Using High-Frequency Evaluations to Estimate Discrimination: Evidence from Mortgage Loan Officers

ISSN: 1962-5361

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Working Papers

Using High-Frequency Evaluations

to Estimate Discrimination: Evidence

from Mortgage Loan Ofﬁcers

Marco Giacoletti

University of Southern California

Rawley Z. Heimer

Boston College

Edison G. Yu

Federal Reserve Bank of Philadelphia Research Department

WP 21-04

Revised April 2021

February 2021

https://doi.org/10.21799/frbp.wp.2021.04

Using High-Frequency Evaluations to Estimate Discrimination:

Evidence from Mortgage Loan Ofﬁcers

∗

Marco Giacoletti

†

USC

Rawley Z. Heimer

‡

Boston College

Edison G. Yu

FRB-Philadelphia

Current Draft: March 1, 2021

First Draft: August 24, 2020

Abstract

We develop empirical tests for discrimination that use high-frequency evaluations to address

the problem of unobserved heterogeneity in a conventional benchmarking test. Our approach

to identifying discrimination requires two conditions: (1) the subject pool is time-invariant in

a short time horizon and (2) there is high-frequency variation in the extent to which evaluators

can rely on their subjective assessments. We bring our approach to the residential mortgage

market, using data on the near-universe of U.S. mortgage applications from 1994 to 2018.

Monthly volume quotas reduce how much subjectivity loan ofﬁcers apply to loans they process

at the end of the month. As a result, the volume of new originations increases by 150% at the

end of the month, while application volume and applicants’ quality are constant within the

month. Owing to within-month variation in loan ofﬁcers’ subjectivity, we estimate that Black

mortgage applicants have 3.5% to 5% lower approval rates, which explains at least half of the

observed approval gap for Blacks. When we use this approach to evaluate policies, we ﬁnd

that market concentration and FinTech lending have had no effect on lending discrimination,

but that shadow banking has reduced discrimination presumably by having a larger presence

in under-served communities.

Keywords: Performance Incentives, Loan Ofﬁcers, Mortgages, FinTech Lending, Lend-

ing Discrimination

∗

Previously titled “To the Back of the (Lending) Bus: How Loan Ofﬁcers’ Performance Incentives Reveal Lend-

ing Discrimination.” We thank Michael Fitzpatrick for excellent research assistance. We thank Pat Akey, Mitchell

Berlin, Greg Buchak, Yulyia Demyanak, Ran Duchin, Andreas Fuster, Antonio Gargano, Hajime Hadeishi, Chris

Parsons, Micah Spector, Phil Strahan, and seminar participants at Baruch, ASU Finance Winter Conference, Boston

College, Federal Reserve Bank of Philadelphia, the Joint Finance Seminar, University of Oregon, and University

of Southern California for helpful feedback. This paper does not reﬂect the views of the Federal Reserve Bank of

Philadelphia or of the Federal Reserve System. Any remaining errors or omissions are the authors’ responsibility.

†

University of Southern California, Marshall School of Business. Phone: +1 (650) 475-6410, Email: mgia-

[email protected]

‡

Boston College, Carroll School of Management. Phone: +1 (216) 774-2623, Email: [email protected]

Federal Reserve Bank of Philadelphia. Phone: +1 (215) 574-6221 Email: [email protected].org

1 Introduction

Racial and gender disparities have been documented in a range of ﬁelds, such as labor markets,

the legal system, and credit markets. Yet whether these disparities are the result of discrimination

by economic decision-makers—deﬁned as an evaluator treating otherwise identical subjects from

minority groups worse than subjects from the majority group—remains in dispute. There has been

a growing trend toward using experiments and correspondence studies to test for discrimination

(Bertrand and Duﬂo, 2017). Nonetheless, tests for discrimination that use observational data have

several advantageous features. Such tests are accessible to a wide range of researchers, they are

easy to replicate and scale, they can be used to estimate aggregate costs of discrimination in a given

market, and policymakers can easily implement them.

However, tests for discrimination based on observational data face a number of economet-

ric challenges that limit their appeal. The most straightforward test for discrimination is an audit

or “benchmarking” test. Benchmarking tests claim to ﬁnd discrimination when minority groups

receive unfavorable evaluations relative to the majority group. But, benchmarking tests are vul-

nerable to criticisms of omitted variable bias—differences in group characteristics, which the re-

searcher does not observe, can cause differences in evaluations across groups.

Alternatively, Becker (1957) proposed an “outcome test.” Instead of comparing differences

in how groups are evaluated, outcome tests compare the ex-post success of these evaluations.

The marginal minority will have better ex-post outcomes than the marginal majority subject be-

cause minority groups face higher thresholds for inclusion when they are subject to discrimination.

Though intuitively appealing, outcome tests are notoriously difﬁcult to implement, most notably

because of the “infra-marginality” problem—the average difference in ex-post outcomes can be

a poor approximation of the difference in marginal outcomes (Ayres, 2002). Recent research has

made signiﬁcant progress to improve econometric methods (e.g., Arnold et al., 2018), but address-

ing the infra-marginality problem requires additional modelling and distributional assumptions

(Simoiu et al., 2017). Furthermore, ex-post outcomes can be the result of self-fulﬁlling prophecies

(e.g., female students underperform in math because gender stereotypes reduce investment in fe-

males’ math education; Bordalo et al., 2016) and ex-post outcomes are often not easily measured

(e.g., worker productivity can be difﬁcult to measure and proxies for productivity, such as wages,

can also be affected by discrimination).

We propose an alternative way to test for discrimination. The approach is motivated by the

observation that evaluators’ subjectivity can often vary substantially within short time intervals.

For example, employers that have immediate stafﬁng needs can ill afford to turn away job appli-

cants. TSA agents might reduce their screening of travelers when they are at the end of their shifts

or there are long queues. Police ofﬁcers that have monthly quotas would issue tickets to all drivers

that exceed the speed limit on the last day of the month. Our approach starts with a benchmarking

test, but addresses the problem of omitted variables by exploiting such high-frequency evaluations.

The approach requires two simple assumptions: time-varying discrimination and time-invariant

unobserved characteristics both in a short time interval (e.g., a month). The identiﬁcation ratio-

nale is straightforward. If the evaluations of a group vary within a short time interval, then these

differences cannot be driven by unobserved subject characteristics, because the unobserved char-

acteristics are time-invariant.

We apply our approach to high-frequency data on mortgage applications, to test for discrim-

ination in the U.S. residential mortgage market.

We obtain the time-stamped version of the Home

Mortgage Disclosure Act (HMDA) data, covering the near-universe of mortgage applications from

1994 to 2018 with 500 million loan applications across more than 28,000 lenders. Crucial to our

empirical approach, we observe the exact application and decision date of each application.

Figure 1 demonstrates our key source of high-frequency variation in the mortgage market

and the foundation of our empirical approach. The ﬁgure shows the volume of new originations

and new applications relative to the ﬁrst day of a given month. The total volume of new mortgage

originations increases by more than 150% on the last day relative to the ﬁrst day of a given month.

The literature can be traced back at least as far as the public release of HMDA data and the work of Munnell

et al. (1996). Ladd (1998) summarizes much of the older literature and frames longstanding debates. Other founda-

tional papers include Berkovec et al. (1994); Tootell (1996); Berkovec et al. (1998). Recent work has begun to study

differences in mortgage rates and fees (e.g., Bhutta and Hizmo, 2020).

100

150

200

percent

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

origination application

Number of loans originated vs applied (relative to first day of month)

Figure 1: The ﬁgure shows average percentage abnormal daily loan origination volume, and loan application vol-

ume (measured as number of originations and applications) in the U.S., for the last eight days of the month, and the

ﬁrst seven days of the following month. The ﬁgure reports the average across all months over the sample period from

January 1994 to December 2018 from the HMDA data. Abnormal volume is computed with respect to loan origina-

tions and applications on the ﬁrst day of the following month.

At the same time, the number of submitted mortgage applications stays constant over the course of

the month. These patterns reveal a crucial feature of the mortgage application process: loans are

processed by individual loan ofﬁcers who have monthly performance targets that determine their

compensation.

Moreover, this within-month pattern in loan approvals unveils the component of

loan ofﬁcers’ decision-making that is orthogonal to observable and unobservable factors affecting

loan originations (e.g., credit market conditions, applicant characteristics, and ﬁrm-level charac-

teristics). Drawing from Becker (1957), a proﬁt-maximizing agent can give disparate treatment

to minority populations until market competition makes discrimination economically untenable.

Though we do not directly measure the compensation of any individual loan ofﬁcer, for the most part, com-

missions are set based on the number of loans and the loan amount originated. And the compensation scheme

is common across employers. For example, see the following link for an article on the website of the Mort-

gage Bankers Association that discusses the industry standards for loan ofﬁcers’ compensation in the U.S.

(https://www.mba.org/publications/insights/archive/mba-insights-archive/2019/is-it-time-to-rethink-compensation-

x253848). Tzioumis and Gee (2013) also note that loan ofﬁcers face disciplinary actions if they fail to meet their

quotas several months in a row. Given this non-linear incentive scheme, Tzioumis and Gee (2013) and Cao et al.

(2020) document end-of-month bunching in a large U.S. commercial bank and in two Chinese banks, respectively.

Loan ofﬁcers have an economic incentive to meet end-of-month performance incentives. As such,

loan ofﬁcers’ subjective favoritism toward applicants has to attenuate at the end of the month

relative to the beginning of the month. Therefore, the within-month pattern, combined with a con-

ventional benchmark test, allows us to estimate the extent to which loan approval decisions can be

attributed to loan ofﬁcers’ subjectivity towards applicants.

-.25

-.2

-.15

-.1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

Average approval rate gap (Black minus white applications)

Figure 2: The ﬁgure reports the difference between the fraction of approved loans, out of all approved and denied

loans in the U.S., for Blacks minus the one for whites, on each of the last eight days of the month and the ﬁrst seven

days of the following month.

Exploiting this within-month variation, our tests for discrimination estimate the difference in

approval rates between Black and white applicants at the start of the month relative to the end of

the month. Our key ﬁnding is summarized in Figure 2, which shows the difference in application

approval rates between Black and white applicants over the course of any given month. In the ﬁrst

seven days of the month, Black applicants have 20 percentage point lower approval rates than white

applicants. The approval gap gets smaller over the course of the month. The approval gap between

Blacks and whites is just 10 percentage points on the last day of the month. The regression tests that

correspond to the graphical evidence in Figure 2 are saturated with a rich set of ﬁxed effects that

control for time-varying economic conditions at precise geographic levels, namely county-month.

The regressions also include lender-month ﬁxed effects that control for factors, such as regulations,

that would affect lending at the institution level. Conﬁrming the graphical evidence, the difference

in the Black-white approval gap between the start and the end of the month is 3 to 5 percentage

points. This constitutes a lower bound on the share of the Black-white approval gap that is due

to loan ofﬁcers’ subjectivity, relative to the approval gap that can be attributed to unobservable

group-differences. We estimate, in our most stringent regressions, that loan ofﬁcers’ subjective

decision-making explains at least half of the overall difference in approval rates between Black

and white applicants even after controlling for observable characteristics. In terms of aggregate

magnitudes, if the approval rate gap for every day of the month was as small as the last day of the

month, about 1.4 million more Black applications would have been approved rather than denied

between 1994 and 2018, which corresponds to a total loan size of about $213 billion in 2018

dollars.

Our approach to estimating discrimination hinges on a set of simple assumptions that we de-

rive and that are easily supportable, either in the data or via narrative, or both. The ﬁrst assumption

is that the loan ofﬁcer has time-varying costs of being subjective. In our setting, loan ofﬁcers have

nonlinear contract incentives.

Loan ofﬁcers that fail to meet their volume quotas will have re-

duced compensation and risk getting ﬁred. The second assumption is that the characteristics of the

subject pool are time invariant. Indeed, we ﬁnd that application volume, the relative share of Black

applications, and loan application quality (for both Black and white applications) are all constant

over the course of the month. The remaining threat to identiﬁcation is that there are differential

trends by race in the quality of applications that get processed over the course of the month. As

evidence against this explanation, we ﬁnd that high-quality and low-quality Black mortgages have

similar amounts of bunching toward the end of the month.

Importantly, with volume quotas, the optimal strategy would be to approve all loan applications. However, in

practice, there are several constraints on this strategy. Lenders set origination standards that an application has to

exceed and loan ofﬁcers may have a ﬁxed quantity of mortgage credit that they can distribute within a month. Loan

ofﬁcers can use their discretion and work to sidestep the origination standards by either using risk-based pricing or

appealing to other “soft” criteria, such as noting that the applicant is a customer of the bank.

In contrast to other methodologies, our approach does not require ex-post outcomes to test

for discrimination. Nevertheless, we show that a conventional outcome test is potentially mislead-

ing about the levels of discrimination in mortgage lending. We ﬁnd that Black mortgages have

signiﬁcantly higher rates of default, which could be interpreted as evidence of reverse discrimina-

tion that favors minorities. Instead, this result is almost certainly caused by the infra-marginality

problem – the fact that Black and white mortgage applicants have different risk distributions. We

compare the subsequent default rates of applications approved at the start of the month to those

approved at the end of the month. The within-month differential signiﬁcantly shrinks the raw dif-

ference between Black and white default rates. As such, these ﬁndings suggest that our approach

potentially counteracts the shortcomings of a conventional outcome test.

Furthermore, our approach offers guidance, relative to both benchmarking and outcome tests,

as to whether observed discrimination is caused by taste-based versus statistical discrimination. We

develop an additional set of assumptions to distinguish between the two theories. Put simply, the

case for statistical discrimination requires asymmetric information between evaluators and sub-

jects. Because of the high-frequency nature of our data, statistical discrimination would require

the loan ofﬁcers’ information set about applicants to change from the start to the end of the month.

This explanation is unlikely because we show that the applicant pool is time invariant. Related,

we consider the role of inaccurate beliefs (i.e., stereotypes Bordalo et al., 2016) and a similar logic

precludes this explanation.

Finally, our approach is advantageous because it can easily be applied to evaluate the effect

of market policies and market innovations on the quantity of discrimination. We consider three im-

portant features of modern mortgage lending: market concentration in banking, FinTech lending,

and shadow banking. We ﬁnd that the amount of discrimination due to loan ofﬁcers’ subjectivity

is unaffected by both market concentration and FinTech lending. This result is largely consistent

with the fact that our regressions include lender-by-month ﬁxed effects and that the component

of loan ofﬁcer subjectivity our approach uncovers occurs within-lender. Moreover, despite these

changes to the banking sector, loan ofﬁcer compensation incentives have largely remained con-

stant throughout our sample, and even mortgage lending at FinTech lenders involves signiﬁcant

discretion from human loan ofﬁcers. On the other hand, we ﬁnd that shadow banks have lower

levels of subjective discrimination against Black applicants. This is likely the result of shadow

banks—owing to their lower regulatory requirements—having a larger presence in under-served

communities.

Related Literature

Our paper is related to advances in the literature on identifying discrimination by economic decision-

makers. Our approach bears closest resemblance to empirical papers that use changes to evaluation

settings to identify discrimination against minority groups. For example, Goldin and Rouse (2000)

shows that blind auditions reduce employment discrimination against female orchestra musicians.

Police ofﬁcers are less likely at night than during the day to pull over Black motorists because

the driver’s race is difﬁcult to identify (Pierson et al., 2020). These empirical papers identify

discrimination by comparing situations in which evaluators know the subject’s gender and race to

situations in which they do not. Our approach is different because there is no change in the loan of-

ﬁcer’s knowledge of applicants’ race. We show that discrimination can be identiﬁed under a set of

simple assumptions about the applicant pool and loan ofﬁcers’ reliance on subjective assessments.

More speciﬁcally, our paper joins a large and important literature on discriminatory lending

practices in consumer credit markets. Our empirical approach is grounded in evidence that loan

ofﬁcers have signiﬁcant discretion in loan processing decisions (see e.g., Engelberg et al., 2012;

Chen et al., 2016; Demiroglu et al., 2019). Most similar to our analysis, Cort

es et al. (2016) also use

conﬁdential HMDA data to disentangle application dates from processing dates to show that loan

ofﬁcers are more likely to approve mortgages on sunny days. Guided by this ﬁnding, we bring the

conﬁdential HMDA data to the question of lending discrimination. Several papers ﬁnd compelling

evidence that individual loan ofﬁcers discriminate against other races and women.

We advance

In no particular order, Fisman et al. (2017, 2020) use data from Indian banks to show that loan ofﬁcers are more

favorable to culturally proximate applicants. Beck et al. (2018) use evidence from an Albanian bank and Montoya

et al. (2019) use a ﬁeld experiment at a Chilean bank to uncover evidence of gender discrimination in consumer lend-

ing. Ambrose et al. (2020) ﬁnd that minorities pay higher fees when they have a white mortgage broker.

this literature in a few ways. With a few exceptions (e.g., Bohren et al., 2019; Dobbie et al., 2020),

most papers are unable to distinguish between taste-based and statistical discrimination. Our ap-

proach can offer guidance about which type of discrimination is most likely. Also, these papers use

evidence from conﬁdential internal data from one or two lending institutions. In contrast, our paper

uses the universe of U.S. mortgage applications over a 25-year period to connect racial disparities

in lending to the incentives of individual loan ofﬁcers. This allows us to address crucial questions

about external validity, investigate the effects of the market structure, and quantify the scope of

racial bias in mortgage markets.

Second, our paper contributes to a growing literature on how market structure and technology

affect consumer lending. First, recent papers ﬁnd support for classic theories arguing that compe-

tition reduces discrimination in consumer lending (Buchak and Jørring, 2017; Butler et al., 2019).

Such papers suggest that racial discrimination declines because of changes to the composition of

lending institutions. We ﬁnd that discrimination by individual decision-makers can persist within

organizations even when there are differences in institution-level competition across markets. Sec-

ond, there is signiﬁcant debate over how the growth of FinTech lending affects the allocation of

credit, with a particular interest in the effects on disadvantaged borrowers. In theory, FinTech can

reduce intermediation costs which can pass through to consumers (e.g., Tang, 2019) or improve

screening (Berg et al., 2020a). However, the literature ﬁnds that FinTech algorithms have either no

effect or negative effects on the supply of credit to disadvantaged consumers (see e.g., Fuster et al.,

2017; Bartlett et al., 2019). Our contribution is to show that biases in human decision-making can

survive advances in loan processing technology (similar to ﬁndings on the introduction of machine

learning to judicial outcomes, as shown by Kleinberg et al., 2018).

Finally, we make a unique contribution to the literature on performance-based compensation,

with a particular focus on ﬁnancial intermediation. The effects of performance-based compensa-

tion have been studied in a range of settings, such as manufacturing (Oyer, 1998), software sales

(Larkin, 2014), government contracts (Liebman and Mahoney, 2017), healthcare (Li et al., 2014;

Gravelle et al., 2010), ﬁrm managers (Bandiera et al., 2007) and accounting (Murphy, 2000). The

literature has also studied how performance incentives within banks affect loan ofﬁcers’ effort

and performance (Agarwal and Ben-David, 2012; Cole et al., 2015), and information production

(Hertzberg et al., 2010; Qian et al., 2015; Berg et al., 2020b). To the best of our knowledge, our

paper is the ﬁrst to study variation in performance incentives combined with racial biases in human

decision-making.

2 Identifying Discrimination

This section presents a formal discussion of our empirical setup. We compare our approach to

existing frameworks for identifying discrimination. Differences in unobserved characteristics of

different subject groups pose a challenge for conventional tests for discrimination. Our approach

is to ﬁlter out these unobserved differences across subject groups by using high frequency data.

Our approach extends conventional tests for discrimination, called either audit or bench-

marking. These tests compare the conditional likelihood that a minority subject group receives

disparate treatment relative to the majority group, after controlling for other observable character-

istics from the point of view of the researcher. Consider the case of a Black mortgage applicant.

The researcher claims to have uncovered discrimination when she rejects the null of no difference

in the conditional likelihood of approval between Blacks and whites, and instead ﬁnds that the

likelihood is signiﬁcantly smaller for Blacks. Speciﬁcally, the researcher claims discrimination

when she ﬁnds that:

P (a|W, X) > P (a|B, X) (1)

where P (a|R, X) is the probability of loan application approval, conditional on race R ∈ {W, B}

(white or Black) and a vector of observable characteristics X to the researcher. However, this

approach is exposed to the criticism that the difference in approval rates between white and Black

applicants might be driven by unobserved characteristics that are relevant for the assessment of

applicants’ credit risk used by the loan ofﬁcers, but are not included in the vector of controls X

used by the researcher. To see that, assume for simplicity that there is a binary unobserved variable

Z ∈ {Z

, Z

}, such that the following assumptions are satisﬁed:

Assumptions Set (A)

No discrimination: P (a|W, X, Z

) = P (a|B, X, Z

)

for k ∈ {H, L}

Higher quality predicts higher approval probability: P (a|R, X, Z

) > P (a|R, X, Z

)

On average white applicants have better unobservables: P (Z

|W, X) > P (Z

|B, X)

The inequality in approval rates formalized by equation (1) holds under the set assumptions above

when omitting the variable Z, even though decision-makers do not discriminate when all of the

characteristics are accounted for (see Appendix A.I). The differences in approval rates for dif-

ferent races simply capture the differences in the unobserved characteristics. In the mortgage-

lending setting, Black and white applicants have substantially different observable characteristics

(see Table 1). Such differences raise concern that there might be also substantial differences in

unobservables.

In this paper, we show that we can reﬁne existing approaches to address the identiﬁcation

problems due to the systematic differences in unobservables across subject groups. Rather than

only testing for the differences in the likelihood of approval between white and Black applicants,

we use high-frequency data to test whether those differences vary over a short period of time.

Because discrimination is determined by the subjective judgment of the evaluators, under the null

of no discrimination, and if applicant characteristics remain constant over time, there shall be no

change in the approval rates over time. On the other hand, discrimination would predict a change

in the relative approval rates over time.

To formalize this idea, let there be two time periods, T ∈ {Start, End}. Assume that

evaluators have more scope to be subjective in period Start relative to period End. Then, in the

presence of time-varying discrimination we expect to ﬁnd:

P (a|W, X, End) − P (a|B, X, End) < P (a|W, X, Start) − P (a|B, X, Start) (2)

where P (a|., X, .) is the probability of approval, conditional on race (white or Black), a vector of

observable characteristics X, and in a speciﬁc period (Start or End). Note that the presence of

unobservable quality characteristics systematically correlated with race cannot alone explain the

effects in equation (2). Consider the following set of assumptions that characterize a situation in

which there is no discrimination:

Assumptions Set (B)

No discrimination: P (a|W, X, Z

, T ) = P (a|B, X, Z

, T )

for k ∈ {H, L}

Higher quality predicts higher approval probability: P (a|X, Z

, T ) > P (a|X, Z

, T )

On average white applicants have better unobservables: P (Z

|W, T ) > P (Z

|B, T )

No time pattern in applications quality: P (Z

|R, X, Start) = P (Z

|R, X, End)

The ﬁrst three assumptions are the same as in Assumptions Set (A), while the last assumption

states that the unobserved characteristics of the applicants, for both whites and Blacks, are on

average constant over time. Jointly, these assumptions imply (see Appendix A.I):

P (a|W, X, End) − P (a|B, X, End) = P (a|W, X, Start) − P (a|B, X, Start).

Thus, the condition in equation (2) indeed amounts to a rejection of the null of no discrimination.

2.1 Distinguishing Taste-Based from Statistical Discrimination

This section explores the extent to which our approach can distinguish between the two broad

categories of discrimination. Under “taste-based” discrimination, minorities are subject to dis-

parate treatment because evaluators have animus toward them. Under “statistical” discrimination,

evaluators are uncertain about the abilities of any given subject. Evaluators form their beliefs after

observing the subject’s race. Minorities are subject to disparate treatment when evaluators have de-

veloped beliefs that minority subjects have worse abilities. Evaluators do not need to have accurate

beliefs about minorities to apply disparate treatment (see e.g., Bohren et al., 2020).

We consider evaluators j who, over a short time-period, for example a month or a week,

evaluate subjects i. Each evaluator j has perceived net beneﬁts from making decisions that favor

subject i equal to U

, Z

, R

, t), where X

and Z

are vectors of observable and unobservable

(from the perspective of the researcher) characteristics, R

is the subjects’ race (e.g., R

= W

for a white applicant and R

= B for a Black applicant), and t is the point in time in which the

evaluation is conducted.

The evaluator’s net beneﬁts can be decomposed into two components:

, Z

, R

, t) = b

, Z

, R

, t) + E

, Z

, R

, t], (3)

where b

, Z

, r

, t) is the subjective net beneﬁts of evaluator j conditional on all characteristics,

and E

, Z

, R

, t] is the statistical component. The statistical component can be written as

, Z

, R

, t] = E[u

, Z

, R

, t] + τ

, t), (4)

where τ

(.) is the bias of decision maker j when forming expectations conditional only on the

information about the race of an applicant.

We can then use our stylized framework to characterize different types of discrimination, for

example against Black subjects with respect to white subjects:

- Taste-based discrimination: b

, Z

, W, t) > b

, Z

, B, t)

- Statistical discrimination: τ

(W, t) > τ

(B, t)

The decision maker will take a decision favorable to subject i as long as the net beneﬁt is

positive:

, Z

, R

, t) + E

, Z

, R

, t] + v

i,j,t

> 0,

where v

i,j,t

is a random preference shock, i.i.d. across subjects and evaluators, and independent of

information on subject characteristics and evaluators’ beliefs. We can then introduce the variable

i,j,t

, which is equal to one if subject i receives a favorable decision from evaluator j at time t, and

has likelihood function:

L(y

i,j,t

) = P r(y

i,j,t

= 1)

I(y

i,j,t

=1)

[1 − P r(y

i,j,t

= 1)]

1−I(y

i,j,t

=1)

P r(y

i,j,t

= 1) = E[y

i,j,t

, Z

, R

, j, t] = F (X

, Z

, R

, j, t).

If we assume the function F (X

, Z

, R

, j, t) can be approximated with a liner speciﬁcation,

then we can write:

i,j,t

= β

+ β

× t) + ηX

+ φZ

+ a

+ 

i,j,t

(5)

where r

= 1 if R

= B. Equation (5) can be estimated in the data. Within this speciﬁc framework,

we can state the predictions of our general discussion in the previous section along the following

lines:

1. The two types of discrimination listed above (driven by taste or statistical) would cause

estimates of β

< 0. However, as the previous section outlines, β

will be a biased estimate

unless the researcher fully controls for observable (X

) and unobservable (Z

) characteristics,

or r

is uncorrelated with any omitted characteristics.

2. Estimates of β

will be different from zero if the magnitude of discrimination changes over

time, regardless of the type of discrimination. If subject pool characteristics (X

and Z

)

are not correlated with the evaluation time t, estimates of β

will be unbiased even if the

researcher does not perfectly control for time-invariant characteristics.

How can this approach distinguish between different theories of discrimination? In principle,

any type of discrimination can be subject to high-frequency ﬂuctuations, and thus produce non-

zero estimates of β

. However, if the unobserved variation across subject pools and the evaluator’s

statistical inference problem are time-invariant, our approach allows the researcher to attribute

discrimination to the source of time-variation in the evaluator’s decision-making.

Consider the case of statistical discrimination. Statistical discrimination is caused by the

evaluators’ statistical inference problem. Therefore, the researcher can reasonably assume the

ﬁndings are caused by statistical discrimination if she can provide evidence of time-variation in the

evaluators’ information set. Now consider taste-based discrimination. The evaluator’s subjective

preferences against minorities causes disparate treatment. The researcher can assume taste-based

discrimination if she has evidence that evaluators’ subjectivity is time-varying.

In the following empirical analysis, we focus on residential mortgage lending in the U.S.

Our source of time-variation in evaluations is the fact that loan ofﬁcers have monthly volume quo-

tas. These monthly volume quotas generate within-month variation in loan ofﬁcers’ subjectivity.

The volume quotas pressure loan ofﬁcers to increase their approval rates at the end of the month,

whereas at the start of the month, loan ofﬁcers have scope to apply their subjective preferences. At

the same time, loan ofﬁcers observe the same information about applications that they process at

the start of the month relative to the end of the month. As such, any ﬁnding of discrimination due to

within-month differences in evaluations can be attributed to loan ofﬁcers’ subjective preferences.

3 Data

The empirical results in this paper are based on the conﬁdential version of the HMDA data available

to researchers in the Federal Reserve System. The dataset contains the largest sample of mortgage

applications available in the U.S. The public version of the data includes information on applicant

characteristics – race, gender, reported income, and location of the property – and identiﬁers for

the lenders that received the applications. The data cover the entire geography of the U.S. over

the period from January 1994 through December 2018. Moreover, the data provide information on

mortgage contract characteristics, such as whether the application is for a new home purchase or

reﬁnancing, the loan amount, the lien, and whether the property is owner-occupied. The primary

distinguishing feature of the conﬁdential version of the HMDA data is that it contains the exact

date on which each application was submitted by a potential borrower and the date on which each

application was processed by the lender (either approved or denied) or withdrawn by the applicant.

This information has been employed in several prior papers (see e.g., Cort

es et al., 2016).

Table 1, panel (a) shows summary statistics of the mortgage applications in our dataset, for

each year from 1994 to 2018. Annual mortgage applications are between 10.1 and 37.3 million,

and originations between 7.2 and 23.7 million. The number of active lenders by year is between

5,700 and 9,800, and the average number of originations per lender is between 750 and 2,900.

Panel (b) shows statistics over the entire period from 1994 to 2018, and across different applicant

groups based on race. Approximately 67% of applicants are white and 7% are Black. Other races

are not separately identiﬁed and are grouped, along with applications that do not specify race, into

a single category called “Other race” that includes 26% of all observations. Black applicants apply

for smaller loans on average, have the highest fraction of low income applicants (59.8%, compared

to 46% for whites and 47.8% for other races), and have the lowest approval rate (63.25%, compared

to 80.72% for whites and 69% for other races). When considering approved loans, 73.7% are to

whites, 5.7% to Blacks and 20.6% to applicants of other races.

To obtain more detailed information on characteristics and performance of originated mort-

gage loans, we merge HMDA with the Black Knight McDash (McDash) dataset. We construct the

merged sample with an algorithm similar to the one used by Rosen (2011). Individual observations

in HMDA and McDash are merged using loan origination date, loan amount, zip code, lien type,

loan type, loan purpose, and occupancy type (owner occupied, absentee or investment property).

The match rate of the merge is about 60%.

McDash provides further information on individual

loan contracts, such as the mortgage interest rate, rate type (ﬁxed or adjustable rate), the mortgage

Lender and consumer identities were anonymized for the merged dataset used in this analysis.

term, whether the loan is conforming, borrowers’ FICO scores, and the quality of the supporting

documentation submitted by the borrower.

4 Identifying Assumptions

Our identiﬁcation strategy relies on high-frequency variation in evaluators’ subjective decision

making. This section provides support for the identiﬁcation assumptions: (1) the pool of mort-

gage applicants is time-invariant and (2) there is time-variation in loan ofﬁcers’ reliance on their

subjective assessments.

4.1 The Applicant Pool is Time-Invariant

The ﬁrst identifying assumption in our tests for discrimination is that the composition of the appli-

cant pool is time-invariant. Figure 3 shows how the composition of new applicants evolves over the

course of the month. Panel (a) plots the average share of Black applicants submitted on each day

of the month. Black applicants’ share of new applications is roughly constant at approximately 7%

on each day of the month. This conﬁrms our identifying assumption that the racial composition of

applicants is time-invariant.

We also verify that other characteristics of the applicant pool—characteristics that could

correlate with race—are constant over the course of the month. The HMDA data has limited infor-

mation on the creditworthiness of applicants. However, the data contain applicants’ income, which

is an important input into lender’s decision-making and is likely correlated with other variables that

determine whether an application is approved (e.g., credit scores). Figure 3, Panel (b) reports the

fraction of applicants that have levels of personal income that are below the median of applicants

within a county during a given year. Panel (c) shows the share of such applicants with the added

restriction that the application becomes a new origination. In both panels, we divide the sample

into applications submitted by Black and white applicants. As such, these ﬁgures explore whether

the quality of applications within and across races changes within the month. These ﬁgures show

that application quality is constant.

Lastly, Panel (d) studies the composition of the applicant pool with outstanding applications

(i.e., applications that have been submitted but have yet to receive an approval decision) in the

lenders’ inventory over the course of the month. We explore this measure of application inventory

because it captures what applications the loan ofﬁcer has the opportunity to work on at any point

during the month. Panel (d) also sorts the outstanding applications by income and by race. Again,

we ﬁnd that the applicant pool is constant over the course of the month, both in terms of the racial

composition of the applicant pool and the quality of the applications outstanding.

4.2 Time-Variation in Subjective Assessments of Applicants

4.2.1 Loan Ofﬁcers Have Monthly Volume Quotas

Mortgage loan ofﬁcers tend to receive commissions calculated as a percentage of the total amount

they originate over the month. They can also receive bonuses for meeting monthly origination

targets, as well as face disciplinary actions or be ﬁred for failing to meet volume targets.

The use

of volume-based incentives is acknowledged by U.S. regulations and directives from the Consumer

Financial Protection Bureau (CFPB). U.S. law permits the use of volume-based incentives, but it

restricts the use of commissions based on the terms and performance of individual loans (see, most

recently, the dispositions of Regulation Z, implementing the Truth in Lending Act).

Seeing as loan ofﬁcers have monthly volume targets, how would these non-linear contract

incentives affect loan ofﬁcer behavior? We consider several theories, even though such theories

are not distinguishable in our data, nor do we intend to establish a single theory. However, many

such theories share a common feature: loan ofﬁcers’ decision criteria vary in a way that lessens

See Tzioumis and Gee (2013), and evidence from practitioners’ research and discussions, such as

what is reported in the following articles on industry standards for loan ofﬁcers’ compensation in the U.S.,

published by the Mortgage Bankers Association (https://www.mba.org/publications/insights/archive/mba-

insights-archive/2019/is-it-time-to-rethink-compensation-x253848), and by consumer websites

(https://www.investopedia.com/ask/answers/120214/whats-average-salary-loan-ofﬁcer.asp and

https://www.thetruthaboutmortgage.com/loan-ofﬁcer-jobs/#salary).

Volume-based incentives are the ﬁrst form of compensation mentioned in the section on

Permissible Methods of Compensation in the most recent revision of Regulation Z, available at

https://www.federalregister.gov/documents/2013/02/15/2013-01503/loan-originator-compensation-requirements-

under-the-truth-in-lending-act-regulation-z.

their scope for subjective decision making as the end of month nears. Instead, in order to meet

their volume quotas, loan ofﬁcers have to approve more loans at the end of month regardless of

their preferences toward any given applicant. Nevertheless, the following outlines these theories to

guide our understanding of the setting.

First, the end-of-month increase in new originations can be caused by rational loan ofﬁcers

that get dis-utility from exerting effort. Assume that loan ofﬁcers prefer to work fewer than a

certain number of hours per day. Whether or not the loan ofﬁcer meets his volume target is a

function of the effort he exerts, as well as how much effort it takes to ﬁnalize a loan approval.

The amount of effort each loan takes is determined by random factors that the loan ofﬁcer does

not control, such as macroeconomic shocks and loan-speciﬁc idiosyncratic shocks. Assuming that

new loan applications arrive randomly over the course of the month, loan ofﬁcers’ optimal strategy

would be to start with a lower effort at the beginning of the month and gradually increase their

effort over the course of the month. And when the end of month nears, they would increase their

effort in order to exceed the volume threshold. This strategy by loan ofﬁcers will cause large

increases in loan originations at month-end. The strategy also implies that loan ofﬁcers can be

more subjective about loans processed at the start of the month, but need to be less discerning and

seek approvals for all loans that they process at the end of the month.

Behavioral biases, such as procrastination (Akerlof, 1991), can also cause loan ofﬁcers to

delay the approval of loans until the end of the month. Alternatively, decision-makers can be

overconﬁdent—they overestimate their own abilities. Loan ofﬁcers that have an overconﬁdence

bias would overestimate their abilities to process loans over the course of the month and would

have to work overtime at the end of the month in order to meet their quotas.

4.2.2 Monthly Volume Quotas Cause End-of-Month Bunching in Mortgage Originations

We ﬁnd that monthly volume quotas cause large increases in new mortgage originations at the

end of the month. Figure 1, described in the introduction, presents the average volume of new

originations per day relative to the ﬁrst day of any given month. The volume of new mortgage

originations grows over the course of the month. The origination volume is more than 150% larger

on the last day relative to the ﬁrst day of a given month. The ﬁgure documents clear evidence of

“bunching” at the end of any given month.

The end-of-month bunching in mortgage originations is robust across time and to seasonal

factors. The end-of-month increase in originations occurs in every year of our sample, which

suggests that the ﬁnding is not caused by business cycles and is therefore unlikely to be caused

by ﬂuctuations in the demand for mortgages (see Appendix Figure A.1). Also, the end-of-month

bunching occurs in every month of the calendar year (see Appendix Figure A.2, which plots the

average number of new originations on the ﬁrst and last seven days of each month within a given

year). This suggests that the ﬁnding is not caused by seasonality in mortgage demand.

Building on our graphical evidence, we use regression analysis to show that the within-month

pattern in originations is not caused by confounding factors. We estimate the following regression:

log(N

) = β

+ β

+ a

dow

+ a

holiday

+ e

(6)

where the dependent variable log(N

) is the log of the number of originated mortgages by lender i

on day t. The regression includes year-month, day-of-week, and bank-holiday ﬁxed effects, which

are a

, a

dow

, and a

holiday

, respectively. I

and I

are dummies equal to one for days in the last

week of the month and the ﬁrst week of the following month. The coefﬁcient of interest, β

(β

measures the difference between the average origination volume in the last (ﬁrst) seven days of the

month, relative to the middle days of the month.

The regression estimates conﬁrm that loan origination volume increases signiﬁcantly in the

last days of the month relative to the middle days. In Table 2, when origination volume is measured

as the log number of loans, the point estimate of β

is 31%, and the estimate of β

is -15%. When

origination volume is measured as the total dollar amount originated per day, the point estimates

are 36% and -14%. This gives us estimates of the increase in origination volume between the

As a testament to the quality of our micro-level data, recurring-day bank-holidays are clearly visible in Figure

A.2. Origination volume is abnormally low on the ﬁrst day of January, on Christmas and on July 4th.

ﬁrst and last week of the month of 46% and 50%, which are qualitatively consistent with the

evidence shown using the raw data in Figure 1. Our ﬁndings are unlikely to be explained by

lending seasonality because the estimates are robust to including a rich set of calendar time ﬁxed

effects (see e.g., Murﬁn and Petersen, 2016).

We also show that the end-of-month bunching in new originations is consistent with loan

ofﬁcers managing the inventory of applications over the course of the month. Figure A.3 in the

Appendix shows the inventory of applications that await a decision (approval, denial, or withdrawal

by the applicant) for each day within the month. There is a sharp drop in inventory over the last

week of the month, driven by the spike in originations, and then a steady increase taking place over

the ﬁrst two weeks of the following month.

4.2.3 Linking Origination Volume to Loan Ofﬁcers’ Performance

Next, we connect loan ofﬁcers’ performance incentives to the end-of-month bunching in new orig-

inations. To do so, we consider how loan ofﬁcers’ monthly volume targets affect their economic

incentive to approve and deny applications. Speciﬁcally, we expect that loan ofﬁcers have to in-

crease the pace of new originations when they are not on track to meet their quotas. Though our

data does not contain the origination targets set by each lender, we infer that loan ofﬁcers’ vol-

ume targets are a function of mortgage lending seasonality and the lender’s internal projections.

As such, we expect that each lender will have their own month-by-month benchmarks that are a

function of their origination volume in prior years (e.g., origination volume in March 2012 is a

reasonable estimate of the volume target in March 2013).

Based on these observations, we construct a measure of whether or not loan ofﬁcers at a

given lender are likely to be on track to meet their performance targets. The measure relates the

The month-end increase in originations is also robust across applicant characteristics. Table A.1 in the Ap-

pendix estimates equation (6) separately for different sub-samples: white applicants, Black applicants, and other

applicants, as well as white and Black samples sorted into income quartiles. New origination volume increases sub-

stantially at the end of the month for all applicant sub-groups.

current month’s origination volume relative to prior year’s:

RelP erf

i,ym

AvgV ol

i,ym

AvgV ol

i,ym

(7)

where AvgV ol

i,ym

is the average daily volume of mortgage loans that have been issued by lending

institution i and in year and month ym, excluding the last 7 days of the month. The denominator

is the average daily volume of mortgage loans issued by the same lending institution in month

, exactly one year before ym. We conjecture that the denominator of equation (7) proxies

for the volume target for institution i, which is based on the performance in the same month of

the previous year. We expect loan ofﬁcers to be behind their volume targets when the value of

RelP erf

i,ym

is small. Loan ofﬁcers that are behind their volume targets would be motivated to

increase their lending at the end of the month.

Indeed, origination volume at the end of the month increases by a larger amount when loan

ofﬁcers are more likely to miss their quotas. Figure 4(a) shows origination volume around the end

of the month. The ﬁgure splits the sample into lenders that have values of RelP erf

i,ym

in the top

quartile of lenders in a given month and lenders with values of RelP erf

i,ym

in the bottom quartile.

The month-end increase in originations is substantially larger when RelP erf

i,ym

is in the bottom

quartile. This provides evidence that loan ofﬁcers increase the pace of new originations at the

end of the month in order to meet their performance targets, and suggests that the end-of-month

increase in origination volume is caused by loan ofﬁcers’ monthly volume quotas.

4.2.4 Alternative Explanation for the End-of-Month Bunching

Though we attribute the increase in new originations at the end of the month to loan ofﬁcers’

monthly volume quotas, we consider alternative explanations. The leading alternative explana-

tion is that consumer lending regulations incentivize lenders to increase origination volume at the

end of the month. Lenders have incentive to “window-dress” prior to regulatory examinations by

increasing originations of certain types of loans.

Figure 4(b) replicates these ﬁndings using approval rates rather than origination volume.

We test the “window-dressing” explanation by exploring how origination volume changes

when lenders are subject to examinations conducted under the Community Reinvestment Act

(CRA). CRA exams are conducted every two years for large banks and every ﬁve years for small

and medium size lenders. Lenders know in advance the exam dates. CRA exams consist of a re-

view of the lender’s fair lending practices, designed to ensure that lenders meet the credit needs of

disadvantaged communities in markets that they serve. The primary alternative explanation for the

month-end effect would be that lenders increase originations to disadvantaged neighborhoods in an

effort to meet the requirements of upcoming CRA examinations. Indeed, prior research shows that

the CRA encourages high-risk lending (see e.g., Bhutta, 2011; Agarwal et al., 2012; Akey et al.,

2020).

We test whether the increase in new originations at the end of the month is caused by upcom-

ing CRA examinations. We sort lenders by whether or not they have a CRA exam scheduled in the

following month. Then, separately for the two samples, we estimate the speciﬁcation in equation

(6) where the dependent variable is the logarithm of daily origination volume. Table 2 reports the

regression estimates in columns (5) and (6). We ﬁnd that the month-end effect occurs regardless of

whether the lenders are subject to CRA examinations. Surprisingly, the end-of-month increase in

lending is smaller for institutions that are subject to CRA exams. Lenders that have (do not have)

CRA exams increase their origination volume by 29% (54%) at the end of the month.

4.2.5 Performance Incentives Affect Loan Ofﬁcers’ Decision-Making

The previous section shows that monthly volume quotas motivate loan ofﬁcers to increase the

volume of originations at the end of the month. Next, we show that such volume quotas affect

loan ofﬁcers’ decision-making on individual loan applications. Speciﬁcally, we study mortgage

approval and rejection decisions and how they vary over the course of the month. Holding constant

the characteristics of the application, a loan approval (denial) implies that the loan ofﬁcer was more

We also use approval rates to conﬁrm that CRA examinations do not cause the increase in originations at the

end of the month. We expand regression equation (8) to include controls for past and upcoming CRA exams. Our

estimates are reported in Table A.2 in the Appendix. We ﬁnd that controlling for CRA exams does not signiﬁcantly

affect the coefﬁcient estimates on the indicator variables for start-of-month and end-of-month loans.

(less) favorable toward the applicant. The within-month variation in loan approval decisions gives

us an estimate of loan ofﬁcers’ subjectivity towards individual loan applications.

Figure 5 shows the average approval rate in the U.S. for mortgage applications processed in

each of the last eight days of the month, and each of the ﬁrst seven days of the following month.

There is roughly a 15% difference in the approval rates between the start and end of the month.

The approval rate gradually increases from 76% seven days before month-end to more than 86%

on the last day of the month. Then, it drops abruptly at the start of the following month, reaching

a bottom value of 71% on the second day of the month.

We use regression analysis to show that the within-month increase in approval rates is robust

to a rich set of ﬁxed effects for time, seasonality, and supply-side factors. We estimate:

Appr

i,t

= γ

last−week

+ γ

first−week

+ a

dow

+ a

holiday

+ u

i,t

(8)

where Appr

i,t

is the approval rate for lender i on day t. a

is a year-month ﬁxed effect, a

is a

lender ﬁxed effect, and a

dow

and a

holiday

are day-of-the-week and holiday ﬁxed effects. The coef-

ﬁcients of interest, γ

and γ

, capture abnormal approval rates in the ﬁrst and last week of the

month, for the same lender in the same month. The speciﬁcation in equation (8) is strict. If month-

end effects are explained by persistent differences across lenders, or by transitory differences in

each speciﬁc month, then estimates of γ

and γ

would be indistinguishable from zero. More-

over, because the dependent variable is the approval rate, if month-end increases in originations

are caused by lagged demand, but not by higher propensity to originate loans, γ

and γ

will not

be different from zero.

Table 3 reports estimates of the coefﬁcients in equation (8). Column (1) reports results

based on approval rates for all processed applications. We ﬁnd that estimates of γ

and γ

are statistically signiﬁcant, and show higher approval rates than average in the last week of the

month, and lower approval rates than average in the ﬁrst week of the month. The difference

− γ

measures the increase in approval rates around month-end, and is equal to 4.5% and

highly statistically signiﬁcant. The other columns sort the data by various applicant characteristics,

namely racial groups, by income quartiles, and by various loan characteristics. We ﬁnd that the

increase in approval rates is present across all groups, but is particularly pronounced for Black

applicants, for which it is equal to 7.6%. Because the average approval rate for Black applicants

is 63%, our estimates imply a 12% relative decline in approval rates for this group of applicants

when comparing the last and ﬁrst week of the month.

5 Testing for Lending Discrimination Using High-Frequency Evaluations

This section uses the framework developed in Section 2 to test for discrimination in the mort-

gage lending data. Our approach exploits a change in the propensity for evaluators (in this case,

mortgage loan ofﬁcers) to rely on their subjective judgment in decision making. In our setting of

mortgage lending, monthly volume quotas compel loan ofﬁcers to generate more originations near

the end of the month. While loan ofﬁcers can reject applications at the start of the month based on

their subjective assessments and personal biases, they will be less willing to do so at the end of the

month when they face pressure to meet their volume quotas.

We can then exploit within-month variation—comparing the ﬁrst to the last week of the

month—in the difference in approval rates between whites and Blacks to conduct the formal dis-

crimination test presented in equation (2). Under the assumption that there is no discrimination,

and that application quality is constant within the month, we should ﬁnd that the difference in

approval rates between Black and white applicants is constant over the course of the month. How-

ever, we ﬁnd that Black applicants are relatively more likely to be approved at the end of the month.

These ﬁndings point toward taste-based discrimination against Black applicants in mortgage loan

approval decisions.

5.1 Empirical Evidence

We start our analysis by examining the aggregate (U.S.-level) differences in mortgage origination

volume for different groups of applicants around month-end. Figure 6 shows daily origination

volume in percentages relative to the ﬁrst day of the month for whites, Blacks and others. All three

groups experience increased origination volume at the end of the month. However, the magnitude

is substantially larger for Blacks—the number of originations is on average more than 240% larger

on the last day of the month than on the ﬁrst day of the following month. Even after controlling

for seasonality, the results in Table A.1 show that the average increase in daily originations from

the ﬁrst week of the month to the last week of the month is 11% larger for Blacks than for whites.

5.2 Testing for lending discrimination

We test for discrimination in mortgage lending by examining within-month differences in approval

rates across races. Our tests use the following regression speciﬁcation:

Appr

= δ

lw,Black

× I

Black

) + δ

fw,Black

× I

Black

) + δ

+ δ

+ (9)

+ δ

Black

+ BX

+ a

ym,c

+ a

ym,i

+ a

dow

+ a

holiday

+ u

j,t

where the unit of observation is the individual loan application. The dependent variable Appr

equals one if the loan is approved. Independent variables I

and I

equal one when the appli-

cation decision is made in the ﬁrst or the last week of the month, respectively. I

Black

is equal to

one for Black applicants. X

is a vector that contains characteristics for mortgage application j

and the corresponding applicant: loan amount, conforming loan status, loan type (conventional, or

government guaranteed or insured, such as FHA, VA, and USDA loans), occupancy type (owner

occupied or absentee), loan purpose (new purchase or reﬁnancing), and applicant income. Year-

month-county, year-month-lender, day of the week, and holiday ﬁxed effects are a

ym,c

, a

ym,i

, a

dow

and a

holiday

, respectively. The coefﬁcients of interest, δ

lw,Black

and δ

fw,Black

, capture the abnormal

approval rate for Black applicants in the last and ﬁrst week of the month.

We begin the regression analysis by reporting split-sample tests of Black and white applicants

that compare approval rates at the start of the month to those at the end of the month (Table 4).

We ﬁnd that approval rates for Black applicants are 12 percentage points larger in the last week of

the month relative to the ﬁrst week (column 1). Approval rates for white (and other) applicants are

8 percentage points larger in the last week (column 2). Comparing these results, Black applicants

gain an additional 4 percentage point increase in approval rates over the course of the month relative

to white applicants.

Next, we use the entire sample of HMDA data to test the regression model in equation (9)

that contains the complete set of interaction terms between Black applicants and applicants of

other races (Table 4, columns 3 through 6). Because we ﬁnd that the estimates are robust across

speciﬁcations, we describe the most restrictive speciﬁcation: column (6). The point estimate of

lw,Black

, the abnormal approval rate for Black applicants in the last week of the month, is equal

to 2.7 ppt. The estimate of δ

fw,Black

, the abnormal approval rate in the ﬁrst week of the month,

is equal to -0.7 ppt. This implies that the relative likelihood of approval for Black applications

increases by 3.4 ppt if the application is processed in the last seven days of the month.

The estimates of the within-month difference in approval rates for Black applicants are large.

For context, we estimate a baseline 6.8 ppt difference in approval rates between Black applicants

and applicants of other races (the coefﬁcient estimate on I

Black

). This estimate is equivalent to what

a conventional benchmarking test would estimate as the amount of discrimination against Black

applicants. However, a conventional benchmarking test is unable to determine whether the 6.8

ppt difference is caused by racial biases or whether it reﬂects the unobserved heterogeneity across

races. On the other hand, because our empirical design suppresses the cross-sectional variation

across applicants’ races, we can conﬁdently attribute the within-month approval gap of 3.4 ppt to

loan ofﬁcers’ subjectivity. As such, the ratio of the within-month difference to the unconditional

difference—3.4 divided by 6.8, or 50%—approximates the share of the observed racial gap in

approval rates that can be attributed to subjective decision-making. In other words, we attribute at

least half of the racial gap in approval rates to racial bias.

Our ﬁnding that the approval gap for Black applicants is reduced at the end of the month is

highly robust (see Appendix Table A.3 for the following robustness tests). The estimates are not

much changed across different types of mortgage applications – new home purchases, conforming

mortgages, and reﬁnances. Controlling for the applicant’s gender and including Black-year ﬁxed

effects also do not affect the estimates. Lastly, the results are robust to replacing calendar month

ﬁxed effects with ﬁxed effects that span the end and start of successive calendar months (e.g.,

January 15 to February 14).

These regression tests conﬁrm the graphical evidence that the approval gap between Black

and other applicants converges over the course of the month (presented in Figure 2 and described in

the Introduction). We augment this aggregate evidence by plotting how the approval gap changes

over the course of the month estimated from the saturated regression model in Table 4, column (6).

Figure 7(b) plots the average day-by-day residual difference in approval rates after controlling for

application characteristics. The approval gap in the ﬁrst seven days of the month is approximately

equal to 7 ppt. The approval gap during the last seven days of the month shrinks to approximately

1 ppt on the last day of the month. Therefore, after controlling for loan characteristics, there is

almost no difference in application approval rates across races on the last day of any given month.

The regressions in Table 4 also convey insight into how differences across lending institu-

tions affect mortgage credit for Black applicants. Notably, the literature has argued that much of

the difference in approval rates between Black and white applicants can be attributed to different

lending institutions catering to different types of borrowers and that different applicants choose to

apply for mortgages at certain types of institutions. We gain insight into the role of selection across

institutions by examining how including lender ﬁxed effects affects the regression estimates. In-

cluding lender ﬁxed effects reduces the magnitude of the un-interacted coefﬁcient on I

Black

from

-0.10 in column (2) to -0.07 in column (3). This result implies that lender ﬁxed effects are a cru-

cial source of unobservable variation driving the Black-white approval gap. On the other hand,

lender ﬁxed effects have a negligible effect on the within-month approval gap. The difference in

approval gaps between the start and end of the month is 0.040 without and 0.035 with lender ﬁxed

effects. These results suggest that we capture a component of loan ofﬁcer decision-making that

exists within lenders and is consistent across institutions. These results are reassuring for our em-

pirical design and the interpretation of the ﬁndings, because loan ofﬁcer compensation schemes do

not vary much across lending institutions.

We also provide evidence that the within-month reduction in approval gap for Black appli-

cants can be linked to the inventory of loan applications that lenders have in their queue. Figure

8(a) plots the share of all approved applications on a given day submitted by Black applicants. On

the ﬁrst day of the month, Black applicants account for approximately 4.4% of approved loans. In

the last week of the month, the share increases steadily, reaching just over 6% on the last day of

the month.

Furthermore, we study whether the within-month convergence in approval gap is sensitive

to the share of Black applicants that a lender processes. Figure 8(b) shows that the within-month

change in approvals occurs across the full range of lenders. The ﬁgure reports the median share

of approved loans from Black applicants, along with the 25th and 75th percentile, across lenders

that issued at least 10 loans per day on average over the year. The median share is close to 5.5%

in the ﬁrst two weeks of the month. However, it steadily increases in the last week of the month.

The shift involves the entire distribution. On the last day of the month, the median share is above

6%, the 25th percentile is approximately 4% and the 75th percentile is close to 10%. On the ﬁrst

day of the month, the median is below 5.5%, the 75th percentile shrinks close to 9% and the 25th

percentile falls below 3.5%.

5.3 Alternative Explanations

The evidence that the approval gap for Black applicants declines at the end of the month is consis-

tent with loan ofﬁcers having less scope for subjective decision-making when they have monthly

volume quotas, as shown by the framework outlined in Section 2. Yet, we consider plausible al-

ternative explanations, other than taste-based discrimination, for the change in approval rates over

the course of the month.

Before considering speciﬁc alternative explanations, we describe how the empirical design

limits the scope for alternative theories. First, it is unlikely that the within-month variation in ap-

proval rates can be explained by variation across lenders, because the estimates are hardly changed

by the inclusion of lender ﬁxed effects.

Second, our empirical strategy rules out the possibility of unobserved differences across

applicant groups. Therefore, any candidate alternative explanation has to have within-month vari-

ation and also has to have differential effects on Black applicants relative to other applicants. Not

only does this conﬁne alternative explanations to factors that vary within the month, it gives us

an avenue to test alternative theories. In particular, suppose that the indicator variable for Black

applicants reﬂects other unobserved characteristics, such as the riskiness of the loan, and that loan

ofﬁcers delay processing high-risk applications. If application risk explains the convergence in

approval rates across races over the course of the month, then the observed riskiness of the loan

application would explain within-month changes in approval rates. Put simply, we would expect

to ﬁnd that originations of observably high-risk applications submitted by Black applicants would

bunch at the end of the month, whereas low-risk applications would be relatively more evenly

distributed throughout the month.

Guided by these bounds on alternative theories, we take a holistic approach to confronting

alternative explanations by examining the within-month quantity of loan originations sorted by

credit scores (and applicant incomes). We study credit scores because they are possibly the most

important ingredient in loan approval decisions and mortgage pricing. They would also corre-

late with the most plausible alternative explanations: they directly measure the ex-ante risk of the

application, and low credit score applicants would be more likely to ﬁle low-documentation ap-

plications. As section 3 describes, the data only contains credit scores for applications that are

approved. As such, we study the quantity of new originations over the course of the month instead

of approval rates. However, such tests would be nearly equivalent to testing approval rates because

we have shown that mortgage demand does not vary within the month.

We ﬁnd that alternative explanations related to application quality are unlikely to explain the

within-month approval gap. Figures 9(a) and 10(a) plot the quantity of new originations sorted by

credit scores and incomes for applications submitted by Blacks and whites, respectively. Strikingly,

the volume of originations for prime-credit-score (FICO ≥ 660) and subprime (FICO < 660) Black

applicants are nearly identical over the course of the month (Figure 9(a)). We would have expected

to ﬁnd relatively more end-of-month bunching for subprime Black applicants if the results simply

reﬂected characteristics—such as risk—that correlate with applicants’ credit scores. Also, the end-

of-month bunching of originations is larger for Blacks than whites for both prime and subprime

applicants (comparing the levels in Figure 9(a) to those in Figure 10(a)). The difference between

Black and white originations would have been attenuated for prime applicants if characteristics

related to credit scores explained the within-month approval gap.

We ﬁnd similar evidence when we sort the volume of new originations into quartiles by appli-

cant incomes (Figure 9(b) and Figure 10(b)). Testing for end-of-month bunching across applicant

incomes not only fortiﬁes evidence from sorting by credit scores but also allows us to present ev-

idence from the full HMDA sample. We ﬁnd that there is substantial end-of-month bunching for

all four income quartiles. Moreover, in each corresponding quartile, the end-of-month bunching

for Black applicants is signiﬁcantly larger than for white applicants. These ﬁndings cast doubt on

alternative explanations related to within-month variation in application quality.

We provide additional evidence that racial differences in approval rates over the course of

the month do not merely reﬂect the possibility that race proxies for other loan characteristics. We

obtain such evidence by directly testing whether certain types of loans are more or less likely to

be approved over the course of the month. Speciﬁcally, Table 5 tests the regression speciﬁcation

in equation (9), but replaces the dependent variable with variables that measure loan quality: an

indicator for subprime loans (column 1), loan-to-value (LTV) ratios (column 2), an indicator for

low-documentation loans (column 3), and the interest rate (column 4). We ﬁnd that, of the four

loan characteristics, only low-documentation loans are more likely to be originated in the last

week of the month, but the effect is only weekly statistically signiﬁcant. Furthermore, Black

applicants with low-documentation applications are relatively less likely than white applicants to

be originated in the last week of the month. These results, combined with the above tests, suggest

that race has effects that are independent from loan characteristics—characteristics that vary by

race in the cross-section—over the course of the month.

Finally, we consider the possibility that our estimates of the within-month approval gap are

caused by the selection of when loan ofﬁcers choose to evaluate loan applications. Notably, if loan

ofﬁcers delay processing applications by Black applicants this would be an act of discrimination.

However, the primary alternative explanation regarding the timing of application processing is that

Black applications are more difﬁcult for lenders to process and therefore, spend a longer time in

inventory. We confront this alternative explanation in a few ways. Table 6, column (1) shows that

controlling for time-to-action (approval or denial) in equation (9) does not affect the regression

estimates of the within-month approval gap. Table 6 also estimates the approval gap using sub-

samples of the data sorting on time-to-action: 1 to 30 days, 31 to 60 days, 61 to 90 days and more

than 90 days (columns 2 through 5, respectively). We ﬁnd that the within-month approval gap

for Black applicants holds in all four sub-samples. Furthermore, there are no patterns across sub-

samples that would suggest that the approval gap is affected by the time that the application is held

in loan ofﬁcers’ inventory. These ﬁndings are inconsistent with the explanation that the approval

gap is caused by the timing of when applications are processed.

5.4 Outcome tests

Four our ﬁnal test, we turn to outcomes, and in particular to the performance of originated loans.

One may argue that there can still be differences in unobservable characteristics of approved loans

around month-end, that are not spanned by FICO, loan-to-value, documentation quality, applicant

and application characteristics, and that are not priced in mortgage interest rates. However, if such

differences, orthogonal to ex-ante observable characteristics, exist, they shall then be reﬂected

in ex-post loan performance. In other words, if loans originated at month-end are riskier due to

any unobservable characteristics correlated with race, then we should see these characteristics re-

Also, Table A.4 in the Appendix tests whether there are differences across races over the course of the month in

time-to-origination, time-to-denial, and time-to-action (approval or denial). We do not ﬁnd economically signiﬁcant

differences for Black applicants.

ﬂected in differences in average loan performance for loans originated in the last and ﬁrst week

of the month, after controlling for observables. Most importantly, we should ﬁnd a stronger dif-

ference in loan performance around month-end for Black applicants, after controlling for all other

characteristics.

We set out to conduct this test in Table 7. We use the same regression speciﬁcation as in Table

5, and set the dependent variable as a dummy equal to one for mortgages that defaulted within

5 years after origination.

In column (1), the sample contains loans across the entire observable

quality distribution, while in columns (2), (3) and (4) the sample is restricted to difﬁcult to evaluate

and risky loans. Estimates are based in column (2) on subprime loans (F ICO < 660), in column

(3) on high loan-to-value loans (LT V > 80%), and in column (4) on low documentation loans.

When considering the baseline differences between the last and ﬁrst week of the month for white

applicants and applicants of other races, we ﬁnd no statistically signiﬁcant effects after controlling

for observables. However, we do ﬁnd that, for Black applicants, after controlling for observables,

default rates are systematically lower than average in the last week of the month, and systematically

higher in the ﬁrst week of the month, both when considering all applications and when considering

only subprime, high LTV and low documentation applications. This effect is not negligible; when

considering the entire sample of application, roughly 1.7% of mortgage loans default within 5-

years. Black applicants’ loans are 0.33% less likely to default when originated in the last rather

than in the ﬁrst week of the month. Thus, the quality of Black applicants approved in the last

week of the month is higher, which is in direct contrast with the predictions of the risk-taking

explanation.

6 Lenders, Market Structure and Discrimination

Our empirical approach to estimating discrimination presents an avenue to study the effects of

policy on the quantity of discrimination. In this section, we explore how two important features

In Table A.5 in the Appendix we repeat the same analysis, but set the dependent variable as a dummy equal to

one for loans terminated (due to default or reﬁnancing) within 5 years after origination. Results are similar to the

ones for defaults reported in Table 7.

of the mortgage lending market—ﬁnancial innovation and competition across lenders—affect the

estimates of the approval gap for Black applicants that can be attributed to loan ofﬁcers’ subjec-

tivity. Intuitively, innovation in ﬁnancial technologies is supposed to mitigate subjective decision-

making by individuals, and the same could be said of innovation promoting more lean and efﬁcient

organizational structures, such as shadow banks. Moreover, according to theory (Becker, 1957),

increased competition should eliminate a proﬁt-maximizing agent’s ability to engage in taste-based

discrimination. Then, both factors should reduce the scope for subjective taste in loan decisions.

The weaker the role of taste-based discrimination in normal days, the weaker the month-end effects

should be, and the narrower the approval gap between whites and Blacks should be.

6.1 FinTech and Shadow Bank Lending

This section studies the effects of the recent growth of ﬁnancial technologies and new forms of

lending institutions on the racial lending gap. The rise of FinTech and shadow banks has been a

major trend in mortgage lending over the last decade in the United States.

First, we compare Fin-

Tech lenders to non-FinTech lenders. FinTech lenders rely on complex models rather than human

decisions in loan approvals and have been shown to improve the speed of the origination process

(Fuster et al., 2019). Second, we compare shadow banks to mortgage originators from “tradi-

tional” depository institutions. Shadow banks are less regulated than traditional banks. Buchak

et al. (2018) show that having fewer regulations allows shadow banks to have a larger operating

presence in underserved communities. However, the overall effect of FinTech and shadow banking

on minorities’ access to credit is still an open question (see e.g., Fuster et al., 2017; Bartlett et al.,

2019). We use our novel empirical strategy to shed new light on this important topic.

Our analysis uses the classiﬁcations of FinTech lenders and shadow banks provided by

Buchak et al. (2018).

Their hand-collected classiﬁcation deﬁnes FinTech lenders as those that

Buchak et al. (2018) show that the market share of shadow banks has nearly doubled, from 30% in 2007 to

more than 50% in 2017.

Fuster et al. (2019) use loan processing times to classify FinTech lenders. Though we ﬁnd this measure appeal-

ing, it would not be well-suited to our analysis. Our analysis focuses on the differences in loan processing across

races. To the extent that there could be differences in the processing times across races, such an analysis would con-

found the classiﬁcation of FinTech lenders.

have a large online presence and that process the majority of mortgage applications online. How-

ever, the authors note that human interaction is not completely absent for FinTech lenders. Mort-

gage applicants have to engage with a loan ofﬁcer during the closing process even if applications

are submitted online. On the other hand, shadow banks have a straightforward classiﬁcation. The

authors deﬁne non-shadow banks as mortgage originators that also take deposits, and classify all

other mortgage lenders as shadow banks. In this section, we restrict the sample of mortgage appli-

cations from HMDA to the period between 2014 and 2018, since the rise in FinTech and shadow

banking is a recent phenomenon.

In Table 8 we study approval patterns around month-end for FinTech lenders and shadow

banks, after carefully controlling for differences in loan and applicant characteristics, using the

same set of controls that we introduce in column (6) of Table 4.

Starting from the comparison

between FinTech and non-FinTech lenders, in columns (1) and (2), we restrict the sample to each

one of these two categories, and separately estimate equation (9). We ﬁnd that for FinTech lenders

the increase in approvals is 9% for whites and 13% for Blacks, while the increases are only 5.6%

and 9.2% for non-FinTech lenders. When considering shadow banks (columns (4) and (5)), the

increase in approval rates is only 5% for whites and 7.3% for Blacks. The same differences are

larger for non-shadow banks, equal to 7.7% and 12%, respectively.

To provide a test for the differences between FinTech and non-FinTech lenders, and shadow

and non-shadow banks, we estimate a new regression equation:

Appr

= δ

lw,Black ,Z

× I

Black

× Z

) + δ

fw,Black,Z

× I

Black

× Z

) + (10)

+ δ

lw,Black

× I

Black

) + δ

fw,Black

× I

Black

) + δ

+ δ

lw,Z

× Z

) + δ

fw,Z

× Z

) + δ

Black

+ δ

Black,Z

Black

× Z

)

+ BX

+ a

ym,c

+ a

ym,i

+ a

dow

+ a

holiday

+ u

j,t

Figures 4(a) and 4(b) in the Appendix provide a ﬁrst look at approval patterns around month-end for FinTech

lenders and shadow banks, based on the raw data.

This speciﬁcation is constructed by augmenting equation (9) with interaction terms, captur-

ing the effect of lender characteristic Z

on approval rates (coefﬁcients δ

lw,Z

and δ

fw,Z

), and on the

approval rates for Black applicants (coefﬁcients δ

lw,Black ,Z

and δ

fw,Black,Z

). The variable Z

will

consist of either a dummy equal to one for FinTech lenders, or a dummy equal to one for shadow

banks.

Our results for FinTech lenders are reported in column (3). Interestingly, the coefﬁcient

lw,Z

is positive and statistically signiﬁcant, and close to 3%. Thus, there is a higher increase in

approval rates for white applicants in the last week of the month for FinTech lenders. However,

the incremental effects on Black applicants are not signiﬁcant. The coefﬁcients on the individual

dummies δ

lw,Black ,Z

and δ

fw,Black,Z

are statistically indistinguishable from 0, and their difference

is also not statistically signiﬁcant at conventional conﬁdence levels.

In column (6) we turn to shadow banks. The coefﬁcient δ

lw,Z

is negative, while δ

fw,Z

positive, thus taking the opposite signs as the baseline month-end ﬂuctuation in approval rates.

Both are statistically signiﬁcant. For white applicants, the increase in approval rates is smaller

for shadow, rather than non-shadow, banks by roughly 2.8%. Moreover, the marginal increase in

approval rates for Black applicants (δ

lw,Black ,Z

− δ

fw,Black,Z

) is smaller by 1.8% (signiﬁcant at the

95% conﬁdence level) for shadow banks. Thus, shadow banks seem to experience smaller month-

end effects in general, and in particular for Black applicants. Consistent with this ﬁnding, the

coefﬁcient on the interaction between the Black applicant and the shadow bank dummy reveals that

in normal days (outside the last and ﬁrst week of the month) approval rates for Black applicants

are 5% higher for shadow banks than for traditional depository institutions. There is again no

difference when comparing FinTech and non-FinTech lenders.

Summing up, shadow banks appear to have smaller month-end effects, and a more equal

treatment of white and Black applicants. This is consistent with our conjecture that more efﬁcient

institutions would leave less room for taste-based discrimination. However, quite surprisingly,

this does not seem to be the case for FinTech lenders, which experience larger month-end spikes in

approvals, and are subject to a similar degree of taste-based discrimination as non-FinTech lenders.

There are two potential explanations for this result. First, the criteria currently used in the

literature to identify FinTech companies might be ﬂawed, or noisy. Second, while up-to-date

statistical and machine learning models may provide loan ofﬁcers with more accurate insights on

credit risk, FinTech lenders may still leave loan ofﬁcers free to blend model insights with their own

subjective judgment. Both explanations have potentially important implications for our current

assessment and understanding of the role of FinTech lenders in the mortgage market, and deserve

further investigation in future research.

6.2 Market Structure and Competition

While the previous section has focused on lender characteristics, we now turn to the relationship

between lending market structure and month-end ﬂuctuations in approval rates, and ultimately the

relationship between market structure and discrimination.

We ﬁrst focus on local (county-level) market concentration. To measure concentration, in

each county and year in our sample we construct two measures based on the number of mortgage

originations by lender using the HMDA data: the share of total mortgages originated by the 4

institutions with the largest number of originations, and the Herﬁndahl-Hirschman Index (HHI)

based on within county shares of mortgage originations in the previous year. Our analysis is

reported in Table 9.

In columns (1) and (2) we restrict the sample to counties with top 4 share

above and below median. We ﬁnd that the magnitude of the increase in approval rates for Blacks is,

in relative terms, 50% larger than the one for whites in both groups. In general, the magnitude of

the increases for Blacks and whites are roughly the same for high and low top 4 share counties. The

same is true when comparing counties with HHI above and below median, as shown in columns (4)

and (5). In columns (3) and (6) we report estimates from the speciﬁcation in equation (10) (with Z

now a dummy equal to one for above median top 4 share or above median HHI counties), which we

use to test the triple interaction effects between last and ﬁrst week of the month, Black applicant

and market concentration. We ﬁnd that these effects are not statistically signiﬁcant. Differences

Results based on the raw data are reported in ﬁgures 5(a) and 5(b) in the Appendix.

between high and low concentration counties in the month-end approval rates increase for whites

are signiﬁcant, but quantitatively negligible.

If we interpret concentrations as a proxy for local competition among lenders (Cetorelli and

Strahan, 2006), then this evidence suggests that local competition among lenders does not translate

into higher competition and smaller room for subjective decision making and biases at the level of

individual loan ofﬁcers.

An alternative channel through which we may capture the effects of local competition is by

comparing large and small lenders. Small lenders are naturally more concentrated in a small num-

ber of markets, and might compete more ﬁercely in those markets. Thus, we construct a proxy for

lender size, equal to the average number of mortgage originations per year. We compute the over-

all average annual mortgage origination volume for each lender and split lenders into two groups,

depending on whether their size is above or below the median across lenders in the United States.

In Table 10 we conduct regression tests analogous to the ones in Tables 8 and 9.

When splitting

the sample between lenders with above and below median size, we ﬁnd that for the former group

the increase in approval rate around month-end is 7.2% for white applicants and 10% for Black

applicants. For the latter group, the increases are smaller: 5.2% and 8.9%. Nonetheless, in col-

umn (3) we ﬁnd that the magnitude of the change in the approval gap for Black applicants around

month-end is indistinguishable between large and small size lenders. Overall, our results suggest

that, even when market forces increase competition across institutions, discriminatory practices

persist within institutions.

7 Conclusions

Tests for taste-based discrimination are often unconvincing because subject groups tend to have dif-

ferent unobserved characteristics. We show that high-frequency evaluations can help address the

omitted variable problem when there is variation in the degree to which decision-makers rely on

subjective evaluations. Under the null that decision-makers do not engage in taste-based discrim-

See ﬁgure A.6 for the results from the raw data.

ination, and assuming that the applicant pool is constant, a decrease in the degree of subjectivity

should have no impact on the likelihood of favorable decisions for minority subjects relative to

majority subjects. A reduction in disparate treatment for minority subjects would instead reveal

the presence of taste-based discrimination.

We use our approach to provide new evidence of discrimination in mortgage lending in the

U.S. First, we document an “end-of-month effect” in which the volume of new mortgage origi-

nations increases by over 150% relative to the start of the month. This increase is caused by the

performance incentives of loan ofﬁcers – the fact that loan ofﬁcers have monthly performance

targets. Next, we show that the within-month pattern of loan approvals varies by the mortgage

applicants’ race. The gap in approval rates between white and Black applicants attenuates by half

at the end of the month, when loan ofﬁcers need to approve more applications to meet their perfor-

mance targets. There are no observable within-month racial patterns in application volume and no

within-month patterns of application quality that could explain the results.

Our ﬁndings have important policy implications for the distribution of credit in consumer

credit markets. Legislation such as the Community Reinvestment Act and the Equal Credit Oppor-

tunity Act has been implemented over the past several decades to counteract historical inequities

in credit access (e.g., red-lining; Appel and Nickerson, 2016; Aaronson et al., 2017). A crucial

aspect of such legislation is that it intends to modify the behavior of lending institutions. We show

that patterns of discriminatory behavior by loan ofﬁcers exist within-institution and such behavior

is not mitigated by important features of the market structure of lending markets—namely Fin-

Tech, institution size, and competition across lenders. This suggests that policies targeted toward

institutions will have limited effects so long as individuals use their discretion to allocate credit.

Seeing as institution-level policies do not eliminate biases held by individuals, it calls into

question what policies would be effective. In accordance with classic economic theories of discrim-

ination (Becker, 1957), competition reduces taste-based discrimination. Such competition occurs

in the labor market for loan ofﬁcers. Loan ofﬁcers have to meet monthly performance targets oth-

erwise they would have less compensation and risk being ﬁred. However, loan ofﬁcers’ preference

for discrimination is not fully undone by labor market competition, suggesting that there are bar-

riers to entry in the labor market. Indeed, loan ofﬁcers need at least a bachelor’s degree in a ﬁeld

related to ﬁnance or business, and they have to obtain and maintain a license.

There are two recommendations that emerge from our study. First, the collection of high-

frequency data on evaluations, combined with our approach, can be used to estimate the amount of

discrimination across a variety of contexts and markets. Second, enhancing the data collection to

go beyond the institution and down to individual decision-makers can provide further insight into

the factors that determine discrimination. Such data can be used by researchers and policy-makers,

as well as by consumers, for instance when shopping for credit in the mortgage market.

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Figures

percent

1 6 11 16 21 26 31

day of month (application)

Percent of applications by Black applicants

(a) Share of Black Applicants

percent

1 6 11 16 21 26 31

day of month (application)

white Black

Percent of below median income applicants by day of application

(b) Originated Loans

percent

1 6 11 16 21 26 31

day of month (application)

white Black

Percent of below median income originated loans by day of application

percent

1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 14 13 12 11 10 9 8 7 6 5 4 3 2 1

days from start of month days from end of month

white Black

Percent of below median income outstanding applicants

(d) Low Income, Outstanding Applications

Figure 3: Panel (a) of the ﬁgure shows the average fraction of applications by Blacks (out of all applications) based

on the day of the month in which the application was ﬁled. Panel (b) shows the fraction of applications by white

and Black applicants with income below the county median in the year, based on the day of the month in which the

applications were ﬁled. Panel (c) shows the fraction of loans originated to white and Black applicants with income

below the county median in the year, based on the day of the month in which the original applications were ﬁled.

Panel (d) shows the fraction of applications with income below the county median in the year, out of all applications

outstanding on each day of the month, for white and Black applicants. The results in all panels of the ﬁgure are based

on the HMDA data from January 1994 to December 2018.

100

150

200

250

percent

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

high year-over-year growth

low year-over-year growth

Number of loans originated (relative to first day of month)

(a) Effects of YoY Performance: Volume

.55

.65

.75

.85

percent

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

high year-over-year growth

low year-over-year growth

Approval rates

(b) Effects of YoY Performance: Approval Rates

Figure 4: Panel (a) of the ﬁgure shows average percentage abnormal daily loan origination volume in the U.S., sep-

arately for lenders that, on each day, have high (top quartile across all lenders in the year) and low (bottom quartile

across all lenders in the year) performance growth relative to the same month in the previous year (deﬁned according

to equation 7). The darker bars are for lenders with high performance growth, while the lighter bars are for lenders

with low performance growth. Abnormal origination volume is reported for the last eight days of the month, and the

ﬁrst seven days of the following month, and is computed with respect to volume on the ﬁrst day of the month. Panel

(b) of the ﬁgure shows the approval rate, across all decisions taken on loan application on each day in the U.S., sepa-

rately for high and low performance growth lenders, and for the last eight days of the month and the ﬁrst seven days

of the following month. The results in both panels of the ﬁgure are based on the HMDA data from January 1994 to

December 2018.

.65

.75

.85

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

Approval rates

Figure 5: The ﬁgure shows the average approval rate (approved applications over approved and denied applica-

tions) at the level of the entire United States, for the last eight days of the month, and the ﬁrst seven days of the fol-

lowing month. The results in the ﬁgure are based on the HMDA data from January 1994 to December 2018.

100

150

200

250

percent

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

white Black other race

Number of loans originated (relative to first day of month)

Figure 6: The ﬁgure shows average percentage abnormal daily loan origination volume in the U.S., by race group

(whites, Blacks and other races). Abnormal volume is reported for the last eight days of the month, and the ﬁrst

seven days of the following month, and is computed with respect to loan origination volume on the ﬁrst day of the

following month, for each group of applicants. The results in the ﬁgure are based on the HMDA data from January

1994 to December 2018.

-.25

-.2

-.15

-.1

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

Average approval rate gap (Black minus white applications)

(a) Approval Gap (Raw Data)

-.1

-.08

-.06

-.04

-.02

residuals

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

Average approval rate gap (Black minus white applications, residuals)

(b) Approval Gap (Residuals)

Figure 7: The ﬁgure shows the approval gap for Blacks. Panel (a) reports the difference between the fraction of

approved loans, out of all approved and denied loans in the U.S., for Blacks minus the one for whites, on each of the

last eight days of the month and the ﬁrst seven days of the following month. Panel (b) reports residual differences

in approval rates after controlling for loan applicant characteristics. The day-by-day difference in approval rates

is attained by ﬁrst estimating the complete speciﬁcation of equation 9 (see column 6 of Table 4), but omitting the

dummies for actions taken in the ﬁrst and last week of the month. We then average regression residuals on each day,

separately for Black and white applicants, and compute the difference between the daily averages to estimate the

(controlled) approval gap on each day. Estimates are based on a 5% sample of the HMDA data from January 1994 to

December 2018.

4.5

5.5

6.5

percent

1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 14 13 12 11 10 9 8 7 6 5 4 3 2 1

days from start of month days from end of month

Share of approved loans by Black applicants out of all loans (by approval date)

(a) United States

percent

1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 14 13 12 11 10 9 8 7 6 5 4 3 2 1

days from start of month days from end of month

median 25-75 percentile range

Distribution of lender approval shares (Black applicants out of all loans)

(b) Individual Lenders

Figure 8: Panel (a) of the ﬁgure shows the share of approved applications from Black applicants, out of all ap-

proved applications on each day in the two weeks before and after the end of the month in the United States. The

results in this panel are based on a 5% random sample of the HMDA data from January 1994 to December 2018.

Panel (b) shows the distribution (median, 25th percentile and 75th percentile) of the share of approved applications

from Blacks at the lender level on each day, for all lenders that originate on average at least 10 loans per-day. The

results in this panel are based on the whole HMDA sample from January 1994 to December 2018.

100

200

300

400

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

prime subprime

Number of loans originated to Black applicants (% relative to first day of month)

(a) Effects for Prime/Subprime Black Applicants

100

150

200

250

percent

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

1st income quartile 2nd income quartile

3rd income quartile 4th income quartile

Number of loans originated to Black applicants (relative to first day of month)

(b) Effects by Income Quartile Black Applicants

Figure 9: Panel (a) of the ﬁgure shows average percentage abnormal daily loan origination volume in the U.S., for

Blacks with prime (660 or higher) and subprime FICO. Abnormal volume is reported for the last eight days of the

month, and the ﬁrst seven days of the following month, and is computed with respect to loan origination volume on

the ﬁrst day of the following month for each applicant group. Estimates are based on the merged sample of HMDA

and Black Knight McDash data from 1994 to 2018. Panel (b) of the ﬁgure shows average percentage abnormal daily

loan origination volume separately for Blacks belonging to different income quartiles within county. The results in

this panel are based on the HMDA sample from January 1994 to December 2018.

100

200

300

400

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

prime subprime

Number of loans originated to white applicants (% relative to first day of month)

(a) Effects for Prime/Subprime White Applicants

100

150

200

percent

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

days around last day of month

1st income quartile 2nd income quartile

3rd income quartile 4th income quartile

Number of loans originated to white applicants (relative to first day of month)

(b) Effects by Income Quartile White Applicants

Figure 10: Panel (a) of the ﬁgure shows average percentage abnormal daily loan origination volume in the U.S.,

for whites with prime (660 or higher) and subprime FICO. Abnormal volume is reported for the last eight days of the

month, and the ﬁrst seven days of the following month, and is computed with respect to loan origination volume on

the ﬁrst day of the following month for each applicant group. Estimates are based on the merged sample of HMDA

and Black Knight McDash data from 1994 to 2018. Panel (b) of the ﬁgure shows average percentage abnormal daily

loan origination volume separately for Blacks belonging to different income quartiles within county. The results in

this panel are based on the HMDA sample from January 1994 to December 2018.

Tables

Panel (a): Statistics by Year

Year Apps Number Orig Number Loan Amount Lenders Average Orig Number Average Loan Size

(Millions) (Millions) ($ Billions) Number Per Lender ($ 1,000)

1994 12.22 8.25 774.16 9876 835.62 93.81

1995 11.22 7.15 648.27 9544 748.90 90.70

1996 14.42 8.61 799.96 9333 922.24 92.94

1997 15.56 8.78 876.75 7931 1106.87 99.87

1998 23.24 13.75 1531.01 7846 1752.67 111.33

1999 21.71 11.68 1315.98 7824 1492.54 112.69

2000 18.42 9.37 1084.18 7705 1215.83 115.73

2001 23.87 13.69 1856.97 7628 1794.62 135.65

2002 29.06 18.12 2739.76 7780 2329.56 151.17

2003 37.26 23.65 3736.00 8117 2913.08 158.00

2004 30.41 16.41 2782.34 8864 1851.35 169.55

2005 32.13 16.78 3077.99 8859 1894.14 183.43

2006 29.28 15.03 2792.80 8893 1689.79 185.85

2007 23.84 12.00 2359.11 8632 1389.98 196.62

2008 16.15 8.16 1617.75 8418 969.82 198.16

2009 15.91 9.34 1903.12 8148 1146.43 203.74

2010 13.52 8.14 1701.14 7929 1026.50 209.01

2011 12.38 7.43 1563.70 7677 968.46 210.32

2012 16.24 10.37 2266.83 7429 1396.37 218.52

2013 15.19 9.52 2086.19 7201 1322.66 219.03

2014 10.12 5.98 1386.26 7050 848.17 231.83

2015 12.27 7.40 1847.68 6907 1071.99 249.54

2016 14.10 8.38 2180.81 6756 1240.07 260.31

2017 12.23 7.36 2042.92 5860 1255.25 277.73

2018 13.12 7.72 1985.78 5678 1359.87 257.18

Panel (b): Statistics by Applicant Race (1994:2018)

Race Share Average Loan Share Low Share Share Primary Share New Approval Share of

of Applications Amount ($ 1,000) Income Apps Conforming Residence Purchases Rate Approved Loans

White 66.95% 156.21 46.03% 87.24% 91.08% 41.64% 80.72% 73.72%

Black 7.34% 125.12 59.75% 89.23% 91.40% 42.73% 63.25% 5.73%

Other Race 25.71% 176.69 47.80% 87.09% 90.25% 32.95% 69.00% 20.55%

Table 1: Summary statistics for the HMDA loan applications data, covering the whole United States. Panel (a) re-

ports statistics for each year from 1994 to 2018. Panel (b) reports statistics by groups based on applicant race. In

panel (b), Share of Applications is the share of applications belonging to each group out of the total, Share Low In-

come Apps is the fraction of applicants with income below the median in the county and year of the application,

within each group, Share Conforming is the fraction of conforming loans, within each group, Share Primary Resi-

dence is the fraction of loans for which the collateral is the primary residence of the applicant, within each group,

Share New Purchases is the fraction of loans for new house purchase, within each group, Approval Rate is the frac-

tion of approved loans, within each group, and Share of Approved Loans is the fraction of approved loans belonging

to each group of applicants, out of the total.

U.S.-Level

(1) (2) (3) (4) (5) (6)

log(Num Loans) log(Num Loans) log(Num Loans) log($ Amount) log(Num Loans) log(Num Loans)

CRA non-CRA

lastweek 0.25*** 0.31*** 0.31*** 0.36*** 0.18*** 0.36***

(0.052) (0.016) (0.012) (0.013) (0.013) (0.013)

firstweek -0.22*** -0.15*** -0.15*** -0.14*** -0.11*** -0.18***

(0.052) (0.016) (0.012) (0.013) (0.013) (0.013)

Holiday FE NO YES YES YES YES YES

Day-of-Week FE NO YES YES YES YES YES

Month FE NO YES NO NO NO NO

Month-Year FE NO NO YES YES YES YES

last − f irst 0.47 0.46 0.46 0.50 0.29 0.54

p − value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

N 9131 9131 9131 9131 9131 9131

r2 0.0064 0.91 0.95 0.95 0.95 0.94

Table 2: The table reports regression estimates of the abnormal loan originations volume in the last and ﬁrst week

of the month (see equation 6). In columns (1) to (3) the dependent variable is the log of the number of originations

per day in the United States. In column (4), the dependent variable is the total dollar amount of loan originations per

day in the United States. In columns (5) and (6) the dependent variable is the log number of originations, respec-

tively, for lenders subject to CRA examination and not subject to CRA examination. lastweek and firstweek are

dummies equal to one, respectively, in the ﬁrst and last week of the month. The different columns present estimates

based on different choices of lender and seasonality ﬁxed effects. Estimates are based on the sample of HMDA mort-

gage originations from 1994 to 2018.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

All Male White Black Other Race Income > Med Income ≤ Med Income Q1 Income Q2 Income Q3 Income Q4 Loan > Med Loan ≤ Med

lastweek 0.029*** 0.028*** 0.026*** 0.050*** 0.028*** 0.024*** 0.034*** 0.038*** 0.031*** 0.026*** 0.023*** 0.031*** 0.028***

(0.00088) (0.00091) (0.00090) (0.0014) (0.00087) (0.00083) (0.0010) (0.0012) (0.0011) (0.00090) (0.00087) (0.0011) (0.00087)

f irstweek -0.016*** -0.016*** -0.016*** -0.025*** -0.016*** -0.015*** -0.019*** -0.021*** -0.019*** -0.016*** -0.013*** -0.018*** -0.017***

(0.0011) (0.0011) (0.0011) (0.0018) (0.0010) (0.00094) (0.0011) (0.0013) (0.0011) (0.00097) (0.00091) (0.00095) (0.0012)

Holiday FE YES YES YES YES YES YES YES YES YES YES YES YES YES

Day-of-Week FE YES YES YES YES YES YES YES YES YES YES YES YES YES

Month-Year FE YES YES YES YES YES YES YES YES YES YES YES YES YES

Lender FE YES YES YES YES YES YES YES YES YES YES YES YES YES

last − f irst 0.045 0.044 0.042 0.076 0.044 0.038 0.052 0.058 0.050 0.043 0.037 0.049 0.045

p − value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

N 5749198 5468592 5457749 2561526 5711340 5209254 5177984 4496837 4541807 4560944 4509888 5027344 5279720

r2 0.35 0.32 0.32 0.26 0.35 0.32 0.31 0.29 0.28 0.28 0.30 0.32 0.32

Table 3: The table reports regression estimates of abnormal approval rates in the last and ﬁrst week of the month (see equation 8). The dependent variable is the

approval rate (approval decisions over approval and denial decisions) per day and lender. Column (1) reports results for all applicants, while the other columns

report results for subgroups of applicants based on sex, race, income and loan amount. Income ≤ Med and Loan ≤ Med are income and loan amount smaller

than or equal to the median in the county and year. Income Q1, Income Q2, Income Q3 and Income Q4 are quartiles of the income distribution in each county and

year. lastweek and firstweek are dummies equal to one, respectively, in the ﬁrst and last week of the month. Standard errors are clustered by lender and year.

Estimates are based on the sample of HMDA mortgage applications and originations from 1994 to 2018.

(1) (2) (3) (4) (5) (6)

approval approval approval approval approval approval

Black White & Other All All All All

lastweek 0.090*** 0.057***

(0.0043) (0.0037)

firstweek -0.032*** -0.022***

(0.0028) (0.0025)

black -0.12*** -0.10*** -0.070*** -0.068***

(0.0069) (0.0062) (0.0053) (0.0043)

lastweek 0.057*** 0.048*** 0.044*** 0.043***

(0.0037) (0.0035) (0.0031) (0.0031)

black × lastweek 0.036*** 0.032*** 0.028*** 0.027***

(0.0021) (0.0023) (0.0022) (0.0023)

firstweek -0.022*** -0.021*** -0.019*** -0.020***

(0.0025) (0.0021) (0.0018) (0.0017)

black × firstweek -0.010*** -0.0081*** -0.0073*** -0.0072***

(0.0015) (0.0014) (0.0024) (0.0015)

log(income) 0.095*** 0.073*** 0.071***

(0.0061) (0.0039) (0.0036)

log(loan amount) 0.031*** 0.0089*** 0.0076***

(0.0075) (0.0029) (0.0023)

is conforming 0.13*** 0.092*** 0.090***

(0.0093) (0.0057) (0.0057)

Loan-Level Controls NO NO NO YES YES YES

Holiday FE YES YES YES YES YES YES

Day-of-Week FE YES YES YES YES YES YES

Month-Year FE YES YES YES YES YES NO

County FE YES YES YES YES YES NO

Lender FE NO NO NO NO YES NO

Month-Year-County NO NO NO NO NO YES

Month-Year-Lender NO NO NO NO NO YES

last − f irst 0.12 0.079 0.079 0.068 0.063 0.063

p − value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

last − f irst (black) 0.13 0.11 0.099 0.097

p − value (bl ack) 0.0000 0.0000 0.0000 0.0000

last − f irst (black − other) 0.046 0.040 0.035 0.034

p − value (bl ack − other) 0.0000 0.0000 0.0000 0.0000

N 1440405 18200483 19641147 18464497 18463245 17898939

r2 0.050 0.034 0.041 0.092 0.23 0.32

Table 4: The table reports individual loan-level regression estimates of abnormal approval rates in the last and ﬁrst

week of the month (see equation 9). The dependent variable is a dummy that takes value 1 if a loan application is

approved and 0 if it is denied. lastweek and f irstweek are dummies equal to one, respectively, if the decision on

the application is taken in the ﬁrst and last week of the month. black is a dummy equal to one for Black applicants.

In columns (1) and (2), the sample is restricted to, respectively, Blacks and whites or other race applicants. The table

also reports estimates of the difference between the coefﬁcients for the dummies lastweek and f irstweek, and

for the difference of the interaction coefﬁcients for Black applicants, along with the p-value of tests of the null that

each difference is equal to 0. Standard errors are clustered by lender and year. Estimates are based on a 5% random

sample of the HMDA data from 1994 to 2018.

(1) (2) (3) (4)

Subprime Origination Low Origination

(FICO < 660) LTV (%) Documentation Interest Rate

lastweek 0.00029 0.0062 0.042* 0.00096

(0.00079) (0.070) (0.023) (0.0011)

f irstweek 0.00059 -0.15*** -0.0012 0.00016

(0.00042) (0.028) (0.0012) (0.00094)

black 0.12*** 3.09*** 0.0014 0.0013

(0.0066) (0.24) (0.0034) (0.0019)

black × lastweek 0.0020 -0.32*** -0.018** -0.00076

(0.0014) (0.081) (0.0068) (0.00068)

black × f irstweek 0.0031* 0.098* -0.00042 0.00022

(0.0016) (0.054) (0.0011) (0.00071)

LTV 0.0016*** 0.00032 0.00043

(0.00035) (0.00055) (0.00044)

log(income) -0.011*** -9.02*** 0.013** 0.000068

(0.0039) (0.84) (0.0051) (0.0081)

log(loan amount) -0.041*** 19.8*** -0.028 -0.049***

(0.0061) (1.60) (0.022) (0.012)

is conforming -0.0061** 7.98*** 0.053*** -0.036***

(0.0030) (0.67) (0.012) (0.0062)

FICO 620:659 -1.59*** 0.019 -0.00015

(0.46) (0.025) (0.010)

FICO 660:719 -2.83*** 0.043 -0.020*

(0.56) (0.040) (0.011)

FICO 720:759 -3.99*** 0.051 -0.036***

(0.71) (0.051) (0.011)

FICO 760:799 -7.34*** 0.052 -0.051***

(0.74) (0.054) (0.0099)

FICO ≥ 800 -10.6*** 0.060 -0.065***

(0.67) (0.052) (0.0081)

last − f irst -0.0003 0.1500 0.0430 0.0008

p − value 0.7600 0.0830 0.0690 0.6800

last − f irst (black) -0.0014 -0.2600 0.0250 -0.0002

p − value (black) 0.6100 0.0077 0.1500 0.9100

last − f irst (black − other) -0.0011 -0.4200 -0.0180 -0.0010

p − value (black − other) 0.6600 0.0005 0.0130 0.3700

N 27701585 27701585 18125835 24187005

r2 0.26 0.51 0.51 0.78

Table 5: The table reports regression estimates of the difference in characteristics between mortgages originated

in the last and ﬁrst week of the month. The dependent variables are a dummy equal to one for subprime loans (with

FICO < 660, see column (1)), the mortgage LTV at origination (column (2)), a dummy equal to one for mortgages

for which the applicant provided low documentation (column (3)), and the mortgage interest rate at origination (col-

umn (4)). lastweek and f irstweek are dummies equal to one in the ﬁrst and last week of the month. black is a

dummy equal to one for Black applicants. The table also reports estimates of the difference between the coefﬁcients

for the dummies lastweek and f irstweek, and for the difference of the interaction coefﬁcients for Black applicants,

along with their p-values. Standard errors are clustered by lender and year. Estimates are based on the merged sam-

ple of HMDA and Black Knight McDash data from 1994 to 2018.

(1) (2) (3) (4) (5)

approval approval approval approval approval

1-30 Days TTA 31-60 Days TTA 61-90 Days TTA > 90 Days TTA

lastweek 0.038*** 0.053*** 0.027*** 0.027*** 0.023***

(0.0026) (0.0033) (0.0031) (0.0030) (0.0034)

firstweek -0.019*** -0.016*** -0.017*** -0.019*** -0.017***

(0.0018) (0.0017) (0.0017) (0.0027) (0.0027)

black -0.056*** -0.072*** -0.043*** -0.037*** -0.030***

(0.0039) (0.0050) (0.0032) (0.0035) (0.0032)

black × lastweek 0.023*** 0.023*** 0.021*** 0.015*** 0.015***

(0.0020) (0.0025) (0.0020) (0.0023) (0.0037)

black × firstweek -0.0094*** -0.0043** -0.015*** -0.0053 -0.0056

(0.0017) (0.0019) (0.0027) (0.0033) (0.0036)

log(TTA) 0.11***

(0.0069)

log(income) 0.058*** 0.083*** 0.038*** 0.040*** 0.036***

(0.0029) (0.0048) (0.0026) (0.0029) (0.0035)

log(loan amount) -0.021*** 0.0022 -0.013*** -0.017*** -0.012***

(0.0026) (0.0029) (0.0020) (0.0026) (0.0035)

is conforming 0.058*** 0.10*** 0.039*** 0.035*** 0.033***

(0.0044) (0.0072) (0.0043) (0.0042) (0.0035)

last − f irst 0.057 0.069 0.044 0.046 0.040

p − value 0.0000 0.0000 0.0000 0.0000 0.0000

last − f irst (black) 0.089 0.096 0.080 0.065 0.061

p − value (bl ack) 0.0000 0.0000 0.0000 0.0000 0.0000

last − f irst (black − other) 0.032 0.027 0.036 0.020 0.021

p − value (bl ack − other) 0.0000 0.0000 0.0000 0.0000 0.0000

N 16503563 9038519 4907587 1420393 1332868

r2 0.35 0.40 0.29 0.37 0.42

Table 6: The table reports individual loan-level regression estimates of abnormal approval rates in the last and ﬁrst

week of the month (see equation 9), controlling for time to action (TTA), deﬁned as the number of days between

the application date and the date in which action (approval or denial) of the loan is taken. In column (1), the log of

TTA is included as a control. In columns (2) to (5), the sample is restricted to loans with TTA, respectively, between

1 and 30 days, between 31 and 60 days, between 61 and 90 days, and longer than 91 days. The dependent variable

is a dummy that takes value 1 if a loan application is approved and 0 if it is denied. lastweek and f irstweek are

dummies equal to one, respectively, if the decision on the application is taken in the ﬁrst and last week of the month.

black is a dummy equal to one for Black applicants. The table also reports estimates of the difference between the

coefﬁcients for the dummies lastweek and f irstweek, and for the difference of the interaction coefﬁcients for

Black applicants, along with the p-value of tests of the null that each difference is equal to 0. Standard errors are

clustered by lender and year. Estimates are based on a 5% random sample of the HMDA data from 1994 to 2018.

(1) (2) (3) (4)

5-Year Default 5-Year Default 5-Year Default 5-Year Default

FICO < 660 LTV > 80% Low Docs

lastweek -0.00011 -0.00016 -0.00031 0.00042

(0.00027) (0.00047) (0.00033) (0.00077)

f irstweek 0.00044 0.0011 0.00097* 0.00049

(0.00027) (0.00064) (0.00054) (0.00041)

black 0.0033** 0.0011 0.0017 0.0075***

(0.0012) (0.0012) (0.0015) (0.0024)

black × lastweek -0.0013** -0.0020 -0.0022*** -0.0039**

(0.00059) (0.0011) (0.00062) (0.0016)

black × f irstweek 0.0020*** 0.0011 0.0025** 0.0033***

(0.00060) (0.00096) (0.00095) (0.0011)

LTV 0.00032** 0.00049** -0.00016 0.00079**

(0.00012) (0.00018) (0.00030) (0.00033)

log(income) -0.0020 -0.011*** -0.012*** -0.0039**

(0.0016) (0.0036) (0.0022) (0.0016)

log(loan amount) -0.0027 0.0021 0.0061*** 0.0029

(0.0035) (0.0076) (0.0021) (0.0038)

is conforming -0.0037** -0.013*** -0.0075** -0.0051**

(0.0016) (0.0044) (0.0032) (0.0021)

FICO 620:659 -0.0063 -0.0040 -0.013*** 0.0030

(0.0045) (0.0042) (0.0030) (0.0050)

FICO 660:719 -0.020*** -0.026*** -0.014***

(0.0048) (0.0044) (0.0038)

FICO 720:759 -0.029*** -0.035*** -0.028***

(0.0058) (0.0063) (0.0073)

FICO 760:799 -0.033*** -0.040*** -0.034***

(0.0069) (0.0077) (0.0096)

FICO ≥ 800 -0.033*** -0.042*** -0.030***

(0.0072) (0.0082) (0.0089)

last − f irst -0.0006 -0.0012 -0.0013 -0.0001

p − value 0.2800 0.2300 0.1400 0.9400

last − f irst (black) -0.0038 -0.0043 -0.0060 -0.0073

p − value (black) 0.0015 0.0036 0.0023 0.0003

last − f irst (black − other) -0.0033 -0.0031 -0.0047 -0.0072

p − value (black − other) 0.0003 0.0380 0.00080 0.0020

N 20732913 3729582 6606008 5617655

r2 0.12 0.16 0.15 0.22

Table 7: The table reports regression estimates of the difference in performance between mortgages originated in

the last and ﬁrst week of the month. The dependent variable is a dummy equal to one for mortgages that defaulted

within 5 years after origination. In column (2), the sample is restricted to subprime loans (FICO < 660). In column

(3) the sample is restricted to high loan-to-value loans (LTV> 80%), and in column (4) to loans with low documen-

tation. lastweek and f irstweek are dummies equal to one in the ﬁrst and last week of the month. black is a dummy

equal to one for Black applicants. The table also reports estimates of the difference between the coefﬁcients for the

dummies lastweek and f irstweek, and for the difference of the interaction coefﬁcients for Black applicants, along

with their p-values. Standard errors are clustered by lender and year. Estimates are based on the merged sample of

HMDA and Black Knight McDash data from 1994 to 2018.

(1) (2) (3) (4) (5) (6)

approval approval approval approval approval approval

Fintech Non-Fintech All Shadowbanks No-Shadowbanks All

lastweek 0.064*** 0.036*** 0.035*** 0.034*** 0.053*** 0.054***

(0.011) (0.0030) (0.0031) (0.0037) (0.0081) (0.0081)

f irstweek -0.026*** -0.020*** -0.020*** -0.017*** -0.024*** -0.024***

(0.0045) (0.0034) (0.0034) (0.0030) (0.0037) (0.0037)

black -0.10*** -0.096*** -0.093*** -0.069*** -0.11*** -0.11***

(0.0059) (0.0037) (0.0043) (0.0050) (0.0035) (0.0038)

black × lastweek 0.034*** 0.028*** 0.027*** 0.021*** 0.031*** 0.031***

(0.0038) (0.0037) (0.0034) (0.0040) (0.0034) (0.0035)

black × f irstweek -0.0063* -0.0086*** -0.0074*** -0.0018 -0.0081*** -0.0087***

(0.0033) (0.0023) (0.0024) (0.0043) (0.0025) (0.0024)

black × f intech -0.013

(0.0089)

f intech × lastweek 0.029***

(0.010)

f intech × f irstweek -0.0069

(0.0046)

black × f intech × lastweek 0.0072

(0.0049)

black × f intech × f irstweek 0.00063

(0.0033)

black × shadowbank 0.050***

(0.0076)

shadowbank × lastweek -0.020**

(0.0086)

shadowbank × f irstweek 0.0075*

(0.0042)

black × shadowbank × lastweek -0.0095**

(0.0046)

black × shadowbank × f irstweek 0.0083*

(0.0049)

log(income) 0.075*** 0.077*** 0.077*** 0.058*** 0.082*** 0.077***

(0.0045) (0.0040) (0.0031) (0.0070) (0.0041) (0.0031)

log(loan amount) 0.022*** 0.0016 0.012** -0.011** 0.015*** 0.012***

(0.0055) (0.0036) (0.0042) (0.0048) (0.0040) (0.0039)

is conforming 0.11*** 0.10*** 0.10*** 0.086*** 0.11*** 0.10***

(0.0097) (0.0080) (0.0067) (0.011) (0.0075) (0.0067)

Loan-Level Controls YES YES YES YES YES YES

Holiday FE YES YES YES YES YES YES

Day-of-Week FE YES YES YES YES YES YES

Month-Year-County FE YES YES YES YES YES YES

Month-Year-Lender FE YES YES YES YES YES YES

last − f irst 0.090 0.056 0.050 0.077

p − value 0.0000 0.0000 0.0000 0.0000

last − f irst (black) 0.13 0.092 0.073 0.12

p − value (black) 0.0000 0.0000 0.0000 0.0000

last − f irst (black − other) 0.040 0.037 0.023 0.040

p − value (black − other) 0.0000 0.0000 0.0004 0.0000

last − f irst (black) 0.089 0.12

p − value (black) 0.0000 0.0000

last − f irst (black, Z) 0.096 0.10

p − value (black, Z) 0.0000 0.0000

last − f irst (black, Z − noZ) 0.0066 -0.018

p − value (black, Z − noZ) 0.15 0.022

N 1869937 2172022 4159023 1046528 3195579 4354784

r2 0.26 0.31 0.26 0.42 0.24 0.26

Table 8: The table reports individual loan-level regression estimates of abnormal approval rates in the last and ﬁrst

week of the month, for lenders with different characteristics (see equation 10). lastweek and firstweek are dum-

mies equal to one, respectively, in the ﬁrst and last week of the month. black is a dummy equal to one for Black

applicants. In columns (1) and (2) the sample is restricted, respectively, to Fintech and non-Fintech lenders, while

in columns (4) and (5) the sample is restricted to shadow banks and non-shadow banks (deposit-taking institutions).

The table also reports estimates of the difference between the coefﬁcients for the dummies lastweek and f irstweek,

and for the difference of the interaction coefﬁcients for Black applicants across lender groups, along with their p-

values. Standard errors are clustered by lender and year. Estimates are based on a 5% random sample of the HMDA

data from 2014 to 2018.

(1) (2) (3) (4) (5) (6)

approval approval approval approval approval approval

High Top4 Sh. Low Top4 Sh. All High HHI Low HHI All

lastweek 0.042*** 0.045*** 0.045*** 0.041*** 0.045*** 0.045***

(0.0031) (0.0031) (0.0030) (0.0031) (0.0031) (0.0030)

f irstweek -0.018*** -0.021*** -0.021*** -0.018*** -0.021*** -0.021***

(0.0015) (0.0019) (0.0019) (0.0015) (0.0019) (0.0019)

black -0.074*** -0.063*** -0.063*** -0.074*** -0.063*** -0.063***

(0.0044) (0.0045) (0.0046) (0.0045) (0.0045) (0.0046)

black × lastweek 0.027*** 0.026*** 0.026*** 0.026*** 0.026*** 0.026***

(0.0024) (0.0022) (0.0022) (0.0023) (0.0023) (0.0023)

black × f irstweek -0.0051** -0.0076*** -0.0079*** -0.0059** -0.0071*** -0.0074***

(0.0021) (0.0015) (0.0015) (0.0022) (0.0015) (0.0014)

black × H(top4) -0.011***

(0.0033)

H(top4) × lastweek -0.0035***

(0.0010)

H(top4) × f irstweek 0.0034***

(0.00088)

black × H(top4) × lastweek 0.0014

(0.0020)

black × H(top4) × f irstweek 0.0027

(0.0020)

black × H(hhi) -0.012***

(0.0033)

H(hhi) × lastweek -0.0040***

(0.0010)

H(hhi) × f irstweek 0.0036***

(0.00084)

black × H(hhi) × lastweek 0.00063

(0.0019)

black × H(hhi) × f irstweek 0.0016

(0.0022)

log(income) 0.071*** 0.069*** 0.071*** 0.072*** 0.069*** 0.071***

(0.0040) (0.0031) (0.0035) (0.0039) (0.0032) (0.0035)

log(loan amount) 0.0075*** 0.0079*** 0.0077*** 0.0078*** 0.0077*** 0.0077***

(0.0022) (0.0025) (0.0023) (0.0022) (0.0025) (0.0023)

is conforming 0.090*** 0.092*** 0.091*** 0.090*** 0.091*** 0.091***

(0.0060) (0.0053) (0.0054) (0.0060) (0.0053) (0.0054)

Loan-Level Controls YES YES YES YES YES YES

Holiday FE YES YES YES YES YES YES

Day-of-Week FE YES YES YES YES YES YES

Month-Year-County FE YES YES YES YES YES YES

Month-Year-Lender FE YES YES YES YES YES YES

last − f irst 0.060 0.066 0.059 0.066

p − value 0.0000 0.0000 0.0000 0.0000

last − f irst (black) 0.092 0.100 0.092 0.100

p − value (black) 0.0000 0.0000 0.0000 0.0000

last − f irst (black − other) 0.032 0.033 0.032 0.033

p − value (black − other) 0.0000 0.0000 0.0000 0.0000

last − f irst (black) 0.100 0.10

p − value (black) 0.0000 0.0000

last − f irst (black, Z) 0.099 0.099

p − value (black, Z) 0.0000 0.0000

last − f irst (black, Z − noZ) -0.0013 -0.0010

p − value (black, Z − noZ) 0.63 0.71

N 8901836 8840521 17898971 8912233 8837435 17898971

r2 0.35 0.30 0.32 0.35 0.30 0.32

Table 9: The table reports individual loan-level regression estimates of abnormal approval rates in the last and ﬁrst week of the month, for

counties with different concentration of the local mortgage market (see equation 10). lastweek and f irstweek are dummies equal to one, re-

spectively, in the ﬁrst and last week of the month. black is a dummy equal to one for Black applicants. In columns (1) and (2) the sample is

restricted, respectively, to counties in which the share of the top 4 originators is above and below median (across counties in the United States in

the same year), while in columns (4) and (5) the sample is restricted to counties in which the HHI index based on lenders’ origination shares is

above and below median (across counties in the United States in the same year). The table also reports estimates of the difference between the

coefﬁcients for the dummies lastweek and f irstweek, and for the difference of the interaction coefﬁcients for Black applicants across lender

groups, along with their p-values. Standard errors are clustered by lender and year. Estimates are based on a 5% random sample of the HMDA

data from 1994 to 2018.

(1) (2) (3)

approval approval approval

Above Med Size Below Med Size All

lastweek 0.050*** 0.036*** 0.035***

(0.0050) (0.0018) (0.0018)

f irstweek -0.022*** -0.016*** -0.016***

(0.0026) (0.0011) (0.0011)

black -0.070*** -0.064*** -0.064***

(0.0058) (0.0039) (0.0040)

black × lastweek 0.025*** 0.029*** 0.029***

(0.0036) (0.0016) (0.0016)

black × f irstweek -0.0057** -0.0086*** -0.0090***

(0.0025) (0.0016) (0.0015)

black × H(size) -0.0069

(0.0066)

H(size) × lastweek 0.015***

(0.0052)

H(size) × f irstweek -0.0065**

(0.0024)

black × H(size) × lastweek -0.0029

(0.0040)

black × H(size) × f irstweek 0.0034

(0.0030)

log(income) 0.070*** 0.070*** 0.071***

(0.0050) (0.0028) (0.0035)

log(loan amount) 0.0079* 0.0076*** 0.0077***

(0.0040) (0.0023) (0.0023)

is conforming 0.092*** 0.088*** 0.091***

(0.0080) (0.0039) (0.0054)

Loan-Level Controls YES YES YES

Holiday FE YES YES YES

Day-of-Week FE YES YES YES

Month-Year-County FE YES YES YES

Month-Year-Lender FE YES YES YES

last − f irst 0.072 0.052

p − value 0.0000 0.0000

last − f irst (black) 0.10 0.089

p − value (black) 0.0000 0.0000

last − f irst (black − other) 0.031 0.037

p − value (black − other) 0.0000 0.0000

last − f irst (black) 0.089

p − value (black) 0.0000

last − f irst (black, Z) 0.082

p − value (black, Z) 0.0000

last − f irst (black, Z − noZ) -0.0064

p − value (black, Z − noZ) 0.27

N 9172101 8532602 17898971

r2 0.31 0.35 0.32

Table 10: The table reports individual loan-level regression estimates of abnormal approval rates in the last and

ﬁrst week of the month, for lenders with size (total originated mortgage amount) above and below median (see equa-

tion 10). lastweek and f irstweek are dummies equal to one, respectively, in the ﬁrst and last week of the month.

black is a dummy equal to one for Black applicants. In columns (1) and (2) the sample is restricted, respectively, to

lenders with size above and below median. The table also reports estimates of the difference between the coefﬁcients

for the dummies lastweek and f irstweek, and for the difference of the interaction coefﬁcients for Black applicants

across lender groups, along with their p-values. Standard errors are clustered by lender and year. Estimates are based

on a 5% sample of the HMDA data from 1994 to 2018.

Appendix to:

Using High-Frequency Evaluations to Estimate Discrimination:

Evidence from Mortgage Loan Ofﬁcers

(intended for online publication)

A.I Identifying Time-Varying Discrimination

We show how under the assumptions in Assumption Set (A) approval probabilities for whites and

Blacks are different. The approval probability, conditional on race and other observable character-

istics, is equal to:

P (a|R, X) =

P (a,R|X)

P (R|X)

P (a,R,Z

|X)+P (a,Z

|X)

P (R|X)

P (a|R,Z

,X)P (Z

|R,X)P (R|X)+P (a|R,Z

,X)P (Z

|R,X)P (R|X)

P (R|X)

= P (a|Z

, R|X)P (Z

|R, X) + P (a|Z

, R, X)P (Z

|R, X)

where Z ∈ {Z

, Z

} is a binary unobservable characteristic, X is a vector of observable char-

acteristics and R ∈ {W, B} is the applicants’ race (white or Black). Then, the difference in

approval probabilities for whites and Blacks is equal to:

P (a|W, X) − P (a|B, X) =

= [P (a|W, Z

, X)P (Z

|W, X) + P (a|W, Z

, X)P (Z

|W, X)] − [P (a|Z

, B, X)P (Z

|B, X) + P (a|Z

, B, X)P (Z

|B, X)]

= P (a|Z

, X)[P (Z

|W, X) − P (Z

|B, X)] + P (a|Z

, X)[P (Z

|W, X) − P (Z

|B, X)] > 0

where P (a|Z

, X) = P (a|W, Z

, X) = P (a|B, Z

, X) and P (a|Z

, X) = P (a|W, Z

, X) =

P (a|B, Z

, X) from the assumption of no discrimination, and P (Z

|W, X) − P (Z

|B, X) > 0

and P (Z

|W, X) − P (Z

|B, X) < 0 due to the assumption of higher unobservable quality char-

acteristics for whites.

We now turn to the comparison of approval rates for whites and Blacks at the beginning and the

end of the month. The difference in the probability between whites and Blacks is equal to:

P (a|W, X, T ) − P (a|B, X, T ) =

= P (a|Z

, W, X, T )P (Z

|W, X, T ) + P (a|Z

, W, X, T )P (Z

|W, X, T ) − P (a|Z

, B, X, T )P (Z

|B, X, T ) − P (a|Z

, B, X, T )P (Z

|B, X, T )

= P (a|Z

, W, X, T )[P (Z

|W, X, T ) − P (Z

|B, X, T )] + P (a|Z

, W, X, T )[P (Z

|W, X, T ) − P (Z

|B, X, T )]

= P (a|Z

, X, T )[P (Z

|W, X, T ) − P (Z

|B, X, T )] + P (a|Z

, X, T )[P (Z

|W, X, T ) − P (Z

|B, X, T )]

where T ∈ {Start, End}. Exploiting the calculations above, we can then derive the properties of

the change in difference between approval probabilities at the beginning and the end of the month:

[P (a|W, X, End) − P (a|B, X, End)] − [P (a|W, X, Start) − P (a|B, X, Start)] =

= P (a|Z

, X, End)[P (Z

|W, X, End) − P (Z

|B, X, End)] + P (a|Z

, X, End)[P (Z

|W, X, End) − P (Z

|B, X, End)]

−P (a|Z

, X, Start)[P (Z

|W, X, Start) − P (X

|B, X, Start)] − P (a|Z

, X, Start)[P (Z

|W, X, Start) − P (Z

|B, X, Start)]

= [P (a|Z

, X, Start) − P (a|Z

, X, Start)][P (Z

|W, X) − P (Z

|B, X)] + [P (a|Z

, X, Start) − P (a|Z

, X, Start)][P (Z

|W, X) − P (Z

|B, X)] = 0

where we set P (Z

|W, X, Start) = P (Z

|W, X, End) based on the assumption that applica-

tions quality does not change over the month, while P (a|Z

, X, T ) = P (a|W, Z

, X, T ) =

P (a|B, Z

, X, T ) and P (a|Z

, X, T ) = P (a|W, Z

, X, T ) = P (a|B, Z

, X, T ), based on the

no discrimination assumption. Thus, the rejection of the null that the counterpart of the equation

above in the data is equal to zero, leads to a rejection of the no discrimination assumption, con-

ditionally on not having changes in application quality between the beginning and the end of the

month.

iii

A.II Additional Figures and Tables

100

150

200

250

percent

1994 1998 2002 2006 2010 2014 2018

year

Origination volume last week of month divided by first week of month by years

Figure A.1: The ﬁgure shows the ratio of average mortgage origination volume in the last week of the month over

average mortgage origination volume in the ﬁrst week of the month, for each year over the period from 1994 to 2018.

The evidence is based on the HMDA data from January 1994 to December 2018.

-100

100

200

300

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Loan volume originated (percentage relative to first day of month)

January December

Figure A.2: The ﬁgure shows average percentage abnormal daily loan origination volume (measured as number

of originations) in the U.S., for the last eight days of the month, and the ﬁrst seven days of the following month,

separately for each calendar month (January to December) over the sample period from January 1994 to December

2018. Abnormal volume is computed with respect to loan origination volume on the ﬁrst day of the following month.

The evidence is based on the HMDA data from January 1994 to December 2018.

-2

-1

standard deviation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 14 13 12 11 10 9 8 7 6 5 4 3 2 1

days from start of month days from end of month

Loan inventory within month (standardized)

Figure A.3: This ﬁgure shows the within-month ﬂuctuation, at the level of the entire United States, in the average

number of loan applications in inventory (awaiting a decision by loan ofﬁcers) by day of the month. Inventory size

is standardized to have mean of zero and standard deviation of one. The evidence is based on the HMDA data from

January 1994 to December 2018.

Approval Gap Dif. (95% CI)FinTech Lenders Not FinTech Lenders

-.1

start-of-month end-of-month start-of-month end-of-month FinTech Not FinTech

White Black change in approval gap

Average approval rate

(a) Fintech

Approval Gap Dif. (95% CI)Shadow Bank Not Shadow Bank

-.1

start-of-month end-of-month start-of-month end-of-month Shadow Bk Not Shadow Bk

White Black change in approval gap

Average approval rate

(b) Shadow banks

Figure A.4: Panel (a) of the ﬁgure shows on the left the approval rates for white and Black applicants, in the ﬁrst

and last week of the month. The rates are shown separately for Fintech and non-Fintech lenders. The right side of

panel (a) shows the change in the approval gap, deﬁned as the difference between the approval rate for white ap-

plicants and the one for Black applicants, between the last and ﬁrst week of the month, separately for Fintech and

non-Fintech lenders. Panel (b) of the ﬁgure shows on the left the approval rates, and on the right the change in the

approval gap, for shadow banks and non-shadow banks (depository institutions). Estimates in this ﬁgure are based on

a 5% random sample of the HMDA data from 2014 to 2018.

vii

Approval Gap Dif. (95% CI)High Top 4 Share Low Top 4 Share

-.1

start-of-month end-of-month start-of-month end-of-month High Top 4 Low Top 4

White Black change in approval gap

Average approval rate

(a) Top 4 Share

Approval Gap Dif. (95% CI)High HHI Low HHI

-.1

start-of-month end-of-month start-of-month end-of-month High HHI Low HHI

White Black change in approval gap

Average approval rate

(b) HHI

Figure A.5: Panel (a) of the ﬁgure shows on the left the approval rates for white and Black applicants, in the ﬁrst

and last week of the month. The rates are shown separately for counties in which the share of the top 4 lenders is

above and below the median (in the year). The right side of panel (a) shows the approval gap, deﬁned as the differ-

ence between the approval rate for white applicants and the one for Black applicants, between the last and ﬁrst week

of the month, separately for counties with above and below median top 4 share. Panel (b) of the ﬁgure shows on the

left the approval rates, and on the right the change in the approval gap, for counties with Herﬁndahl-Hirschman Index

(HHI) above and below the median (in the year). Estimates in this ﬁgure are based on a 5% random sample of the

HMDA data from 1994 to 2018.

viii

Approval Gap Dif. (95% CI)Lender Size, Above Median Lender Size, Below Median

-.1

start-of-month end-of-month start-of-month end-of-month Above Below

White Black change in approval gap

Average approval rate

Figure A.6: The ﬁgure shows on the left the approval rates for white and Black applicants, in the ﬁrst and last

week of the month. The rates are shown separately for lenders above and below median size (for each year across

the United States), measured as the total volume of loans originated per year. The right side of the ﬁgure shows the

change in the approval gap, deﬁned as the difference between the approval rate for white applicants and the one for

Black applicants, between the last and ﬁrst week of the month, separately for lenders above and below median size.

Estimates in this ﬁgure are based on a 5% random sample of the HMDA data from 1994 to 2018.

U.S.-Level

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

White Black Other White Inc Q1 White Inc Q2 White Inc Q3 White Inc Q4 Black Inc Q1 Black Inc Q2 Black Inc Q3 Black Inc Q4 Other Inc Q1 Other Inc Q2 Other Inc Q3 Other Inc Q4

lastweek 0.30*** 0.38*** 0.31*** 0.31*** 0.31*** 0.29*** 0.26*** 0.35*** 0.38*** 0.37*** 0.33*** 0.31*** 0.32*** 0.30*** 0.27***

(0.012) (0.013) (0.012) (0.012) (0.012) (0.012) (0.012) (0.012) (0.013) (0.013) (0.012) (0.012) (0.012) (0.012) (0.012)

f irstweek -0.15*** -0.19*** -0.15*** -0.15*** -0.16*** -0.16*** -0.13*** -0.16*** -0.18*** -0.17*** -0.16*** -0.16*** -0.17*** -0.16*** -0.13***

(0.012) (0.013) (0.012) (0.012) (0.012) (0.012) (0.012) (0.012) (0.013) (0.013) (0.013) (0.012) (0.012) (0.012) (0.012)

Holiday FE YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES

Day-of-Week FE YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES

Month-Year FE YES YES YES YES YES YES YES YES YES YES YES YES YES YES YES

last − f irst 0.45 0.56 0.46 0.46 0.47 0.45 0.39 0.51 0.55 0.54 0.48 0.47 0.48 0.46 0.40

p − value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

N 9131 9131 9131 9131 9131 9131 9131 9131 9131 9131 9131 9131 9131 9131 9131

r2 0.95 0.95 0.95 0.95 0.95 0.95 0.95 0.94 0.94 0.94 0.94 0.95 0.95 0.95 0.95

Table A.1: The table reports regression estimates of the abnormal loan originations volume in the last and ﬁrst week of the month (see equation 6) for borrowers

of different race and income level. The ﬁrst three columns report results for white, Black and other race applicants, while the remaining columns show, within

each of the three ethnicity groups, breakdown based on income: ﬁrst, second, third and fourth quartile of income within the county of the loan application (Inc

Q1, Inc Q2, Inc Q3 and Inc Q4). lastweek and f irstweek are dummies equal to one, respectively, in the ﬁrst and last week of the month. The dependent variable

is the log of the number of originations for each group, at the U.S. level. Standard errors are clustered by lender and year. Estimates are based on the sample of

HMDA mortgage originations from 1994 to 2018.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

All Approvals Male White AFA Other Race Income > Med Income ≤ Med Income Q1 Income Q2 Income Q3 Income Q4 Loan > Med Loan ≤ Med

lastweek 0.024*** 0.023*** 0.021*** 0.049*** 0.023*** 0.019*** 0.030*** 0.035*** 0.028*** 0.022*** 0.018*** 0.026*** 0.022***

(0.0012) (0.0012) (0.0012) (0.0020) (0.0011) (0.0012) (0.0014) (0.0016) (0.0014) (0.0012) (0.0012) (0.0015) (0.0012)

f irstweek -0.013*** -0.013*** -0.013*** -0.020*** -0.013*** -0.011*** -0.017*** -0.018*** -0.016*** -0.014*** -0.010*** -0.015*** -0.013***

(0.0012) (0.0013) (0.0013) (0.0023) (0.0012) (0.0012) (0.0014) (0.0016) (0.0015) (0.0012) (0.0012) (0.0012) (0.0014)

CRA month -0.0012 -0.00069 -0.000057 0.0023 -0.0014 -0.0012 -0.00036 -0.000051 -0.00031 -0.00090 -0.000022 -0.00070 -0.0016

(0.0011) (0.00093) (0.00081) (0.0022) (0.0011) (0.0012) (0.0017) (0.0020) (0.0015) (0.0014) (0.0010) (0.00068) (0.0015)

CRA month(+1) -0.00032 -0.00043 0.00056 0.0032 -0.00028 -0.00014 -0.000019 0.000085 -0.00029 -0.00022 0.00020 0.00014 -0.00059

(0.0013) (0.0011) (0.00095) (0.0023) (0.0014) (0.0010) (0.0013) (0.0016) (0.0014) (0.0014) (0.0010) (0.0013) (0.0013)

CRA month(+2) -0.00049 -0.00042 -0.00050 -0.0013 -0.00079 -0.00018 -0.00098 -0.0019 -0.00020 -0.00090 -0.00034 0.000098 -0.0014

(0.0013) (0.0012) (0.0012) (0.0028) (0.0012) (0.0014) (0.0016) (0.0019) (0.0014) (0.0020) (0.0012) (0.0010) (0.0017)

CRA month(+3) -0.0023* -0.0021 -0.0018 0.00039 -0.0020 -0.0018* -0.0017 0.0011 -0.0030 -0.00064 -0.0011** -0.00067 -0.0016

(0.0013) (0.0013) (0.0011) (0.0024) (0.0013) (0.0010) (0.0020) (0.0024) (0.0018) (0.0017) (0.00049) (0.0011) (0.0019)

CRA month(-1) -0.0020** -0.0016 -0.0012* -0.0022 -0.0017** -0.0013 -0.0020* -0.0019 -0.0019 -0.0014 -0.0015** -0.0018* -0.0020*

(0.00071) (0.00098) (0.00057) (0.0028) (0.00069) (0.00080) (0.0010) (0.0014) (0.0018) (0.0011) (0.00064) (0.00098) (0.00096)

CRA month(-2) -0.0011 -0.0015* -0.00075 0.0021 -0.0010 -0.00099 -0.00059 0.00074 -0.0015 -0.00092 -0.00030 -0.00068 -0.0015

(0.00088) (0.00083) (0.00081) (0.0028) (0.00090) (0.00100) (0.0014) (0.0017) (0.0019) (0.0013) (0.0010) (0.0011) (0.0013)

CRA month(-3) -0.00074 -0.0010 -0.00076 -0.0013 -0.00063 -0.00065 -0.00088 -0.00062 -0.0021 -0.0019 0.00040 0.00027 -0.0014

(0.0010) (0.00098) (0.00091) (0.0025) (0.0011) (0.00085) (0.0016) (0.0017) (0.0018) (0.0012) (0.0011) (0.00065) (0.0012)

Holiday FE YES YES YES YES YES YES YES YES YES YES YES YES YES

Day-of-Week FE YES YES YES YES YES YES YES YES YES YES YES YES YES

Month-Year FE YES YES YES YES YES YES YES YES YES YES YES YES YES

Lender FE YES YES YES YES YES YES YES YES YES YES YES YES YES

N 2216169 2116758 2122995 823391 2205077 2020223 1976495 1711880 1694957 1717338 1779768 1878114 2049297

r2 0.25 0.22 0.22 0.16 0.25 0.22 0.21 0.19 0.19 0.19 0.20 0.22 0.22

Table A.2: The table reports regression estimates of abnormal approval rates in the last and ﬁrst week of the month. The dependent variable is the approval rate

(approval decisions over approval and denial decisions) per day and lender. Column (1) reports results for all applicants, while the other columns report results

for subgroup of applicants based on sex, race, income and loan amount. Income ≤ Med and Loan ≤ Med are income and loan amount smaller than or equal to the

median in the county and year. Income Q1, Income Q2, Income Q3 and Income Q4 are quartiles of the income distribution in each county and year. lastweek and

firstweek are dummies equal to one, respectively, in the ﬁrst and last week of the month. We include controls accounting for whether the lender is subject to a

CRA examination in the current month, or the previous or next three months. Estimates are based on the sample of HMDA mortgage applications and originations

from 1994 to 2018.

(1) (2) (3) (4) (5) (6) (7)

approval approval approval approval approval approval approval

All All New Purchases Reﬁnancing Conforming All

lastweek 0.043*** 0.043*** 0.035*** 0.051*** 0.043*** 0.043***

(0.0030) (0.0030) (0.0021) (0.0049) (0.0032) (0.0031)

f irstweek -0.020*** -0.020*** -0.014*** -0.025*** -0.020*** -0.019***

(0.0017) (0.0017) (0.0011) (0.0026) (0.0018) (0.0017)

black -0.067*** -0.070*** -0.056*** -0.067*** -0.068*** -0.064***

(0.0043) (0.0036) (0.0059) (0.0043) (0.0044) (0.0043)

black × lastweek 0.027*** 0.027*** 0.028*** 0.025*** 0.026*** 0.028***

(0.0021) (0.0021) (0.0018) (0.0041) (0.0022) (0.0021)

black × f irstweek -0.0074*** -0.0073*** -0.0063*** -0.0096*** -0.0067*** -0.0072***

(0.0015) (0.0015) (0.0015) (0.0024) (0.0015) (0.0015)

f emale -0.017***

(0.0025)

lastday 0.081***

(0.0068)

f irstday -0.020***

(0.0031)

black × lastday 0.046***

(0.0039)

black × f irstday -0.0069**

(0.0033)

log(income) 0.071*** 0.069*** 0.058*** 0.068*** 0.071*** 0.071*** 0.071***

(0.0035) (0.0034) (0.0038) (0.0038) (0.0034) (0.0036) (0.0036)

log(loan amount) 0.0076*** 0.0073*** 0.0031 -0.010* 0.0089*** 0.0077*** 0.0079***

(0.0023) (0.0023) (0.0021) (0.0050) (0.0024) (0.0023) (0.0023)

is conforming 0.090*** 0.090*** 0.058*** 0.084*** 0.091*** 0.091***

(0.0054) (0.0054) (0.0038) (0.0056) (0.0055) (0.0055)

black-Year YES NO NO NO NO NO NO

Loan-Level Controls YES YES YES YES YES YES YES

Holiday FE YES YES YES YES YES YES YES

Day-of-Week FE YES YES YES YES YES YES YES

Lender FE YES YES YES YES YES YES YES

Month-Year-County YES YES YES YES YES YES YES

Month-Year-Lender YES YES YES YES YES YES YES

last − f irst 0.063 0.063 0.049 0.076 0.063 0.062 0.10

p − value 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

last − f irst (black) 0.097 0.097 0.084 0.11 0.096 0.097 0.15

p − value (black) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

last − f irst (black − other) 0.034 0.034 0.035 0.034 0.033 0.035 0.053

p − value (black − other) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

N 17898971 17898971 7046904 8705784 16392963 17893870 17893870

r2 0.32 0.32 0.33 0.35 0.32 0.32 0.32

Table A.3: The table reports individual loan-level regression estimates of abnormal approval rates in the last and

ﬁrst week of the month (see equation 9). The dependent variable is a dummy that takes value 1 if a loan application

is approved and 0 if it is denied. For all columns the regression speciﬁcation includes all the controls used in column

6 of Table 4. In column (3) the sample is restricting to new mortgages issued for home purchases, in column (4)

it is restricted to reﬁnanced mortgages, and in column (5) to conforming mortgages. Columns (6) and (7) redeﬁne

month ﬁxed effects so that a month breaks at the 15th day. This helps comparing differences in approval rates in

weeks or days immediately adjacent to the calendar month cutoff. lastweek and firstweek are dummies equal to

one, respectively, if the decision on the application is taken in the ﬁrst and last week of the month, while lastday and

firstday are dummies equal to one, respectively, if the decision on the application is taken in the ﬁrst and last day

of the month. black is a dummy equal to one for Black applicants and f emale is a dummy equal to one for female

applicants. The table also reports estimates of the difference between the coefﬁcients for the dummies lastweek and

firstweek (lastday and f irstday), and for the difference of the interaction coefﬁcients for Black applicants, along

with the p-value of tests of the null that each difference is equal to 0. Standard errors are clustered by lender and

year. Estimates are based on a 5% random sample of the HMDA data from 1994 to 2018.

xii

(1) (2) (3) (4)

Time to Time to Time to Time to

Origination Origination Denial Action

lastweek -0.49***

(0.15)

f irstweek -0.55***

(0.13)

black 3.08*** -0.85*** 0.76**

(0.39) (0.16) (0.29)

lastweek -0.51*** 0.72*** 0.13

(0.15) (0.12) (0.24)

f irstweek -0.54*** 0.73*** 0.53

(0.13) (0.16) (0.49)

black × lastweek 0.26* 0.13 0.82***

(0.13) (0.13) (0.14)

black × f irstweek -0.26** -0.063 -0.052

(0.11) (0.15) (0.100)

log(income) -1.01*** -0.94*** 1.35*** 0.95***

(0.17) (0.17) (0.12) (0.15)

log(loan amount) 5.38*** 5.41*** 3.16*** 4.56***

(0.31) (0.32) (0.37) (0.31)

is conforming 1.08** 1.10** 1.74*** 1.54***

(0.40) (0.41) (0.32) (0.35)

last − f irst 0.0590 0.0240 -0.0083 -0.4000

p − value 0.7900 0.9100 0.9700 0.3300

last − f irst (black) 0.5400 0.1800 0.4800

p − value (black) 0.02800 0.2900 0.3000

last − f irst (black − other) 0.5200 0.1900 0.8800

p − value (black − other) 0.0031 0.2500 0.0000

N 11924971 11924971 3915189 20683438

r2 0.29 0.29 0.40 0.25

Table A.4: The table reports individual loan-level regression estimates of abnormal mortgage processing time in

the last and ﬁrst week of the month. We use the same speciﬁcation as in equation 9. In column (1), the sample is

restricted to applications from Black applicants, while in all other columns the sample includes all applicants. In

columns (1) and (2), the sample is restricted to originated loans, and the dependent variable is the time to origina-

tion, deﬁned as the number of days between the application date and the origination date. In column (3), the sample

is restricted to denied applications, and the dependent variable is the time to denial. In column (4), the sample in-

cludes both approved and denied loans, and the dependent variable is time to action (time to approval). lastweek

and firstweek are dummies equal to one, respectively, if the decision on the application is taken in the ﬁrst and last

week of the month. black is a dummy equal to one for Black applicants. The table also reports estimates of the dif-

ference between the coefﬁcients for the dummies lastweek and f irstweek, and for the difference of the interaction

coefﬁcients for Black applicants, along with the p-value of tests of the null that each difference is equal to 0. Stan-

dard errors are clustered by lender and year. Estimates are based on a 5% random sample of the HMDA data from

1994 to 2018.

xiii

(1) (2) (3) (4)

5-Year Termination 5-Year Termination 5-Year Termination 5-Year Termination

FICO < 660 LTV > 80% Low Docs

lastweek -0.0026 -0.00060 -0.0041* 0.0023

(0.0022) (0.0012) (0.0020) (0.0038)

f irstweek 0.0010 0.00032 0.0018 -0.00028

(0.0014) (0.0020) (0.0016) (0.0017)

black -0.054*** -0.038*** -0.061*** -0.044***

(0.0083) (0.0063) (0.0091) (0.0086)

black × lastweek -0.0024* -0.0043*** -0.0014 -0.0088**

(0.0014) (0.0012) (0.0015) (0.0039)

black × f irstweek 0.0018 0.0013 0.0033 0.0036**

(0.0018) (0.0019) (0.0021) (0.0014)

LTV -0.0015*** -0.0011*** -0.0029*** -0.0016***

(0.00043) (0.00031) (0.00061) (0.00050)

log(income) 0.025*** 0.0018 0.028*** 0.023**

(0.0073) (0.011) (0.0080) (0.0086)

log(loan amount) 0.096*** 0.068*** 0.12*** 0.11***

(0.018) (0.010) (0.016) (0.021)

is conforming 0.087*** 0.080*** 0.090*** 0.13***

(0.027) (0.011) (0.018) (0.035)

FICO 620:659 0.016 0.024* 0.011 0.0042

(0.013) (0.012) (0.012) (0.0059)

FICO 660:719 0.028 0.030 0.010

(0.020) (0.020) (0.0080)

FICO 720:759 0.039 0.044* 0.034**

(0.025) (0.024) (0.012)

FICO 760:799 0.048 0.051* 0.067***

(0.031) (0.028) (0.017)

FICO ≥ 800 0.032 0.029 0.066***

(0.032) (0.029) (0.018)

last − f irst -0.0036 -0.00092 -0.0059 0.0026

p − value 0.2900 0.7700 0.0780 0.6200

last − f irst (black) -0.0078 -0.0066 -0.0110 -0.0099

p − value (black) 0.1100 0.0440 0.0067 0.1200

last − f irst (black − other) -0.0042 -0.0057 -0.0047 -0.0120

p − value (black − other) 0.1200 0.0410 0.1000 0.0047

N 20732913 3729582 6606008 5617655

r2 0.22 0.28 0.25 0.32

Table A.5: The table reports regression estimates of the difference in performance between mortgages originated

in the last and ﬁrst week of the month. The dependent variable is a dummy equal to one for mortgages that were

terminated (due to default or reﬁnancing) within 5 years after origination. In column (2), the sample is restricted to

subprime loans (FICO < 660). In column (3) the sample is restricted to high loan-to-value loans (LTV> 80%),

and in column (4) to loans with low documentation. lastweek and firstweek are dummies equal to one in the ﬁrst

and last week of the month. black is a dummy equal to one for Black applicants. The table also reports estimates

of the difference between the coefﬁcients for the dummies lastweek and f irstweek, and for the difference of the

interaction coefﬁcients for Black applicants, along with their p-values. Standard errors are clustered by lender and

year. Estimates are based on the merged sample of HMDA and Black Knight McDash data from 1994 to 2018.

xiv