The Causal Effects of Credit Supply on Housing Prices
Aurel Hizmo
Edward Kung
September 2, 2013
Abstract
We quantify the separate causal effects of changes in interest rates and changes in
underwriting standards on house prices. The first contribution is to construct a new
direct measure of underwriting standards based on the maximum DTI ratio a borrower
could obtain conditional on his/her FICO score and on market characteristics. We then
use the dissagregate nature of our underwriting standards measure to construct Bartikstyle instruments for changes in this measure and interest rates. Our IV estimates show
that a one percent change in the average maximum DTI that banks are willing to lend,
increases prices by 2.6%, while a one percent change in interest rates leads to a four
percent drop in house prices. These effects are stronger after the financial crisis and
are stronger in areas where housing supply is less elastic.
1
Introduction
In the wake of the financial and housing crisis of 2008, there has been a push to better understand the role of credit markets in determining house prices. Traditionally, policymakers
have focused most on the role of interest rates. The mechanism that leads from interest rates
to house prices is clear: lower interest rates lead to lower borrowing costs on mortgages and
hence higher demand, ceteris paribus, for owner-occupied housing. Recently, more attention
is also being drawn to the role of underwriting standards (for example, the down payment
required for approval of a loan). The ease or tightness of underwriting standards determines
the degree to which a prospective buyer may leverage the purchase of their home. To the
extent that there are buyers whose access to credit is rationed in equilibrium, a loosening of
underwriting standards would increase the demand for housing and translate to higher house
prices. Which dimension, interest rates or underwriting standards, has a greater marginal
effect on house prices is an empirical question. The answer will depend on the reason that
1
a marginal buyer has not bought a bigger home, or a marginal renter has decided not to
buy. Is it because borrowing costs are too high or is it because they could not get a loan of
the desired size? The goal of this research agenda is to empirically address these questions
in a rigorous and convincing way. It is a question of both academic and practical interest:
academic because it advances our understanding of the interactions between credit markets
and real markets, and practical because it informs policymakers of the relative strengths and
weaknesses of interest rates versus underwriting standards as policy variables. This point has
been emphasized by Geanakoplos (2003, 2010, 1997), who develops the theory of endogenous
collateral requirements and argues that leverage ratios play an especially important role in
times of price collapse and should be monitored closely by policymakers.
The current literature on the role of credit markets in housing has not been able to
satisfactorily address the relative role of interest rates versus underwriting standards. As
noted in Glaeser, Gottlieb, and Gyourko (2010), there are two main challenges to overcome in
order to understand the relative role of mortgage interest rates and underwriting standards.
The first is that there are few direct measures of underwriting standards that accurately
reflect a potential borrower’s true constraints. To understand this problem, consider three
potential measures of underwriting standards: the conforming loan limit, the observed loanto-value ratios of newly originated loans, or the approval rate of loan applications. The
conforming loan limit is problematic as a measure of collateral constraints because there is
little variation in it across time and space, and because for many individuals it does not
accurately reflect the menu of loans that are available to them; many borrowers willingly
take out loans greater than the conforming loan limit in exchange for a higher interest
rate. Observed loan-to-value ratios are problematic because at least a subset of buyers are
borrowing less than they could have, causing observed LTVs to understate true borrowing
limits. Finally, observed approval rates are problematic because the decision of what loan to
apply for is endogenous (potential borrowers are unlikely to apply for loans for which they
are likely to be rejected) and can overstate the true approval rate for any given combination
of borrower and loan characteristics.
The second challenge is the simultaneity between house prices and credit market conditions. Simultaneity arises due to the unique nature of housing as collateral for loans. House
prices, and in particular expectations of house price growth, are important determining factors of interest rates and underwriting standards. Interest rates and underwriting standards
in turn influence demand for housing which affects house prices and house price expectations.
Any study which seeks to estimate the effects of interest rates and underwriting standards
on house prices therefore needs a source of exogenous variation to credit market conditions.
Moreover, in order to separately disentangle the direct effect of interest rates versus the
2
direct effect of underwriting standards, one needs two sources of exogenous variation which
orthogonally impact interest rates and underwriting standards.
The current paper is the first one in the literature to tackle both of these challenges simultaneousy. To overcome the first challenge, we propose a definition of underwriting standards
based on the maximum debt-to-income ratio loan a borrower could obtain conditional on his
or her FICO score and conditional on market level variables such as interest rates and house
prices. The data we use to construct our measures come from the Freddie Mac Single Family
Loan-Level Dataset. This is a dataset that includes the universe of fully amortizing, 30-year
fixed rate single family mortgages purchased or guaranteed by Freddie Mac with origination
dates between 1999Q1 and 2011Q4.1 We construct our measure of underwriting standards
as the answer to an analogous question: “For a given level of credit score (FICO), what is
the highest level of debt-to-income ratio (DTI) that a borrower with that credit score can
obtain?” We shall therefore be thinking of the credit score as an input, the debt-to-income
ratio as an output, and the underwriting standards as the production function. The shape
of the maximum DTI boundary we estimate contains information that supports the idea
that this boundary is determined by credit supply rather than credit demand. First of all,
the boundary is upward sloping. This observation is in line with the idea that banks make
higher DTI loans to people with higher FICO scores. It doesn’t seem plausible that this
slope is driven by demand since it seems unlikely that people with marginally higher FICO
scores would want to spend a higher proportion of their income in housing. One would
either expect FICO score to be uncorrelated with the share of housing expenditure, or to be
negatively correlated with it if FICO is positively correlated with household wealth. In the
latter scenario, higher FICO individuals would tend to be wealthier and would need to lever
themselves less than poorer individuals. This would should lead to a negative slope rather
than the positive slope we observe in the data. Secondly, the boundary we estimate is very
sharp. There is a large amount of data points clustered around the boundary, also indicating
that the boundary is likely to be a constraint rather than result from credit demand.
To overcome the second challenge, we need a source of exogenous variation in local
underwriting standards. We exploit the disaggregated nature of our measure for underwriting
standards by using it to construct instrumental variables for msa-by-year level regressions of
house prices on underwriting standards. The spirit of the instruments we create is closely
1
The dataset is obviously not representative of the mortgage market as a whole. Our constructed measure
therefore cannot be said to representing the minimum underwriting standard that borrowers face, but rather
the underwriting standards they would face on a conforming 30-year fixed rate mortgage. Nevertheless, we
will find that even this measure has explanatory power in the determination of house prices. We plan to
extend this paper in the near future to include data on non-agency mortgages, which would then allow us
to construct underwriting measures that are more representative of the mortgage market as a whole.
3
related to Bartik instruments used in labor economics. The main identification idea is to
use the fact that shocks to the national credit markets are exogenous to the local conditions
in one particular metropolitan area. Additionally, a shock to national credit markets will
have different effects on different metropolitan areas. If, for example, willingness to lend
to subprime borrowers increases nationally, the impact of such change will be greater in
MSA’s where there are a large number of people with low credit scores. Controlling for
what happens to the credit markets as a whole through year fixed effects, we can exploit
the cross-sectional variation in how these shocks affect different locations. More specifically,
to compute the instrument for a particular MSA, we first create a national measure as the
average (across different markets) maximum DTI a borrower with a particular FICO, while
excluding the contribution of the MSA in question. We then construct our instrument by
weighting this national measure according to the FICO distribution of the population in the
MSA in question. This instrument can be interpreted as the part of the local credit supply
shocks that can be attributed to national supply shocks and as such it is uncorrelated with
local conditions. We repeat the same procedure to construct an instrument for local interest
rates, allowing us to identify our parameters of interest.
Using the instrumental variables approach described above we estimate the causal effect
of underwriting standards on local house prices. In our main specification we regress house
prices on the instrumented weighted average maximum DTI, the instrumented weighted
interest rates, on local fundamentals while controlling for year and metro fixed effects. We
find that a one percent change in the population weighted maximum DTI in a MSA leads
to a 2.67 percent change in local house prices holding constant everything else. On the
other hand, one percent change in the level of interest rates will lead to a drop of about
four percent in local house prices. We also conduct a similar analysis for the growth rates
in our variables of interest. In these regressions we find that a one percent change in the
growth rate of the weighted maximum DTI in one particular area will lead to a 0.422 percent
change in the growth rate of local house prices holding constant everything else. Also, a one
percent change in the growth rate of interest rates will lead to a drop of about 0.8 percent
in the growth rate of local house prices. These findings are not only interesting because
they confirm what one would expect, but also because they quantify the separate effects of
underwriting standards and interest rates on house prices. To our knowledge this is the first
paper to do so in the literature.
To test the robustness of our findings, we also confirm that the effects that we identified
are not driven by the financial crisis. We interact our variables of interest with dummy
variables for the crisis and the result stand almost identically. While, as one would expect,
the effects became stronger during the crisis, they were present even in the precrisis period.
4
We also explore the cross-sectional variation in the size of the coefficients. One plausible
hypothesis is that a shock to underwriting standards should have more of a price effect in
areas where housing supply is less elastic than in areas where it is more elastic. To test
this, we interact our variables of interest with a measure that captures how difficult it is to
construct new homes in an area: the Wharton’s index for Land Regulation. The interaction
with the supply elasticity proxy is positive, indicating that a shock to credit condition are
will lead to higher prices in areas where it is more difficult for supply to react. The same
pattern also emerges when we look at the effect of the Weighted Rate: a shock to interest
rates has a higher effect in places where it is difficult to increase the supply of housing.
The rest of the paper is organized as follow: section 2 presents and constructs our new
measure of underwriting standards. Section 3 discusses our estimation strategy and presents
our main estimation results and section 4 concludes.
2
2.1
A new measure of underwriting standards
Methodology
The first goal of this paper is to construct an index that can reasonably be interpreted as
a measure of mortgage underwriting standards, free of demand side factors. To this end,
commonly used proxies for underwriting standards, such as average LTVs, average approval
rates, or subprime shares in a market are inadequate because they reflect both credit supply
and housing demand. Instead of using such population aggregates, our method will draw
from the literature on estimating nonparametric production frontiers, particularly the robust
nonparametric method of Cazals, Florens, and Simar (2002) (henceforth CFS). The frontier
estimation literature is an appropriate place to begin because it is interested in answering the
question: “Given a certain level of inputs, what is the maximum output that is attainable?”
Applied to mortgages, we construct our measure of underwriting standards as the answer to
an analogous question: “For a given level of credit score (FICO), what is the highest level
of debt-to-income ratio (DTI) that a borrower with that credit score can obtain?” We shall
therefore be thinking of the credit score as an input, the debt-to-income ratio as an output,
and the underwriting standards as the production function.
To formalize this idea, suppose that the population of mortgage originations with FICO X
and DTI Y is described by distribution FX,Y (x, y). Our measure of underwriting standards
for credit score x is given by:
Ï (x) = sup {y|P (Y Ø y|X Æ x) > 0}
5
(1)
In words, Ï (x) is the highest y such that a person with a FICO x or lower is observed with
a DTI greater than y, with positive probability. 2 Let us now define
Ïm (x) = E [max {Y1 , . . . , Ym } |X Æ x]
(2)
as the expected maximum of DTI out of m draws, where the draws are conditioned on FICO
less than x. The construction of Ïm (x) is useful because it approaches Ï (x) as m æ Œ,
and because it has an easy-to-compute finite sample analogue. Specifically, suppose we have
n random draws from the population of mortgage originations: {xi , yi }ni=1 . Following CFS,
we construct:
n
1ÿ
I [yi Æ y, xi Æ x]
n i=1
Ŝn (x, y) =
Ŝn (x, y)
Ŝn (x̄, y)
Ŝc,n (y|x) =
(3)
(4)
which respectively are the empirical analogs of P (Y Æ y, X Æ x) and P (Y Æ y|X Æ x) (x̄
is the maximum of the support of X). Noting that:
P (max {Y1 , . . . , Ym } Æ y|X Æ x) = P (Y Æ y|X Æ x)m
(5)
we can express the empirical analogs of Ï (x) and Ïm (x) as:
Ó
Ô
Ï̂n (x) = sup y|Ŝc,n (y|x) > 0
ˆ Ï̂n (x) Ë
Èm
Ï̂m,n (x) = Ï̂n (x) ≠
Ŝc,n (u|x) du
0
(6)
(7)
Equations (3)-(7) tells us how to compute Ï̂m,n (x) non-parametrically from the data. CFS
establish the asymptotic properties of the estimator, but the key point to note is that Ï̂m,n (x)
Ô
is a n-consistent estimator for Ïm (x). Ï̂m,n (x) is therefore a consistent estimator of the
expected maximum DTI available to a borrower with FICO less than x, out of m draws. As
2
One complication in our setting is the possibility that persons with FICO x or lower are not observed
with DTI higher than Ï (x) due to reasons unrelated to credit supply. For example, borrowers with high
FICO’s may not be observed obtaining high DTI’s because they do not want high DTI loans, not because
they are unable to obtain them. This possibility is not typically a concern in production frontier estimation
because free disposal is assumed, and therefore a firm would always produce as much as possible for a given
level of input. Although free disposal cannot be assumed our setting, in the appendix we give conditions
under which we may still interpret Ï (x) as the supply-driven maximum DTI for FICO x. We will also show
be able to show that features of our data appear consistent with those assumptions.
6
m grows large, Ï̂m,n (x) æ Ï̂n (x), which means the estimator approaches the largest DTI
observed out of observations with FICO less than x. The reason to use a finite m is that
choosing a smaller m makes the estimator more robust to outliers, will still maintaining the
interpretation as an expected maximum out of m draws.3
There are a number of advantages to estimating Ïm (x), the expected maximum DTI
that borrowers with FICO less than x could obtain. First, it is readily interpretable as
a credit constraint that borrowers face, imposed upon them by lending standards in the
credit market. In comparison, a measure such as the average DTI that borrowers with
FICO less than x actually obtain is also affected by borrowers’ demand for credit. A second
advantage of using Ïm (x) is that it is a disaggregated measure of underwriting standards. It
therefore allows us to measure borrowing constraints separately for borrowers with different
characteristics. These measures can then be used as inputs into a structural model that allows
for rich heterogeneity in individual agents’ credit constraints. In the current paper, we exploit
the disaggregated nature of our measure by using it to construct Bartik-style instrumental
variables for msa-by-year level regressions of house prices on underwriting standards. We
elaborate more on this point in section 3.
2.2
2.2.1
Construction of the underwriting measure
Estimation of the maximum DTI boundary
The data we use to construct our measures come from the Freddie Mac Single Family LoanLevel Dataset. This is a dataset that includes the universe of fully amortizing, 30-year fixed
rate single family mortgages purchased or guaranteed by Freddie Mac with origination dates
between 1999Q1 and 2011Q4.4 There are a total of about 16 million unique loans in the
dataset. The dataset includes many details about the loan, including the FICO score of the
borrower and the original DTI of the loan. The dataset also includes date of origination
and location of the property, down to 3-digit zip code. We will construct our measures
Ïmjt (x) separately for each MSA j and each year t, with m = 1000, using the method
3
Our exposition of the estimator has focused on estimating a single input, single output production
frontier. The method is easily generalizable to allow multiple inputs and multiple outputs. For example,
a full specification of the underwriting function may include all characteristics of the collateral and of the
borrower as inputs, and all characteristics of the mortgage loan as outputs. However, the resulting frontier
is a higher dimensional object which is more difficult to summarize for use in subsequent analysis. For now,
in this paper, we focus on FICO-DTI frontier.
4
The dataset is obviously not representative of the mortgage market as a whole. Our constructed measure
therefore cannot be said to representing the minimum underwriting standard that borrowers face, but rather
the underwriting standards they would face on a conforming 30-year fixed rate mortgage. Nevertheless, we
will find that even this measure has explanatory power in the determination of house prices. We plan to
extend this paper in the near future to include data on non-agency mortgages, which would then allow us
to construct underwriting measures that are more representative of the mortgage market as a whole.
7
outlined in section 2.1 above. In order to focus on a more homogeneous set of loans in
terms of risk characteristics, we use only loans with original loan-to-value ratio between 60
to 100%. Cutting the sample in this way does not have a significant effect on our estimates
for underwriting standards, because most of the data already lies in this range of LTV.
Because our constructed underwriting measures are two-dimensional objects, it is easier
to show them in pictures than in tables. Figures 1-3 show our constructed measures for three
MSAs: Los Angeles, Phoenix and Dallas, for all the years in our data. Superimposed on
our measures of underwriting standards are scatter plots of the data used to construct the
measures. It is easy to see from the tables how our measure forms an envelope around the
data that can be interpreted as the maximum DTI an individual with a certain FICO could
obtain. Reassuringly, the envelope formed around the data is upward sloping with respect to
FICO, which is consistent with the envelope representing a credit constraint imposed from
the supply side. From these figures, a number of observations bear commenting.
First, the measure assigns a value of 0 to FICO scores in which no originations are
observed. One could interpret this to mean that borrowers with these credit scores were
unable to obtain conforming loans in these time periods. According to this interpretation,
it would appear that underwriting standards for low-FICO borrowers on conforming loans
were loosest in the earliest years of our sample, from 1999 to 2003, and then tightened later
in the sample, with especially sharp tightening occurring in 2009 and 2010. An alternative
interpretation would be that low-FICO borrowers migrated away from conforming loans in
the 2004-2006 period and were increasingly in the market for non-agency loans. Currently,
without additional data from the non-agency side of the market, we are unable to distinguish
between the two interpretations. For this reason, in later sections of the paper we will focus
our analysis on the underwriting measure for higher FICO borrowers. Nevertheless, these
figures demonstrate the importance of extending our analysis to include data on non-agency
loans.
A second important observation about figures 1-3 is that there is little heterogeneity
in the underwriting measure across metros, especially at very low and very high FICOs.
This suggests that underwriting standards, at least for the conforming market, may be
set nationally without regard to local housing market conditions. Despite this, we should
note that nationally set underwriting standards may still affect different cities differently,
depending on the FICO composition of its residents. Moreover, there is substantially more
cross-sectional variation in the changes to the underwriting standard over time, especially
for borrowers with FICO between 600 and 700, than appears from simple visual inspection
of the graphs. This can be more easily seen in the next subsection when we aggregate this
data in a single index for each city.
8
The shape of the maximum DTI boundary in figures 1-3 also contains information that
supports the idea that this boundary is determined by credit supply rather than credit
demand. First of all, notice that the boundary is upward sloping, especially for the lower
to mid range of the FICO scores. This observation is in line with the idea that banks make
higher DTI loans to people with higher FICO scores. It doesn’t seem plausible that this
slope is driven by demand since it seems unlikely that people with marginally higher FICO
scores would want to spend a higher proportion of their income in housing. One would
either expect FICO score to be uncorrelated with the share of housing expenditure, or to
be negatively correlated with it, if FICO is positively correlated with household wealth. In
that scenario higher FICO individuals would tend to be wealthier and would need to lever
themselves less than poorer individuals. This would should lead to a negative slope rather
than the positive slope we observe in the data. Secondly, notice that the boundary is very
sharp. There is a large amount of data points clustered around the boundary, also indicating
that the boundary is likely to be a constraint.
2.2.2
Construction of the measure of the underwriting standards
In the subsection above we show that we can estimate a nonparametric function for the
maximum DTI that a person i in market j at time t with a particular FICO score can get:
DT¯Ijt = Ïjt (F ICO)
There is many ways to create measures of underwriting standards that summarize the information contained in function Ïjt . One way to construct a measure is to take the weighted
average of maximum DTI over the local FICO distribution:
Ujt =
ÿ
F ICO
Ïjt (F ICO) · sjt (F ICO)
where we are weighting the function fjt according to the share of people in market j at
time t that have a particular FICO score sjt (F ICO). Therefore this measure has the clear
interpretation as the weighted average of the maximum DTI that the local population can
get. This calculation allows us to create a time series for each metropolitan area. The result
from such procedure is shown for a few cities in figure 4.
In table (1) we explore how our measure, the population weighed maximum DTI, correlates with local fundamentals and how it is different from a more naive measure of supply,
such as the average DTI. In specification (1) we regress the log weighted max DTI on log
rents, unemployment and wages and also include MSA fixed effects. Here we can see that
9
Figure 1: Underwriting Measures for Los Angeles, 1999-2011
Note: These figures show our constructed underwriting measures from 1999 to 2011, alongside the
scatter plots of the data used to create the measures. The x axis is FICO and the y axis is DTI. The
interpretation of the underwriting measure is the expected maximum DTI that would be observed
for borrowers with FICO less than x, out of 1,000 draws.
10
Figure 2: Underwriting Measures for Dallas, 1999-2011
Note: These figures show our constructed underwriting measures from 1999 to 2011, alongside the
scatter plots of the data used to create the measures. The x axis is FICO and the y axis is DTI. The
interpretation of the underwriting measure is the expected maximum DTI that would be observed
for borrowers with FICO less than x, out of 1,000 draws.
11
Figure 3: Underwriting Measures for Phoenix, 1999-2011
Note: These figures show our constructed underwriting measures from 1999 to 2011, alongside the
scatter plots of the data used to create the measures. The x axis is FICO and the y axis is DTI. The
interpretation of the underwriting measure is the expected maximum DTI that would be observed
for borrowers with FICO less than x, out of 1,000 draws.
12
Figure 4: The Average Maximum DTI Underwriting Standards Index
100
Underwriting Index
110
120
130
140
The Underwriting Index (=100 in year 2000)
2000
2005
year
Dallas, TX
Miami, FL
2010
Los Angeles, CA
Phoenix, AZ
13
Table 1: Explaining Underwriting Measures with Market Fundamentals
Log Weighted Max DTI
Log Average DTI
(1)
(2)
(3)
(4)
0.301***
-0.000319
0.417***
0.329***
(0.0466)
(0.0324)
(0.0336)
(0.0240)
-0.00534
-0.177***
0.00823*
(0.00537)
(0.00674)
(0.00388)
(0.00496)
-0.0193
0.00963
0.0952***
0.0815***
(0.0373)
(0.0284)
(0.0266)
(0.0209)
MSA F.E.
Yes
Yes
Yes
Yes
Year F.E
No
Yes
No
Yes
N
1909
1909
2088
2088
No. MSA
232
232
258
258
R2 within
0.200
0.733
0.649
0.876
R2 between
0.284
0.0993
0.273
0.464
R2 overall
0.200
0.345
0.301
0.574
Log Rent
Log Unemployment -0.0861***
Log Wage
Note - The dependent variable for the first two columns is the logarithm of the average
maximum DTI for a particular MSA. The sample consists of annual data from 1999 to 2011.
The clustered robust standard errors are given in parentheses.
ú
statistical significance at the 90% level
úú
statistical significance at the 95% level
úúú
statistical significance at the 99% level
14
our measure is correlated with rents and negatively correlated with local unemployment.
Similar correlations can be seen in column (3) where the dependend variable is the average
DTI. In specification (2) and (4) we include year fixed effects in order to take out any national trends. From these specifications we can see that once we control for national trends,
our measure is not correlated with market fundamentals anymore, while the average DTI
still is. Comparing the coefficients reveals that the coefficients in in specification (2) are
very economically small and not statistically different from zero, while those in specification
(4) are economically larger and statistically significantly different from zero. This finding is
consistent with the idea that the weighted maximum DTI measure captures credit supply,
which is mostly determined at a national level, while the log average DTI also incorporates
the effects of local credit demand which vary by MSA.5
3
Estimates of the effect of underwriting standards on
house prices
3.1
Model and Identification Strategy
The regression we want to run is:
pjt = –Ujt + —rtj + Xjt “ + dj + dt + Ájt
(8)
where pjt is the log house price in metro j at time t, U is a measure of the underwriting
standards, r is a measure of local log interest rates, and Xjt are additional controls. The
coefficient – here can be interpreted as the percent change in prices for a one percent change
in underwriting standards. Ultimately we want to get a sense for the sizes of the parameters
– and —.
We could also run a similar regression in percent changes:
pjt = – Ujt + — rtj + Xjt “ + dj + dt + Ájt
(9)
Here – can be interpreted as the percent change in the growth rate of prices for a one percent
change in the growth rate of the underwriting standards.
In order to run regression (8) we need a measure for underwriting standards and interest
rates that:
5
Notice that this does not mean that there is no cross-sectional or time-series differences in the weighted
average maximum DTI. Such differences can be seein in Figure (4).
15
1. Captures the supply side of credit rather than the demand side
2. Has exogenous variation, or in our regression is not correlated with Ájt
In the next subsection we describe how we could describe such an instrument. The spirit of
the instruments we create is closely related to Bartik instruments used in labor economics.
The main identification idea is to use the fact that shocks to the national credit markets
are exogenous to the local conditions in one particular metropolitan area. Additionally, a
shock to national credit markets will have different effects on different metropolitan areas.
If, for example, willingness to lend to subprime borrowers increases nationally, the impact
of such change will be greater in MSA’s where there are a large number of people with low
credit scores. Controlling for what happens to the credit markets as a whole through year
fixed effects, we can exploit the cross-sectional variation in how these shocks affect different
locations as exogenous shocks to local credit supply.
3.1.1
Construction of the instrument
We need to construct two instruments: one for the maximum DTI and one for interest rates.
The construction of the index is identically therefore we only discuss the construction of the
maximum DTI index here.
Suppose that we have estimated a nonparametric function for the maximum DTI that a
person i in market j at time t with a particular FICO score can get:
DT¯Ijt = Ïjt (F ICO)
For each MSA i, we can average this function over all the different markets to get a national
measure of underwriting standards while excluding the contribution of the MSA in question:
J
Ë
È
1ÿ
E≠i DT¯ Iit =
Ïjt (F ICO) · 1(i”=j) = gt≠i (F ICO)
J j=1
This function will change over time depending on the credit markets demand for different
credit quality loans. We can interpret this measure as being related to the demand by
investors in capital markets for different credit product types. Any shock to preferences of
investors to hold a particular mortgage type will be reflected in the changes in the shape of
gt≠i ().
A shock to the national credit markets will affect each market differently: if there is an
increase in demand for product types with FICO<700 then the areas with populations with
such FICO scores should benefit the most. We construct our instrument as the local effect
16
that shocks to the national underwriting standards will have. To do this first we compute:
¯ I I = gt≠j (F ICOjt ) · sjt (F ICO) = g I (F ICO)
DT
jt
jt
where gt≠j is the national measure of the credit standards calculated while excluding market
j, and sjt (F ICO) is the share of the population in market j at time t that has a particular
FICO score.
All is left to do now is to aggregate the information in the function fjtI () into one measure
for underwriting standards:
UjtI =
ÿ
I
gjt
(F ICO)
F ICO
Notice that this is a valid instrument for Ujt in regression (8). Since we are including time
specific fixed effects, our estimates are identified from differences from a national trend. Any
shocks to UjtI are orthogonal to what is happening in the particular market j at time t and
should be uncorrelated with the error term in our regression. We construct the instrument
I
for interest rates rjt
similarly using the same procedure.
3.2
Results
In this section we present instrumental variables estimates of equations (8) and (9). Table (2)
presents the results for regressions in log levels for equation (8). The regression is estimated
using data from 1999-2011 for an unbalanced panel of MSA’s. The independent variable in
this regression is the log of house prices. All the independent variables are also in logs. We
instrument for the Weighted Max DTI variable (Ujt ) and for the Weighted Rate (rjt ) by
I
using the proccedure described in the previous subsection (the instruments are UjtI and rjt
respectively). In specification (5) we present our main result. Specification (5) controls for
year and MSA fixed effects as well as for local fundamentals such as the log rent, wages and
unemployment rates. In this regression we find that a one percent change in the weighted
maximum DTI in one particular area will lead to a 2.67 percent change in local house prices
holding everything else constant. On the other hand, one percent change in the level of
interest rates will lead to a drop of about four percent in local house prices. Both of these
estimates are statistically significantly different from zero at the 99% level. We also notice
that the fundamentals included in this regression also enter significantly with the expected
signs.
In specifications (1) to (4) we include first only year fixed effects, then metro fixed effect
17
and then the fundamentals progressively. In all of these cases the magnitude of the coefficients
of interest varies, however it is always of the expected sign and it is statistically different from
zero. In specifications (6)-(8) we include additional variables that are potentially endogenous
to see how our coefficients change. Even when we include variables such as average interest
rates, average DTI and average FICO, our coefficients remain statistically significant and
the magnitude does not change significantly. We take this as evidence for the robustness of
the results.
Table (3) repeats the same excercise as the previous table except that all the variables are
not in growth rates. Our main results are presented in specification (5). This specification
controls for year and MSA fixed effects and also includes as controls the growth rates in
rents, wages and unemployment. In this regression we find that a one percent change in
the growth rate of the weighted maximum DTI in one particular area will lead to a 0.422
percent change in the growth rate of local house prices holding everything else constant. On
the other hand, one percent change in the growth rate of interest rates will lead to a drop
of about 0.8 percent in the growth rate of local house prices. Both of these estimates are
statistically significantly different from zero. We also notice that the fundamentals included
in this regression also enter significantly with the expected signs.
In specifications (1) to (4) of table (3) we include first only year fixed effects, then metro
fixed effect and then the fundamentals progressively. In all of these cases the magnitude
of the coefficients of interest varies, however it is always of the expected sign and it is
statistically different from zero. In specifications (6)-(8) we include additional variables
that are potentially endogenous to see how our coefficients change. Even when we include
variables such as average interest rates, average DTI and average FICO, our coefficients
remain statistically significant and the magnitude does not change significantly.
3.3
Robustness and Alternative Explanations
In this subsection we explore the robustness of our findings. First we explore whether our
results are mainly driven by the financial crisis. Secondly we want to explore cross-sectional
heterogeneity in the magnitude of our coefficients.
Specifications (1) and (2) of Table (4) reproduce our main findings corresponding to
specifications (5) and (8) in table (2). In specification (3) we interact our variables of interest
with indicator variables for the financial crisis. The coefficient on Weighted Max DTI is still
statistically significant and not different from the baseline specification (1). The interaction
with the crisis dummy is positive, indicating that credit condition became more important
during the crisis, although this is not statistically significant. The coefficient on Weighted
18
Table 2: IV Estimates of the Effect of Underwriting Standards on Housing Prices
Weighted Max DTI
Weighted Rate
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
1.697***
7.913***
4.157***
3.186***
2.664***
2.701***
2.911***
2.677***
(0.248)
(1.413)
(0.819)
(0.715)
(0.586)
(0.573)
(0.791)
(0.772)
-4.329*** -8.582*** -5.441*** -4.497*** -4.012***
(0.297)
(1.149)
Rent
-3.971*** -4.197*** -3.212***
(0.725)
(0.645)
(0.541)
(0.547)
(0.748)
(0.829)
1.397***
1.016***
1.137***
1.149***
1.192***
1.237***
(0.204)
(0.171)
(0.145)
(0.148)
(0.175)
(0.182)
1.075***
0.520***
0.507***
0.511***
0.440***
(0.181)
(0.162)
(0.161)
(0.166)
(0.156)
Wage
Unemployment
-0.300***
-0.296*** -0.293*** -0.260***
(0.0357)
(0.0348)
(0.0363)
(0.0338)
-0.781
-0.564
-1.570**
(0.590)
(0.736)
(0.778)
-0.163
-0.355
(0.260)
(0.227)
Avg. Rate
Avg. DTI
Avg. FICO
-4.621***
(1.135)
Metro F.E.
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year F.E
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N
2043
2029
1895
1895
1895
1895
1895
1895
220
218
218
218
218
218
218
0.379
0.568
0.669
0.665
0.638
0.681
0.154
0.351
0.313
0.327
0.326
0.321
0.336
0.159
0.317
0.295
0.346
0.345
0.334
0.361
No. MSA
R2 within
R2 between
R overall
2
0.386
Note - All the variables in this regression are in logs. The dependent variable is the log of the FHFA house price index. The average
max DTI and weighted interest rates are instrumented with a Bartik type instrument. The sample consists of annual data from 1999 to
2011. The clustered robust standard errors are given in parentheses.
ú
statistical significance at the 90% level
úú
statistical significance at the 95% level
úúú
statistical significance at the 99% level
19
Table 3: IV Estimates of the Effect of Growth in Underwriting Standards on the Growth of Housing Prices
Weighted Max DTI
Weighted Rate
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0.904***
0.462*
0.339
0.429*
0.422*
0.820***
1.050***
0.916***
(0.348)
(0.281)
(0.272)
(0.235)
(0.234)
(0.256)
(0.310)
(0.304)
-1.391*** -0.931*** -0.775*** -0.908*** -0.800***
(0.335)
(0.264)
Rent
-1.159*** -1.384*** -1.198***
(0.262)
(0.230)
(0.230)
(0.247)
(0.294)
(0.292)
0.421***
0.457***
0.509***
0.446***
0.505***
0.408**
(0.159)
(0.136)
(0.151)
(0.165)
(0.175)
(0.166)
0.877***
0.599***
0.641***
0.634***
0.582***
(0.131)
(0.124)
(0.137)
(0.142)
(0.132)
Wage
Unemployment
-0.186***
-0.147*** -0.145*** -0.141***
(0.0246)
(0.0241)
Avg. FICO
(0.0244)
(0.0238)
-4.134*** -4.465*** -4.927***
(0.519)
Avg. DTI
(0.557)
(0.571)
-0.370*** -0.314***
(0.110)
Avg. Rate
(0.106)
-1.229***
(1.135)
Metro F.E.
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Year F.E
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
N
1787
1761
1629
1629
1629
1629
1629
1629
No. MSA
0.441
0.537
0.537
0.567
0.603
0.583
0.530
0.576
R within
0.441
0.537
0.537
0.567
0.603
0.583
0.530
0.576
2
Note - All the variables in this regression are in growth rates. The dependent variable is the growth rate of the FHFA house price index.
The average max DTI and weighted interest rates are instrumented with a Bartik type instrument. The sample consists of annual data
from 1999 to 2011. The clustered robust standard errors are given in parentheses.
ú
statistical significance at the 90% level
úú
statistical significance at the 95% level
úúú
statistical significance at the 99% level
20
Table 4: Exploring the Robustness of the IV Effects of the Underwriting Standards on Housing
Prices
Weighted Max DTI
(1)
(2)
(3)
(4)
(5)
(6)
2.664***
2.677***
2.500***
2.766**
2.311***
2.414***
(0.586)
(0.772)
(0.633)
(1.176)
(0.531)
(0.706)
0.611
1.325*
(0.517)
(0.709)
0.709***
0.737***
(0.116)
(0.132)
◊I (year Ø 2006)
◊RE Supply Elast.
Weighted Rate
-4.012*** -3.212***
(0.541)
(0.829)
◊I (year Ø 2006)
-3.603***
-3.125**
(0.651)
(1.380)
-1.607**
-2.675***
(0.685)
(1.006)
◊RE Supply Elast.
Rent
Wage
Unemployment
-3.862*** -3.146***
(0.502)
(0.792)
-0.119*** -0.132***
(0.0257)
(0.0289)
1.137***
1.237***
0.910***
0.855***
0.984***
1.067***
(0.145)
(0.182)
(0.189)
(0.186)
(0.137)
(0.161)
0.520***
0.440***
(0.162)
(0.156)
-0.300*** -0.260***
-0.274*** -0.206***
-0.274*** -0.231***
(0.0320)
(0.0390)
(0.0340)
(0.0318)
0.514***
0.451***
0.611***
0.551***
(0.0357)
(0.0338)
(0.105)
(0.113)
(0.140)
(0.140)
Other Controls
No
Yes
No
Yes
No
Yes
Metro F.E.
Yes
Yes
Yes
Yes
Yes
Yes
Year F.E
Yes
Yes
Yes
Yes
Yes
Yes
N
1895
1895
1909
1909
1799
1799
R2 within
0.669
0.681
0.667
0.596
0.727
0.730
Note - All the variables in this regression are in logs. The dependent variable is the log of the FHFA house
price index. The average max DTI and weighted interest rates are instrumented with a Bartik type instrument. In
specifications (3) and (4) we interact our variables of interest with a dummy variable for years after the financial
crisis. In specifications (5) and (6) we interact the variables of interest with Wharton’s index for Land Regulation
which is large for places where it is more difficult to build new homes. In specifications (2), (4) and (6) we also control
for average DTI, average interest rates and average FICO scores. The sample consists of annual data from 1999 to
2011. The clustered robust standard errors are given in parentheses.
ú
statistical significance at the 90% level
úú
statistical significance at the 95% level
úúú
statistical significance at the 99% level
21
Table 5: Exploring the Robustness of the IV Effects of the Underwriting Standards on Housing
Prices
Weighted Max DTI
(1)
(2)
(3)
(4)
(5)
(6)
0.422*
0.916***
0.456***
0.492***
0.381*
0.904***
(0.234)
(0.304)
(0.158)
(0.167)
(0.229)
(0.302)
-0.169
0.773
(0.477)
(0.699)
0.244***
0.301***
(0.0540)
(0.0496)
◊I (year Ø 2006)
◊RE Supply Elast.
Weighted Rate
-0.800*** -1.198***
(0.230)
(0.292)
◊I (year Ø 2006)
-0.678*** -0.638***
(0.173)
(0.166)
-0.128
-1.160
(0.506)
(0.723)
◊RE Supply Elast.
Rent
Wage
Unemployment
-0.775*** -1.187***
(0.230)
(0.301)
0.00188
0.0130
(0.0216)
(0.0199)
0.509***
0.408**
0.527***
0.366**
0.425**
0.319*
(0.151)
(0.166)
(0.163)
(0.163)
(0.173)
(0.185)
0.599***
0.582***
(0.124)
(0.132)
-0.186*** -0.141***
-0.187*** -0.143***
-0.191*** -0.149***
(0.0244)
(0.0234)
(0.0248)
(0.0241)
0.591***
0.575***
0.554***
0.543***
(0.0246)
(0.0238)
(0.122)
(0.131)
(0.119)
(0.127)
Other Controls
No
Yes
No
Yes
No
Yes
Metro F.E.
Yes
Yes
Yes
Yes
Yes
Yes
Year F.E
Yes
Yes
Yes
Yes
Yes
Yes
N
1629
1629
1629
1629
1564
1564
R2 within
0.603
0.576
0.607
0.585
0.605
0.576
Note - All the variables in this regression are in growth rates. The dependent variable is the growth rate of the
FHFA house price index. The average max DTI and weighted interest rates are instrumented with a Bartik type
instrument. In specifications (3) and (4) we interact our variables of interest with a dummy variable for years after
the financial crisis. In specifications (5) and (6) we interact the variables of interest with Wharton’s index for Land
Regulation which is large for places where it is more difficult to build new homes. In specifications (2), (4) and (6)
we also control for average DTI, average interest rates and average FICO scores. The sample consists of annual data
from 1999 to 2011. The clustered robust standard errors are given in parentheses.
ú
statistical significance at the 90% level
úú
statistical significance at the 95% level
úúú
statistical significance at the 99% level
22
Interest Rates is also still positive and statistically significantly different from zero. The
interaction with the crisis dummy reveals that changes in the interest rates became more
important during the crisis: a one percent change in interest rates during the crisis led to
an aditional 1.6 percent drop in house prices as compared to the non-crisis period. Similar
results can be also seen in specification (4) when we include additional variables such as
average fico scores, average DTI and average interest rates.
Next we turn to exploring the cross-sectional variation in the size of the coefficients. One
plausible hypothesis is that a shock to underwriting standards should have more of a price
effect in areas where housing supply is less elastic than in areas where it is more elastic. The
idea is that in areas whith elastic supply, relaxing credit would result in more construction
rather in higher house prices. To test this, we interact our variables of interest with a measure
that captures how difficult it is to construct new homes in an area: the Wharton’s index for
Land Regulation. This index is higher in areas where there is a lot of regulation about how
much and where to construct and it is lower in areas with less restrictions. The main results
are presented in specification (5) of table (4). The coefficient on Weighted Max DTI is still
statistically significant and not different from the baseline specification (1). The interaction
with the supply elasticity proxy is positive, indicating that a shock to credit condition are
will lead to higher prices in areas where it is more difficult for supply to react The coefficient
on Weighted Interest Rates is also still positive and statistically significantly different from
zero. The same pattern also emerges when we look at the effect of the Weighted Rate: a
shock to interest rates will have a higher effect in places where it is difficult to increase
the supply of housing. Similar results can be also seen in specification (4) when we include
additional variables such as average fico scores, average DTI and average interest rates.
Similar results can be seen in table (5) where all the variables are in growth rates. We find
that interacting our main variables with a crisis dummy does not qualitatively change our
results indicating that our results are not driven by a particular time period. In specifications
(5) and (6) we also find that changes in the growth of underwriting standards have a higher
impact on price growth in places where it is more difficult for housing construction to readily
react to such shocks.
3.4
Extensions
We would expect that shocks to the underwriting standards for low (high) credit quality
borrowers affect house prices for lower (high) quality homes. To test this hypothesis, our
measure of credit standards can be refined to be the average maximum DTI for a range of
FICO scores. We can create a measures of underwriting standards for different percentiles
23
of the FICO distribution:
Ujt (q) =
b
ÿ
F ICO=a
Ïjt (F ICO) · sjt (F ICO)
where q is the measure of credit standards for a < F ICO < b. From Dataquick we could
construct house price indexes for different percentiles of the house prices so we have pjt (q).
We then can run the following regressions separately for each q:
pjt (q) =
Q
ÿ
–q Ujt (q) + —rtj + Xjt “ + dj + dt + Ájt
(10)
q=1
If we stack the estimated parameters, we would have a matrix of – that is q ◊ q. What we
would expect is that the diagonal of this matrix would have the highest coefficients. The
off the diagonal coefficients would inform us of the spillover effect of underwriting standards
across various segments of the housing market. We could think of things like: suppose we
get a shock to underwriting standards for only the low end, how does that spill over to other
housing segments? This could be quite interesting if the results are precise.
4
Conclusion
Using an instrumental variables approach we estimate the causal effect of underwriting standards on local house prices. In our main specification we regress house prices on the instrumented weighted average maximum DTI, the instrumented weighted interest rates, on local
fundamentals while controlling for year and metro fixed effects. We find that a one percent
change in the population weighted maximum DTI in a MSA leads to a 2.67 percent change in
local house prices holding constant everything else. On the other hand, one percent change
in the level of interest rates will lead to a drop of about four percent in local house prices.
We also conduct a similar analysis for the growth rates in our variables of interest. In these
regressions we find that a one percent change in the growth rate of the weighted maximum
DTI in one particular area will lead to a 0.422 percent change in the growth rate of local
house prices holding constant everything else. Also, a one percent change in the growth rate
of interest rates will lead to a drop of about 0.8 percent in the growth rate of local house
prices. These findings are not only interesting because they confirm what one would expect,
but also because they quantify the separate effects of underwriting standards and interest
rates on house prices. To our knowledge this is the first paper to do so in the literature.
To test the robustness of our findings, we also confirm that the effects that we identified
24
are not driven by the financial crisis. We interact our variables of interest with dummy
variables for the crisis and the result stand almost identically. While, as one would expect,
the effects became stronger during the crisis, they were present even in the precrisis period.
We also explore the cross-sectional variation in the size of the coefficients. One plausible
hypothesis is that a shock to underwriting standards should have more of a price effect in
areas where housing supply is less elastic than in areas where it is more elastic. To test
this, we interact our variables of interest with a measure that captures how difficult it is to
construct new homes in an area: the Wharton’s index for Land Regulation. The interaction
with the supply elasticity proxy is positive, indicating that a shock to credit condition are
will lead to higher prices in areas where it is more difficult for supply to react. The same
pattern also emerges when we look at the effect of the Weighted Rate: a shock to interest
rates has a higher effect in places where it is difficult to increase the supply of housing.
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and S. J. Turnovsky. Cambridge University Press.
(2010): “The Leverage Cycle,” in NBER Macroeconomics Annual 2009, Volume
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Glaeser, E. L., J. D. Gottlieb, and J. Gyourko (2010): “Can Cheap Credit Explain
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25