Working Paper No. HF-021

Temporary Loan Limits as a Natural 

Experiment in FHA Insurance

Kevin A. Park

Working Paper No. HF-01 9

THE GSEs’ FUNDING OF AFFORDABLE LOANS:

A 2004-05 UPDATE 

Harold L. Bunce 

December 2012 

Office of Policy 

Development 

and Research

Housing Finance 

W O R K I N G P A P E R S E R I E S

U.S. Department of Housing and Urban Development

May 2016

U.S. Department of Housing and Urban Development | Office of Policy Development and Research
Temporary Loan Limits as a Natural 

Experiment in FHA Insurance

Kevin A. Park1

The Economic Stimulus Act of 2008 dramatically but temporarily increased the mortgage 

loan amount eligible for insurance through the Federal Housing Administration. We use the 

implementation and expiration of these loan limits as a source of exogenous variation in the 

availability of FHA insurance to measure the impact on the overall mortgage market and conventional lending. We find that the introduction of higher loan limits increased the number of 

mortgages newly eligible for FHA financing, but that the expiration of those loan limits roughly 

six years later did not significantly decrease affected loan originations. Moreover, the degree of 

substitution between FHA and conventional market segments was lower in 2008-09 than in 

2014, when substitution was nearly one-for-one. The smaller impact on the overall mortgage 

market and greater degree of substitution when the ESA loan limits expired may be explained 

by the return of a stronger conventional lending industry than existed during the housing crisis.

1

 U.S. Department of Housing and Urban Development, 451 Seventh Street SW, Washington, DC, 20410 (kevin.park@hud.gov). The opinions expressed are those 

of the author, and do not necessarily reflect the policies of the Department of Housing and Urban Development or the Administration. The author thanks Josh Miller 

and William Reeder for invaluable comments and suggestions. Any omissions and errors belong solely to the author.
Housing Finance Working Paper Series 1

Temporary Loan Limits as a Natural 

Experiment in FHA Insurance

Introduction

Section 203 of the National Housing Act of 1934 created the 

Federal Housing Administration (FHA) to provide federallybacked insurance of home mortgages against the risk of 

default. FHA insurance typically serves borrowers with higher 

perceived credit risk, including first-time homebuyers and 

minority borrowers. FHA is also restricted to loan amounts 

less than a maximum limit. Historically, these loan limits 

have tended to not keep pace with house price appreciation, 

further focusing FHA insurance on a narrowing segment of 

the mortgage market. But in response to the collapse of house 

prices and rising foreclosures, Congress enacted legislation 

in 2008 that drastically increased the maximum loan amount 

eligible for FHA insurance. Although subsequently extended, 

the higher loan limits expired at the end of 2013. The changes 

in loan limits create a natural experiment to measure the effect 

of the availability of FHA mortgage insurance on the mortgage 

market. The exogenous variation in FHA eligibility provides 

an improvement over previous research on the substitution between FHA and conventional (i.e., not insured by the Veterans 

Administration, Department of Agriculture, or FHA) mortgage 

lending.

Literature Review 

FHA has typically maintained less stringent underwriting 

than the conventional mortgage market, accepting borrowers 

with smaller downpayments and worse credit histories. In 

the extension of the theoretical model used by Ferguson and 

Peters (1995) by Ambrose, Pennington-Cross and Yezer (2002), 

this creates an FHA “wedge” between borrowers served by 

the conventional market and borrowers deemed unacceptable 

credit risks, with a clear delineation between market segments. 

Under this conception, there is very little room for product 

substitution because borrowers will always select the least expensive option available at any given point in time. Bunce et al. 

(1995) argue, “[O]verlap is only possible when the lender and 

borrower fail to take advantage of a bonafide [private mortgage 

insurance] offer of the same service at lower cost.” And given 

the complexity of the underwriting process, even observed 

incidences are only evidence of potential, not actual, overlap. 

Not surprisingly, indicators of greater credit risk are associated 

with greater reliance on FHA insurance. Pennington-Cross and 

Nichols (2000) find that a 10-point increase in credit score 

lowers the probability of using FHA insurance by 2.8 percent. 

Decomposing credit scores into specific components of credit 

history such as revolving credit balance, ever delinquent, and 

derogatory public notices provides even more explanatory 

power. Lacour-Little (2004) supports the finding that credit 

score predominantly distinguishes FHA and subprime mortgages from conventional prime mortgages, but also notes that 

documentation requirements appear to separate subprime and 

FHA loans. 

Neighborhood characteristics and economic conditions impact 

risk assessments given their potential to affect the value of the 

collateral securing the mortgage. Ambrose, Pennington-Cross 

and Yezer (2002) find that the FHA rejection rate is less sensitive to cyclical economic risk factors than the conventional 

rejection rate and actually inversely related to some permanent 

risk factors like house price volatility. Holmes and Horvitz 

(1994) find that the neighborhood default rate is negatively 

associated with conventional mortgage lending activity but 

positively associated with FHA activity. Immergluck (2011) also 

notes that falling house prices are associated with an increase in 

the likelihood of FHA insurance. 

However, evidence suggests the mortgage market is not nearly 

as segmented as theory would dictate. One US Department of 

Housing and Urban Development study from 1986 noted, “It 

appears, therefore, that Section 203(b) and private insurers are 

less different...than may be commonly believed.” Ambrose, 

Pennington-Cross and Yezer (2002) attribute the overlap to 

applicants’ tolerance for rejection. For example, risk-averse applicants might apply for FHA insurance even when they would 

qualify for typically less expensive conventional mortgage credit 

alternatives. 

Institutional factors appear to influence the likelihood of 

FHA financing. Karikari, Voicu and Fang (2011) find loans 

originated through depository institutions (commercial banks, 

thrifts and credit unions) are more likely to use FHA insurance 

compared to independent mortgage companies. In contrast, 

Immergluck (2011) finds wholesale or correspondent lending 

channels were associated with an increased likelihood of 

being an FHA loan. The difference may be due to the fact that 

Karikari, Voicu and Fang use data from 2005, at the peak of the 

housing bubble, while Immergluck uses data from 2008, when 

conventional mortgage credit was becoming less available. 
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Housing Finance Working Paper Series 2

Immergluck also notes that FHA’s historical market share 

increases the likelihood of FHA insurance, indicating lenders’ 

familiarity with FHA lending may have a legacy effect.

Even after controlling for these factors, the race and ethnicity 

of borrowers continues to be associated with differences in 

credit channel. Early empirical studies (e.g., Fullerton and 

MacRae 1978; Canner, Gabriel and Woolley 1991; Gabriel and 

Rosenthal 1991; Holmes and Horvitz 1994) typically found 

minorities were disproportionately more likely to rely on FHA 

insurance than conventional mortgages. However, later studies 

find different patterns, possibly reflecting changes in the mortgage industry such as the introduction of greater risk-based 

pricing in the form of subprime loans. Pennington-Cross and 

Nichols (2000) find that Hispanics are more likely to use FHA 

insurance but Blacks are less likely. Karikari, Voicu and Fang 

(2011) find minority borrowers and neighborhoods were more 

likely to receive subprime mortgages than FHA-insured loans. 

Several studies have tried to empirically quantify the degree of 

overlap between FHA insurance and the conventional mortgage 

market. Rodda, Schmidt and Patrabansh (2005) estimate an 11 

percent overlap in the combined borrower risk distributions of 

FHA endorsements and conventional loans purchased by the 

government-sponsored enterprises Fannie Mae and Freddie 

Mac. However, Gyourko and Hu (2002) find spatial differences, 

with Fannie and Freddie focusing on lower income borrowers 

in relatively high income neighborhoods and a large FHA presence associated with fewer conventional loans. Karikari, Voicu 

and Fang (2011) estimate that 29 percent of subprime loans 

made in 2005 could have qualified for FHA insurance. Results 

presented in Spader and Quercia (2012) indicate that every 

ten subprime loans in a Census tract between 2002 and 2006 

was associated with roughly three fewer FHA-insured loans, 

although the opposite effect is observed between 1998 and 

2001. There is also evidence that the market share of FHA was 

negatively impacted by other public policies, including affordable housing goals for the government-sponsored enterprises 

(An and Bostic 2008) and the Community Reinvestment Act 

(Spader and Quercia 2012). On the other hand, Ding et al. 

(2008) find FHA and subprime loans are complements at the 

neighborhood level, with the share of FHA loans in a census 

tract positively correlated with the share of subprime loans. 

These different findings suggest that the role of FHA may 

change over time depending on the context of the broader 

mortgage market.

A concern with many of these studies is that any observed 

inverse correlation between FHA and conventional mortgage 

market activity cannot prove causation. This study builds on 

the existing literature by exploiting an exogenous change in 

the availability of FHA insurance caused by restrictions on the 

maximum loan amount FHA is allowed to insure. 

FHA Loan Limits

FHA is prohibited by section 203(b)(2) of the National Housing Act from insuring loans above certain amounts. Vandell 

(1995) provides a detailed history of FHA and these loan limits. 

At the creation, FHA was allowed to insure loan amounts up 

to $16,000 compared to a median house price in 1930 of only 

$4,778. Even after the limit was reduced to $6,000 in 1938, 

more than 85 percent of owner-occupied homes were eligible 

for FHA financing. Consequently, the loan limits were not 

exceptionally restrictive early in FHA’s history.

FHA loan limits were periodically increased through the mid20th century, but often failed to keep pace with house price 

appreciation. Although an exception was made for high cost 

areas2, the national loan limit was $67,500 from 1980 through 

1993 while the median sales price of a single-family home 

increased from $62,200 to $106,800. “While still intended to 

be actuarially sound, the Section 203(b) program was gradually 

targeted lower and lower in the income distribution by means 

of both more lenient terms ... and binding loan ceilings” 

(Vandell 1995). 

A new loan limit formula was adopted in 1994. The loan limit 

was set at 95 percent of the area median house price, as determined by the U.S. Department of Housing and Urban Development. However, the loan limit could not be less than 38 percent 

(the “floor”) nor greater than 75 percent (the “ceiling”) of the 

conforming loan limit used by the government-sponsored 

enterprises, Fannie Mae and Freddie Mac (Mortgagee Letters 

1994-15; 1994-52). Loan limits were increased in 1998, raising 

the floor to 48 percent and the ceiling to 87 percent of the 

comparable Freddie Mac conforming loan limit (Mortgagee 

Letter 1998-28). 

This loan limit formula remained in effect for the next decade. 

But in response to the collapse of the housing market in the mid2000s, Section 202 of the Economic Stimulus Act of 2008 (ESA) 

increased the loan limit formula to 125 percent of the median 

2

 Loan limits in high cost areas were set at 95 percent of the area median sales price up to $90,000. The maximum amount was increased to $101,250 in 1988 and 

$124,875 in 1989.
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Housing Finance Working Paper Series 3

house price, not to exceed 175 percent of the comparable 

Freddie Mac limit nor be less than 65 percent, effective for loans 

endorsed on or after March 6, 2008. Moreover, the Freddie Mac 

conforming loan limit was increased to 125 percent of the area 

median, not to decline below the 2008 limit nor exceed 175 

percent of the 2008 limit.3 Overall, 3,141 counties had their FHA 

loan limits increased, often dramatically, in March 2008.

These temporary limits expired at the end of 2008 but were 

reinstated by the American Recovery and Reinvestment Act of 

2009 (ARRA). Continuing resolutions further extended the ESA 

loan limit standard for FHA (Mortgagee Letters 2009-50; 2010-40; 

2011-39; 2012-26). However, the temporary increase in the high 

cost area “ceiling” for loans acquired by the government-sponsored 

enterprises was allowed to expire in October 2011, creating the 

anomalous condition for 27 months of FHA loan limits exceeding 

those of Fannie Mae and Freddie Mac in many counties. 

The temporary FHA loan limits ultimately expired at the end of 

2013, at which time loan limits did not revert to their pre-ESA 

formula but instead change to a new formula described in the 

Housing and Economic Recovery Act of 2008 (HERA)4. HERA 

maintains the ESA floor but lowers the loan limit from 125 

percent of the median house price to 115 percent and lowers 

the ceiling from 175 percent of the Freddie Mac limit to 150 

percent.5 The lower loan limits were effective for applications 

for FHA insurance with case numbers assigned on or after 

January 1, 2014 (Mortgagee Letter 2013-43). Figure 1 shows 

the recent history of FHA loan limits.

Loan limits in 2014 were also affected by a revision of metropolitan areas by the Office of Management and Budget. Because loan 

limits for a metropolitan area are defined by the county in that 

area with the highest median house price, a change in boundaries 

can affect the loan limits for all counties in that metropolitan area. 

Over 600 counties had their loan limits decreased in January 

2014. Goodman, Seidman and Zhu (2014) find that the 

decline in house prices since 2006 was the primary factor in 

lower loan limits, affecting 389 counties, followed by changes 

the house price multiplier from 125 percent to 115 percent 

(157 counties), decline in the loan limit ceiling (73 counties), 

and changes in metropolitan area boundaries (33 counties).6

Figure 1. FHA Loan Limits

Note: National Average Sales Price estimated by applying Case-Shiller National 

Home Price Index to average sales price of existing single-family homes, condominiums and cooperatives between 2013 and 2015 reported by the National 

Association of Realtors®, weighted by the number of sales.

The metropolitan areas most impacted by the change include 

Winchester, VA-WV, Salt Lake City, UT, Worcester, MA, NorwichNew London, CT, and Stockton, CA. In 16 of the 30 most 

affected census tracts, more than half of borrowers are minority.

The implementation and expiration of the temporary loan limits 

under ESA creates a natural experiment of the effect of the availability of FHA mortgage insurance on the mortgage market. 

Data and Methodology

Detailed information on home mortgage loan originations is 

available through the Home Mortgage Disclosure Act of 1975 

(HMDA). Most mortgage lending institutions are required to 

submit a loan-application register to be compiled for public 

use by the Federal Financial Institutions Examination Council 

(FFIEC). Although reporting is not required of smaller lenders, 

the HMDA data is estimated to cover 90 to 95 percent of FHA 

endorsements and between 75 and 85 percent of conventional 

originations (HUD 2011). The loan-application register lists the 

loan amount and purpose as well as the occupancy and type 

of the property securing the mortgage. This study focuses on 

loan applications7 and originations of first lien mortgages for 

3

 Prior to ESA, the conforming loan limit for the government-sponsored enterprises was determined by adjusting the previous limit by the change in average house 

prices.

4

 HERA was passed subsequent to but also superseded by ESA.

5

 FHA loan limits were also governed by HERA during short lapses in continuing resolutions in early 2009 and late 2011 (Mortgagee Letters 2008-36; 2009-07; 

2011-29; 2011-39).

6

 Goodman, Seidman and Zhu include territories of the United States in their tabulations while this study is restricted to states and the District of Columbia.

7

 Applications are limited to those for which the financial institution made a credit decision, including loan originations, denied applications and applications approved but not accepted, but not including applications withdrawn by the applicant and applications closed for incompleteness.
Temporary Loan Limits as a Natural Experiment in FHA Insurance

Housing Finance Working Paper Series 4

purchase of owner-occupied, site-built, one-to-four unit properties. Up-front mortgage insurance premiums are assumed to be 

financed into all FHA-insured loans8; consequently, loan amounts 

for FHA originations are discounted by the prevailing insurance 

premium in order to identify the estimated base loan amount. 

Table 1 shows that the changes in loan limits mandated by 

ESA affected the distribution of FHA endorsements. The 

share of FHA-insured loan originations with loan amounts 

above the pre-ESA limit increased from 2.9 percent in 2007 

to 10.8 percent in 2008 and the corresponding number of 

originations increased from 7,300 to 79,400 (Table 1A). The 

expiration of ESA caused the share of FHA loans above the 

2014 loan limits to fall from 4.0 percent to 2.5 percent and 

the number to fall from 25,200 to 13,500 (Table 1B). Table 1 

also shows the share of conventional loans above the 2007 

FHA loan limits increased slightly from 29.1 percent in 2007 

to 31.6 percent in 2008; however, the number of originations fell 

drastically from 848,900 to 491,200. When the ESA loan limits 

expired, the share of conventional loans above the 2014 FHA 

loan limits remained relatively constant at roughly 19 percent. 

Loans affected by the policy change are those with loan 

amounts between loan limit standards. For example, the 

FHA single-family loan limit in Los Angeles County increased 

from $362,790 in 2007 to $729,750 in 2008, and then fell 

to $625,500 in 2014. Loan originations after 2007 with balances less than $362,790 were not affected by the loan limit 

increase in ESA. Similarly, “jumbo” loans with balances greater 

$729,750 were never eligible for FHA insurance. However, 

loans with balances above the pre-ESA loan limit and less 

than or equal to the ESA loan limit (i.e., between $362,790 

and $729,750) were affected by the increase. And loans with 

balances less than or equal to the ESA loan limits but above 

the HERA limits (i.e., between $625,500 and $729,750) were 

affected by the decrease. Figure 2 shows the total number and 

share of loans in this “intra-limit range” for the implementation 

(Figure 2A) and expiration of ESA loan limits (Figure 2B). 

Table 1. Loan Applications and Originations Above FHA Loan Limits (Thousands)

ESA HERA

2006 2007 2008 2009 2010 2011 2012 2013 2014

A. Over 2007 Loan Limits

Applications 1,502 1,274 832 618 601 566 708 947 1,000

Percent 26% 28% 25% 21% 22% 22% 25% 29% 30%

Originations 1,071 882 608 489 489 461 592 793 853

Percent 25% 27% 24% 21% 23% 23% 26% 30% 31%

Conventional 1,044 849 491 321 321 321 430 603 658

Percent 27% 29% 32% 30% 32% 32% 35% 37% 38%

FHA 3 7 79 119 118 85 91 95 82

Percent 1% 3% 11% 12% 13% 12% 13% 15% 14%

B. Over 2014 Loan Limits

Applications 774 638 384 261 259 252 313 443 484

Percent 13% 14% 11% 9% 10% 10% 11% 14% 15%

Originations 539 428 271 197 205 200 257 365 405

Percent 13% 13% 11% 8% 10% 10% 11% 14% 15%

Conventional 531 418 237 154 160 163 211 303 343

Percent 14% 14% 15% 14% 16% 16% 17% 19% 20%

FHA 0 1 21 27 28 18 21 25 16

Percent 0% 1% 3% 3% 3% 3% 3% 4% 3%

8

 The upfront mortgage insurance premium was 1.5 percent prior to July 2008. Between July 14 and October 1, the rate varied by loan-to-value ratio and credit 

score. These risk factors are not reported in HMDA, but the average upfront insurance premium remained roughly 1.5 percent according to internal FHA data. The 

premium increased to 1.75 percent in October. 

In April 2010, the premium was rose to 2.25 percent then fell to 1 percent a few months later. The upfront premium was reset to 1.75 percent on April 9, 2012, 

which was the rate through 2013 and 2014.
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Figure 2. Share of Loan Originations in Intra-Limit Range

A. 2007-2008

B. 2013-2014

[]=Month excluded from analysis
Temporary Loan Limits as a Natural Experiment in FHA Insurance

Housing Finance Working Paper Series 6

There are two reasons why the FHA-insured origination volume in 

the intra-limit range before or after ESA is not zero. First, HMDA 

data does not distinguish single-family homes from properties with 

two- to four-units, which have a higher FHA loan limit. Second, 

HMDA data rounds loan amounts to the nearest thousand dollars. 

According to internal FHA data, the intra-limit range share of FHA 

endorsements of single-family properties is approximately zero 

in years when ESA was not in effect. Adjusting by rounding the 

loan amount and including two-to-four unit properties closely 

resembles the volumes found in the HMDA data.

Following how FHA adopted changes in loan limits, the effect 

of the implementation of ESA loan limits is modeled using the 

origination date while the effect of their expiration is modeled 

using the application date (Mortgagee Letters 2008-06; 2013-

43). Specifically, the analysis of the enactment of ESA loan 

limits uses loans with a date of origination between January 

2006 and December 2009. The analysis of the expiration of 

ESA limits uses loans with a date of application between January 2012 and September 2014. The last three months of 2014 

are excluded because applications late in the year may not be 

acted on and therefore reported until the following calendar 

year and the HMDA data for 2015 has not been released. 

For example, over 60 percent of loan applications submitted 

between October and December in 2013 were not acted upon 

and therefore disclosed until 2014. 

In addition, the month that loan limit changes were announced 

is excluded from the analysis. There is evidence that some 

borrowers, for example, rushed to apply for FHA mortgage 

insurance in December 2013 before the expiration of the ESA 

loan limits (see Figure 3B).The spike in applications shows that 

the decline in FHA loan limits was unexpected after several 

years of continuing resolutions that preserved the ESA formula. 

In addition, pulling demand forward may depress applications 

in the following month, which is therefore also excluded. These 

patterns bolster the argument that the changes in loan limits 

represent a discontinuity in policy necessary for the natural 

experiment research design, but short-term sorting around the 

effective date of the new loan limits obscures the long-term 

trend. Removing the transition period results in a more conservative estimate of the effect of the change in loan limits.

We use a research design in which monthly mortgage originations with loan amounts in the intra-limit range are compared 

before and after ESA loan limits were effective, controlling for 

applications, the loan origination rate outside the intra-limit 

range, and a general time trend. The total number of mortgage 

originations with loan amounts in the intra-limit range in time 

t is modeled as

where 

 is the number in hundreds of mortgage applications with 

loan amounts in the intra-limit range,

 is the number of mortgage originations with loan 

amounts in the exo-limit range (i.e., outside the intra-limit 

range),

 is the number in hundreds of mortgage applications with 

loan amounts in the exo-limit range,

 is a linear time trend centered on the month that ESA 

loan limits went into effect or expired (e.g., 3/5/2008=-1, 

3/6/2008=0, 3/7/2008=1, etc.), 

 is a series of binary variables indicating month of application/origination, and

 is a binary indicator of whether the ESA loan limit 

formula was in effect

The coefficient of interest (δ) measures the effect of the 

temporary ESA loan limits. Including the number of applications accounts for changes in demand for loan amounts in the 

intra-limit range over time. The origination rate in the exo-limit 

range controls for general changes in the supply of mortgage 

credit. Monthly fixed effects account for seasonality and the 

trend for secular changes in the market.

After estimating the effect on the overall mortgage market, the 

specific impacts on FHA-insured and conventional mortgage 

originations are also estimated using a seemingly unrelated 

regression (SUR) model9, which allows errors to be correlated 

across equations. The system of equations can be represented as

9

 A Breusch-Pagan test presented in the findings confirms that residuals across the two models are not independent. Unfortunately, the sureg command in Stata currently does not allow for correlation in error terms both across and within models, such as correlation within a county across loan amount ranges. However, the 

results are robust to alternative specifications of the error terms, including fixed effects models and ordinary least squares clustered by county. 
Temporary Loan Limits as a Natural Experiment in FHA Insurance

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where we assume

but allow

A second SUR model is estimated in which FHA-insured loan 

originations are included as an explanatory variable of conventional loan originations. Including in the model of 

 should moderate the estimated impact of because 

it is not the change in FHA loan limits that affects conventional 

originations but the change in FHA endorsements directly.

Findings

Table 2 presents the results of estimating the impact of the 

enactment of higher loan limits under ESA. The first column 

shows the estimated effect on the overall number of mortgage 

originations with loan amounts in the intra-limit range. Overall, 

the model is statistically significant. Further, Breusch-Godfrey 

and Durbin10 tests did not find evidence of autocorrelation in 

the error terms.

The volume of originations is affected by the demand for mortgage credit: there are roughly 72 additional mortgages made 

in this loan range for every 100 applications, all else equal. 

However, it should be noted that the number of applications 

was falling precipitously over this period, contributing to a 

decline in new mortgages. Originations in the intra-limit range 

are also affected by broader trends in the supply of mortgage 

credit: a 10 percentage point increase in the exo-limit range 

origination rate (originations per hundred applications with 

loan amounts outside the intra-limit range) leads to 82 additional loan originations in the intra-limit range. In addition 

to these factors, there is also a time trend indicating nearly 

100 fewer loan originations in the intra-limit range per month. 

Most importantly, the ESA indicator shows that the increase in 

loan limits that went into effect at the beginning of March 2008 

increased the number of loan originations newly eligible for 

FHA insurance by 1,698 per month. All of these variables are 

statistically significant at the 1 percent level.

The second column of Table 2 shows the results of the first SUR 

model that includes estimates of both FHA and conventional 

loan originations. Both models are statistically significant and 

the Breusch-Pagan test confirms a statistically significant negative correlation in the error terms across models. In the model 

of FHA originations, the exo-limit range origination rate is statistically significant at the 1 percent level, although the effect is 

more modest than in the model of all originations, as expected. 

The estimated effect of ESA loan limits is negative, contrary to 

expectation, but not statistically significant. 

In the model of conventional loan originations, both the 

intra-limit applications and exo-limit range origination rate are 

Table 2. Estimated Impact of Enactment of ESA Loan Limits

(1) (2) (3)

All FHA Conventional Conventional

Coeff. Std. Err. Coeff. Std. Err. Coeff. Std. Err. Coeff. Std. Err.

Applications (00s) 71.66*** 1.99 4.01 3.23 71.75*** 4.17 75.95*** 3.25

Exo-Limit Origination Rate (%) 823.79*** 65.11 435.41*** 45.43 269.23*** 60.49 -1.22 66.68

Linear Time Trend -99.87*** 28.57 -53.70 43.92 12.01 55.48 -21.24 42.64

ESA Loan Limits 1697.10*** 482.20 -459.65 933.49 1019.59 1189.89 518.07 933.38

FHA Originations . . . -0.55*** 0.13

Month Fixed Effects Yes Yes Yes Yes

N 46 46 46 46

F 1732.6*** 52.7*** 591.4*** 960.7***

RMSE 623.8 1288.5 1624.7 1267.3

Breusch-Pagan χ2 . 29.54*** 2.74*

Statistically significant at the ***0.01 level **0.05 level *0.10 level.

FHA component of SUR model presented in Column 3 is not shown.

10 The estimated Durbin-Watson statistic is 1.585.
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Housing Finance Working Paper Series 8

statistically significant at the 1 percent level, but also smaller 

than in the model of all originations. The estimated effect of 

ESA loan limits on conventional originations is positive, also 

contrary to expectation, but again not statistically significant. 

When the number of FHA originations in the intra-limit range 

is included in the SUR model, the estimated effect of ESA 

loan limits on conventional originations declines but remains 

not statistically significant. On the other hand, the estimated 

direct effect of FHA originations is statistically significant at 

the 1 percent level and indicates 55 fewer conventional loan 

originations for every 100 additional FHA loans. Including 

FHA originations also reduces the degree of correlation in error 

terms across models.

Table 3 presents the results of estimating the impact of the 

expiration of the higher loan limits. The first column shows the 

estimated effect on the overall number of mortgage originations 

with loan amounts in the intra-limit range. The model is statistically significant without evidence of autocorrelation in the 

error terms.11 The volume of originations is again responsive to 

the demand for mortgage credit, with 87 additional mortgages 

for every 100 applications, and reflects general trends in the 

supply of mortgage credit, with a 10 percentage point increase 

in the exo-limit range origination rate associated with 17 

additional originations in the intra-limit range. A negative time 

trend persists, indicating 12 fewer loan originations per month. 

The estimated effect of the ESA loan limits is negative, meaning 

loan originations in the intra-limit range increased after the 

expiration of the higher loan limits, but the coefficient is not 

statistically significant. 

The second column of Table 3 shows the results of the first SUR 

model that includes estimates of both FHA and conventional 

loan originations. Both models are statistically significant and 

the Breusch-Pagan test confirms a statistically significant correlation in the error terms across models. In the model of FHA 

originations, the positive effects of intra-limit applications and 

exo-limit origination rate as well as a negative time trend are all 

statistically significant at the 1 percent level. Most importantly, 

the estimated effect of ESA loan limits on FHA originations is 

also statistically significant at the 1 percent level and indicates 

694 additional FHA loans per month under the ESA loan limit 

formula compared to after its expiration, all else equal. 

In the model of conventional loan originations, the effect of 

intra-limit applications remains statistically significant at the 

1 percent level but the exo-limit origination rate is not statistically significant. A positive time trend is statistically significant. 

The estimated effect of ESA loan limits on conventional 

originations is also statistically significant and indicates 671 

fewer conventional loan originations per month under the ESA 

loan limit regime. Note that the magnitude of the positive effect 

of loan limits under ESA on FHA originations is similar to the 

magnitude of the negative effect on conventional originations. 

Table 3. Estimated Impact of Expiration of ESA Loan Limits

(1) (2) (3)

All FHA Conventional Conventional

Coeff. Std. Err. Coeff. Std. Err. Coeff. Std. Err. Coeff. Std. Err.

Applications (00s) 87.36*** 1.84 11.66*** 3.26 65.21*** 3.26 76.00*** 1.52

Exo-Limit Origination Rate (%) 167.02*** 34.24 62.90*** 17.32 31.21 21.27 -36.61*** 11.53

Linear Time Trend -11.87** 4.45 -39.63*** 6.18 38.65*** 8.40 10.50** 4.12

ESA Loan Limits -70.81 48.26 693.42*** 78.93 -671.05*** 83.51 -19.79 63.05

FHA Originations . . . -0.91*** 0.07

Month Fixed Effects Yes Yes Yes Yes

N 31 31 31 31

F 3679.0*** 76.8*** 905.2*** 5605.4***

RMSE 47.5 121.3 121.7 48.9

Breusch-Pagan χ2 . 26.32*** 0.03

Statistically significant at the ***0.01 level **0.05 level *0.10 level.

FHA component of SUR model presented in Column 3 is not shown.

11 The estimated Durbin-Watson statistic is 2.01
Temporary Loan Limits as a Natural Experiment in FHA Insurance

Housing Finance Working Paper Series 9

In fact, the third column confirms the substitution effect. 

Including the number of intra-limit range FHA originations 

sharply reduces the estimated effect of ESA loan limits, which is 

also no longer statistically significant. Meanwhile, the estimated 

direct effect of FHA originations is statistically significant at 

the 1 percent level and indicates 9 fewer conventional originations for every 10 additional FHA originations. In fact, the 95 

percent confidence interval includes 1, indicating a possible 

one-for-one substitution cannot be rejected. Including FHA 

originations also eliminates the statistically significant correlation between models of FHA and conventional originations.

Conclusion

The housing crisis created a vicious cycle in which falling house 

prices led to financial distress in the conventional mortgage 

market, which restricted mortgage lending, further exacerbating the declines in house prices. The government guarantee 

provided through FHA mortgage insurance helped stabilize the 

mortgage market. Although most of the increase in FHA’s market share occurred below the pre-ESA loan limits, the increase 

in the maximum loan amount eligible for FHA insurance was 

in keeping with FHA’s counter-cyclical role. FHA was able to 

help increase loan originations without substantially displacing 

conventional lending. We find that the introduction of higher 

loan limits under ESA increased the overall number of loan 

originations newly eligible for FHA financing by nearly 1,700 

per month. The direct effect on the specific number of FHA 

and conventional loan originations is less clear, although every 

two FHA endorsements appears to have displaced roughly one 

conventional loan in 2008 and 2009. According to Moody’s 

Analytics, homes sales would have fallen an additional 2.4 million and prices depressed by nearly another 20 percent if FHA 

had stopped insuring loans in October 2010. “Arguably the 

most important policy response to the housing crash has been 

the dramatic expansion of Federal Housing Administration 

lending” (Zandi and deRitis 2010).

The conventional market had sufficiently recovered by 2014 such 

that FHA could lower loan limits without harming the overall 

mortgage market. Conventional lending replaced FHA-insured 

lending in that market segment nearly one-for-one and the overall 

volume of affected loan originations did not change significantly. 

However, caution is still warranted for calling for faster or 

greater retrenchment. First, reducing FHA business before it 

had a chance to recapitalize would create an inter-temporal 

form of adverse selection, wherein FHA is most concentrated in 

the worst performing years of the housing cycle. The Office of 

Management and Budget projects that forward loans endorsed 

between fiscal years 2007 and 2009 will ultimately cost FHA 

nearly $23 billion (OMB 2016). From 2009 until 2015, FHA’s 

capital ratio12 was below the two percent required by the 

National Affordable Housing Act of 1990. More recent books of 

business are needed to replenish FHA’s capital reserves and in 

order to weather the next crisis.

Second, the findings are based on a relatively small, unusual 

segment of FHA’s portfolio. The estimated local area treatment effects may not be completely generalizable to lower 

loan amounts that constitute the bulk of FHA endorsements. 

Moreover, it is difficult to disentangle the impact of change in 

FHA loan limits from concurrent changes in the loan limits for 

Fannie Mae and Freddie Mac as well as the overall turbulence 

in the mortgage market over this period.

Relative pricing also affects the level of substitution. FHA insurance is typically more expensive than conventional mortgage 

credit offered to qualified consumers. And FHA premiums 

have been raised multiple times, with the annual premium 

rising from 0.55 percent in early 2010 to up to 1.35 percent 

by mid-2013 (see Mortgagee Letters 2008-22; 2010-02; 

2010-28; 2011-10; 2012-04; 2013-04). However, the degree 

of substitution in 2014 suggests that the cost of FHA insurance 

to consumers was still lower than offered in the conventional 

market. Otherwise, borrowers would have already shifted 

towards conventional mortgage credit prior to the expiration 

of FHA loan limits. Indeed, Moody’s Analytics finds that FHA 

was less expensive at the start of 2015 than conventional loans 

financed through the government-sponsored enterprises for 

borrowers with credit scores under 680 and a downpayment of 

five percent or less (Zandi and deRitis 2015). 

Prematurely forcing FHA out of parts of the market by lowering 

loan limits may harm homebuyers and homeowners by restricting mortgage credit as well as taxpayers by interrupting the 

process of rebuilding reserves sufficient to withstand the next 

housing crisis. On the other hand, a recovering conventional 

mortgage lending industry shows evidence of supporting an 

increasing share of the market as FHA scales down from the 

counter-cyclical position it assumed at the height of the housing crisis.

12 FHA’s capital ratio is defined as the economic value as a share of insurance in-force.
Temporary Loan Limits as a Natural Experiment in FHA Insurance

Housing Finance Working Paper Series 10

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