Finance and Economics Discussion Series
Divisions of Research & Statistics and Monetary Affairs
Federal Reserve Board, Washington, D.C.
The Effect of Interest Rates on Home Buying: Evidence from a
Discontinuity in Mortgage Insurance Premiums
Neil Bhutta and Daniel Ringo
2017-086
Please cite this paper as:
Bhutta, Neil, and Daniel Ringo (2017). “The Effect of Interest Rates on Home Buying:
Evidence from a Discontinuity in Mortgage Insurance Premiums,” Finance and Economics
Discussion Series 2017-086. Washington: Board of Governors of the Federal Reserve System,
https://doi.org/10.17016/FEDS.2017.086.
NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary
materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth
are those of the authors and do not indicate concurrence by other members of the research staff or the
Board of Governors. References in publications to the Finance and Economics Discussion Series (other than
acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.
The Effect of Interest Rates on Home Buying: Evidence from a Discontinuity in Mortgage
Insurance Premiums
Neil Bhutta and Daniel Ringo
1
Abstract: We study the effect of interest rates on the housing market by taking advantage of a
sudden and unexpected price change in a large government mortgage program. The Federal
Housing Administration (FHA) insures most mortgages to lower-downpayment, lower-credit
score borrowers, including a majority of first-time homebuyers. The FHA charges borrowers an
annual mortgage insurance premium (MIP), and in January, 2015 the FHA abruptly reduced the
MIP, and thus FHA borrowers’ effective interest rate, by 50 basis points. Using a regression
discontinuity design, we find that the MIP reduction increased the number of home purchase
originations among the FHA-reliant population by nearly 14 percent. The response to the
premium cut was negatively correlated with borrower income, with no observable response
among relatively high income borrowers. We trace part of the jump in home buying to the MIP
reduction helping ease binding debt payment-to-income ratio limits thus allowing more
applications to be approved. Finally, we find no evidence that the MIP reduction increased
house prices.
1
Both authors are at the Board of Governors of the Federal Reserve System, K93, Washington DC 20551,
neil.bhutta@frb.gov, daniel.r.ringo@frb.gov
. Jimmy Kelliher provided excellent research assistance. We thank
Peter Blair, Felipe Carozzi, Pedro Gete, John Krainer, Doug McManus, Raven Molloy, Karen Pence, David
Rappoport, Paul Willen, and seminar participants at Clemson University, Freddie Mac, and the Federal Reserve
Board for helpful comments. The views and analysis are solely those of the authors, and do not necessarily
represent Federal Reserve Board or staff.
1
Introduction
How do interest rates affect the housing market? Understanding this link is important for
gauging the potential effects of monetary policy, and is central to the debate about the causes of
the recent housing boom of the 2000s (e.g. Taylor 2007; Bernanke 2010). Understanding this
link also matters for evaluating U.S. housing policy. Through government-sponsored enterprises
(Fannie Mae and Freddie Mac, or GSEs) and institutions such as the Veteran’s Administration
(VA) and the Federal Housing Administration (FHA), the government insures or guarantees
most residential mortgages in the U.S., with the aim of lowering mortgage rates and promoting
homeownership.
2
In addition, the mortgage interest tax deduction is a major federal expenditure
intended to boost homeownership by reducing mortgage costs (e.g. Glaeser and Shapiro 2003;
Hilber and Turner 2014; Sommer and Sullivan 2017).
Standard theory indicates that housing demand could be quite sensitive to interest rates, as the
user cost of home ownership varies directly with the cost of credit (Poterba 1984; Himmelberg,
Mayer, and Sinai 2005; Boivin, Kiley, and Mishkin 2010). However, estimating the causal
effect of interest rates on housing demand is difficult because of the endogeneity of interest rates
to an array of economic forces that could also be correlated with housing demand. In general,
without a clear identification strategy, estimates of the effect of interest rates on house prices and
other housing indicators are likely to be biased toward zero, and possibly even have the wrong
sign. For example, over the two year period from April 2007 to April 2009, the prime mortgage
rate fell from approximately 6.2 to 4.8 percent. Despite falling rates, home purchase originations
dropped by about 50 percent as the financial crisis, recession, and expectations for continued
house price declines set in. The difficulty of empirically controlling for confounding factors may
underlie the somewhat weak correlations between home prices and interest rates typically found
in macro data (e.g. Dokko et al. 2011; Glaeser, Gottlieb, and Gyourko 2013; Kuttner 2012).
In this paper, we identify the effect of interest rates on home buying by studying a sharp,
unexpected drop in 2015 in the cost of mortgages insured by the FHA. For borrowers with
below-average credit scores and limited funds for a down payment, which includes many first-
time homebuyers, FHA loans have been just about the only financing option since the financial
2
A number of papers explore the effect of the GSEs on mortgage rates. See, for example, Passmore, Sherlund, and
Burgess (2005). Statistics in Bhutta, Popper, and Ringo (2015) imply that in 2014 the Federal Government insured
or guaranteed at least half of owner-occupied home purchase mortgage originations (see Table 13).
2
crisis. In 2014, the FHA insured about one-fifth of all home purchase loans originated in the
U.S., or nearly 600,000 loans, with about eight-in-ten FHA loans going to first-time homebuyers.
The FHA charges borrowers an annual mortgage insurance premium (MIP) – a percentage of the
expected average loan balance in the coming year – and this premium is added to the borrower’s
monthly interest and principal payments. Thus, the MIP mimics an interest rate risk premium,
and the FHA determines the size of this risk premium.
3
Following a surprise executive order
from the Obama administration in January 2015, the FHA lowered the annual MIP by 50 basis
points. For lower credit score, liquidity-constrained households, the MIP reduction represented a
direct drop in the cost of mortgage credit they faced.
Using this policy change, we implement a regression discontinuity design where the cost of
mortgages for a large subgroup of the population dropped discontinuously, while all other
economic conditions that might affect home buying decisions evolved smoothly or remained
constant. Using detailed loan-level data, we find that the total number of home purchase loans to
“FHA-likely” borrowers jumped discontinuously by nearly 14 percent when the new premiums
went into effect. As explained in Section 2, this estimate nets out any shifts into FHA from
alternative options such as private mortgage insurance (PMI). This discontinuity can be clearly
seen in Figure 1, which we will discuss in more detail later and replicate in other datasets.
4
Only one other paper, to our knowledge, estimates the extensive margin response of mortgage
borrowing and home buying to interest rates in the United States using quasi-experimental
methods. Adelino, Schoar, and Severino (2012) find a small increase in home sales among
houses that recently became easier to purchase with cheaper GSE financing due to changes in the
conforming loan limit. In addition, Martins and Villanueva (2006, 2009) study a program in
Portugal and find that interest rate encouraged household formation and mortgage borrowing.
3
The base interest rate for FHA loans is market determined and, because FHA assumes the credit risk, is typically a
little lower than the prime mortgage rate.
4
This paper builds on initial work in Bhutta and Ringo (2016). Two other papers also study the FHA MIP cut. Park
(2017) studies the effect of the 2015 FHA MIP cut on mortgage maturity choice. Davis et al. (2016) estimate that
about half of the rise in FHA loans from 2014 to 2015 was a result of borrowers shifting into FHA from other
programs like PMI. However, their data makes it difficult to disentangle how much of the remaining FHA growth
stems from the MIP cut as opposed to trend growth. In contrast, our high frequency data allows us to employ an RD
design that generates a direct estimate of the MIP cut’s causal effect on borrowing.
3
Other researchers have used time series methods to estimate the effect of interest rates on home
sales and homeownership, including Painter and Redfearn (2002) and Hamilton (2008).
The discontinuous jump in home buying evident in Figure 1 implies a surprisingly quick
response by households, in contrast to previous time-series based evidence (Hamilton 2008). We
view it as unlikely that the MIP drop would cause people who were not already shopping for a
home to immediately go out and apply for a mortgage. Instead, the drop in the MIP would
probably be salient to those already shopping (almost surely their real estate agent or loan officer
would know about it) and encourage more of them to bid on a house and get a mortgage. In
other words, the MIP reduction may generate a higher “yield” of homebuyers from the pool of
people shopping for a home at the time of the MIP cut.
Another reason for an immediate rise in home buying is that a reduction in the FHA’s MIP, by
lowering a mortgage applicant’s expected monthly payment, could ease borrowing constraints
due to limits on borrowers’ debt-payment-to-income (DTI) ratios, which would increase the
fraction of applications that can be accepted. Indeed, we provide evidence that DTI limits bind,
and, more importantly, find a discontinuous drop in denial rates among FHA-likely borrowers
after the MIP reduction. We estimate that this drop in denials could account for up to 40 percent
of the overall rise in lending. While higher down payment requirements can dampen the
response of housing demand to interest rates, as shown in Glaeser, Gottlieb, and Gyourko (2012),
we provide novel evidence that binding DTI constraints amplify the response to interest rates.
5
New regulations under Dodd-Frank that discourage lending to borrowers with DTI ratios in
excess of 43 percent add to the importance of understanding the extent to which DTI limits bind
and how such limits influence the response of housing markets to interest rates (Bhutta and
Ringo 2015; DeFusco, Johnson, and Mondragon 2016).
We also find that the effect of the MIP reduction on home buying shrinks as household income
rises, with the top-quartile of FHA-likely households (those with annual incomes of nearly $100k
and higher) largely insensitive to the premium cut. As Glaeser and Shapiro (2003) argue in the
5
Feldman (2001) simulates the effect of interest rates on homeownership through changes in DTI. Others have
studied the likelihood of homeownership as a function of the likelihood of being credit constrained due to low
income, low wealth or low credit score (e.g. Acolin et al. 2016). Other studies have shown the effect of credit
constraints, including DTI constraints, on house prices, such as Anenberg et al. (2017) and Kuttner and Shim (2016).
Johnson and Li (2010) show that a high DTI is predictive of the consumer having been denied credit.
4
context of the mortgage interest deduction, high-income households are likely to be homeowners
regardless of interest rates as larger, detached homes tend not to be available for rent due to
agency problems in home maintenance (Henderson and Ionnides 1983). Instead, interest rates
may only influence intensive margin housing and mortgage decisions among high-income
households.
However, using the same RD design, we find no evidence that borrowers took out larger loans or
paid more for their home (either by buying a larger home or by bidding up the price of a given
home) in response to the reduced cost of credit. The lack of an intensive-margin response may
stem from binding down payment constraints among FHA-likely borrowers, even those with
relatively high incomes. That said, previous research has also found – among arguably less
constrained borrowers – small intensive-margin responses to mortgage interest rates. DeFusco
and Paciorek (2017) use a discontinuity in interest rates at the GSE conforming loan limit (the
“jumbo-conforming spread”) to estimate a semi-elasticity of loan size to interest rates of only
about 2 percent. Best et al. (2015) similarly exploit mortgage rate discontinuities in the U.K. and
generate estimates slightly larger than DeFusco and Paciorek (2017). Moreover, survey
estimates under hypothetical interest rate changes suggest small intensive-margin and
willingness-to-pay elasticities (Fuster and Zafar 2015).
6
We also employ a difference-in-difference design to test for longer-run effects on house prices,
comparing FHA-reliant neighborhoods to less-reliant neighborhoods, but find little evidence that
the MIP cut led to faster home price growth over the subsequent 12 months.
7
Altogether, our
findings suggest that the reduction in FHA premiums increased home buying among lower
income households, without much, if any, of the MIP cut being capitalized into house prices.
The lack of house price effects in FHA-reliant neighborhoods differs somewhat from what has
been found in higher-income markets. Adelino, Schoar, and Severino (2012) find modest price
increases among relatively high-priced homes as their eligibility for cheaper, GSE-based
financing increases. That said, Anenberg and Kung (2017) argue that house prices may not
6
One other paper, Jappelli and Pistaferri (2006), finds that mortgage borrowing in Italy was largely unresponsive to
changes in the tax treatment of mortgage interest in the early 1990’s. See Zinman (2015) for a review of literature
on the interest rate elasticity of non-mortgage of borrowing.
7
Davis et al. (2016) estimate that quality-adjusted sales prices grew slightly more from 2014 to 2015 for FHA-
financed homes compared to non-FHA-financed homes.
5
always react strongly to interest rates because home sellers can respond to demand shocks along
non-price dimensions such as the time to sell.
8
The rest of the paper proceeds as follows. In the next section we provide more background about
the FHA premium cut. In section 2 we lay out the identification strategy. In section 3 we
describe our data sources. Section 4 provides the main estimation results. Section 5 describes
evidence supporting key identifying assumptions. Section 6 investigates the mechanisms by
which reduced premiums lead to greater home buying. In section 7 we test for effects of the MIP
cut on house prices. Finally, section 8 concludes.
1. Mortgage Insurance and the Surprise FHA Premium Cut in 2015
The ratio of the amount of a mortgage loan to the market value of the property securing the loan
(known as the loan-to-value, or LTV ratio) is an important underwriting factor. High LTV loans
default at higher rates, and creditors tend to suffer greater losses given default on such loans. To
get approved, applicants with low down payments often need to pay for mortgage insurance,
which helps protect creditors against losses in the event of default.
In addition to several large private mortgage insurance (PMI) companies, the FHA, a Federal
agency within the Department of Housing and Urban Development (HUD), is an important
provider of mortgage insurance. The FHA does not extend credit, but insures loans extended by
private lenders if the loan meets or exceeds the FHA’s underwriting standards, and is within
statutory loan size limits.
9
Since 2012, 20-30 percent of all home purchase originations for 1-4
family owner-occupied properties in the U.S. have carried FHA insurance. FHA-insured loans
require a down payment as low as 3.5 percent of the property value, which can ease the transition
into homeownership for first time homebuyers with little in the way of accumulated assets. In
2014, more than 80 percent of FHA-insured home purchase loans went to first-time homebuyers,
8
Hilber and Turner’s (2014) finding of a negative effect of the mortgage interest deduction on homeownership in
highly regulated housing markets implies capitalization of the deduction in such markets, but the actual effect of
interest rates on house prices is not estimated.
9
The 2015 maximum loan size for a one-family house was $271,050 in most counties, and as high as $625,500 in
high-cost areas such as counties in San Francisco.
6
and over three-quarters of FHA-insured loans had down payments of less than 5 percent.
10
FHA
mortgage insurance premiums can also be substantially lower than those from PMI companies
for many borrowers, particularly those with lower credit scores.
11
The FHA charges a one-time upfront premium, set as a percentage of the original loan amount
(and which can be financed). The FHA also charges an annual premium, set each year during
the life of the loan as a fixed percentage of the expected average outstanding balance during the
year. The premium rates are generally the same for all borrowers, regardless of credit risk.
12
On January 7, 2015, the Obama administration announced that the FHA would be reducing its
annual mortgage insurance premiums by 50 basis points, from 135 basis points to 85 basis points
for typical FHA loans.
13
This reduction would lead to a decline in premium payments of about
$1,000 for a $200,000 loan in the first year of the loan, and about $4,700 in the first five years.
The FHA provided additional details two days later, indicating that the new premiums would
apply in less than three weeks to loans that close on or after January 26, 2015, regardless of loan
application date.
The 2015 premium cut came after several increases in FHA’s premiums, beginning with a small
rise in late 2008, and larger increases starting in 2010 (Figure 2). During the financial crisis and
recession, FHA insurance became heavily used, and FHA suffered sizeable losses on the 2008
vintage of loans in particular (Avery et al. 2010; HUD 2012). FHA began raising premiums to
help rebuild reserves more quickly. Prior to 2010, the annual MIP was essentially flat for at least
a decade.
Because FHA’s reserves were still below target levels, the announcement on January 7
th
of the
FHA premium cut appears to have been a real surprise. In its annual actuarial report released in
10
Source: HUD (2015).
11
See the June 2016 Housing Finance at a Glance monthly chartbook published by the Urban Institute. Over half
of FHA-insured mortgages in 2014 went to borrowers with credit scores under 680 (HUD, 2015). Fannie Mae and
Freddie Mac, which purchased just under half of all new mortgage loans by dollar volume in 2015 according to
Inside Mortgage Finance, by statute can only purchase loans with an LTV in excess of 80 percent if they have PMI.
12
Currently, annual insurance premiums differ very slightly if the loan amount exceeds $625,000 (add 5 basis
points), or the LTV ratio at origination exceeds 95 percent (add 5 basis points). Premiums are significantly lower
for loans with a maturity of 15 years or less, but 15-year FHA loans are rare.
13
Typical means a loan amount under $625,000 and LTV over 95 percent, but annual premiums were lowered by 50
basis points for all 30-year loans.
7
November, 2014, the FHA noted that the economic value of its insurance fund had increased in
2014, but its capital ratio still stood at just 0.41 percent, well below the congressionally
mandated 2 percent target (HUD 2014). Earlier in 2014, FHA Commissioner Carol Galante told
the Washington Post, “[I]t’s not the time to do a wholesale rollback of the premiums. FHA’s
financial condition is not where it should be yet.”
14
Additionally, a Housing Wire article in
December, 2014 remarked, “Industry analysts said that despite the increased health of the [FHA],
changes in the FHA mortgage insurance premiums were unlikely in 2015,”
15
Finally, the Urban
Institute released an analysis on January 6, 2015 – the day before the announcement of the
premium cut – arguing that, despite slower-than-expected improvements in their finances, the
FHA could reduce its premiums (Bai, Goodman and Zhu 2015). The tone and timing of their
discussion underscores the lingering questions around FHA’s finances and suggests there was
little expectation for the announcement that would come the next day. Indeed, data from Google
Trends are consistent with the announced FHA premium cuts being a surprise, with searches for
“FHA mortgage” and “FHA mip reduction” being steady for several months and then suddenly
spiking on January 8, 2015 – the day after the announcement.
16
Overall, we have not found any
news article or blog indicating any expectation among real estate and mortgage industry
participants for an FHA premium cut in the weeks and months just before the announcement.
17
2. Identification and Estimation
Our primary goal in this paper is to use the sharp 2015 FHA MIP cut to study the causal response
of home buying to interest rates in a regression discontinuity (RD) design. Two key attributes of
the FHA MIP cut, as discussed in the previous section, are, first, that it was a surprise and,
second, that there was little time between its announcement and implementation that might
encourage strategic delays in home buying.
14
ElBoghdady, Dina. “Why a government agency won’t lower mortgage fees for borrowers.” Washington Post,
April 21, 2014.
15
Lane, Ben. “18 Senators, mortgage bankers tell HUD: Time to lower FHA premiums.” Housing Wire, December
18, 2014.
16
See Appendix Figure A1
17
We searched for FHA-related articles available on the internet prior to January 7, 2015 using Google’s date-
specific search tool.
8
The MIP cut mimics an interest rate decline, but helps avoid a central difficulty in estimating the
effect of interest rates, which is the endogeneity of rates to a host of aggregate- and individual-
level confounding factors. A closer examination of one recent shock to interest rates illustrates
these difficulties. In the late summer of 2016, the prevailing prime mortgage rate stood at around
3.5 percent. Following the surprising results of the U.S. presidential election on November 8
th
,
rates jumped by approximately 50 basis points over a few days, superficially providing a case
study to examine the response of mortgage borrowing to higher rates. However, the sudden
jump in rates reflected a shift in market expectations about the future of the economy. The value
of the stock market and indexes of consumer confidence and small business confidence all
jumped upon news of the election, likely in response to expectations of expansionary policies.
This surge in confidence likely affected housing demand. Furthermore, as rates moved up, so did
consumers’ expectations of the future path of rate increases. These updated expectations may
have pulled future home buying demand forward, as can be seen in the representative Surveys of
Consumers run by the University of Michigan. Between August 2016 and January 2017 the
number of homeowners who responded that it was a good time to buy a house due to low interest
rates fell from 53 to 38 percent. Nearly offsetting this change, however, the number who
responded that it was a good time to buy because rates were likely to rise soon rose from 6
percent to 20 percent. In contrast to endogenous interest rate changes, the discontinuous drop in
the FHA MIP in January 2015 occurred while other determinants of housing demand evolved
more smoothly (as we will show later).
Our main empirical approach tests for a discontinuity at the time of the MIP cut in the share of
home purchase loans going to borrowers with below-average credit scores and less than a 20
percent down payment – characteristics that make them most sensitive to FHA premiums. In our
primary dataset from Optimal Blue, which we describe in the next section, about 85 percent of
borrowers with a FICO score below 680 and an LTV over 80 percent used FHA insurance during
the sample period. We refer to such borrowers throughout the paper as “FHA-likely” borrowers,
or “treatment group” borrowers. All other borrowers (implicitly the control group) used FHA
insurance only 17 percent of the time.
18
18
We also examine several alternative definitions of the treatment and control groups in the appendix.
9
Our approach of testing for a discontinuity in the share of loans to lower-score, higher-LTV
borrowers is motivated by two issues. First, a more straightforward approach of simply testing
for a discontinuity in the total volume of home purchase loans is confounded by the strong
seasonal cyclicality of the mortgage market. In practice, a discontinuity can be hard to
distinguish from a sufficiently steep slope. To illustrate the difficulty, in Figure 3 we plot the
volume of home purchase loans from mid-2012 through 2015 by week of application, with
vertical lines representing the week of January 26 for each year. The rate of change in loan
volume is typically rapid through the late January/early February period, so distinguishing any
discontinuity in lending, even one of substantial size, from the prevailing upward trend would be
challenging. Instead, we test for a discontinuity in the share of all home purchase loans going to
treatment group borrowers, which displays almost no seasonality as the control group absorbs
seasonal trends.
A second issue is that some borrowers seeking a high-LTV loan may have a choice between PMI
and FHA mortgage insurance, and the decrease in FHA premiums may have pulled some of
these borrowers away from PMI and into FHA. Figure 4 shows a clear discontinuity in the FHA
share of home purchase loans, from about 22 percent to 27 percent, but this discontinuity likely
overstates the effect of the MIP cut on new borrowing. Although seasonality is not an issue with
the FHA share, the discontinuity in the FHA share is confounded by borrowers shifting from
PMI into FHA. In contrast, our treatment group share of home purchase loans is not affected by
such shifting. If, for instance, a borrower with a FICO score of 670 got FHA insurance instead
of PMI after the MIP cut, our treatment group share would not change – that borrower would
contribute one loan to the numerator regardless.
Focusing on home purchase loans for owner-occupied properties, we estimate the equation:
=
0
+
1
+
(
|
)
+
(1)
where y is an indicator for the borrower being a member of the treatment group. The variable x is
a dummy for either the date of application or the date of interest rate lock, depending on our
dataset, being within or after the week of January 26, 2015. Observing the application date in the
data is key to our study because this date marks the point when a decision to borrow occurs, as
10
opposed to the closing date of a loan which can occur weeks or months after application.
19
Finally, g(t|x) is a flexible function in the week of application or rate lock. The function g(·) is
specified relative to the week of rate lock, rather than the exact date, to absorb day-of-the-week
effects (mortgage applications exhibit strong periodicity within the week). Assuming y is a
continuous function of t in the absence of the MIP cut, least-squares estimation of (1) yields a
consistent estimate of β
1
, the effect of the FHA MIP reduction on the treatment group share of
home purchase loans. Following Imbens and Lemieux (2008), we model g(·) as a local linear
function with different slopes on either side of the January 26 breakpoint. We try a variety of
bandwidths, and cluster all standard errors by week of rate lock.
A key concern in any RD design is whether the “running variable”—in our case the week of
application or rate lock—would have been manipulated (McCrary 2008). As already
emphasized, the MIP cut was a surprise and was quickly implemented, limiting concerns about
borrowers strategically delaying their mortgage applications. However, a remaining concern is
that existing mortgage applicants at the time of the announcement may have had an incentive to
re-apply for a mortgage after January 26
th
to get the lower premium. Later in Section 6 we
discuss how the FHA explicitly mitigated such incentives, and present empirical evidence
supporting this exogeneity assumption.
Finally, the consistency of our estimator requires that membership in the treatment group be
exogenous to the FHA MIP reduction. We believe this assumption is a fair one. The primary
threat to this assumption is if low-FICO borrowers with the liquid assets to potentially make a
down payment of 20 percent or more decided to put less down and take an FHA loan when the
MIP dropped. Sub-680 FICO score borrowers with a down payment of 20 percent or more were
relatively uncommon even before the MIP cut, however. Furthermore, the decision to put less
than 20 percent down would be quite costly, as the borrower would then have to pay mortgage
insurance on the entire loan, as well as interest and insurance on the additional borrowed funds.
Later in Section 6 we discuss an explicit test of this exogeneity assumption, providing evidence
that there was little or no switching into the treatment group as a result of the reduced FHA
premiums.
19
Rate locks usually occur shortly after application.
11
3. Data
Data for this project come from several sources. One source is loan-level data reported under the
Home Mortgage Disclosure Act (HMDA). These data cover nearly the entire residential
mortgage market, and data collected include FHA status, the dates of application and origination,
loan amount, loan purpose (home purchase, refinance or home improvement), property type,
occupancy status, lien status and application outcome (originated, denied, withdrawn by
applicant, etc.), borrower socioeconomic characteristics including income, race and ethnicity,
and the census tract of the securing property.
20
In addition, we draw on loan-level rate lock data provided by Optimal Blue.
21
Optimal Blue is a
lending services company that provides mortgage lenders with a software platform that can be
used during the interest rate lock process. Optimal Blue retains the data entered by lenders, and
these data can be purchased for research. In 2014 and 2015 they recorded approximately
1,600,000 rate locks for owner-occupied home purchase loans, about one quarter of the number
of mortgage originations reported in HMDA over that period. Lenders using the Optimal Blue
platform tend to be smaller and thus the data do not include loans originated by the largest banks
such as Wells Fargo and JPMorgan Chase. The Optimal Blue data include borrower FICO score,
DTI and LTV ratios as well as the contract rate, FHA status, date of rate lock, loan amount,
occupancy and the ZIP Code of the securing property. Unlike HMDA, the final disposition of the
application is not available in this data – some applications may be withdrawn or denied after the
borrower locks in a rate.
In order to assess how our estimated elasticity varies with borrowers’ income, we perform a
merge of home purchase loans in the HMDA and Optimal Blue data sets. Loans are merged
based on loan amount (rounded to the nearest thousand), location (as determined by the overlap
between ZIP Code Tabulation Areas and census tracts) and loan type (i.e. FHA, VA, RHS or no
government insurance). We also require that the date of rate lock from Optimal Blue fall
20
The public version of the HMDA data does not include application and origination dates. See Bhutta and Ringo
(2016) for more details on the information available in the HMDA data.
21
The data from Optimal Blue do not contain lender or customer identifies, or complete rate sheets. We report only
aggregate statistics.
12
between the dates of loan application and origination from HMDA. We then drop all non-unique
matches. This leaves about 600,000 matches for 2014 and 2015, 540,000 of which were for
owner-occupied properties.
Finally, to verify that our results are robust to the choice of data set, we replicate our estimation
on a large sample of loans provided by McDash Analytics. The McDash data are composed of
the servicing portfolios of the largest mortgage servicers in the U.S. These data cover over half
of one- to four-family mortgage loans originated in 2014 and 2015, and, in contrast to the
Optimal Blue data, coverage is skewed towards larger lenders.
The McDash data include information on the origination date, loan amount, contract rate and
LTV ratio of the loan, as well as ZIP Code of the securing property and FICO score and back-
end DTI ratio of the borrower. To get the associated application dates for these loans, we must
merge these data with HMDA data. The merge is performed on loan amount, county, origination
date, loan purpose and loan type.
22
McDash has records for 1.6 million home purchase loans
originated in a 50 week window around the 2015 FHA MIP reduction, and we match over
900,000 to HMDA after dropping observations that were non-unique on the matching criteria in
either data set.
Summary statistics for each loan-level data source are presented in Table 1, for both all home
purchase loans and for those with FHA insurance. FHA loans tend to be for smaller dollar
amounts and carry higher LTV ratios, while FHA borrowers tend to have lower incomes and
weaker credit scores than the overall borrower population. The HMDA data are the most
representative, as the vast majority of residential mortgages are covered. Loans in the Optimal
Blue data are slightly smaller on average and more likely to have FHA insurance. FHA loans or
those with otherwise risky characteristics were less likely to have a unique match between the
two data sets – the merged HMDA/Optimal Blue sample has a lower FHA share, lower DTI and
LTV ratios, and a higher average FICO score. Relative to Optimal Blue, McDash covers a
higher loan amount, higher income and a generally less risky borrower population.
22
In accordance with our contract with Black Knight, the data provider, institutional identifying information was
dropped before the merge and was not available to researchers in the final, merged data set.
13
4. The Effect of the MIP Cut on Home Buying
As mentioned earlier, Figure 1 illustrates our main finding, plotting the share of owner-occupied,
home purchase loans going to the treatment group against the week of rate lock, using the
Optimal Blue data. Rate lock typically occurs about one week after the loan application is
recorded, and should therefore provide a good proxy for the FHA pricing regime the borrower
faced. A local polynomial curve is fitted over the weekly data, and a vertical line represents the
week of January 26, 2015. There is only a muted seasonality to the treatment group share (which
peaks in the late fall and bottoms out in the early summer), in comparison to the large
fluctuations in total lending apparent in Figure 4. A jump in lending to the treatment group
coincident with the FHA MIP reduction is quite apparent, with approximately 18 percent of
loans going to treatment group borrowers before the change and 20 percent after.
Estimates of the discontinuity in treatment group share based on the Optimal Blue data are
presented in the first row of Table 2. The function g(·) is estimated separately on either side of
the breakpoint with a triangular weighting kernel. We show results for a variety of bandwidths,
and find a statistically significant effect in all of them. At the narrowest bandwidths of 12 and 25
weeks, the point estimates match Figure 1, suggesting the new premiums increased the treatment
group share of loans by about 2 percentage points, from 18 percent to 20 percent. The estimate
at a bandwidth of 50 weeks is smaller at 1.2 percentage points. Overall, we estimate from these
data that the MIP reduction led to an increase in borrowing of 8 to 14 percent by the treatment
group. While these estimates assume total borrowing by the control group was unaffected by the
reduced annual MIP, results are quite similar when we use more restrictive definitions for the
control group, including specifications under which the control group has FHA utilization rates
below 2 percent. See Appendix Table A1 for results under various different treatment and
control group specifications.
Next, we verify that the observed discontinuity in lending is not peculiar to the Optimal Blue
data. For example, it is conceivable that a large group of borrowers switched lenders as a result
of the new premiums, and only their new lenders are covered by Optimal Blue. To rule out such
possibilities, we turn to the matched HMDA/McDash data, which tends to cover the largest
lenders whereas Optimal Blue tends to cover smaller lenders. We plot the share of owner-
14
occupied, home purchase loans in the HMDA/McDash dataset against the week of application in
Figure 5. A large discontinuity in lending to the treatment group at the week of January 26 is
apparent in these data as well. Estimates of the discontinuity from equation (1) are presented in
the second row of Table 2. The RD estimates are stable and statistically significant across the
choice of bandwidth, and similar to the estimates from Optimal Blue – the share of lending to the
treatment group increased by approximately 13 percent around January 26, 2015.
Going back to Figure 5, we can see that after the week of January 26 the treatment group fraction
declines and returns to the pre-MIP-cut level within 20 weeks. While it is tempting to try and
draw conclusions about the persistence of the effects of the MIP cut (or lack thereof) from
Figures 1 and 5, it is important to keep in mind that our RD estimates only identify the effects of
the MIP cut near the dates when the cut was announced and went into effect. Thus, Figure 5
does not necessarily imply the effect died out within 20 weeks, nor does Figure 1 necessarily
imply that the effect was persistent.
To help ensure that the estimated discontinuity is not an artifact of the time of year, we run
placebo RD tests around the week of January 26 the year before the MIP reduction (2014) and
the year after (2016; year after estimates are only available with the Optimal Blue data since
2016 HMDA data were not yet available at the time of writing). The estimates, also presented in
Table 2 across three bandwidths, are all close to zero, inconsistent in sign, and statistically
insignificant in all but one instance. Seasonality does not appear to be driving our main results.
4.1 Heterogeneous Responses by Borrower Income
We test for a heterogeneous response to the reduced premiums by dividing treatment group
borrowers in the merged Optimal Blue/HMDA data into four quartiles based on HMDA reported
applicant income. The cutoffs are annual incomes of $46,000, $66,000 and $96,000. We
estimate a discontinuity in the share of all lending going to each treatment group subsample as in
(1). Results are reported in Table 3.
23
The discontinuity is strongest in the lowest income
23
Summing over the four income categories, the estimated discontinuities, in percentage point terms, are smaller in
the merged Optimal Blue/HMDA data than those in the Optimal Blue data alone (Table 2). This is because the
merged data contains a lower proportion of FHA and treatment group borrowers (see Table 1). The estimated
discontinuity as a percent of the 2014 treatment group share is similar in both the merged and non-merged data.
15
sample, and weakens as income increases. We repeat the analysis on the merged
HMDA/McDash data, and find very similar results, also shown in Table 3. In both data sets, the
estimated effect decreases with borrower income. It appears that among households with annual
incomes above $96,000, the demand for home purchase loans is essentially rate inelastic.
Applicants with lower incomes may be relatively more sensitive to reduced premiums for two
reasons. First, lower-income borrowers may have higher DTI ratios, and therefore more likely to
be on the margin of denial. Reduced premiums could then have a greater effect on their
probability of being approved for a loan. Second, lower income households may have more
price-elastic demand for owner-occupied housing, in which case reducing premiums would bring
relatively more lower-income applicants into the market.
5. Validity of the Identification Strategy
Before we move on to discussing the mechanisms behind the discontinuity in home buying, in
this section we address four potential issues related to the validity of the RD design. They
include: exogeneity in the timing of the MIP reduction with respect to other macroeconomic
trends; the extent to which lenders pass-through the MIP cut to borrowers, exogeneity of the
assignment variable; and selection into the “treatment” group.
5.1 Was the Timing of the MIP Reduction Exogenous?
To be certain that we can attribute the increase in treatment group share of borrowing to the
reduced FHA premiums, we need to make sure that the other economic drivers of housing
demand did not vary discontinuously around January 26. In Figure 8 we plot a variety of
economic indicators across time around the date of the premium cut. These are the yields on 1-,
and 10-year Treasury securities, the S&P 500 stock market index, and the seasonally adjusted
unemployment rate. None of these measures show evidence of a discontinuity around January
26. In addition, we rerun our main RD specifications including these macro series as control
variables. The results, shown in Table 2, are robust to adding these controls.
16
5.2 Pass-Through of the MIP Reduction to Borrowers
Was the MIP cut fully passed through to borrowers? Previous research, for instance, has found
that price reductions in the mortgage backed securities market are not fully passed through to
consumer-facing interest rates, particularly in times of high mortgage borrowing volume (Fuster,
Lo, and Willen 2017). This research attributes this incomplete pass through to capacity
constraints, as mortgage retailers become overwhelmed with demand.
To be sure that the MIP cut was passed through, we test for a discontinuity in the contract
interest rate among treatment group borrowers relative to control group borrowers. Full pass
through of the MIP reduction to borrowers would imply no change in this rate. Because the
premium cut changed the composition of treatment group borrowers by inducing more marginal
households into the pool of borrowers, we try specifications with and without controls for
various underwriting factors that could influence the rate. Results are presented in Table 4.
There appears to be little or no effect on the interest rates treatment group borrowers paid,
regardless of specification, implying full pass through of the MIP reduction to borrowers.
Notably, the FHA MIP cut we study occurred in January, near the trough of the highly cyclical
mortgage market, when there may have been slack capacity for lenders to originate more loans
and allow for full pass through.
5.3 Did Borrowers Shift their Loan Application Date?
As noted earlier, the validity of our RD design depends on whether borrowers delayed their loan
applications upon hearing the news to take advantage of the lower premiums. A related concern
is that, by the time of the announcement, those who had already submitted an application but not
yet reached settlement could withdraw their application and reapply to get the lower premiums.
The jump we see in treatment group lending might represent these delayers and withdrawers,
rather than a true increase in lending.
However, the implementation of the MIP reduction removed most of the incentive for borrowers
to withdraw and re-apply for and FHA loan. Eligibility for the lower FHA premium depends on
the FHA “case assignment date” rather than the loan application date. When the new MIP was
announced, FHA also announced that existing FHA mortgage applicants who had not yet closed
17
could simply cancel their existing case number and get a new one in order to receive the lower
MIP, without withdrawing the loan application (as long as they close on or after January 26
th
).
24
Indeed, many borrowers appear to have moved their case number assignment dates. In Figure 6,
using loan-level data obtained from HUD on all FHA loans originated from 2011 through 2015
merged to HMDA, we plot the average number of days between loan application and case
number assignment for all FHA home purchase loans by week of loan application. While the
typical gap is approximately one week, the gap rose substantially for loans with application dates
in December 2014 and early January 2015. This pattern is consistent with many borrowers
getting new case numbers assigned post-January 26, despite their much earlier loan application
dates.
While there was no incentive for FHA applicants to withdraw in response to the MIP news, and
most treatment group borrowers were FHA applicants, it is still possible some treatment group
applicants withdrew and then reapplied. Using the merge between HMDA applications and
Optimal Blue rate locks, we can test for an increase in the withdrawal rate of treatment group
applications (among those that made it to rate lock before withdrawing).
In Figure 7 we plot the share of all withdrawn loans for which the applicant was a treatment
group household, by the week of application. A rise in treatment group withdrawals in late 2014
and early 2015, or a sharp fall in withdrawals after January 26, 2015, might suggest that
borrowers were manipulating their application date in response to the lower premiums. No such
pattern is apparent, however, as the share of withdrawn loans by treatment group applicants
holds steady for the months around the MIP reduction.
In addition to withdrawals, we may be concerned about the possibility that some borrowers
delayed applying in response to the news of the lower premiums. Again, there was no actual
incentive to do so, as borrowers could always get a case number assignment after the 26
th
even
with an earlier application date. There was also very limited scope for delay – the White House
announced the premium reduction less than 3 weeks before it was implemented. Inspection of
Figures 1 and 5 also reveals no indication of a sudden dip in applications or rate locks in the few
24
FHA made clear the ability for borrowers to get a new case number assignment date in an FAQ released at the
time they announced the new premium structure. See Appendix Figure A2.
18
weeks just before the premium reductions, suggesting that borrowers were not delaying their
applications.
5.4 Is Selection into the Treatment Group Exogenous?
We demonstrate above that the fraction of home purchase loans going to borrowers with a FICO
score below 680 and an LTV ratio in excess of 80% jumped discontinuously when the FHA
reduced its premiums. A concern with our interpretation of this finding is that the amount of
down payment is a choice made by the borrower, so there is potential for endogenous selection.
If borrowers who counterfactually would have put 20% of the purchase price or more down
under the old FHA premiums put down less than 20% given the new MIP, our estimates would
be biased upward.
We believe endogenous selection into the treatment group is at most a minor source of bias, for
several reasons. First, borrowers with a FICO score below 680 were very likely to be part of the
treatment group regardless of the FHA’s policy—in 2014, only 10 percent of these low-score
borrowers had an LTV ratio less than or equal to 80 percent in the Optimal Blue data.
Essentially all of these households would have had to “switch” into the treatment group in
response to the MIP reduction to explain the magnitude of the discontinuity seen in Figure 1.
Second, the cost of borrowing jumps discontinuously at an 80% LTV ratio, as borrowers have to
pay annual and upfront insurance premiums on the entire loan balance once they cross that
threshold, in addition to interest and insurance on the additional amount borrowed. Borrowers
with the liquid assets available for a 20% down payment who chose to put less down and get an
FHA loan would be costing themselves a substantial amount of money.
Third, while we cannot theoretically rule out the existence of borrowers who respond to the MIP
reduction by getting an FHA loan despite being able to afford a 20 percent down payment, we
can test for their presence. For a given house value, borrowers face a budget constraint, trading
off between the amount of down payment (conversely, the LTV ratio) and the amount of their
monthly mortgage payments. With mortgage insurance required above an 80 percent LTV ratio,
both the total and marginal “cost” of a higher LTV ratio jump at this threshold. This notch in the
budget constraint at 80 percent LTV explains the commonly observed bunching of borrowers
19
right at this threshold. In the Optimal Blue data, over half of borrowers with a FICO score below
680 and an LTV less than or equal to 80 percent in 2014 had an LTV exactly equal to 80 percent.
If we assume that borrowers have convex preferences over combinations of LTV ratio and
monthly payments (i.e. if the disutility from the marginal dollar of down payment and debt
service payments is increasing in their respective levels) then we can show:
1) Any borrower whose optimal LTV under the old (higher) MIP was less than 80 percent
will have the same optimal LTV under the new (lower) MIP.
2) For any borrower whose optimal LTV under the new MIP is above 80 percent, and whose
optimal LTV under the old MIP was less than or equal to 80 percent, the optimal LTV
under the old MIP was exactly 80 percent.
We can therefore test for endogenous selection into the treatment group, as any such “switching”
borrowers should be of the second type described above – coming from the group who would
choose exactly 80 percent LTV under the old MIP.
We redefine the treatment group as households with a FICO score below 680 and an LTV ratio
in excess of 79 percent and re-estimate equation 1. Results are quite similar to those presented in
Table 2, indicating that there was not a significant shift of borrowers from an 80% LTV ratio to
the treatment group in response to the lower MIP. We therefore conclude that the assumption of
exogeneity of treatment group status is sound. A graphical demonstration of points 1) and 2)
above, and a table of results using the redefined treatment group are included in the appendix.
6. Mechanism
Understanding the mechanism by which reduced FHA MIPs increased lending to the treatment
group is necessary for the extrapolation of these results to other contexts and the broader
population. We posit that two distinct channels are responsible. First, more applicants may have
decided to buy homes in response to lower premiums (the typical quantity-demanded response to
a price decrease). Second, reduced premiums mechanically improve applicants’ DTI ratios and
could thereby have led to many borrowers being approved for loans that they would otherwise
have been denied. In this section we provide evidence that both mechanisms were at work.
20
6.1 Denial Rates and the DTI Ratio
A reduction in DTI ratios leading to a reduction in denials is an intuitively appealing channel,
given the rapid effect of the new premiums. According to 2014 HMDA data, about 18 percent of
FHA home purchase loan applications were denied, and lenders cited DTI as a reason for denial
in 31 percent of denied applications with a reported reason. DTI ratios on FHA loan applications
should drop mechanically with the annual premiums, without requiring borrowers to change their
behavior. Was the reduction in annual premiums large enough to change denials to acceptances
for an appreciable number of mortgage applicants? Using the loan level data, we can calculate
how much a 50 basis point change in mortgage insurance premiums means for borrower DTI
ratios. Taking FHA borrowers in 2015 (after the MIP reduction), we approximate their
counterfactual DTI ratio as:
=
+ 0.005
(2)
where DTI
c
is the counterfactual DTI ratio, DTI
f
is the ratio in the data, L is the loan amount at
origination and Y is the borrower’s income as reported in HMDA. In the merged
HMDA/Optimal Blue data, the average FHA borrower in 2015 would have a DTI 1.6 percentage
points higher under the old premiums than under the reduced premiums. In the merged
HMDA/McDash data, average DTI ratios would have been 1.4 percentage points higher. If
many applicants have a DTI ratio within a percentage point or two of the margin for denial, a 50
basis point change in premiums is certainly enough to swing the outcome for a sizable
population.
The FHA imposes underwriting standards that tighten in a stepwise manner as the applicant’s
DTI ratio increases. A basic cap of 43 percent is imposed on manually underwritten loans with
no compensating factors. For borrowers with an additional compensating factor, this limit may
be raised to 47 percent. With two factors, it is raised again to 50 percent (see the FHA Single
Family Housing Policy Handbook, 2016).
25
Using the FHA’s automated underwriting tool,
25
Acceptable compensating factors include cash reserves, residual income not included in the DTI calculation and
proof that the new mortgage payment represents a minimal increase over previous housing payments.
21
borrowers may be approved with a DTI ratio up to 57 percent. Additionally, lenders may impose
overlays and, in particular, tighten the availability of credit at DTI ratios of 45 and 55 percent.
FHA borrowers just under one of these thresholds in 2015 would have been over the threshold if
they had to pay the old, higher premiums. In Figure 9 we plot the sample frequency of DTI
ratios for all FHA home purchase loans in 2014 and 2015, in bins of a single percentage point.
For borrowers with a FICO score below 620, the 43 percent DTI cutoff is clearly relevant. For
borrowers with a higher FICO score, we can see substantial drop-offs in the sample density at 45,
50, 55 and 57 percent. A significant fraction of FHA borrowers have a DTI ratio close enough to
an underwriting cutoff such that a 50 basis point change in their insurance premiums could affect
their probability of getting denied.
If the new premiums caused increased lending to the treatment group by reducing DTI-based
denials, we would expect to see a discontinuous drop in the overall denial rate around January
26, 2015. Unfortunately, a direct test of this prediction is confounded once again by the
seasonality of mortgage markets. Denial rates fall rapidly through the early months of every
year, violating the continuity assumption necessary for consistency of an RD estimator.
As a next-best alternative, we turn to the logic of comparing treatment and control groups.
Denial rates should only be affected for borrowers limited to FHA loans. Unfortunately, HMDA
is our only source for data on denied loan applications. We therefore do not have FICO score or
LTV ratio information for these applicants, and so we cannot use our previously defined
treatment and control groups.
26
While we do not have credit score or LTV data for HMDA applications, HMDA data do provide
applicant race, which is highly correlated with credit score and FHA status. Among black
applicants, about 53 percent of home purchase applications (excluding VA applications) in 2014
were for FHA loans, compared to just 10 percent among Asian applicants, and previous research
has found large gaps in credit scores between black and Asian borrowers.
27
If the MIP reduction
26
In Appendix Table A3, we show that the denial rate for FHA loan applications dropped discontinuously on
January 26, 2015, relative to all other applications. However, the reduction in premiums may have led to changes in
the composition of the FHA applicant pool, so the fall in denial rates may reflect stronger FHA applicant
underwriting factors in addition to any easing of DTI constraints.
27
Bhutta and Canner (2013) document large differences in credit scores between black and Asian homebuyers of
70-80 points, on average.
22
made any given FHA application more likely to qualify, the denial rate of black applicants
should have fallen relative to Asian applicants around January 26, 2015.
We test for a relative decline in the black/Asian denial rate in the HMDA data. Taking
individual loan applications in HMDA as our unit of observation, we estimate:
=
0
+
1
+
2
∙ +
(
|
)
+ ℎ(
|
) ∙ +
(3)
where Black is an indicator that the applicant or co-applicant was black, and d
i
indicates that the
application was denied. The running variable t is again the week of application, while x
i
indicates
the application date was on or after January 26, 2015. The functions g and h are flexible
functions of time, with slopes that can vary discontinuously across the January 26 thresholds and
allow for different levels and time trends in black and Asian denial rates. We restrict the sample
to applications for which all applicants were recorded as being either black or Asian, and for
which a credit decision was reached. The parameter of interest, β
2
, represents the discontinuous
change in black denial rates, relative to Asian denial rates, when the premiums were reduced.
The results, presented in Table 5, indicate that black applicants became approximately 1
percentage point less likely to be denied after the MIP reduction, relative to Asian applicants. As
can also be seen in Table 5, no statistically significant discontinuity appeared around January 26,
2014 – when there was no MIP cut – suggesting the estimated effect is not an artifact of
seasonality. The reduced premiums appear to have increased overall borrowing at least in part
by reducing the denial rate of borrowers who rely heavily on FHA insurance.
About half of home purchase applications from black applicants were for FHA loans. Assuming
the reduction in FHA premiums had no effect on the denial probability of a non-FHA
application, conditional on risk characteristics, these estimates suggest the MIP cut reduced the
probability of any given FHA applicant being denied by about 2 to 3 percentage points.
Approximately 736,000 applications for home purchase FHA loans for owner-occupied single
family homes reached a credit decision and were recorded in the HMDA data in 2014.
Extrapolating from the previous estimates, the reduced premiums could have turned
approximately 15,000 to 22,000 of these from denials into originated loans. With about 2.7
million total home purchase originations in 2014, the denial rate channel could therefore explain
23
from 28 to 40 percent of the two percent total increase in lending we previously estimated the
FHA premium reduction was responsible for.
Potentially confounding these results on denial rates is the possibility that the MIP reduction
altered the composition of the pool of applicants. If marginal applicants tend to be better
qualified, that could explain the reduction in the denial rate. However, as demonstrated in
Section 5.1, the increase in lending was particularly concentrated among lower-income
households and such borrowers may be relatively less qualified. To check for compositional
changes, we test for a discontinuity in the FICO scores of black borrowers relative to Asian
borrowers on January 26, 2015. Equation (3) is re-estimated on the Optimal Blue/HMDA
merged data, using reported FICO score as the outcome variable. Results are presented in Table
5. We estimate that the average FICO score of black borrowers dropped a small amount, a few
points on a scale that runs from 300 to 850. The estimated discontinuity is also only statistically
significant under one of the three bandwidth specifications we use. This data is inherently
censored – we only observe FICO scores for applications that made it to rate lock – but the pool
of black borrowers shows at most a minor weakening of creditworthiness following the MIP
reduction.
6.2 Volume of Applications
In addition to a change in the denial rate, the MIP reduction could have increased treatment
group borrowing by encouraging a greater quantity of demand for loans. While home buying
can be a lengthy process, Figures 1 and 5 indicate that there was a nearly immediate response to
reduced premiums. If marginal applicants respond to changes in the cost of credit within a week
or two, this suggests there is a substantial pool of potential home buyers that are actively
searching but uncommitted to applying for a mortgage. Such households may only learn about
their total borrowing costs when they are close to the decision point and contact a broker or loan
officer.
In this section, we provide evidence that the reduction in FHA premiums caused more
households to submit home purchase mortgage applications. As we discussed previously, the
seasonality of the mortgage market makes looking for discontinuities in the overall volume of
24
applications or originations tricky. One way of dealing with the seasonality is to identify a
treatment and control group, as we do in section 4. FICO and LTV information is not available
in HMDA, so this method won’t work for estimating the effect on the number of applications. A
second option is to control for seasonal effects and estimate a discontinuity in the deviations
from the seasonal trend.
To test for an effect of the reduced premiums on demand, we follow the second option,
controlling for seasonal variation by estimating a discontinuity in the year-over-year change in
the log of the weekly volume of home purchase loan applications and originations. We re-
estimate (1) with these weekly growth rates as the outcome variable. Results are presented in
Table 5. The estimates are somewhat imprecise and sensitive to choice of bandwidth, however,
they are consistent with the reduced MIPs causing a jump in total applications and originations
of 3 to 5 percent.
28
The estimates of the effect on loan volume are greater than on application
volume, which fits the theory that denial rates dropped. Standard errors are too large to
distinguish the effect sizes from each other statistically, however. As can also be seen in Table
5, there is no evidence of discontinuity in total lending or applications around January 26, 2014,
suggesting the discontinuity at the time of the MIP cut in 2015 are not driven by residual
seasonal factors. In Figure 10, the annual growth in the number of applications is plotted by
week around the premium cut on January 26, 2015 and around a placebo date on January 26,
2014.
7. The Effect of the MIP Cut on Loan Amounts and Home Prices
In addition to the extensive margin of home buying, borrowers may respond to a reduction in
their cost of credit along the intensive margin by bidding more for a given home, purchasing
more expensive properties, and/or taking out larger loan amounts. Increasing demand along both
the extensive and intensive margins could lead to higher house prices. In this section we estimate
28
For the volume regressions, we omit estimates using the 50 week bandwidth due to an artifact of data collection.
Loan applications are reported under HMDA in a given year only if a credit decision is made prior to December 31
of that year. For 2015, the most recent year HMDA data is available at the time this writing, the volume of
applications therefore spuriously appears to drop off in the late fall and early winter, disrupting the estimated
discontinuity when using the widest bandwidth.
25
borrowers’ responses along the intensive margin, as well as whether the shock to housing
demand caused an increase in the overall level of house prices.
To begin, we test for a discontinuity in (log) amount borrowed and in (log) purchase price
around January 26, 2015. Note that an unconditional discontinuity test is likely to pick up the
effect of a change in the composition of treatment group borrowers. As shown earlier, new
borrowers induced into home buying by the MIP reduction tended to have relatively low
incomes. These lower income households may buy less expensive homes, which would tend to
pull the average loan amount of treatment group borrowers down after the premium cut. Indeed,
Table 6 indicates that treatment group mortgages and purchase prices dropped 7 to 9 percent, on
average, after January 26. However, when we control for borrower income and FICO scores, the
RD estimates for loan amount and purchase price are close to zero and statistically insignificant.
With the caveat that residual compositional effects may still be biasing our estimates downward,
we find no evidence that lower FHA premiums caused households to borrow and spend more,
conditional on getting a mortgage.
These results reflect RD estimates for the treatment group (FHA-likely borrowers) relative to the
control group (all other borrowers). However, if FHA-likely borrowers bid up house prices, that
might affect the prices and loan amounts in the control group, biasing the RD estimates toward
zero. To check for this issue, we restrict the sample to only treatment group borrowers and
estimate the discontinuity in loan size and purchase price without the control group. Results are
presented in Table 6. We again find no evidence of house price or loan size effects.
One possible explanation for the lack of an intensive margin response is binding underwriting
constraints. While the MIP cut reduced DTI ratios for any given FHA loan, LTV ratio limits
may still have bound. FHA loans have a maximum LTV ratio of 96.5 percent, and the median
LTV ratio among treatment group FHA borrowers in 2014 was 95.7 percent. Even if home
buyers would have liked to borrow more in response to the lower premiums, many had little
scope to do so without producing a larger down payment.
The FHA premium reduction could have led to a more gradual rise in home prices, which the RD
approach may not pick up. Therefore, in addition to these RD estimates, we also test if home
prices accelerated after the premium cut more rapidly in areas that are more reliant on the FHA.
In some neighborhoods, the FHA share of loans tends to be much higher than the national
26
average. If lowering interest rates drives up home prices by spurring housing demand, then the
reduction in FHA premiums may similarly drive up prices in areas where a greater portion of the
population relies on FHA financing.
First, we demonstrate that areas with higher pre-period FHA participation experienced a greater
demand shock following the premium reduction. To do so, we re-estimate equation (1)
separately for each of the 50 U.S. states and Puerto Rico. In Figure 11, we plot these state-
specific coefficients against the state’s 2014 FHA share of home purchase loans. There is a clear
positive correlation between the two, confirming that the jump in treatment group lending shown
in Figure 1 and Table 2 was concentrated in areas that were more FHA reliant prior to the
premium cut.
Next, we test if house prices began to grow faster after the FHA premium cut in census tracts
that had a higher 2014 FHA share (and therefore experienced a greater surge in home buying
demand). We estimate equations of the form:
∆ =
0
ℎ +
1
+
3
ℎ × + + (4)
where ΔP is local house price growth (in log points), FHAshare is the fraction of all home
purchase loans in 2014 that carried FHA insurance, and Post is an indicator for the period after
the premium cut. The vector θ contains a set of fixed effects described below. We compare
price growth in windows of 6, 12 and 24 months prior to the premium cut to matching post-cut
windows. FHA shares are observed in the HMDA data at the census tract level. For house price
data, we use the ZIP code level single-family home house price index from Zillow. Estimates of
house prices at the census tract level are produced by averaging across the price levels of ZIP
codes that intersect with the target tract, weighted by the fraction of housing units in that tract
that appear in each ZIP code.
Equation (4) describes a difference-in-differences estimator with a continuous measure of
treatment status (the FHA share). A key identification concern is that neighborhoods with high
FHA shares may experience different economic conditions and be on different price trends than
neighborhoods with low shares.
To deal with this issue, we try a number of specifications controlling for various fixed effects.
First, we include county-by-time period fixed effects. This specification absorbs any regional
27
differences in economic conditions that might affect high and low FHA share areas differently.
Second, we use a matching estimator to compare tracts to their peers with nearly identical pre-
trends in home price growth. We place each tract into buckets based on the growth rate in house
prices across 2014, with bin widths of a single percentage point, and then control for fixed
effects of these buckets interacted with the pre/post dummy. The final specification uses fixed
effects for the combination of time, county and price growth bins.
The coefficient of interest, β
3,
indicates how acceleration in house prices after the MIP reduction
correlates with the tract’s 2014 FHA share. Estimates of β
3
are presented in Table 7 for various
time windows. The FHA share is measured between 0 and 1, so the coefficients represent the
estimated difference in post-MIP cut log price growth between a hypothetical tract whose
population was completely reliant on FHA insurance to one whose population did not use FHA
insurance at all. Overall, the estimates do not provide strong evidence that FHA reliant areas
experienced more rapid price growth as a result of the FHA premium reduction. The estimates
in the second column suggest a modest positive effect after 12 and 24 months, but these are not
robust to matching on pre-trend growth, as seen in columns 3 and 4.
Our finding of an elastic demand response with little change in prices may be reconciled to some
extent by the mechanism outlined in Anenberg and Kung (2017). They argue that the average
time-on-market of homes for sale could absorb demand shocks from interest rates, with house
prices showing little change. In addition, our finding of no intensive margin response to the MIP
reduction may have mitigated any upward pressure on prices.
29
7.2. The Effect of the MIP Cut on Loan Performance
Earlier, we found that the reduced premiums affected the composition of the borrower pool by
pulling in lower-income and marginal borrowers. If marginal borrowers have a higher than
average propensity to miss payments, the overall delinquency rate could rise and act as a drag on
neighborhood home prices. However, at the same time, the reduced MIP lowers payments for all
29
Rappoport (2016) models the process by which interest rate subsidies get capitalized into house prices, offsetting
much of the benefit of the subsidy to borrowers.
28
new borrowers, which could help borrowers stay current. Thus, ex-ante, the overall effect of the
MIP cut on delinquency is ambiguous.
We test for an effect of the 50 basis point reduction in MIPs on delinquencies using the McDash
data, which tracks loan performance over time. We estimate (1) on the probability a payment for
a treatment-group loan is ever 30 days or more past due within the first 12 months after
origination. Results are presented in Table 8. We cannot reject the null hypothesis that there
was no change in the delinquency rate among the treatment group, despite the influx of new
borrowers and the lower insurance premiums. It is possible that these two opposing forces
cancel each other out, or that the net effect is simply too small to be detected.
8. Conclusion
This paper uses a sudden drop in the pricing of government-provided mortgage insurance to
identify how the volume of home buying responds to the cost of credit. Using a regression
discontinuity design and loan-level data, we find that a 50 basis point reduction in the FHA’s
annual mortgage insurance premium increased home purchase borrowing by FHA-likely
borrowers (those with below-average credit scores and less than a 20 percent down payment) by
about 14 percent. Further evidence suggests that the reduced premiums improved applicants’
debt payments-to-income ratios, and the easing of underwriting constraints along this dimension
was an important – but not the only – channel by which more lending occurred.
We also find heterogeneity in the borrowing response by income, with lower-income borrowers
exhibiting a strong response to the premium cut, and higher-income borrowers demonstrating
little or no response. Although we study the FHA market, many homebuyers outside the FHA
market (those getting VA-guaranteed loans and conventional, or non-government, loans) may
have similar liquidity positions and be responsive to interest rates. In 2014-2015, about 30
percent of non-FHA home buyers had incomes below the median of $60,000 for FHA borrowers;
roughly 45 percent made a down payment of less than 20 percent; and the distribution of DTIs
29
suggests many borrowers bump up against DTI constraints in the non-FHA market.
30
Thus, we
believe the evidence in this paper demonstrates that policies, including monetary policy, that
influence the cost of mortgage credit can have a significant and immediate effect on housing
demand. That said, the overall demand response to an interest rate shock that applies to all
households will be more muted than the response to the MIP cut we estimate, as our target
population contains a higher proportion of relatively low-income, low-wealth borrowers. In this
sense, our findings suggest that subsidizing FHA premiums may be more effective at increasing
home buying than subsidizing interest rates in general, as the FHA implicitly targets a borrower
population with more elastic demand. General equilibrium effects could also attenuate the
benefits or costs to borrowers of interest rate shocks as rate changes may be capitalized into
home values, although evidence provided in this paper and others in the literature suggest that
interest rates exert only weak influence over house prices. Furthermore, capacity constraints
could mitigate the effect of lower interest rates on home purchase lending, as discussed in Sharpe
and Sherlund (2016). Finally, our results suggest that home buying responses to policies that
tend to target higher-income households, like the mortgage interest deduction, may be quite
limited.
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Figure 1. Treatment Group Share of Home Purchase Loans by Week of Rate Lock
Note: Treatment group defined as borrowers with a FICO score less than 680 and an LTV above 80 percent. The
vertical line marks the week of January 26, 2015, the date of the FHA annual MIP reduction. Curve of best fit
overlaid on weekly data.
Source: Optimal Blue
35
Figure 2. Mortgage Rate and FHA Premium, 2001-2015
Source: Freddie Mac and HUD.
36
Figure 3. Count of Home Purchase Loan Originations for 1- to 4-Family, Owner-Occupied
Properties, by Week of Loan Application
Note: Vertical lines mark the weeks of January 26, 2013, 2014 and 2015.
Source: Data reported under HMDA.
37
Figure 4. FHA Share of Home Purchase Loans by Week of Loan Application
Note: The vertical line marks the week of January 26, 2015, the week of the FHA annual MIP reduction. Curve of
best fit overlaid on weekly data.
Source: Data reported under HMDA.
38
Figure 5. Treatment Group Share of Home Purchase Loans by Week of Loan Application
(HMDA/McDash Merge)
Note: The vertical line marks January 26, 2015, the date of the decrease in annual FHA MIP referenced in Table 1.
Estimated curve of best fit overlaid on weekly data.
Source: McDash Analytics and data reported under HMDA.
39
Figure 6. Average Time between Loan Application and Case Number Assignment, by
Week of Loan Application
Note: Vertical lines indicate the week January 26 for the years 2012-2015.
Source: HUD loan-level data and data reported under HMDA.
40
Figure 7. Treatment Group Share of Withdrawn Home Purchase Applications, by Week of
Loan Application
Source: Data collected under HMDA and Optimal Blue
41
Figure 8. Continuity of Other Economic Indicators
42
Figure 9. Distribution of DTI Ratios for FHA Home Purchase Loans
FICO Score < 620
FICO Score ≥ 620
Note: Sample densities in one-percentage point bins.
Source: HUD loan-level data.
43
Figure 10: Year-over-Year Log Growth in the Number of Home Purchase Applications, by
Week of Loan Application
2015
2014
Source: Data collected under HMDA
44
Figure 11: Correlation between Effect of FHA MIP Reduction on Treatment Group
Borrowing and 2014 FHA Share, by State
Note: Figure plots state-specific point estimates of the coefficient β
1
from equation 1. The red line plots a
linear fit of the estimate effect to the state’s proportion of FHA loans among its home purchase borrowing
in 2014.
Source: Optimal Blue and data collected under HMDA.
45
Table 1. Summary of Loan Level Data for 2014-15
Data Source
HMDA Optimal Blue
HMDA/Optimal
Blue Merge
HMDA/McDash
Merge
A. All Loans
Loan Amount ($, 000's)
244
236
241
241
(210)
(155)
(158)
(220)
FHA
0.24
0.3
0.09
0.21
(0.42)
(0.45)
(0.3)
(0.41)
Income ($, 000's)
101
97
117
(125)
(89)
(162)
LTV Ratio
89
87.7
84
(13.3)
(14.1)
(17.1)
FICO Score
719
730
740
(57)
(54)
(52)
N
5,865,166
1,574,184
542,794
1,679,119
B. FHA Loans
Loan Amount ($, 000's)
185
190
181
169
(97)
(97)
(84)
(87)
Income ($, 000's)
67
65
64
(40)
(39)
(38)
LTV Ratio
95.2
95.4
94.9
(5.5)
(4.8)
(16.5)
FICO Score
679
678
689
(45)
(44.8)
(44)
N
1,371,074
469,577
49,350
458,485
Note: Sample means shown. Sample standard deviations in parentheses.
46
Table 2: Regression Discontinuity Estimates of the Effect of the FHA
MIP Reduction on Treatment Group Share of Lending
Bandwidth (Weeks)
Year
Data Source
Macro controls
12
25
50
2015
Optimal Blue
No
0.021**
0.019**
0.012**
(0.006)
(0.005)
(0.003)
HMDA/McDash
No
0.015**
0.016**
0.013**
(0.004)
(0.003)
(0.002)
Optimal Blue
Yes
0.015**
0.018**
0.014**
(0.005)
(0.003)
(0.003)
HMDA/McDash
Yes
0.011*
0.014**
0.013**
(0.005)
(0.003)
(0.002)
2014
Optimal Blue
No
-0.004
-0.002
-0.005*
(0.004)
(0.004)
(0.003)
HMDA/McDash
No
0.004
0.006
0.002
(0.003)
(0.003)
(0.003)
2016
Optimal Blue
No
-0.006
0.006
0.004
(0.005)
(0.005)
(0.003)
Note: Table shows the estimated discontinuity at January 26, 2015 in the share of
home purchase loans going to the treatment group. Estimated placebo tests for
discontinuities on January 26 in 2014 and 2016 are also shown. Effects estimated
using a local linear regression and a triangular weighting kernel. Treatment
group share refers to the fraction of total home purchase loans for the borrower
had a FICO score below 680 and an LTV ratio between 80 and 100 percent.
Macro controls are the national unemployment rate, the yield on 1 year and 10
year treasury securities, and the value of the S&P 500 stock market index.
Standard errors, shown in parentheses, are adjusted for clustering at the weekly
level, calculated using the method of White (1980) and Froot (1989).
* p < 0.05
** p < 0.01
47
Table 3: Effect of FHA MIP Reduction on Treatment Group Share, by
Borrower Income
Bandwidth (Weeks)
Data Source
Borrower Income
12
25
50
Optimal Blue
Less than $46,001
0.005**
0.005**
0.006**
(0.002)
(0.002)
(0.001)
$46,001-$66,000
0.003*
0.004**
0.004**
(0.002)
(0.001)
(0.001)
$66,001-$96,000
0.002*
0.002*
0.002**
(0.001)
(0.001)
(0.001)
Greater than $96,000
-0.004
-0.002
-0.002
(0.002)
(0.002)
(0.001)
HMDA/McDash
Less than $46,001
0.008**
0.008**
0.005**
(0.002)
(0.001)
(0.001)
$46,001-$66,000
0.004
0.004**
0.003**
(0.002)
(0.001)
(0.001)
$66,001-$96,000
0.003
0.003**
0.003**
(0.002)
(0.001)
(0.001)
Greater than $96,000
0.0002
0.001
0.003**
(0.001)
(0.001)
(0.001)
Note: Table shows the estimated discontinuity at January 26, 2015 in the fraction of total
home purchase loans going to borrowers with FICO scores below 680 and LTV ratios
between 80 and 100 percent in each of the income categories. Standard errors, shown in
parentheses, are adjusted for clustering at the weekly level, calculated using the method of
White (1980) and Froot (1989).
* p < 0.05
** p < 0.01
48
Table 4: Effect of the FHA MIP Reduction on Contract Rates
Bandwidth (Weeks)
Outcome Variable
Underwriting Controls
12
25
50
Contract Rate (Percentage Points)
No
0.009
0.015
-0.002
(0.068)
(0.071)
(0.058)
Yes
0.002
0.011
-0.01
(0.025)
(0.017)
(0.012)
Note: Table shows the estimated discontinuity at January 26, 2015 in the contract rate on treatment group
loans, relative to the control group. Data is from Optimal Blue merged with data collected under the
Home Mortgage Disclosure Act. Effects estimated using a local linear regression and a triangular
weighting kernel. Treatment group refers to borrowers with a FICO score below 680 and an LTV ratio
between 80 and 100 percent. Control variables consist of flexible functions of borrower income and
FICO score. Standard errors, shown in parentheses, are adjusted for clustering at the weekly level,
calculated using the method of White (1980) and Froot (1989).
* p < 0.05
** p < 0.01
49
Table 5: Effect of the FHA MIP Reduction on Denial Rates, Average FICO Scores and
Application Volume
Bandwidth (Weeks)
Year
Outcome Variable
12
25
50
2015
Denial Rate Difference between Black and
Asian Applicants
-0.012**
-0.009**
-0.014**
(0.004)
(0.004)
(0.003)
FICO Score Difference between Black and
Asian Applicants
-7.36*
-4.91
-2.13
(2.72)
(2.55)
(1.84)
Log Total Loans (Seasonally Adjusted)
0.032
0.051**
(0.033)
(0.019)
Log Total Applications (Seasonally
Adjusted)
0.027
0.041*
(0.033)
(0.018)
2014
Denial Rate Difference between Black and
Asian Applicants
-0.002
-0.0005
0.0008
(0.006)
(0.004)
(0.003)
FICO Score Difference between Black and
Asian Applicants
5.28
1.80
-0.56
(4.61)
(3.38)
(2.37)
Log Total Loans (Seasonally Adjusted)
-0.0001
-0.003
-0.031
(0.110)
(0.058)
(0.034)
Log Total Applications (Seasonally
Adjusted)
0.006
0.006
-0.025
(0.110)
(0.058)
(0.034)
Note: Table shows the estimated discontinuity at January 26, 2015 in the outcome variable.
Estimated placebo tests for discontinuities on January 26 in 2014 and 2016 are also shown.
Effects estimated using a local linear regression and a triangular weighting kernel. Standard
errors, shown in parentheses, are adjusted for clustering at the weekly level, calculated using
the method of White (1980) and Froot (1989).
* p < 0.05
** p < 0.01
50
Table 6: Effect of the FHA MIP Reduction on Loan Amounts and Purchase Prices
Bandwidth (Weeks)
Outcome Variable
Include Control
Group?
Underwriting
Controls
12
25
50
Log Loan Amount
Yes
No
-0.089**
-0.070**
-0.074**
(0.016)
(0.014)
(0.012)
Yes
Yes
-0.027
-0.019
-0.018*
(0.020)
(0.013)
(0.009)
Log Purchase Price
Yes
No
-0.094**
-0.069**
-0.073**
(0.017)
(0.017)
(0.014)
Yes
Yes
-0.015
-0.004
0.001
(0.019)
(0.013)
(0.009)
Log Loan Amount
No
No
-0.089**
-0.064**
-0.045**
(0.019)
(0.014)
(0.012)
No
Yes
-0.016
-0.002
0.011
(0.018)
(0.012)
(0.008)
Log Purchase Price
No
No
-0.094**
-0.070**
-0.052**
(0.019)
(0.014)
(0.012)
No
Yes
-0.019
-0.006
0.006
(0.019)
(0.012)
(0.008)
Note: Table shows the estimated discontinuity at January 26, 2015 in the outcome variable for the
treatment group. Data is from Optimal Blue merged with data collected under the Home Mortgage
Disclosure Act. Effects estimated using a local linear regression and a triangular weighting kernel.
Treatment group refers to borrowers with a FICO score below 680 and an LTV ratio between 80 and
100 percent, while the control group is all others. Control variables consist of flexible functions of
borrower income and FICO score. Standard errors, shown in parentheses, are adjusted for clustering
at the weekly level, calculated using the method of White (1980) and Froot (1989).
* p < 0.05
** p < 0.01
51
Table 7: Effect of Local FHA Share on Census Tract House Price Growth after
MIP Reduction
Time Window
(1)
(2)
(3)
(4)
6 Months
-0.002
-0.00001
-0.001
-0.001
(0.003)
(0.002)
(0.002)
(0.001)
12 Months
0.002
0.011**
0.0001
0.0002
(0.005)
(0.004)
(0.0001)
(0.0002)
24 Months
0.014
0.030**
-0.016
0.004
(0.014)
(0.009)
(0.013)
(0.005)
County-by-Time Fixed Effects
X
Pre-Period Growth Rate-by-Time Fixed
Effects
X
County-by-Pre-Period Growth Rate-by-Time
Fixed Effects
X
N=55,743
Note: Table shows the estimated influence of the share of loans in 2014 that used FHA
insurance on the subsequent growth in house prices at the census tract level. Prices are
measured in logs. The FHA share takes values between 0 and 1. The time window refers to the
number of months before and after January 2015 house price growth is measured over.
Standard errors, shown in parentheses, are adjusted for clustering at the county level, calculated
using the method of White (1980) and Froot (1989).
* p < 0.05
** p < 0.01
52
Table 8: Effect of the FHA MIP Reduction on
Delinquencies
Bandwidth (Weeks)
12
25
50
Delinquency Rate for
Treatment Group
0.009
0.0002
-0.004
(0.005)
(0.006)
(0.004)
Note: Table shows the estimated discontinuity at January
26, 2015 in the delinquency rate of treatment group
loans. Effects estimated using a local linear regression
and a triangular weighting kernel. Treatment group
refers to borrowers with a FICO score below 680 and an
LTV ratio between 80 and 100 percent. Delinquency
rate is the fraction of loans with a payment that was 30
days or more past due within 12 months after origination.
Standard errors, shown in parentheses, are adjusted for
clustering at the weekly level, calculated using the
method of White (1980) and Froot (1989).
* p < 0.05
** p < 0.01
