9%

Select ARIMAX (A)

125

19.1%

145

13.5%

Select ARIMAX (B)

113

17.2%

116

11.5%

Expanded ARIMAX (A)

91

11.7%

140

11.0%

Expanded ARIMAX (B)

94

11.9%

146

11.7%

Counties with higher rents (top 20th percentile)

529

HUD FMR

151

14.3%

176

11.0%

ARIMA (A)

129

11.8%

135

9.8%

ARIMA (B)

130

11.9%

140

10.1%

Select ARIMAX (A)

136

13.9%

157

11.5%

Select ARIMAX (B)

132

13.7%

124

9.3%

Expanded ARIMAX (A)

138

12.4%

163

11.7%

Expanded ARIMAX (B)

144

13.0%

169

12.5%

Counties with rapidly rising rents

597

HUD FMR

140

20.4%

198

12.5%

ARIMA (A)

100

13.2%

117

9.7%

ARIMA (B)

101

13.2%

126

10.2%

Select ARIMAX (A)

140

21.6%

135

11.9%

Select ARIMAX (B)

134

20.3%

116

11.2%

Expanded ARIMAX (A)

107

13.9%

156

12.1%

Expanded ARIMAX (B)

113

14.4%

160

12.9%

Counties in metropolitan areas

1,038

HUD FMR

140

17.8%

160

11.1%

ARIMA (A)

105

11.6%

123

9.6%

ARIMA (B)

106

11.6%

128

9.9%

Select ARIMAX (A)

128

16.6%

147

12.4%

Select ARIMAX (B)

120

15.7%

117

10.3%

Expanded ARIMAX (A)

110

11.9%

148

11.1%

Expanded ARIMAX (B)

114

12.2%

153

11.8%

Counties in nonmetropolitan areas

1,596

HUD FMR

87

15.3%

79

12.5%

ARIMA (A)

68

10.2%

70

9.5%

ARIMA (B)

69

10.2%

70

9.5%

Select ARIMAX (A)

123

20.6%

124

19.5%

8 8

N OTES

Select ARIMAX (B)

108

18.1%

110

17.5%

Expanded ARIMAX (A)

76

11.5%

75

10.4%

Expanded ARIMAX (B)

78

11.8%

78

10.7%

Counties with SAFMRs

139

HUD FMR

225

21.5%

223

13.1%

ARIMA (A)

128

10.2%

134

9.7%

ARIMA (B)

129

10.5%

137

10.1%

Select ARIMAX (A)

135

12.7%

148

11.2%

Select ARIMAX (B)

127

12.7%

116

9.1%

Expanded ARIMAX (A)

144

11.4%

161

12.1%

Expanded ARIMAX (B)

151

12.3%

176

13.7%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error. SAFMR = Small Area Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors calculated between HUD’s two-bedroom FMR or proposed alternatives and actual 40th percentile gross rents for two-bedroom units. Weights are based on the number of rental units in each county. Alternative FMRs are the average of the four quarters of the fiscal year. Categories are not mutually exclusive.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; HUD FMR

program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

Exhibit 55. Alternative Calculations of Root Mean Squared Error, 2018

Population-Weighted

RMSE

RMSE

Item

(dollars)

(percent)

(dollars)

(percent)

Observations

All counties

2,613

HUD FMR

109

15.3%

148

10.8%

ARIMA (A)

90

10.5%

126

10.0%

ARIMA (B)

90

10.5%

121

10.0%

Select ARIMAX (A)

113

16.0%

175

13.4%

Select ARIMAX (B)

107

15.0%

118

10.8%

Expanded ARIMAX (A)

95

11.0%

146

11.3%

Expanded ARIMAX (B)

101

11.5%

175

13.0%

Counties with higher rents (top 20th percentile)

529

HUD FMR

153

14.1%

171

10.7%

ARIMA (A)

143

12.2%

143

10.2%

ARIMA (B)

144

12.4%

137

10.3%

Select ARIMAX (A)

143

13.3%

201

13.0%

Select ARIMAX (B)

139

13.3%

128

9.4%

Expanded ARIMAX (A)

151

12.7%

169

12.0%

Expanded ARIMAX (B)

165

13.7%

204

14.2%

N OTES

8 9

Counties with rapidly rising rents

593

HUD FMR

124

18.5%

124

10.4%

ARIMA (A)

92

10.5%

126

9.2%

ARIMA (B)

90

10.4%

109

8.9%

Select ARIMAX (A)

126

17.6%

226

15.5%

Select ARIMAX (B)

120

17.0%

122

10.9%

Expanded ARIMAX (A)

94

10.9%

146

10.2%

Expanded ARIMAX (B)

99

11.3%

170

11.5%

Counties in metropolitan areas

1,035

HUD FMR

138

17.0%

156

10.7%

ARIMA (A)

116

11.7%

132

10.1%

ARIMA (B)

116

11.8%

126

10.2%

Select ARIMAX (A)

125

14.8%

183

13.1%

Select ARIMAX (B)

119

14.4%

120

10.0%

Expanded ARIMAX (A)

122

12.1%

154

11.6%

Expanded ARIMAX (B)

130

12.7%

185

13.4%

Counties in nonmetropolitan areas

1,578

HUD FMR

84

14.1%

73

11.2%

ARIMA (A)

68

9.6%

73

9.3%

ARIMA (B)

68

9.5%

73

9.2%

Select ARIMAX (A)

105

16.7%

104

15.6%

Select ARIMAX (B)

97

15.5%

100

14.8%

Expanded ARIMAX (A)

72

10.2%

76

9.8%

Expanded ARIMAX (B)

75

10.5%

80

10.1%

Counties with SAFMRs

139

HUD FMR

226

21.5%

221

13.1%

ARIMA (A)

165

13.1%

148

10.4%

ARIMA (B)

169

13.5%

150

10.8%

Select ARIMAX (A)

158

14.3%

143

10.7%

Select ARIMAX (B)

149

14.0%

113

8.6%

Expanded ARIMAX (A)

179

14.4%

174

12.9%

Expanded ARIMAX (B)

194

15.5%

194

14.6%

ARIMA = Autoregressive Integrated Moving Average. ARIMAX = Autoregressive Integrated Moving Average with Exogenous Variables. FMR = Fair Market Rent. RMSE = root mean squared error. SAFMR = Small Area Fair Market Rent.

Notes: Exhibit displays root mean squared prediction errors calculated between HUD’s two-bedroom FMR or proposed alternatives and actual 40th percentile gross rents for two-bedroom units. Weights are based on the number of rental units in each county. Alternative FMRs are the average of the four quarters of the fiscal year. Categories are not mutually exclusive.

Sources: Urban Institute analysis of Federal Housing Finance Agency House Price Index; Federal Reserve mortgage interest data; Zillow observed rent index; Bureau of Labor Statistics Consumer Price Index and unemployment statistics; HUD FMR

program data and U.S. Postal Service vacancy data; Census Bureau American Community Survey, Building Permits Survey, and Population Estimates Program data

9 0

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References

2M Research. 2019. Deriving Local Trend Factors for Fair Market Rent Estimation . Washington, DC: U.S.

Department of Housing and Urban Development.

https://www.huduser.gov/portal/publications/LocalTrendFactor.html.

Boeing, Geoff, Jake Wegmann, and Junfeng Jiao. 2020. “Rental Housing Spot Markets: How Online Information Exchanges Can Supplement Transacted-Rents Data,” Journal of Planning Education and Research.

https://journals.sagepub.com/doi/10.1177/0739456X20904435.

Collinson, Robert, and Davin Reed. 2018. The Effects of Evictions on Low-Income Households . New York: New York University School of Law.

https://www.law.nyu.edu/sites/default/files/upload_documents/evictions_collinson_reed.pdf.

Desmond, Matthew, and Carl Gershenson. 2016. “Housing and Employment Insecurity among the Working Poor,”

Social Problems 63: 46–67 . https://scholar.harvard.edu/mdesmond/publications/housing-and-employment-

insecurity-among-working-poor.

Federal Register. 2016a. Establishing a More Effective Fair Market Rent System; Using Small Area Fair Market Rents in the Housing Choice Voucher Program Instead of the Current 50th Percentile FMRs . Washington, DC: U.S. Department of Housing and Urban Development.

https://www.federalregister.gov/documents/2016/11/16/2016-27114/establishing-a-more-effective-fair-

market-rent-system-using-small-area-fair-market-rents-in-the.

——. 2016b. Small Area Fair Market Rents in Housing Choice Voucher Program Values for Selection Criteria and Metropolitan Areas Subject to Small Area Fair Market Rents. Washington, DC: U.S. Department of Housing and Urban Development. https://www.huduser.gov/portal/datasets/fmr/fmr2016f/SAFMR-Final-Rule-

Criteria-Notice.pdf.

——. 2019. Fair Market Rents for the Housing Choice Voucher Program, Moderate Rehabilitation Single Room Occupancy Program, and Other Programs Fiscal Year 2020. Washington, DC: U.S. Department of Housing and Urban Development.

Feldman, Joshua, and Graham MacDonald. 2019. “Rents Are Too High. Here Are Three Ways to Get the Data We Need to Fix That.” Urban Wire (blog). Urban Institute. https://www.urban.org/urban-wire/rents-are-too-high-

here-are-three-ways-get-data-we-need-fix.

Glaeser, Edward L., Joseph Gyourko, and Raven E. Saks. 2005. “Why Have Housing Prices Gone Up?” American Economic Review 95 (2): 329–333 . https://www.aeaweb.org/articles?id=10.1257/000282805774669961.

Glaeser, Edward L., and Bryce A. Ward. 2009. “The Causes and Consequences of Land Use Regulation: Evidence from Greater Boston,” Journal of Urban Economics 65: 265–278.

https://www.sciencedirect.com/science/article/abs/pii/S0094119008000582.

Hagen, Daniel A., and Julia L. Hansen. 2010. “Rental Housing and the Natural Vacancy Rate,” Journal of Real Estate Research 32 (4): 413–434. https://www.jstor.org/stable/24888355.

Harrison, Austin, Dan Immergluck, Jeff Ernsthausen, and Stephanie Earl. 2021. “Housing Stability, Evictions, and Subsidized Rental Properties: Evidence From Metro Atlanta, Georgia.” Housing Policy Debate 31: 411–24 .

https://www.tandfonline.com/doi/full/10.1080/10511482.2020.1798487.

Hatef, Elham, Hadi Kbarrazi, Karin Nelson, Philip Sylling, Xiaomeng Ma, Elyse C. Lasser, Kelly M. Searle, Zachary Predmore, Adam J. Batten, Idamay Curtis, Stephan Fihn, and Jonathan P. Weiner. 2019. “The Association Between Neighborhood Socioeconomic and Housing Characteristics with Hospitalization: Results of a National Study of Veterans,” Journal of the American Board of Family Medicine 32 (6): 890–903 .

R EFER EN CES

9 1

Kirkpatrick, Sharon I., and Valerie Tarasuk. 2011. “Housing Circumstances are Associated with Household Food Access Among Low-Income Urban Families,” Journal of Urban Health 88 (2): 284–296 .

https://pubmed.ncbi.nlm.nih.gov/21286826/.

Kushel, Margot B., Reena Gupta, Lauren Gee, and Jennifer S. Haas. 2005. “Housing Instability and Food Insecurity as Barriers to Health Care Among Low-Income Americans,” Journal of General Internal Medicine 21 (1): 71–77 .

https://pubmed.ncbi.nlm.nih.gov/16423128/.

Mankiw, N. Gregory, and David Weil. 1989. “The Baby Boom, the Baby Bust, and the Housing Market,” Regional Science and Urban Economics 19: 235–258. https://scholar.harvard.edu/files/mankiw/files/baby_boom.pdf.

Meyers, Alan, Diana Cutts, Deborah A. Frank, Suzette Levenson, and Anne Skalicky. 2005. “Subsidized Housing and Children’s Nutritional Status: Data from a Multisite Surveillance Study,” Archives of Pediatrics and Adolescent Medicine 159 (6): 551–556 . https://jamanetwork.com/journals/jamapediatrics/fullarticle/486034.

Mueller, Elizabeth J., and J. Rosie Tighe. 2007. “Making the Case for Affordable Housing: Connecting Housing with Health and Education Outcomes,” Journal of Planning Literature 21 (4): 371–385 .

https://libres.uncg.edu/ir/asu/f/Tighe_Rosie%20_2007_Making_the_case_for_Affordable.pdf.

Quigley, John M., and Steven Raphael. 2005. “Regulation and the High Cost of Housing in California,” American Economic Review 95 (2): 323–328. https://www.aeaweb.org/articles?id=10.1257/000282805774670293.

Reid, Kristen W., Eric Vittinghoff, and Margot B. Kushel. 2008. “Association Between the Level of Housing Instability, Economic Standing and Health Care Access: A Meta-Regression,” Journal of Health Care for the Poor and Underserved 19 (4): 1212–1228 . https://pubmed.ncbi.nlm.nih.gov/19029747/.

Robinson, David, and Justin Steil. 2020. “Eviction Dynamics in Market-Rate Multifamily Rental Housing,” Housing Policy Debate 31: 647–669 .

https://www.tandfonline.com/doi/abs/10.1080/10511482.2020.1839936?journalCode=rhpd20.

Rosen, Kenneth T., and Lawrence B. Smith. 1983. “The Price-Adjustment Process for Rental Housing and the Natural Vacancy Rate,” American Economic Review 73 (4): 779–786 . https://www.jstor.org/stable/1816576.

Saiz, Albert. 2003. “Room in the Kitchen for the Melting Pot: Immigration and Rental Prices,” Review of Economics and Statistics 85 (3): 502–521.  https://repository.upenn.edu/cgi/viewcontent.cgi?article=1025&context=real-

estate_papers.

——. 2010. “The Geographic Determinants of Housing Supply,” The Quarterly Journal of Economics, 125 (3): 1253–

1296. https://mitcre.mit.edu/wp-content/uploads/2014/03/The-Quarterly-Journal-of-Economics-2010-Saiz-

1253-96.pdf.

Smith, Lawrence B. 1974. “A Note on the Price Adjustment Mechanism for Rental Housing,” American Economic Review 64 (3): 779–786. https://www.jstor.org/stable/1808904.

Suglia, Shakira Franco, Christiane S. Duarte, and Megan T. Sandel. 2011. “Housing Quality, Housing Instability, and Maternal Mental Health,” Journal of Urban Health 88 (6): 1105–1116 .

https://pubmed.ncbi.nlm.nih.gov/21647798/.

U.S. Department of Housing and Urban Development (HUD). n.d. “Fair Market Rents (40th Percentile Rents).”

https://www.huduser.gov/portal/datasets/fmr.html.

——. 1999. “Fair Market Rents.” U.S. Housing Market Conditions (4th Quarter 1998).

https://www.huduser.gov/periodicals/ushmc/winter98/summary-2.html.

——. 2015. “Multidisciplinary Research Team.” HUDUser.

https://www.huduser.gov/portal/publications/mdrt_reports.html.

——. 2018. Proposals to Update the Fair Market Rent Formula . Washington, DC: U.S. Department of Housing and Urban Development. https://www.huduser.gov/portal/sites/default/files/pdf/Proposals-To-Update-the-Fair-

Market-Rent-Formula.pdf.

9 2

R EFER EN CES

Verma, Nandita, and Rick Hendra. 2003. “Comparing Outcomes for Los Angeles County’s HUD-Assisted and Unassisted Welfare Leavers,” Cityscape 6 (2): 89–102 .

https://www.huduser.gov/periodicals/cityscpe/vol6num2/2comp_outcomes.pdf.

R EFER EN CES

9 3

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

Washington, DC 20410-6000

April 2023

Document Outline

- Alternative Fair Market Rents for Local Housing Markets

- DISCLAIMER

- Acknowledgments

- Contents

- List of Exhibits

- Executive Summary

- Findings

- Alternative Fair Market Rents for Local Housing Markets

- Background

- How HUD Forecasts Fair Market Rents

- Improving FMR Estimates

- Research Design

- Data

- Defining Areas with Rapidly Rising Rents

- Predicting Areas with Rapidly Rising Rents

- Estimating Rent Time Series Models with Local Data

- Creating Alternative FMR Calculations

- Assessing Alternative FMR Calculations

- Limitations

- Findings

- Defining Areas with Rapidly Rising Rents

- Predicting Areas with Rapidly Rising Rents

- Estimating Rent Time Series Models with Local Data

- Assessing Alternative FMR Calculations

- Implications for Policy and Future Research

- Conclusion

- Appendix A. Exploring Alternative Definitions of Rapidly Rising Rents

- Appendix B. Supplemental Exhibits

- Predicting Areas with Rapidly Rising Rents

- Estimating Rent Time Series Models with Local Data

- Assessing Alternative FMR Performance

- References

Table of Contents

Alternative Fair Market Rents for Local Housing Markets

DISCLAIMER

Acknowledgments

Contents

List of Exhibits

Executive Summary

Findings

Alternative Fair Market Rents for Local Housing Markets

Background

How HUD Forecasts Fair Market Rents

Improving FMR Estimates

Research Design

Data

Defining Areas with Rapidly Rising Rents

Predicting Areas with Rapidly Rising Rents

Estimating Rent Time Series Models with Local Data

Creating Alternative FMR Calculations

Assessing Alternative FMR Calculations

Limitations

Findings

Defining Areas with Rapidly Rising Rents

Predicting Areas with Rapidly Rising Rents

Estimating Rent Time Series Models with Local Data

Assessing Alternative FMR Calculations

Implications for Policy and Future Research

Conclusion

Appendix A. Exploring Alternative Definitions of Rapidly Rising Rents

Appendix B. Supplemental Exhibits

Predicting Areas with Rapidly Rising Rents

Estimating Rent Time Series Models with Local Data

Assessing Alternative FMR Performance

References