Language Frictions in Consumer Credit ∗

Chao Liu†

February 21, 2023

Abstract

This paper studies how language barriers between lenders and borrowers translate into diferences in borrower outcomes in the U.S. mortgage market. I use

survey data to infer and machine learning techniques to predict borrowers’ English profciency. I document signifcant descriptive diferences in perceptions

of mortgages, application experiences, and mortgage rates between limited English profcient (LEP) and non-LEP borrowers. To measure the causal efects of

language frictions, I exploit a Federal Housing Finance Agency policy that provided translated mortgage documents in Spanish to mortgage lenders. After the

policy change, LEP Hispanic borrowers had a streamlined application process,

contacted more lenders, understood mortgage contracts better, and enjoyed

lower borrowing costs. Reducing language frictions also led to expanded access

to credit for LEP borrowers. Overall, my fndings highlight a cost-efective

way to create a responsible inclusion of well-qualifed LEP borrowers in the

mortgage market.

∗I am deeply indebted to my advisors Gregor Matvos, Paola Sapienza, Anthony DeFusco, and

John Mondragon for their extensive guidance and support. I thank Gene Amromin, Scott Baker,

Vivek Bhattacharya, Nicolas Crouzet, Carola Frydman, Shi Gu, Menaka Hampole, W. Walker Hanlon, Sean Higgins, Chao Jin, Hyunseob Kim, Jake Liu, Lu Liu, Edmund Y. Lou, Tianshi Mu,

Charles G. Nathanson, Nicola Persico, Jacopo Ponticelli, Enrichetta Ravina, Mar Reguant, Tim

Seida, Ritwika Sen, Yongxiang Wang, Wei Xiang, Brandon Zborowski, and Yi Zhang, as well as

seminar participants at Northwestern University, the Federal Housing Finance Agency, Freddie Mac,

Federal Reserve Bank of Chicago, Lake Forest College, Urban Institute, Peking University, Shanghai

Advanced Institute of Finance, Chinese University of Hong Kong, City University of Hong Kong,

and Lingnan University for valuable comments and suggestions. I am also thankful to Sika Pryor at

FHFA for providing useful details on the FHFA Language Access Plan. All errors are my own.

†Liu: Kellogg School of Management, Northwestern University, 2211 Campus Dr, Evanston, IL

60208. Email: chao.liu1@kellogg.northwestern.edu.
Households make fnancial decisions afected by various frictions in consumer

credit markets. For example, costly search in the auto loan market results in higher

interest rates, smaller loan sizes, and distorted consumption (Argyle, Nadauld and

Palmer, 2023). Households respond slowly to mortgage refnancing opportunities because they are reluctant to incur current time costs for the sake of future benefts

(Andersen et al., 2020). Information frictions restrain people from reducing their use

of payday lending, as they are not fully aware of the borrowing costs (Bertrand and

Morse, 2011).

In this paper, I study a fundamental yet often overlooked type of friction in consumer credit markets: language frictions. Specifcally, I investigate the language barriers between fnancial institutions and consumers with limited English profciency

(LEP). With restricted abilities to read, speak, write, or understand English, LEP

individuals may misunderstand fnancial contracts, have limited access to information, or miss opportunities in consumer credit markets. Importantly, LEP individuals

are far from being a negligible group in the U.S. The census data reveal that nearly

one in ten working-age U.S. adults falls into this category. A majority of this substantial group, approximately 64 percent, speaks Spanish as their primary language,

followed by Chinese, Vietnamese, Korean, and Tagalog. Figure 1 plots the geographic

distribution of LEP individuals across the U.S., highlighting large variation in the proportion of LEP individuals, LEP Hispanic, and LEP Chinese people at the county

level.

I focus on the U.S. mortgage market because language frictions are particularly

salient in this market for three reasons. First, acquiring a mortgage is perhaps the

most important fnancial decision for many households. Given the loan size relative to

household budgets and the loan duration relative to household life cycle, even minor

misunderstandings can translate into signifcant fnancial consequences over time. By

the end of 2019, mortgage balances accounted for 68 percent of total household debt,

with about 42 percent of families having debt secured by their primary residence

(Bhutta et al., 2020). Therefore, beyond individual implications, mortgage decisions

also have a pivotal infuence on broader economic stability.

Second, language frictions exacerbate the challenges of the already intricate mortgage application process for LEP borrowers. In addition to the lengthy process (Ellie

Mae, 2016), mortgage forms and disclosures can be overwhelming even for native English speakers. For instance, disclosures for alternative mortgage products are written

at reading levels ranging from 9th to 12th grade, but 43 percent of U.S. adults read

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below these levels (United States Government Accountability Ofce, 2006). Recent

studies have found that lenders can exploit borrowers’ confusion and steer them to

certain products (Agarwal, Ben-David and Yao, 2017; Di Maggio, Kermani and Korgaonkar, 2019; Guiso et al., 2022). As mortgage disclosures are generally not available

in non-English languages, LEP borrowers encounter more obstacles in learning about

and accessing mortgage products and services, comprehending and completing key

application documents, and resolving issues with mortgage lenders and servicers.

Finally, compliance risks and uncertainty deter fnancial institutions from fully

serving LEP borrowers. Mortgage lenders may acknowledge the importance of ofering

products and services to LEP borrowers, but they remain cautious about violating

statutes and regulations in practice. For instance, they are concerned about fair

lending risks under the Equal Credit Opportunity Act (ECOA) when determining

how and in which languages to ofer products and services.1

Although LEP individuals represent a substantial segment of the U.S. population

and have considerable credit needs, there is little empirical research that systematically addresses language frictions in the mortgage market (e.g., Kleimann Communication Group (2017) as a qualitative study). In this paper, I attempt to fll this

gap by answering three questions: (1) Do language frictions afect access to mortgage

credit? On the intensive margin, I examine how challenging the process can be for

LEP borrowers who fnally manage to apply for a mortgage. On the extensive margin,

I examine whether LEP borrowers can take out mortgages in the frst place. (2) How

do language frictions afect the price of credit? (3) Does reducing language frictions

afect the quality of credit?

To answer these questions, I confront two key empirical challenges. First, researchers rarely observe borrowers’ English profciency in conventional mortgage data

sets. To overcome this data challenge, I leverage the newly available National Survey

of Mortgage Originations (NSMO). If borrowers believe that it is important for a

lender to speak their primary language, which is not English, I classify them as LEP

borrowers. Furthermore, I construct a novel loan-level data set from Home Mortgage

Disclosure Act (HMDA) data and employ supervised learning to predict borrowers’

LEP status. Therefore, I can use this novel data set to complement my analysis using

the survey data.

Second, it is difcult to isolate the role of language frictions from confounding fac1See Recent Requests for Information (RFIs) of ECOA at https://www.consumerfinance.gov/

rules-policy/notice-opportunities-comment/archive-closed/request-informationequal-credit-opportunity-act-and-regulation-b/.

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tors (e.g., fnancial literacy and cultural identity), as LEP borrowers often difer from

non-LEP borrowers in many observable and unobservable aspects. To overcome this

identifcation challenge, I exploit the implementation of the Federal Housing Finance

Agency (FHFA) Language Access Plan in 2018. The government agency provided a

centralized collection of translated mortgage documents to assist lenders, servicers,

and housing counselors in serving LEP borrowers. This simple intervention addresses

three issues: which documents to provide translations for, in which languages to provide translations, and the accuracy of translations. By alleviating lenders’ concerns

about compliance risks, this policy efectively reduced language barriers for LEP borrowers while having no impact on their creditworthiness.

My analysis begins by using the survey data to document large descriptive differences in perceptions, experiences, and real outcomes between LEP and non-LEP

mortgage borrowers. Prior to applying, LEP borrowers often have more concerns

about mortgage qualifcation and possess less product and market knowledge. During the application process, they engage with fewer lenders and are more likely to

encounter additional problems, such as resolving credit report errors, having extra

home appraisals, and redoing mortgage paperwork. Notably, they pay about 3.2 basis points higher interest rates than risk-equivalent non-LEP counterparts for similar

mortgages, but they do not exhibit a higher likelihood of missing mortgage payments. This fnding suggests that language frictions may prevent some well-qualifed

LEP borrowers from obtaining favorable loan terms. After successfully taking out

their mortgages, they appear to be less familiar with their own mortgage contracts.

For example, a higher proportion of LEP borrowers remain unaware of key mortgage

features, such as adjustable interest rates, prepayment penalties, escrow accounts, or

balloon payments. These results still hold after accounting for borrower demographic

characteristics such as race, ethnicity, income, and education.

To identify the causal efects of language frictions more rigorously, I use a triplediference strategy, which leverages the fact that the FHFA Language Access Plan

was frst launched with only Spanish translations. Specifcally, I compare changes in

outcomes of interest around the policy shock for Hispanic borrowers who are limited

English profcient and those who are not, using similar changes among non-Hispanic

borrowers as a counterfactual for what would have occurred in the absence of the

policy shock.

I frst apply the triple-diference strategy to the NSMO sample. I fnd that LEP

Hispanic borrowers had a streamlined application process and a better understanding

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of their mortgage products following the policy shock. There was a 43% decrease in

their likelihood of redoing mortgage paperwork—a decline of 13.7 percentage points

from the pre-treatment level. They were 16.4 percentage points less likely to be

unaware of whether their mortgages had a balloon payment, representing a 47%

improvement relative to the pre-treatment level. Mortgage interest rates decreased

by roughly 14.9 basis points for LEP Hispanic borrowers. This reduction was larger

for borrowers with less experience transacting with lenders, such as purchase loan

borrowers and frst-time borrowers. My estimates suggest that increased borrower

search could partially explain the price efect: LEP Hispanic borrowers were 16.2

percentage points more likely to seriously consider multiple lenders after the policy

shock, indicating a 35% increase from the pre-treatment level. Additionally, the

motivation of borrower search changed from seeking approval or learning information

to fnding better loan terms. On the other hand, mortgage performance, measured by

the 90-day delinquency rate, did not change signifcantly. Most of these fndings are

evident by only comparing sample means of the treatment and control groups before

and after the policy change. Moreover, these results remain consistent when I use

diferent control groups, but they vanish in a series of placebo tests, where I simulate

fake policy interventions.

The survey is a sample of current mortgage holders, so it cannot capture the full

picture of LEP consumers who might be excluded from even entering the mortgage

market due to language frictions. Therefore, I turn to the 2011-19 HMDA data to

investigate the efects of reducing language frictions on access to credit on the extensive margin. Since I cannot observe each applicant’s LEP status, I use a diference-indiferences framework, which leverages a time-varying treatment intensity measured

by the proportion of potentially treated LEP people at the county level. I fnd that

the propensity of LEP people to apply for conventional purchase loans increased by

roughly 1.1 percentage points after the policy shock. The policy also reduced LEP

borrowers’ probability of submitting incomplete applications or being denied by 6.2

and 15.5 percentage points, respectively. If we assume that the fraction of potentially treated LEP people rises by 4 percentage points (i.e., one standard deviation

of the LEP fraction), then mortgage originations will increase by approximately 5.4

percent. These results are robust to using a two-way fxed efects estimator with

heterogeneous treatment efects and a series of placebo tests where I randomly assign

the share of LEP people to each county within each state. Further analysis of the

heterogeneous efects shows that the policy had a larger efect in areas where the

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demand for translated documents was higher.

Using the same diference-in-diferences framework, I show that the policy lowered

the interest rates of GSE and FHA loans while maintaining mortgage performance,

which is consistent with the loan-level estimates. Additionally, I fnd a positive impact

on borrowers’ creditworthiness, measured by the average credit scores. This result,

along with the result about greater mortgage credit access, suggests that the policy

not only expanded fnancial inclusion but also targeted the appropriate population.

Translations provided by government agencies could reduce lenders’ operational costs

and potential regulatory risks, so the policy might encourage lender competition for

LEP borrowers. Consistent with this reasoning, I show that areas with a larger share

of LEP Hispanic and Chinese people witnessed an increase in the number of active

lenders and a decline in the Herfndahl-Hirschman index (HHI). This efect only took

place in the market of Hispanic and Asian borrowers instead of the whole market,

suggesting that my results capture the efect of this specifc policy for LEP borrowers.

In the last part of this paper, I use a novel loan-level data set to revisit the estimated efect on the price of credit and the quality of credit. The analysis using

the survey data has strongly suggested that mortgage rates decreased and mortgage

performance did not worsen. However, the limited sample size and the absence of

lender and location information may raise concerns about my fndings. To address

this concern, I assemble a large and representative loan-level data set named HMDA+.

This data set combines demographic, lender, and location information from HMDA

data with mortgage origination and performance information from Fannie Mae, Freddie Mac, and Ginnie Mae data. To implement the triple-diference strategy in the

HMDA+ sample, I employ machine learning techniques to predict individual-level

LEP status. Remarkably, my machine learning model achieves an overall accuracy

of nearly 99% in the test sample. Although the application of the machine learning

model to the prediction sample inevitably results in misclassifed cases, I show that

under several assumptions that are likely to hold in my research, I can recover a lower

bound of the true treatment efect on the treated (ATT) from the triple-diference

regression. In my case, unlike traditional measurement error, I can exploit the performance of machine learning model to quantify how severe the measurement error

is.

Using the HMDA+ data set, I show that the interest rates of purchase loans paid by

risk-equivalent LEP Hispanic borrowers dropped by at least 4.9 basis points. Again, I

fnd no evidence of a decline in mortgage performance. The granularity of the HMDA+

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data set allows me to estimate the policy efect on up-front costs and heterogeneous

efects across counties with varying needs for translated documents. First, I fnd that

the decrease in interest rates was not ofset by an increase in discount points, implying

lower total borrowing costs for LEP borrowers. Second, the decrease in interest rates

was larger in counties with a lower level of social capital. This result suggests that

the FHFA Language Access Plan was particularly efective on its intended targets,

since LEP borrowers in these counties typically receive less community support.

My paper contributes to three strands of literature. First, it is closely related to

the literature on various types of frictions in consumer credit markets. Behavioral

frictions can afect 401(K) plan participation (Madrian and Shea, 2001), investment in

individual stocks (Puri and Robinson, 2007), credit card repayment (Keys and Wang,

2019), and mortgage refnancing (Andersen et al., 2020). Many studies establish

the existence of search frictions and explore their role in explaining price dispersion,

such as Stango and Zinman (2016) in the credit card market and Argyle, Nadauld

and Palmer (2023) in the auto loan market. In the mortgage market in particular,

Woodward and Hall (2012), Alexandrov and Koulayev (2018), and Bhutta, Fuster

and Hizmo (2021) show that borrowers pay excessive mortgage fees because they do

not shop for lower-cost mortgages.

Information frictions between borrowers and lenders are pervasive in consumer

credit markets. On one hand, a growing empirical literature documents the presence

of adverse selection and moral hazard, arising from information asymmetries where

borrowers have private knowledge. Recent examples include Gupta and Hansman

(2022) on mortgages, Adams, Einav and Levin (2009) on auto loans, Agarwal, Chomsisengphet and Liu (2010) on credit cards, and Dobbie and Skiba (2013) on payday

loans. On the other hand, lenders may possess superior information, capitalizing on

the borrowers’ lack of understanding of fnancial products. Several papers reinforce

this perspective by arguing that fnancial sophistication is a key driver of diferential

outcomes in household fnance (Agarwal and Mazumder, 2013; Hastings, Madrian

and Skimmyhorn, 2013; Lusardi and Tufano, 2015; Gomes, Haliassos and Ramadorai, 2021). This paper complements this literature by studying the role of important

yet less emphasized language frictions in the mortgage market. Language frictions

might be a deeper source of borrowers’ search and information frictions, because they

can infuence search behavior and fnancial literacy but not the other way around. I

provide evidence that reducing language frictions can induce LEP mortgage borrowers to search more. A government report fnds that a lack of English-language skills

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hinders LEP individuals’ fnancial literacy, making it difcult to conduct everyday

fnancial afairs (United States Government Accountability Ofce, 2010).

Second, this paper contributes to the burgeoning body of research that examines the real efects of government interventions in credit markets, especially on

disadvantaged households. Recent examples include the Community Reinvestment

Act (Bhutta, 2011), bank branch deregulation (C ́elerier and Matray, 2019), credit

card regulation (Agarwal et al., 2015), and broader regulation of consumer protection (Campbell et al., 2011; Posner and Weyl, 2013). Since the Great Recession, a

large amount of rules and policies have been proposed and implemented in the mortgage market. DeFusco, Johnson and Mondragon (2020) study how the Dodd–Frank

“Ability-to-Repay” rule afected the price and availability of credit. Kielty, Wang

and Weng (2021) estimate the efect of the integrated disclosure rule, which streamlines mortgage disclosures. This paper contributes to the literature by examining a

mortgage-related policy targeting at a previously overlooked but non-trivial group of

people. Unlike many of the above-mentioned regulations, the policy studied in this

paper did not impose mandates on fnancial institutions, did not explicitly control

fnancial product design, and did not involve any cash transfers. Nevertheless, I fnd

a signifcantly benefcial policy impact on various outcomes throughout the mortgage

origination life cycle. My fndings support the ongoing eforts by government agencies to make information on mortgages available, comparable, and comprehensible

for LEP individuals.2 Given the close nexus between English profciency, race, and

national origin, my fndings also ofer important insights into the racial wealth gap

and immigrant assimilation.

Finally, this paper contributes to the research on the economic efects of language

ability. Previous studies mainly fnd that workers with limited English skills earn less

than comparable workers who are profcient in English (McManus, Gould and Welch,

1983; Tainer, 1988; Chiswick, 1991; Zavodny, 2000; Dustmann and Fabbri, 2003).

In addition to the earning efects, Bleakley and Chin (2010) estimate the efect of

English profciency on marriage, fertility, and residential choice. Guven and Islam

(2015) study the impact of English profciency on individuals’ health and satisfaction

with partners and jobs. My contribution is to extend this stream by examining the

efects of English ability in an important consumer loan market.

2In early 2021, the Bureau of Consumer Financial Protection (CFPB) issued Statement Regarding

the Provision of Financial Products and Services to Consumers with Limited English Profciency to

encourage fnancial institutions to better serve consumers with limited English profciency and to

provide principles and guidelines to assist fnancial institutions in complying with applicable laws.

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The remainder of this paper proceeds as follows. Section I introduces the data

used in this paper. Section II documents descriptive diferences between LEP and

non-LEP borrowers throughout the mortgage application process. Section III outlines

the policy shock that I use to study the causal efects of reducing language frictions

and the triple-diference strategy. Section IV presents my empirical results using the

survey data. Section V shows the estimated policy impact using aggregate data in a

diference-in-diferences framework. Section VI extends the triple-diference analysis

to a novel loan-level data set and provides a lower bound of the ATT. Section VII

concludes.

I Data

My loan-level data come from four sources described below. Details of the sample

selection are available in Section A of the Online Appendix.

National Survey of Mortgage Originations (NSMO): My main data source

is this quarterly mail survey, which draws a nationally representative sample from

newly originated closed-end frst-lien residential mortgages between 2013 and 2019.

Important for my analysis, this data set provides rich information on borrowers’

demographic characteristics and unique information on borrowers’ experiences getting

a mortgage and their perceptions of the mortgage market. This data set also contains

common underwriting variables drawn from administrative sources, including credit

score, loan-to-value ratio (LTV), loan term, interest rate, loan type (conventional

or FHA), loan purpose (purchase or refnance), occupancy (primary residence or

investment property), and origination quarter.

Home Mortgage Disclosure Act (HMDA): The HMDA database cover the

near universe of mortgage applications in the United States. Supplemented with the

HMDA lender fle (a.k.a. “the Avery File”), it can provide lender identity, loan type,

loan purpose, loan size, and detailed property location for each home mortgage application or purchased loan. Using the 2011-19 HMDA data, I calculate measures

of credit access and market concentration by race and county. This database also

provides applicants’ demographic features (e.g., race, ethnicity, gender, and income),

which are useful for me to predict borrowers’ LEP status. However, it lacks information on borrowers’ credit scores and subsequent loan performance.

Fannie Mae and Freddie Mac Single-Family Loan Level Data (GSE): I

combine the Fannie Mae and Freddie Mac loan-level data together. The resulting data

8
set covers the majority of fully amortizing fxed-rate single family mortgages that the

Enterprises acquired with origination dates from 2015 to 2019. It contains detailed

information on origination characteristics (e.g., origination date, interest rate, FICO

score, LTV ratio, and 3-digit ZIP code of the property), mortgage performance, and

some large originators’ identities.3

Ginnie Mae MBS Single-Family Loan Level Disclosure Data: This loanlevel data set is similar to the GSE data set in content (similar origination and

performance variables), but it covers federally insured or guaranteed mortgages in

the pool of Ginnie Mae mortgage backed securities. My fnal data set only includes

the most prevalent federally insured mortgage type—FHA loans originated between

2015 and 2019. I clean this data set so that it has the same data structure as the

above GSE data set.

Each of the aforementioned mortgage data sets contains important information

about some aspects of a mortgage or borrower. However, none of them ofers a full set

of loan and borrower characteristics, and there is no unique loan identifcation number

to connect these data sets. This problem is especially important in my context,

because my research question and identifcation strategy call for a representative

sample with detailed borrower demographic and mortgage contract variables. To

overcome this data challenge, I use the above data sources to construct two novel

loan-level data sets.4 A detailed description of the matching procedure is available in

Section A of the Online Appendix.

FHA Snapshot+: The most granular property location in the Ginnie Mae data

is at the state level, which is too coarse for a precise empirical analysis. To solve

this problem, I merge Ginnie Mae data with FHA Snapshot data, which record

detailed property location of FHA loans. The fnal merged data set, named as

FHA Snapshot+, covers about 65% of FHA loans sold to Ginnie Mae in HMDA data

during 2015-19. The analysis weight in this data set represents how many FHA loans

in HMDA data are represented by each observation. I use this data set to calculate

average mortgage rates, delinquency rate, and average FICO scores at the 5-digit ZIP

code level.

HMDA+: The NSMO data set provides the richest information about the bor3This GSE data set only identifes the originator that sold the loan to the Enterprises in cases

where the originator had sufciently high origination market share in the reporting period.

4Previous literature has used diferent mortgage data and matching methods to solve this problem

(Bartlett et al., 2022; Saadi, 2020). Section A of the Online Appendix discusses the advantages of

my matching method compared to existing eforts.

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rower and the mortgage, but it lacks location and lender information. To complement

the analysis using the NSMO sample, I assemble a new loan-level data set by merging HMDA data with GSE and FHA Snapshot+ data. The fnal HMDA+ data set

covers nearly half of GSE and FHA loans in the 2015-19 HMDA data, which contains

a broad set of borrower, property, mortgage contract, mortgage performance, and

lender information. It has approximately 9.5 million mortgages originated between

2015 and 2019, including about 5.1 million purchase loans and 4.4 million refnance

loans, or about 8.2 million conventional loans and 1.4 million FHA loans. To make

this data set representative, I use the reciprocal of the likelihood of being sampled

from HMDA data as the analysis weight for each observation.

Supplemental Data: I use the micro-level 2015–19 ACS to construct a training

sample for my machine learning algorithm to predict borrowers’ LEP status in the

HMDA+ data set. For county level information, I collect the share of LEP people

from the aggregate ACS fles, other population data from the Population and Housing Unit Estimates Tables, income data from the Small Area Income and Poverty

Estimates (SAIPE) Program, and single family appraisal data from the Uniform Appraisal Dataset (UAD) Aggregate Statistics.

II LEP Borrowers in the Mortgage Market

This section uses NSMO data to describe LEP borrowers, their mortgage application experiences, and their mortgage results.

A Demographic Characteristics of LEP Borrowers

The survey does not directly ask respondents how well they speak English, so I

assign borrowers’ LEP status based on their answer to this question: “Is speaking my

primary language, which is not English, important in choosing the mortgage lender

or broker?” Following this defnition, about 10% of the respondents in this sample

are LEP borrowers.5 Figure B1 shows an increasing trend in the proportion of LEP

mortgage borrowers from 8.5% in 2013 to 11% in 2019.

Panel A of Table 1 reports summary statistics of demographic characteristics for

all borrowers, LEP borrowers, and non-LEP borrowers, respectively. In terms of

gender, marital status, and age at the time of taking out their current mortgage, bor5For reference, servicers in Dallas averaged having 15% of LEP borrowers as customers (Kleimann

Communication Group, 2017).

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rowers with limited English profciency are similar to native borrowers. As expected,

LEP borrowers typically have lower socioeconomic status. Only 53.4% of LEP borrowers hold a bachelor’s degree or higher, compared to 65.8% of non-LEP borrowers.

Around 21.8% of LEP borrowers have an annual household income less than $50,000,

compared to 14.3% of non-LEP borrowers. The average FICO scores of LEP borrowers is 722, 11 points lower than that of non-LEP borrowers. This diference is

not large, roughly one-sixth of the FICO score standard deviation in the full sample.

Figure B2 plots the distribution of educational achievement, age at mortgage origination, income, and credit scores for both LEP and non-LEP borrowers, exhibiting

analogous patterns as summarized by the sample means.

B Perceptions and Experiences

I next use regression analysis to show that borrowers with limited English profciency have diferent mortgage application experiences even conditional on a variety

of borrower and mortgage characteristics. In particular, I estimate the following

specifcation:

yit = α + βLEPi + γXi + δt + εit (1)

where yit is an outcome of interest for loan i originated in quarter t. LEPi is an

indicator denoting English profciency of borrower i. Xi is a vector of borrower

demographic characteristics (e.g., gender, race, ethnicity, marital status, age, income,

education, and FICO score) and mortgage characteristics (e.g., loan-to-value ratio,

loan type, loan purpose, loan term, property type, occupancy type, interest type, and

census tract type).6 Origination quarter fxed efects δt account for market conditions

across time.

I start with borrowers’ anxiety when they begin the application process. Column

1 of Table 2 reports the estimate from a univariate regression, implying that LEP

borrowers are more concerned about qualifying for a mortgage than non-LEP borrowers. The remaining columns of this table add a series of control variables that

increasingly remove the infuence of other confounding factors. Column 2 includes

origination quarter and census tract type fxed efects, which control for market conditions. Column 3 directly controls for race, ethnicity, gender, education, and other

demographic characteristics. This addresses the concern that the diference in de6The NSMO public use fle does not provide detailed location information. Instead, it reports 3

types of census tract: metropolitan Community Reinvestment Act (CRA) low- and moderate-income

(LMI) tract, metropolitan CRA non-LMI tract, and non-metropolitan tract.

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mographic characteristics, instead of the diference in English profciency, leads to

the diference in borrower behavior. This column shows that the efect of English

profciency is comparable to the efect of a college degree. Column 4 further includes

borrowers’ risk fxed efects, which are the full pairwise interactions between LTV

bins and FICO score bins.7 Finally, column 5 adds predetermined loan characteristics, such as loan purpose, property type, and occupancy status. The coefcient of

interest from columns 2 to 5 remains statistically signifcant at the 1% level. The

most demanding specifcation in the last column demonstrates that LEP borrowers

are about 6 percentage points more likely to worry about qualifying for a mortgage,

and this magnitude is about twice the efect of college education. These results suggest that the efect of English ability cannot be fully captured by race, gender, or

education.

Using the specifcation in column 5, Figure 2 compares the perceptions and experiences of LEP and non-LEP borrowers throughout the mortgage application process.

This comparison is visualized through red bars representing the estimated βˆ in Equation (1).8 To provide perspective on the magnitude of these diferences, I also include

green bars to represent the raw diferences between LEP and non-LEP borrowers,

and blue bars to represent the conditional diferences between borrowers with and

without college degrees.

Before the application process: LEP borrowers tend to have less knowledge

about the mortgage product and market. As Panel A of Figure 2 shows, borrowers

with limited English profciency are less familiar with diferent types of mortgages

available, the down payment needed to qualify for a mortgage, their own credit histories, and the current mortgage rate. To put this into perspective, these knowledge

gaps are roughly 60% of the diferences between borrowers with and without college

degrees. Panel B of this fgure illustrates that LEP borrowers value established banking relationships and personal connections a lot when selecting mortgage lenders or

brokers. For instance, 39% of non-LEP borrowers, compared to 55% of LEP borrowers, believe that a friend or relative’s recommendation is very important. This

disparity remains essentially the same even after accounting for borrower and mortgage characteristics. On the other hand, college education does not have as signifcant

an impact on these preferences.

7I follow the Loan-Level Price Adjustment Grid of Fannie Mae to group FICO scores and LTV

into bins. See https://singlefamily.fanniemae.com/media/33201/display. 8Figure 2 plots the diferences in outcomes between LEP and non-LEP borrowers. For level

information of each type of borrowers, see Figure B3.

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In the application process: Borrowers with limited English profciency search

less compared to native borrowers. In the frst two columns of Table 3, I fnd that

LEP borrowers seriously consider and fnally apply to fewer lenders. Interestingly, as

shown in Table B1, the coefcients of race and ethnicity have the opposite sign to

that of LEP status, suggesting that English profciency, race, and ethnicity have quite

diferent impact on borrower search behavior. In columns 3 to 5 of Table 3, I explore

the motivations behind LEP borrowers’ shopping behavior. The regression results

show that they do shop around not because they try to fnd better loan contracts,

but because they have concerns about qualifying for a loan or they hope to learn

information from the Loan Estimate form.9

Panel C of Figure 2 further shows that LEP borrowers face more challenges in

the application process. Conditional on relevant borrower and mortgage features,

LEP borrowers are about 3-6 percentage points more likely to resolve credit report

errors, have more than one home appraisal, and redo their paperwork due to processing delays. On the other hand, borrowers’ educational level has a limited efect on

the probability of encountering problems in the process of getting a mortgage. One

exception is that the probability of answering follow-up requests for more information about income or assets does not signifcantly difer between LEP and non-LEP

borrowers. However, borrowers without a college degree are signifcantly less likely

to do so compared with college graduates.

After the application process: Although each respondent in the survey has

taken out a mortgage successfully, LEP borrowers seem less familiar with their own

mortgage contracts. Interviews and focus groups with LEP borrowers reveal that

they are particularly confused with the meaning of “balloon” as a terminology in

mortgage-related documents (Kleimann Communication Group, 2017). Panel D of

Figure 2 shows that LEP borrowers are roughly 5 percentage points more likely to

report that they do not know if their mortgage has a balloon payment. They also

tend to be less familiar with other nonstandard mortgage features such as adjustable

interest rate, prepayment penalties, and escrow account. In contrast, the diferences

between borrowers with and without college degrees are much smaller. Furthermore,

despite completing the application process, LEP borrowers struggle to explain some

complex mortgage concepts to others. As shown in Figure B4, fewer LEP borrowers

can articulate the diference between a fxed- and an adjustable-rate mortgage, explain

9Lender must provide borrowers a Loan Estimate form within three business days of receiving

the application. This form provides important information, including the estimated interest rate,

monthly payment, and total closing costs for the loan.

13
why payments into an escrow account can change, or describe the process of taking

out a mortgage.

The above fndings are robust within a specifc group of people. For example,

Figures B5 and B6 document signifcant diferences in perceptions and experiences

across English profciency among Hispanics and Asians, respectively. Figures B7 and

B8 show the disparities between LEP and non-LEP borrowers among both college

and non-college graduates. Figures B9 and B10 highlight these diferences within high

income and low income borrowers. Figures B11 and B12 extend this observation to

borrowers who accessed mortgages via brokers and lenders. Taken together, language

frictions lead to distinctive mortgage application experiences for LEP borrowers.

C Mortgage Outcomes

Finally, I use administrative data in NSMO to compare mortgage outcomes between LEP and non-LEP borrowers. Panel B of Table 1 reports the comparison using

the raw data. About 74.2% non-LEP borrowers take out conventional loans, while

only 67% of LEP borrowers do the same. LEP borrowers tend to take out smaller

mortgages than non-LEP borrowers: the proportion of mortgage amount less than

$200,000 is 2.3 percentage points higher. In addition, LEP borrowers have slightly

higher loan-to-value ratios by 1.3 percentage points and debt-to-income ratios by 2.5

percentage points relative to non-LEP borrowers. Figure B13 confrms these results

by plotting the distribution of loan amount, LTV, and DTI for LEP and non-LEP

borrowers, respectively.

Panel B of Table 1 also shows that the average raw interest rate for LEP borrowers is approximately 7 basis points higher than that for non-LEP borrowers. Since

interest rate is largely determined by borrowers’ credit scores and mortgage choices,

I control for these features and estimate Equation (1) for a more precise comparison.

In addition to predetermined loan characteristics such as loan purpose, property type,

and occupancy status, I also control for loan type, loan term, and interest type. In

Panel A of Table 4, column 1 suggests that the interest rate of a similar mortgage

product is 3.2 basis points higher for LEP borrowers than risk-equivalent non-LEP

borrowers. From columns 2 to 4, I further include race, ethnicity, gender, and education as control variables. The diference in mortgage rate associated with language

frictions is still statistically signifcant. Panel A of Table B2 shows that the price dispersion ranges from 2.7 to 3.8 basis points across diferent loan purposes or borrowers

with diferent borrowing histories.

14
On the other hand, LEP borrowers are not ex-post riskier than ex-ante riskcomparable non-LEP borrowers. As can be seen from Panel B of Table 1, the unconditional probability of 90-day delinquency of LEP borrowers is slightly higher than

that of non-LEP borrowers. However, the regression results presented in Panel B

of Table 4 show that the diference in mortgage performance is insignifcant after I

control for ex-ante risk factors, mortgage characteristics, and demographic features.

Furthermore, Panel B of Table B2 confrms that this result is unrelated to loan purpose or prior borrowing experience.

III Empirical Design

Although I have included a comprehensive list of borrower and mortgage characteristics in the above analysis, it is still possible that the observed diferences between

LEP and non-LEP borrowers are caused by unobservables, such as cultural background and social relationships. To address this issue, I exploit the implementation

of the FHFA Language Access Plan as an exogenous shock to language frictions in

the mortgage market. In this section, I introduce the policy shock and outline my

main identifcation strategy.

A The FHFA Language Access Plan

In 2017, FHFA required Fannie Mae and Freddie Mac to identify major obstacles

for LEP borrowers in accessing mortgage credit, analyze potential solutions, and

develop a multi-year plan. The interviews and focus groups with LEP borrowers

and mortgage lenders revealed two key fndings (Kleimann Communication Group,

2017). First, accurate translations and standardized mortgage terminology are key

to any further action. Second, borrowers and lenders may not be able to fnd existing

language resources and are hesitant to use them. Because these language materials

are not centrally collected or uniformly considered reliable, consumers lack trust in

them, and lenders are afraid of potential legal issues.

Based on these fndings, in May 2018, FHFA and the Enterprises published a

multi-year plan to improve the ability of mortgage-ready LEP borrowers to understand and participate in all facets of the mortgage life cycle. The plan lists two key

measures:

(1) Disclosure: The mortgage translation disclosure, published in the third quarter

of 2018, is used by lenders and servicers to clarify that mortgage transactions are likely

15
to be conducted in English and that not all communications related to a mortgage

transaction will be in the borrower’s preferred language. It also refers borrowers to the

multilingual housing counseling services that may be available from HUD-approved

housing counseling agencies. Figure F1 shows the disclosure in both English and

Spanish. Lenders and servicers can customize the disclosure with their own logo and

formatting. By explicitly stating the limitations of potential language assistance, this

disclosure serves as a protection for fnancial institutions.10

(2) Clearinghouse: The Mortgage Translation Clearinghouse is an online centralized collection of language resources, which is designed to assist lenders, servicers,

and housing counselors in serving LEP borrowers. It provides translated glossaries,

forms, disclosures, and other documents and materials from the Enterprises and other

government agencies involved in the mortgage process. When the clearinghouse website was initially launched in 2018, it only provided translated mortgage documents in

Spanish. Figure F2 shows a snapshot of the clearinghouse website in early 2019. Chinese translations were added to the website in 2019, followed by Vietnamese, Korean,

and Tagalog translations in 2020.

I use the implementation of the FHFA Language Access Plan to perturb language

frictions faced by LEP borrowers. For borrowers, the government provides translated

documents, enhancing their trust in these translations. For lenders, this simple policy

intervention alleviates their concerns by addressing three key issues: which documents

to provide translations, in which languages to provide translations, and the accuracy

of translations. As a result, fnancial institutions face smaller regulatory uncertainty

and compliance risks.

I use Google Trends data to show the usage of FHFA language resources in practice. Figure 3 plots monthly search interest for search term “mortgage translation”

and “mortgage” between July 2018 and December 2019.11 I normalize two series

relative to its value in July 2018, separately. Following the addition of a foreign language to the Mortgage Translations Clearinghouse, the Google searches for “mortgage

translation” would increase by two to three times. In contrast, the Google searches

for “mortgage” did not exhibit a similar change, which suggests that the sharp rise in

the social interest in “mortgage translation” was not driven by the overall sentiment

10A policy expert at FHFA said that the mortgage translation disclosure was designed to alleviate

lenders’ concerns about compliance risks when serving LEP borrowers.

11The Mortgage Translation Clearinghouse appears at the top of the frst result page when the

keyword is “mortgage translation”, but it is not in the frst 20 results when the keyword is “mortgage.”

16
in the mortgage market. Moreover, the web trafc data from Semrush implies that

the clearinghouse web page had taken up about 5.52% of the total web trafc of the

FHFA website by the end of 2019.

B Triple-Diference Model

To identify the causal efect of language frictions, a diference-in-diferences model

can compare the outcomes of interest around the policy shock between LEP and nonLEP borrowers. Such a comparison could capture the efect of other LEP-specifc

shocks instead of the FHFA Language Access Plan. To address this concern, I exploit the fact that the initial translated mortgage documents were only available in

Spanish. I expect the changes in outcomes of interest to be concentrated among LEP

Hispanic borrowers, which suggests a triple-diference analysis. Specifcally, I compare

the double diferences (as described above) among Hispanic borrowers to the same

double diferences among non-Hispanic borrowers. Alternatively, the triple-diference

model can be interpreted as comparing changes in outcomes before and after the

policy change across Hispanic and non-Hispanic LEP borrowers while using similar

changes in non-LEP borrowers as a counterfactual. This specifcation controls for

any unobserved common shocks that afected all LEP people or all Hispanic people

in a given year. For example, shocks to the mortgage market that difer across LEP

status but not diferentially by ethnicity would not lead to bias in this specifcation,

and neither would shocks that difer across ethnicity but not diferentially by LEP

status.

Figure 4 presents the main idea of the triple-diference strategy. It plots the proportion of diferent types of borrowers who had to redo mortgage paperwork before

and after the policy change.12 I divide borrowers into four groups based on their

ethnicity and LEP status. The treatment group consists of LEP Hispanic borrowers

(Panel A). The control group consists of non-LEP Hispanic (Panel B), LEP nonHispanic (Panel C), and non-LEP non-Hispanic borrowers (Panel D). As can be seen

in Panel A, there is a salient drop of the proportion among LEP Hispanic borrowers.

We can reject the null hypothesis that the reduction is smaller than 5 percentage

points at the 1% level. On the other hand, the proportion in Panels B to D declines by roughly the same amount, and the decline is not signifcantly smaller than

12In the Online Appendix, Figure F3 plots the same triple-diference graphical evidence for other

outcomes of interest.

17
5 percentage points.13 Although not conclusive, this fgure implies that LEP Hispanic borrowers were about 14 percentage points less likely to redo their mortgage

paperwork after the policy shock.

I formally implement this approach by estimating the following regression:

yit = α + β0LEPi + β1Hispanici + β2LEPi × Hispanici + β3LEPi × Postt

+ β4Hispanici × Postt + β5LEPi × Hispanici × Postt + γXit + δt + εit. (2)

In this specifcation, Postt equals one if the mortgage was originated after June 2018,

and Hispanici equals one if borrower i is Hispanic.14 I interact census tract type and

mortgage characteristics with Postt to allow these controls to have time-varying efect

on the dependent variable. All other terms are as previously defned in Equation (1).

The coefcient of interest is β5, which measures the diference in the outcome for

LEP Hispanic borrowers relative to non-LEP Hispanic borrowers around the policy

change, relative to the same diference across LEP and non-LEP borrowers among

non-Hispanic borrowers. This triple-dimension comparison is based on a broad set

of borrower and mortgage characteristics as well as origination quarter fxed efects.

The sign of β5 depends on which outcome I examine. For instance, when I use

the probability of confronting additional problems in the application process as the

dependent variable, I expect to fnd β5 < 0. On the other hand, when I use search

intensity as the dependent variable, I expect to fnd β5 > 0 if the policy reduced

search costs.

Recall that the NSMO sample includes mortgages originated between 2013 and

2019. During this period, Spanish translations were made available online in the

second half of 2018, followed by Chinese translations in the second half of 2019.

However, I can only observe borrowers’ race (e.g., Asian) rather than their primary

language (e.g., Chinese or Tagalog), which prevents me from precisely defning the

treatment group in 2019. Therefore, for my main results, I drop Asian borrowers

to obtain a longer post-policy period, and the triple-diference model identifes the

average treatment efect on LEP Hispanic borrowers. As a robustness check, I drop

13LEP non-Hispanic borrowers have a higher socioeconomic status than LEP Hispanic borrowers,

which explains why the pre-policy proportion of redoing paperwork is lower in Panel C than in Panel

A.

14According to the timeline in the multi-year plan, FHFA and the Enterprises prepared and

reviewed the necessary materials in the frst and second quarters of 2018. The disclosure and the

clearinghouse were fnalized and launched in the third and fourth quarters. Thus, I treat July 2018

as the frst post-policy month.

18
observations after the introduction of Chinese translations and re-estimate Equation

(2).

IV Results Using NSMO

In this section, I frst use the survey data to estimate the causal efects of language

frictions on borrowers’ application experience, mortgage rate, and loan performance.

I then examine borrower search as the mechanism through which LEP borrowers paid

lower interest rates after the policy shock. Finally, I provide robustness tests of my

main results.

A Efect on Perceptions and Experiences

Having mortgage documents translated made it less likely that LEP borrowers

would have extra problems when they applied for a mortgage. The frst two columns

in Panel A of Table 5 show that the probabilities of resolving credit report errors

and answering follow-up requests on income or asset information both decreased by

about 16 percentage points for LEP Hispanic borrowers. They correspond to a 48%

and 25% drop relative to the pre-treatment level among LEP Hispanic borrowers,

respectively. The most time-consuming part of getting a mortgage is home appraisal,

which usually takes between one and two weeks to fnish.15 The estimate in column 3

implies a statistically signifcant 12.5 percentage points reduction in the probability

of having more than one home appraisal following the policy change. Before the

implementation of the FHFA Language Access Plan, nearly 22% of LEP Hispanic

borrowers had extra home appraisals, while only 8% of non-LEP Hispanic borrowers

did. My estimate suggests that the policy change almost eliminated the gap caused by

language frictions.16 The last column shows that LEP Hispanic borrowers were 13.7

percentage points less likely to redo mortgage paperwork subsequent to the policy

change, or a 42% decrease from the pre-treatment level. These results demonstrate

that translations could help LEP borrowers save time and reduce psychological costs

associated with an important and complicated fnancial transaction. The results also

ofer suggestive evidence that lenders and servicers indeed provided language help

15See https://pacresmortgage.com/your-loan-timeline-from-offer-through-closing/. 16In Section C.1 of the Online Appendix, I use another data source, the Uniform Appraisal Dataset

(UAD), to provide suggestive evidence of the positive policy impact on LEP borrowers’ experience

with property appraisals. Table C1 reports the results.

19
to LEP borrowers following the policy change; otherwise, LEP borrowers would not

have experienced a streamlined mortgage application process.

The positive policy impact also existed after the application process. LEP Hispanic borrowers’ ex-post knowledge of their own mortgage contracts improved following the policy change. Column 1 in Panel B reveals that LEP Hispanic borrowers were

8 percentage points more likely to know if their mortgage has an adjustable interest

rate, implying a 76% improvement relative to the pre-treatment level. Columns 2

and 3 report small impacts on their familiarity with prepayment penalty and escrow

account. Column 4 indicates that LEP Hispanic borrowers were about 16 percentage

points more likely to know whether their own mortgage had a balloon payment. In

the NSMO sample, about 38% of LEP Hispanic borrowers did not know this prior

to the policy shock, suggesting an approximately 42% decrease in the unawareness of

balloon payment among the treatment population.

B Efect on Mortgage Rate and Performance

The foregoing estimates suggest that providing Spanish mortgage-related documents greatly improved the origination experience for LEP Hispanic borrowers. Next,

I explore how language frictions afect mortgage rates and performance. To do this, I

frst present graphical evidence showing that only LEP Hispanic borrowers paid lower

conditional interest rates after the policy shock. The conditional interest rate is the

mean of raw interest rate plus the residual after regressing the raw rate on origination

quarter fxed efects, census tract type fxed efects, loan type, loan term, loan purpose, property type, occupancy type, and interest type. Figure 5 plots the average

conditional interest rates for 8 samples, partitioned by ethnicity, English profciency,

and origination time. In Panel A that focuses on the LEP Hispanic group, there is

a noticeable diference in interest rates before and after the policy change at the 5%

level. However, Panels B to D show no such distinction. Formally, I cannot reject

the null hypothesis that the pre-policy mean is equivalent to the post-policy mean in

these control groups at conventional levels.

I then quantify the changes in interest rates demonstrated by Figure 5 with a

regression analysis. Panel A of Table 6 shows that risk-equivalent LEP Hispanic

borrowers paid lower interest rates for similar mortgages product after the policy

shock. The coefcient of interest in column 1 implies a reduction in interest rates

by about 14.9 basis points. To put this magnitude in more context, consider a typical LEP Hispanic borrower who took out a 30-year fxed rate mortgage in January

20
2019 with a loan amount of $249,000 and a mortgage rate of 4.5%.17 Converting

the estimate of the interest rate efect into dollars implies a reduction of $22 per

month in mortgage payments. In the remaining columns of Panel A, I fnd that the

drop in mortgage rate was larger for purchase loans compared with refnance loans,

and larger for frst-time borrowers compared with repeat borrowers. Although the

estimates have relatively wide confdence intervals, there is a noticeable diference

in both coefcient magnitude and statistical signifcance. This heterogeneity across

loan purpose and borrowing history ofers additional validity to my results. Compared to frst-time (purchase) borrowers, repeat (refnance) borrowers should have

more experience applying for a mortgage, so we would expect them to beneft less

from translated mortgage documents.

To capture loan performance, I use an indicator that takes the value of one if the

borrower was ever 90 or more days late in making payments, and zero otherwise. As

shown in Panel B of Table 6, I do not fnd a signifcant efect on mortgage performance across diferent loan types. The coefcients are all negative but statistically

insignifcant, suggesting, if anything, a weak positive efect on loan performance. Table C2 reports similar results when I use indicators of 60-day delinquency and default

to measure mortgage performance. This is not surprising since borrowers received

a better price following the policy change. Consistent with this, Table F1 shows

that LEP Hispanic borrowers had lower debt-to-income ratios (DTI) after the policy

shock.

To summarize, the results in Tables 5 and 6 provide evidence that language frictions were a substantial barrier for borrowers with limited English profciency in the

mortgage market. Providing translated mortgage documents to these borrowers could

greatly improve their welfare without introducing additional risks to the residential

mortgage market.

C Mechanism of the Price Efect: Borrower Search

Why did LEP borrowers pay a lower interest rate when they had access to mortgage documents in their primary languages? Using the survey data, I ofer suggestive

evidence indicating that the reduction in interest rates could be attributed to increased borrower search, rather than an improvement in fnancial literacy.

17The average loan amount for Hispanic borrowers was $249,000 in 2019. The average rate of a

30-year fxed rate mortgage was 4.5% in January 2019.

21
Agarwal et al. (2014) fnd that fnancially sophisticated households are less likely

to pay too high mortgage rates. However, the FHFA Language Access Plan seemed

to have a limited efect on LEP borrowers’ ex-ante knowledge of the U.S. mortgage

market. As shown in Table F2, I do not fnd a statistically signifcant efect on LEP

borrowers’ knowledge of mortgage types available, down payments needed, personal

credit history, or market rate when they began the application process. These results

suggest that borrowers with limited English profciency did not improve their fnancial literacy in advance, which is consistent with how the policy was designed and

implemented. Both the disclosure and the clearinghouse website were designed for

lenders and servicers, and LEP borrowers were probably unaware of language help

until they actually contacted a lender.

Several papers fnd that obtaining multiple mortgage quotes may help borrowers

get a mortgage with better fnancial terms (Woodward and Hall, 2012; Alexandrov

and Koulayev, 2018; McManus, Liu and Yi, 2018).18 However, borrowers seem to

conduct little search in the mortgage market despite the large potential beneft (Cai

and Shahdad, 2015). The NSMO sample also suggests that more than half of borrowers did not search before taking out a mortgage. Since LEP borrowers have difculty

processing complicated mortgage documents and negotiating with mortgage lenders,

it is not surprising that they search even less compared to non-LEP borrowers (see

Table 3). Reducing language frictions for LEP borrowers can efectively reduce their

search costs, since translated documents can help them better understand paperwork

and compare multiple ofers. As a result, they are more likely to take out a mortgage

with a lower interest rate.

I frst provide graphical evidence that uses unadjusted data and summarizes my

triple-diference strategy. Figure 6 plots the pre- and post-policy distributions of

borrower search intensity for diferent types of borrowers. Panel A clearly illustrates

that more LEP Hispanic borrowers seriously considered multiple lenders when they

faced lower language frictions in the mortgage market. The Kolmogorov-Smirnov test

rejects the null hypothesis that the pre- and post-policy distributions are the same at

the 5% level. In contrast, we do not observe such a pattern among non-LEP Hispanic

borrowers or non-Hispanic people regardless of LEP status. Although not conclusive,

this fgure suggests that reducing language frictions can induce LEP borrowers to

18Agarwal et al. (2020) fnd a non-monotonic relationship between consumer search and realized

interest rates due to the fact that ex-ante risky borrowers search for approval. As LEP borrowers tend

to have lower creditworthiness, for borrower search as a valid channel, I show that LEP borrowers

can get cheaper mortgages when they consider more lenders in Figure F4.

22
search more.

Motivated by the above graphical evidence, I estimate Equation (2), which allows

me to control for factors that are correlated with both LEP status and search behavior.

Table 7 reports the regression results. The dependent variable in column 1 is a dummy

variable indicating that the borrower seriously considered multiple lenders. The point

estimate in column 1 implies that LEP Hispanic borrowers were 16.2 percentage points

more likely to do so following the policy shock. Column 2 uses the number of lenders

seriously considered as the dependent variable to reinforce this fnding. In columns 3

to 5, I examine the policy impact on the reasons why borrowers search. As noted in

Section II, LEP borrowers shop around mainly because they try to get approval or

to gain experience. Although the estimates are imprecise, columns 3 and 4 suggest

that more LEP Hispanic borrowers started to shop for better loan terms rather than

for application approval. Column 5 shows that LEP Hispanic borrowers were 26.9

percentage points less likely to report learning information as the goal of search after

the policy shock. Given that about 60% of pre-treatment LEP Hispanic borrowers

applied to multiple lenders due to this reason, the FHFA Language Access Plan had

a large impact on borrowers’ search motivation.

D Robustness Checks

This subsection summarizes a suite of specifcation tests using diferent control

groups and a suite of placebo tests exploiting diferent fake policy shocks. I focus on

four outcomes that I have found signifcant efects in the above analysis: the likelihood

of redoing mortgage paperwork, awareness of balloon payments, mortgage rate, and

borrower search.

Choice of control group: In the above analysis, I drop Asian borrowers to

avoid the misclassifcation of borrowers’ treatment status. Alternatively, I can drop

observations after the addition of Chinese translations to the Mortgage Translations

Clearinghouse, so Asian borrowers are also included in the control group. Table

C3 presents the triple-diference estimates following this sample selection, which are

similar to my main fndings.

The second row (Panels C and D) of Figures 4 through 6 suggests that LEP and

non-LEP borrowers within the non-Hispanic population would have evolved similarly

in the absence of the policy change. Likewise, the second column (Panels B and D)

suggests that the parallel trends between Hispanics and non-Hispanics among nonLEP people are likely to hold. This motivates three alternative choices of the control

23
group. First, I use non-LEP Hispanic borrowers as the control group to run diferencein-diferences regressions. Second, I use LEP non-Hispanic borrowers as the control

group to run diference-in-diferences regressions. Finally, I directly compare LEP

Hispanic borrowers with all other borrowers in the same sample used for my main

results. Table C4 shows that all three specifcations lead to similar estimated policy

impact as my triple-diference estimation.

To give a sense of the dynamics of the policy impact, Figure C1 plots estimates

from a fexible diference-in-diferences specifcation. These estimates are obtained

from a regression that employs the same specifcation as Panel C of Table C4, but

allows the policy impact to vary every six months, relative to the frst half of 2018.

Outcomes of interest diverge from their pre-policy trends following the policy shock.

Importantly, the trends are statistically indistinguishable before the policy shock.

The policy impact grows over time, which refects the fact that lenders need time to

learn about the policy and adjust their services for LEP borrowers.

Placebo Tests: Given the framework of the triple-diference setting, I intentionally change each item in LEPi × Hispanici × Postt to make up fake policy interventions. As the treatment status is completely misclassifed, I do not expect to fnd a

statistically or economically signifcant efect.

First, I assume that the FHFA Language Access Plan was implemented in July

2016, which is a perturbation to Postt. I drop mortgages originated after June 2018

and re-estimate Equation (2). Panel A of Table C5 reports a small and statistically

insignifcant efect of the fake policy shock. Second, I assume that the clearinghouse

website initially published Asian language translations, which is a perturbation to

Hispanici. I replace LEPi × Hispanici × Postt with LEPi × Asiani × Postt when

estimating the triple-diference model. Panel B of Table C5 shows that the estimated

efect is indeed statistically and economically insignifcant. Third, I randomly assign

borrowers’ LEP status, which is a perturbation to LEPi.

19 In each iteration, I randomly select a group of people as LEP borrowers. To preserve the market share of

LEP borrowers in reality, the simulated sample has the same number of LEP borrowers as the real NSMO sample. I then estimate Equation (2) and get one placebo

coefcient, βˆ5. Figure C2 plots the distribution of this coefcient arising from 1000

iterations. All panels present a bell shaped distribution of the placebo coefcient,

19Bertrand, Dufo and Mullainathan (2004) recommend using the empirical distribution of estimated placebo efects to evaluate the results from diference-in-diferences studies. As a triplediference model can be transformed into a diference-in-diferences model (Olden and Møen, 2022),

their argument is also valid in my context.

24
which centers close to 0. Furthermore, the vertical red line indicating the true estimated efect lies in the extreme tail of the whole distribution, which leads to a small

empirical p-value. Taken together, all robustness checks provide confdence that my

empirical results are not statistical artifacts.

V Results Using Aggregate Data

In this section, I use county or ZIP code level data and an accompanying diferencein-diferences model to estimate the efects of reducing language frictions. This aggregate level analysis complements the triple-diference analysis in two ways. First

and foremost, it allows me to explore the policy impact on LEP consumers who were

discouraged from participating in the mortgage market due to language frictions. As

individual-level LEP status is not required, I can use the county-level HMDA data

that contain loan application information. Second, this empirical design is fexible

enough to incorporate the efect of providing Chinese translations in late 2019 by

changing the local treatment intensity. Below, I present the estimated policy impact

on credit access on the extensive margin, mortgage rate, mortgage risk, and lender

competition.

A Identifcation Strategy

My diference-in-diferences strategy leverages the fact that native speakers do not

beneft from the translations of mortgage-related documents into other languages. I

compare the changes in outcomes of interest around the policy shock between areas

with varying proportions of treated LEP people. Specifcally, I estimate the following

model:

Yct = α + βDct + γXct + δc + δst + εct (3)

where



0, if t ≤ 2017,

Dct = Hispanic LEP sharec, if t = 2018,  Hispanic LEP sharec + Chinese LEP sharec, if t = 2019.

In Equation (3), c, s, and t index county, state, and year respectively. The key

independent variable of interest, Dct, which comes from the county-level ACS fles,

measures the share of potentially treated LEP people in county c in year t. This

25
variable captures the gradual introduction of Spanish translations in 2018 and Chinese

translations in 2019. I exclude small counties with a population under 5,000 so that

the share of LEP people is relatively precise at the county level. Xct is a vector of

county-year level controls, including total population, median household income, the

proportion of Hispanics, Asians, and Black people. These control variables account

for the racial and ethnic composition and local housing market demand, which may be

correlated with both the share of treated LEP borrowers and local mortgage market

outcomes. δc and δst are county fxed efects and state-year fxed efects, which absorb

county-specifc time-invariant characteristics and state-level time-specifc shocks.

The standard identifcation assumption in this framework is that the trends in

outcomes in areas with varying fractions of LEP people would have evolved in parallel in the absence of the policy shock. I provide graphical evidence showing the

plausibility of this assumption by estimating a more fexible version of the above

model as follows:

X Yct = α + βτLEP Sharect × 1(t = τ ) + γXct + δst + δc + εct (4)

τ̸=2017

where 1(t = τ ) is an indicator variable taking the value of one if year t is equal to τ .

LEP Sharect is the share of LEP Hispanic people before 2019 and the share of LEP

Hispanic and LEP Chinese people in 2019. I normalize the coefcient for τ = 2017 to

zero, so that all estimates of βτ can be interpreted as the diference in the outcome

of interest between areas with varying shares of treated LEP people relative to the

corresponding diference in the year just before the policy shock. If βτ is statistically

insignifcant before but signifcant after the policy change, this provides evidence of

the validity of the parallel trends assumption and suggests that the discrete jump in

coefcients is induced by the policy shock studied in this paper.

B Efect on Access to Mortgage Credit

First, I investigate the efect of reducing language frictions on mortgage credit

access. Since refnance loan borrowers have more prior experience in the mortgage

market, I focus on purchase loans in my analysis.20 Using 2011-19 HMDA data,

I follow the borrower funnel in the mortgage market to calculate four outcomes of

interest at the county level: the number of applications, the share of incomplete

20Table F3 reports the regression results for conventional refnance loans, showing that the policy

shock had much smaller efect on refnance loans.

26
applications, the denial rate, and the number of originations. If some LEP borrowers

have a more user-friendly application procedure after the policy shock, they may

encourage more people in their communities to apply for mortgages. LEP borrowers

are more likely to submit complete and accurate applications if they have access to

mortgage documents in their primary language, so I expect a decrease in the share of

incomplete applications and the denial rate for treated LEP borrowers after the policy

shock. Finally, more applications and a lower denial rate will lead to an increase in

mortgage originations.

Panel A of Table 8 shows that the FHFA Language Access Plan had a positive

efect on credit access of conventional purchase loans. Column 1 implies that a 4

percentage point increase in the proportion of potentially treated LEP borrowers

(i.e., one standard deviation of the proportion) could result in 48 more applications

after the policy change. The economic magnitude of this efect is sizable relative to

the proportion of LEP individuals. Given that the average number of applications

in my sample is 905, my estimate implies an increase in mortgage applications by

approximately 5.3 percent. As an alternative way to interpret this result, I convert

the diference-in-diferences coefcient into the implied change in the latent propensity

to apply for mortgages among LEP people. Let APP0 and APP1 denote the number

of applications before and after the policy shock, respectively. If we assume that

DLEP percent of LEP and DNLEP percent of non-LEP people would like to apply for

a mortgage before the policy shock, then we can express APP0 and APP1 as weighted

averages of the demand among LEP and non-LEP people:

APP0 = DLEP × LEP × POP + DNLEP × (1 − LEP) × POP

APP1 = (DLEP + ∆) × LEP × POP + DNLEP × (1 − LEP) × POP,

where LEP and POP denote the share of LEP people and total population, respectively.21 The second line arises from the assumption that reducing language frictions

would boost the propensity by ∆ among LEP people but not among non-LEP people. Then the diference-in-diferences coefcient actually identifes ∆ × POP. Since

the average population is around 113,000 in my sample, the diference-in-diferences

estimate in column 1 implies that the policy shock increased the propensity to apply

for a mortgage among LEP people by approximately 1.1 percentage points.

Consistent with my expectation, column 2 shows that the policy led to a reduction

21For simplicity, here I ignore the population growth from pre-policy to post-policy period.

27
in the probability of submitting an incomplete application by 6.2 percentage points for

treated LEP borrowers. Column 3 shows that the denial rate also dropped by roughly

15.5 percentage points. Given these estimated efects on the frst three stages of the

borrower funnel, it is not surprising that if the share of potentially treated LEP people

increased by 4 percentage points, there would be 36 additional originated conventional

purchase loans. As the sample mean of mortgage originations is 665, this estimated

efect corresponds to a roughly 5.4% increase in mortgage originations.

As shown in Panel B of Table 8, LEP borrowers were also less likely to submit

incomplete applications or be denied for FHA loans. However, there was a slight

drop in FHA loan applications and originations, which suggests a substitution efect

between conventional and FHA loans. Thus, the overall supply of purchase loans

might remain largely unchanged. I confrm this point in Table F4, which provides the

regression results using all types of purchase loans (conventional, FHA, VA guaranteed, and FSA/RHS loans). Columns 2 and 3 in Table F4 show that the incomplete

share and denial rate of all types of purchase loans still decreased signifcantly. Based

on the above results, the following analysis will only use the sample of conventional

purchase loans.

To present the dynamics of the policy impact on the extensive margin, I estimate

Equation (4) that allows the policy impact to vary by year. Figure 7 plots the series

of βτ along with their 95% confdence intervals. Almost all coefcients prior to the

policy shock are close to zero and statistically insignifcant, lending support to the

validity of the parallel trends assumption required for the identifcation in a diferencein-diferences research design. In contrast, the coefcients after the policy shock are

economically large and statistically signifcant for all outcomes. For example, there

is a discrete drop in the application denial rate when the FHFA Language Access

Plan began. The magnitude of this drop is roughly 14 percentage points, which is

similar to the point estimate in Table 8. The results so far have shown that providing

translated mortgage documents addressed the credit access issue faced by borrowers

with limited English profciency.

Heterogeneous Efects: The magnitude of the policy impact should be a function of the extent to which borrowers with limited English profciency need translated

mortgage documents. Therefore, I investigate how the credit access efects vary across

counties in this regard.

Section II has demonstrated that LEP borrowers largely rely on their friends and

relatives when applying for a mortgage. If LEP borrowers have high trust in their

28
I

communities, providing translations will hardly change their behavior. Therefore,

I expect a stronger policy impact in counties with lower levels of social capital.

split the sample based on a county-level community health index, which measures

local civic engagement and the health of associational life.22 Figure 8 presents the

diference-in-diferences results by social capital. Consistent with my expectation,

counties that had a community health index below the national median experienced

a larger increase in the number of applications and originations and a larger decline

in application denial rate. The share of incomplete applications in these counties also

dropped signifcantly at the 5% level, though the magnitude is slightly smaller than

that in counties with higher levels of social capital.

The demand of LEP borrowers for translated mortgage documents also depends

on racial composition and lender competition. If a county has a large fraction of

Hispanic and Chinese people, local lenders may already have well-trained bilingual

agents and translated documents prior to the policy shock. As shown in Table F5, I

fnd a large and statistically signifcant policy efect in counties where the proportion

of Hispanics and Chinese is below the national median. By contrast, there is little

change in counties with a proportion above the national median. Moreover, the efect

on mortgage credit access is likely to be smaller in less competitive counties for two

reasons. First, if the market for LEP borrowers is concentrated among several lenders,

these lenders may have expertise in serving LEP borrowers. Second, lenders with

greater market power have less incentive to provide better service for LEP borrowers.

I divide the sample by the county-level HHI of conventional purchase loan originations

for Hispanic and Asian borrowers in 2017. Table F6 shows that the increase in

credit supply and decrease in failed applications concentrated in counties with a more

competitive mortgage market for Hispanic and Asian borrowers. Taken together, the

FHFA Language Access Plan was more efective in counties where the demand for

translations was higher.

Robustness Checks: Recent applied econometrics literature fnds that two-way

fxed efects (TWFE) estimations of diference-in-diferences coefcients can lead to

substantial bias when there are heterogeneous treatment efects (De Chaisemartin

and d’Haultfoeuille, 2020; Callaway and Sant’Anna, 2021; Sun and Abraham, 2021).

In my application, Equation (3) is a prototype of this regression with a time-varying

continuous treatment status. Following De Chaisemartin and d’Haultfoeuille (2020), I

22The county-level community health index combines non-religious non-profts per capita, congregations per capita, and the informal civil society index. See U.S. Congress Joint Economic

Committee (2018) for more details.

29
estimate the diference-in-diferences model with a TWFE estimator allowing heterogeneous treatment efects.23 Table C6 shows that my main fndings are robust to this

approach and actually underestimate the policy impact. The reason why the TWFE

estimator behaves this way is that the treatment efect was larger in counties with

a smaller share of LEP people.24 Following the policy change, some counties experienced a smaller increase in the treatment level, but these counties also experienced

a larger change in credit expansion for a given change in the treatment level. The

traditional TWFE estimator only accounts for the frst efect, so it underestimates

the efect of the policy shock (Sun and Shapiro, 2022).

Furthermore, I conduct three falsifcation tests to ensure that my diference-indiferences results are robust. I frst assume that the policy shock happened in 2016

and re-estimate Equation (3) using the 2011-17 HMDA data. As shown in Panel A of

Table C7, I fnd little efect of this fake policy intervention on mortgage credit access.

Second, I estimate the efect of providing Spanish translations on Asian borrowers.

In the diference-in-diferences model, the treatment intensity is determined by the

share of LEP Hispanics, but the outcomes are calculated using only Asian borrowers

in HMDA data. Panel B of Table C7 reports an insignifcant policy efect on Asian

borrowers. On the other hand, Table C8 reports an economically and statistically

signifcant efect when the outcomes are calculated using Hispanic borrowers. Finally,

I randomly assign the share of LEP Hispanics and LEP Chinese at the county level

within each state, and then I use this simulated treatment level and true data of

outcomes and control variables to run diference-in-diferences regressions. Figure C3

plots the distribution of 1000 placebo estimates following the above steps. The fgure

shows that the true estimate, denoted by the red vertical line, lies in the extreme tail

of the distribution of placebo estimates. The corresponding empirical p-values are

smaller than 1% in all panels.

C Efect on Mortgage Rate and Risk

In this subsection, I exploit across-ZIP code variation in exposure to the FHFA

Language Access Plan to identify the efect of reducing language frictions on interest

rates and mortgage risk. I frst use GSE data to construct a ZIP code-level measure

of interest rates. In particular, I regress the raw interest rate on a set of loan char23This approach can take care of continuous treatment status. In practice, the estimation uses

counties whose treatment level changed in absolute value by less than 0.5% as control groups.

24Table F7 shows that the treatment efect was larger in counties with a smaller share of LEP

people.

30
acteristics, retrieve the residual as the conditional interest rate for each mortgage,

and average this variable at the 3-digit ZIP code level at a monthly frequency. Motivated by the heterogeneous efects found in Table 6, I use diferent types of mortgages

when aggregating the conditional interest rate. To accommodate this data structure,

I estimate a modifcation of Equation (3) as follows:

Yzm = α + βDzm + γXzy + δz + δm + εzm (5)

where



 0, if m ≤ June 2018,

Dzm = Hispanic LEP share , if July 2018 ≤ m ≤ June 2019,  z

Hispanic LEP sharez + Chinese LEP sharez, if m ≥ July 2019.

In this expression, z, m, and y index 3-digit ZIP code, month, and year respectively.

The treatment intensity Dzm in this specifcation can vary within a year because of

the monthly data. Xzy is the same collection of demographic control variables as

above at the 3-digit ZIP code-year level. δz and δm are ZIP code fxed efects and

month fxed efects.

Panel A of Table 9 shows that reducing language frictions helped LEP borrowers

fnd cheaper GSE loans. Column 1 indicates that providing translated mortgage

documents led to a decrease in interest rate for LEP borrowers by 12.7 basis points.

This magnitude is comparable to that from a triple-diference estimation in the NSMO

sample. Consistent with the triple-diference results, columns 2 to 5 demonstrates that

the efect on purchase loans was about 34% larger than that on refnance loans, and

the price efect on frst-time borrowers was roughly 27% larger than that on repeat

borrowers. As shown in the last two columns of Panel A, the efect on mortgages

originated through retailers was both economically and statistically more signifcant

than that on mortgages originated through brokers. These results imply two key

conditions under which the policy had a greater impact: (1) borrowers or lenders

lacked experience; and (2) borrowers and lenders had direct interactions.

I next fnd that the policy did not increase the overall risk of the local mortgage

market. To measure mortgage performance, I follow the same steps as described above

to calculate the monthly ZIP code-level conditional 90-day delinquency rate for GSE

loans. As can be seen in Panel B of Table 9, there is little evidence that the policy

change had an impact on local mortgage performance. The conditional delinquency

31
rate has partialled out borrowers’ ex-ante risk factors, so the above fnding does

not take into account the potential efect on borrowers’ risk composition. If the

policy introduced more subprime LEP borrowers to the mortgage market, the overall

stability of the mortgage market would be at greater risk. I address this concern in

two steps. First, I estimate the policy efect on the average credit scores of originated

mortgages, which is a measure of ex-ante mortgage risk. Panel C of Table 9 shows that

instead of deteriorating origination standards, the FHFA Language Access Plan had a

positive impact on borrowers’ creditworthiness. This suggests that some well-qualifed

LEP borrowers were excluded from the mortgage market due to language frictions

before the policy change. Combined with the fndings about the extensive margin

efect, this result implies that the policy not only expand fnancial inclusion, but

also expand to the appropriate population. Second, I use an unconditional measure,

the CFPB monthly delinquency rate, as the dependent variable to re-estimate the

diference-in-diferences model. This unconditional delinquency rate is defned as the

number of records where the borrower has missed mortgage payments divided by the

total number of outstanding mortgages in the National Mortgage Database (NMDB).

Table F8 presents an insignifcant estimated efect on 90-day delinquency rate and a

measure of early stage delinquencies, 30–89 day mortgage delinquency rate, at both

the county and CBSA levels. In sum, these results imply that reducing language

frictions did not introduce extra risks to the mortgage market.

In addition, I use the FHA Snapshot+ data set to repeat the above analysis for

FHA loans.25 The only diference is that I aggregate the outcomes of interest at the

5-digit ZIP code level at a monthly frequency. Table F9 reports a very similar pattern

of results for FHA loans. After the policy shock, the interest rates dropped, the exante mortgage risk decreased, and the mortgage performance remained unchanged.

Similar to my above fndings, the policy impact on interest rates was larger for less

experienced borrowers.

D Efect on Lender Competition

Finally, I provide suggestive evidence of the positive policy impact on local lender

competition for LEP borrowers. Conceptually, the policy studied in this paper can

promote lender competition by reducing two types of service costs. First, it can reduce

25The original FHA Snapshot data have detailed location information but lack key variables about

origination and performance. The Ginnie Mae data have these variables but the mortgage location

is at the state level. Therefore, I match FHA Snapshot with the Ginnie Mae data to construct the

FHA Snapshot+ data set.

32
communication costs as LEP borrowers will understand and complete key fnancial

documents better. Second, it can reduce compliance risks and regulatory uncertainty

as the translations are provided by government agencies.

Following the above analysis using HMDA data, I focus on the conventional purchase loan market. To measure lender competition at the county level, I calculate the

number of active lenders and the HHI in diferent market segments divided by borrowers’ race and ethnicity. Panel A of Table 10 reports the diference-in-diferences

results for the market of Hispanic and Asian borrowers. The frst two columns show

that, after the policy shock, more lenders received applications from and originated

mortgages to Hispanic and Asian borrowers in counties with a larger share of treated

LEP people. As a result, the HHI of mortgage applications and originations in these

counties declined. In contrast, Panel B shows that there did not exist a similar impact on lender competition in the markets of all borrowers. Since the majority of LEP

borrowers are Hispanic or Asian, Panel B actually serves as a placebo test, which suggests that the result in Panel A captures the efect of the FHFA Language Access

Plan.

The policy studied in this paper might also curb lenders’ market power, since it

would be more difcult for lenders to exploit language frictions to take advantage of

LEP borrowers. However, due to unobserved marginal costs, the documented decrease

in market concentration does not defnitely imply a decrease in market power. This

reasoning is especially plausible in my context, as lenders could have lower service

costs after the FHFA started to provide translations. Therefore, it is unclear to

what extent the decline in marginal costs and market power contributed to a more

competitive mortgage market. This issue calls for further research to identify the

underlying mechanisms.

VI Empirical Analysis Using HMDA+

The NSMO data set ofers rich and unique information about borrowers’ mortgage market experiences, but its small sample size could restrict the precision of my

estimation. Another concern is that the NSMO data set does not contain location or

lender information. The direction of the potential bias is not ex-ante obvious. On one

hand, if some lenders took advantage of LEP borrowers before and then the predatory lending practices were curbed, the NSMO results would have a negative bias.

On the other hand, if some lenders were more productive than others in serving LEP

33
borrowers before and then the cost advantage diminished, the NSMO results would

have a positive bias. To address these issues, I use machine learning to predict borrowers’ LEP status in the HMDA+ data set and then implement the triple-diference

strategy using this data set. Although this approach generates measurement error of

LEP status, I can exploit the misclassifcation to provide a lower bound of the ATT

under several plausible assumptions. The detailed lender and location information

in the HMDA+ data set enables me to identify the efect of language frictions in a

more refned specifcation than that used in Section IV, and explore diferential efects

based on the cross-county heterogeneity. In this section, I introduce how I predict

individual-level LEP status, discuss how I recover the lower bound of the ATT, and

present the empirical results using this unique data set.

A Use Machine Learning to Predict LEP Status

The HMDA+ data set has included borrowers’ ethnicity and mortgage origination

time, but the implementation of the triple-diference strategy further requires borrowers’ LEP status. Predicting this variable in the HMDA+ data set has three challenges.

First, it is difcult to fnd a large labeled database as the training sample. The training sample should consist of mortgage borrowers and include their LEP status, but

few loan-level data sets can meet both requirements simultaneously. Second, as one

can expect, education, country of birth, and age at migration are useful predictors for

this classifcation task, but these variables are not available in the HMDA+ data set.

Third, traditional classifers (e.g., the Logit model) are prone to classify all borrowers

as non-LEP in an imbalanced classifcation task. Since the fraction of LEP borrowers

is small, this conservative prediction can achieve a decent accuracy rate in nature,

but it lacks sufcient variation in treatment status for a triple-diference regression.

Below, I briefy introduce how I solve these problems and leave the details of my

machine learning model in Section D of the Online Appendix.

I start from the micro-level 2015-19 ACS to construct the training sample, because this data set directly provides individual-level LEP status based on the census

defnition. To ensure that the training sample mimics the population in the HMDA+

data set, I only keep adult household heads who own their homes with mortgages.

In addition, only people who moved into the current residence within a year are selected, so that I use the survey year as their mortgage origination year. Finally, I

expand the sample based on individual weights in the ACS. Table D1 reports summary statistics for this sample. Similar to the NSMO sample, LEP borrowers have a

34
lower educational and income level. It is important to note that the training sample

tries to represent home buyers between 2015 and 2019, so the prediction sample will

only include purchase loans in the HMDA+ data set.

The input variables for the training process should be available in both the training

sample and the prediction sample. Therefore, I pick gender, race, ethnicity, household

income, and a series of state × year fxed efects as inputs for the classifcation task.

Although this is a short list of features that does not appear to be directly related to

borrowers’ English profciency, it turns out that these variables have enough predictive

power to produce relatively accurate results. The success relies on the use of a machine

learning algorithm that can efciently learn non-linear decision boundaries.

To solve this imbalanced classifcation problem, I employ XGBoost, a leading machine learning library for regression, classifcation, and ranking problems. XGBoost

implements machine learning algorithms under the Gradient Boosting framework in

a highly efcient, fexible, and portable way. I randomly allocate 80% of the ACS

sample for training, while the remaining 20% (i.e., the test sample) is used to evaluate

the performance of my model. Specifcally, I frst use the full training sample to train

a classifer Cf , and then I only use Hispanics to train another classifer Ch. Following the convention in machine learning literature, class 1 stands for LEP and class

0 stands for non-LEP. For non-Hispanic people, classifer Cf completely determines

the prediction of LEP status. For Hispanic people, if either classifer Cf or classifer

Ch predicts a positive class, then they are LEP borrowers. This two-step procedure

results in improved performance for the sample of Hispanic borrowers, which is crucial

for accurately recovering the ATT through a triple-diference regression.

My XGBoost model outperforms the traditional Logit model. Table D2 reports

three useful evaluation metrics for the full sample and the sample of Hispanics in Panels A and B, separately. For each class, precision is the fraction of relevant instances

among the retrieved instances, recall is the fraction of relevant instances that are retrieved, and accuracy is the ratio of correct predictions to all instances. As expected,

the Logit model predicts almost all people as non-LEP borrowers. Therefore, it only

detects 0.5% and 2.3% of LEP people in the full sample and the Hispanic sample.

In contrast, my model can fnd approximately 78.7% and 83.1% of LEP borrowers in

two samples. The precision rate of the Logit model in the full sample is only 0.54,

which means that nearly half of the predicted LEP people are actually profcient in

English. In contrast, my model can achieve a precision rate of 0.89 in the full sample.

Overall, the accuracy rate of my model increases by 3.2 percentage points in the full

35
sample and 15.4 percentage points in the Hispanic sample.

I then use this fne-tuned machine learning model to predict purchase loan borrowers’ LEP status in the HMDA+ data set. Table D3 compares several key characteristics between LEP and non-LEP borrowers, based on the machine learning prediction.

Consistent with the NSMO sample, a typical LEP borrower has a lower income, credit

score, and mortgage amount but a higher DTI, mortgage rate, and delinquency rate.

This suggests that the prediction is defnitely better than a random guess. About

4.9% of the training sample are LEP borrowers, but the machine learning model predicts that only 3.3% of the HMDA+ sample are LEP borrowers. This is probably

because the prediction sample has a smaller share of minorities and low-income Hispanic people than the training sample.26 Fortunately, as long as the misclassifcation

is not too severe, it can be used to back out a lower bound of the ATT under several

assumptions that are likely to hold in my case.

B Recover the Lower Bound of the ATT

Since the machine learning prediction generates measurement error of the key independent variable, it is necessary to gauge the bias of the triple-diference estimation

that uses the predicted LEP status. In this subsection, I lay out the assumptions and

explain the intuition of how I recover the lower bound of the ATT from a triplediference model with treatment status misclassifcation. The formal discussion is

presented in Section E of the Online Appendix.

For the sake of exposition, I summarize the empirical framework in the language

of potential outcomes. Consider a canonical triple-diference model with a 2 × 2 × 2

setup. Three dummy variables, P, L, H, indicate post-policy period, LEP status,

and Hispanic ethnicity in the data, respectively. However, L is a misclassifed version

of the unobserved true LEP status, L∗. I use a latent variable, ρ, as an indicator for

misclassifcation, so ρ = 1 when L ̸= L∗. The treatment status D is also a dummy

variable, which takes the value of one only when P = 1, L∗ = 1, and H = 1. Let Yt

and Yt(D) represent the observed outcome and the potential outcome in period t if

the treatment status is D. I am interested in identifying the ATT that can be written

as:

ATT = E[Y1(1) − Y1(0) | L∗ = 1, H = 1].

When I run triple-diference regressions using the HMDA+ data set, I implicitly

26See Section D.3 of the Online Appendix for a more detailed discussion.

36
⊥

proceed with:

Assumption 1. Parallel trends between the misclassifed treatment status (L).27

If there is no misclassifcation of L∗, then this assumption helps to identify the ATT

(Olden and Møen, 2022). On the other hand, when there exists misclassifcation,

lemma E.1 in the Online Appendix reveals that the triple-diference estimator cannot recover the ATT under this assumption. The triple-diference estimator can be

written as a weighted average of the ATT for the correctly classifed and misclassifed

treatment groups, but the sum of two weights is not guaranteed to be one. Thus,

the bias direction is ambiguous. However, I then show that a reasonable assumption on the structure of misclassifcation can help to identify both the direction and

magnitude of the bias.

Assumption 2. Non-diferential Misclassifcation: ρ ⊥ (Y1(1), Y1(0)) | L∗, H

This assumption states that misclassifcation is not correlated to potential outcomes conditional on the true treatment status. It is likely to hold in my context,

because the misclassifcation mechanically comes from a pure statistics exercise. Then

the following proposition holds.

Proposition 1. In a 2 × 2 × 2 canonical triple-diference design, if Assumptions 1

and 2 hold, the triple-diference estimator can be written as:

θDDD = ATT(P(ρ = 0 | L = 1, H = 1) + P(ρ = 0 | L = 0, H = 1) − 1). (6)

If 1 − P(ρ = 1 | L = 1, H = 1) − P(ρ = 1 | L = 0, H = 1) ∈ (0, 1], then the

triple-diferences estimator has attenuation bias.

Proposition 1 shows that the triple-diference estimate is smaller than the true

ATT when the misclassifcation problem is not too severe. It also links the performance of machine learning models to the bias magnitude. As shown in Equation (6),

the relationship between the triple-diference estimate and the ATT depends on the

precision metrics (i.e., P(ρ = 0)). Because non-Hispanic people are always untreated,

the bias is only determined by the precision in the Hispanic sample. However, the

true LEP status is not observable in the prediction sample, so I cannot evaluate the

prediction performance in this sample. To convert the triple-diference estimate to

27In the interest of space, the formal expression of this assumption is presented in Section E of

the Online Appendix.

37
the ATT, I impose two additional assumptions that allow me to pin down the range

of the prediction precision.

Assumption 3. The fraction of LEP people among Hispanic borrowers in the prediction sample is lower than that in the training sample.

Assumption 4. The machine learning model does not perform better in the prediction

sample than in the test sample.

Figure D1 provides supporting evidence for Assumption 3, as it shows that the

training sample has a larger fraction of low-income Hispanic households than the

prediction sample. Then Assumption 4 also stands because the prediction sample does

not represent the test sample perfectly. This assumption implies that the precision

and recall metrics in the prediction sample should be smaller than those in the test

sample.

Under these two assumptions, I can calculate a lower bound of the ATT. Table

E1 presents the confusion matrix of Hispanic borrowers in the HMDA+ sample. Each

element of this matrix, as well as the precision and recall metrics, can be expressed by

two unknowns: the number of true positive instances (denoted as x) and the number

of LEP Hispanic borrowers in reality (denoted as y). Finding the lower bound of the

ATT is equivalent to solving a constrained optimization problem: maximize the sum

of prediction precision for two classes (i.e., P(ρ = 0 | L = 1, H = 1) + P(ρ = 0 | L =

0, H = 1)) while subject to a system of constraints implied by Assumptions 3 and 4.

Solving this problem, I obtain the maximum value of 1.72 for the sum of prediction

precision for two classes.28 Therefore, according to Proposition 1, the ATT in this

case is the triple-diference coefcient multiplied by 1.39. Notice that this is the lower

bound of the ATT. Given the same triple-diference coefcient, any deviation of the

machine learning performance (x) or the actual number of LEP Hispanic borrowers

(y) from the value that achieves the maximum will generate a larger ATT.

C Results

The results from the previous two parts allow me to implement the triple-diference

strategy in the HMDA+ sample and calculate a lower bound of the ATT. For the same

reason, I drop Asian borrowers as I did in the NSMO sample. Since the HMDA+ data

set includes precise property location and lender information, I can further add post

28See Section E.2 of the Online Appendix for the calculation.

38
policy-county fxed efects and post policy-lender fxed efects in Equation (2). Table

11 reports the triple-diference results and the implied lower bound of the ATT.

First, I confrm that the policy decreased interest rate across diferent types of

purchase loans. After converting the coefcient to the ATT, the point estimate in

column 1 of Panel A implies a decrease in interest rate by at least 4.9 basis points

for risk-equivalent LEP Hispanic borrowers after the policy shock.29 Bartlett et al.

(2022) report that the average lender’s proft per mortgage is 10 basis points of the

interest rate, so the efect I document corresponds to nearly half of the average lender’s

proft. The economic magnitude is also comparable to other research evaluating the

efect of diferent shocks on the mortgage interest rate. For example, Allen, Clark

and Houde (2014) fnd a 6-bps increase in interest rates after a merger between two

lenders in Canada. Kielty, Wang and Weng (2021) fnd that simplifying mortgage

disclosures led to an interest rate reduction of 1.8 bps. The heterogeneous efects

presented in columns 2 and 3 are consistent with the fndings using the survey data:

frst-time borrowers benefted more from the language help. Columns 4 and 5 show

that the price impact on mortgages originated through retailers was roughly 78%

larger than that on mortgages originated through brokers. LEP borrowers probably

will choose brokers who can speak their primary languages, so the efect of translated

documents is largely substituted by mortgage brokers. Using this unique loan-level

data set, I also fnd that the FHFA Language Access Plan was more efective in

counties where translated documents were more needed. Figure 9 plots the results

from estimating the triple-diference model in two groups of counties with diferent

levels of social capital. The efect of reducing language frictions on interest rate was

larger in counties with a level of social capital below the national median, which is

consistent with the heterogeneity in aggregate quantity efects.

Second, I show that the drop in interest rates was not ofset by an increase in

up-front costs. Bhutta and Hizmo (2020) fnd that Black and Hispanic borrowers pay

higher interest rates but lower up-front costs, so interest rate gaps alone do not refect

the whole picture of borrower costs. To address this concern, I estimate Equation (2)

using the discount points scaled by mortgage amount as the dependent variable. The

sample only includes the mortgages originated in 2018 and 2019, as HMDA started

to disclose discount points in 2018. As shown in Panel B of Table 11, there was little

efect of reducing language frictions on the up-front discount points, suggesting that

29In Section E.2 of the Online Appendix, I provide a reasonable bundle of values of x and y so that

the magnitude of the ATT in the HMDA+ sample is comparable to the triple-diference estimates

in the NSMO sample.

39
the decline in interest rates cannot be attributable to borrowers purchasing discount

points to get a cheaper interest rate. Using the results in column 2 of Panels A and B,

I conduct a back-of-the-envelope calculation of total borrowing costs. The discount

points paid by a frst time home buyer insignifcantly increased by only 0.049% of

the mortgage principal. This would decrease the interest rate by 1.2 bps, since each

point costs 1 percent of the loan amount and can reduce interest rate by about 25

basis points.30 However, I fnd a 7.2 bps reduction in interest rate, suggesting lower

overall borrowing costs for frst time LEP Hispanic borrowers.

Third, I do not fnd a signifcant efect on mortgage performance, which is consistent with previous results using NSMO and the ZIP code level data. Panel C of Table

11 reports the triple-diference estimates using the 90-day delinquency incidence as

the dependent variable. If anything, providing Spanish mortgage documents to LEP

Hispanic borrowers slightly improved their mortgage performance.

Finally, I provide indirect evidence of the borrower search mechanism behind the

price efect. As the competing channel here is the reaction of lenders to the policy

change, I show that the price efect still remains when I block the competing channel.

Specifcally, I add Post × Lender × County fxed efects in Equation (2), so the

resulting specifcation absorbs how lenders reacted to the policy shock diferently

across their operating markets. Table F10 reports the results from estimating this

modifed specifcation. The magnitude of most coefcients decreases, but they are

still statistically signifcant at the 1% level. This means that lenders’ response to

the policy shock cannot fully explain the decrease in interest rate, suggesting the

existence of the borrower search channel.

Overall, my fndings using the HMDA+ sample are consistent with those using the

survey data. The triple-diference estimates in this section, which provide the lower

bound of the ATT, suggest that the FHFA Language Access Plan reduced borrowing

costs for borrowers with limited English profciency. At the same time, the policy did

not worsen mortgage performance conditional on ex-ante risk factors.

VII Conclusion

Many consumers with limited English profciency have difculty accessing the fnancial market, despite making up a signifcant portion of the U.S. population. This

paper quantifes the language frictions faced by LEP borrowers in the U.S. mortgage

30See, for example, https://bettermoneyhabits.bankofamerica.com/en/home-ownership/

buying-mortgage-points-lower-rate.

40
market. I document that LEP borrowers encounter more challenges in the application process and pay higher interest rates for similar mortgages than similar non-LEP

borrowers. To estimate the causal efects of language frictions, I exploit the implementation of the FHFA Language Access Plan in 2018. Using a triple-diference design, I

fnd that LEP Hispanic borrowers had a better mortgage application experience and

gained a better understanding of mortgage contracts after the policy shock. They

paid lower interest rates, and one possible explanation is that they searched more

after they had mortgage documents in their primary language. Using a diferencein-diferences design, I fnd that the credit supply of conventional purchase loans

increased, the average conditional interest rate decreased, and the lender competition

for LEP borrowers increased in counties with a larger fraction of potentially treated

LEP people after the policy shock. At the same time, the more inclusive credit access

did not introduce extra risks, as measured by both ex-ante and ex-post indicators.

This paper ofers clear policy implications. Providing translations can better equip

borrowers with limited English profciency to navigate the mortgage application process, thereby fostering a more inclusive and equitable mortgage market. Compared

to direct fscal transfers, this policy is a much more cost-efective way to help LEP

borrowers. Moreover, the heterogeneous efects that I fnd suggest that the policy

has the greatest positive efect on those LEP borrowers who need translations the

most. Broadly speaking, lowering language barriers is an efort to reduce information asymmetry in the mortgage market. Borrowers engage in mortgage transactions

only a few times in their lives, so they have an information disadvantage relative to

lenders. Since each transaction involves a large portion of borrowers’ budget, addressing asymmetric information problems can signifcantly improve borrowers’ decision

making and generate substantial welfare improvements.

As English profciency is closely related to immigration and race, my results also

highlight that language help in the mortgage market could be benefcial to address

three important social issues. First, many creditworthy LEP people are fnancially

underserved, so reducing language frictions creates an efective and responsible integration of LEP consumers into the fnancial marketplace. Second, many LEP borrowers are immigrants, so reducing language frictions facilitates their assimilation into

society and helps them achieve the American dream of homeownership. Finally, many

LEP borrowers are minorities, so reducing language frictions ofers opportunities for

them to build their fnancial capabilities and potentially close the racial wealth gap.

41
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46
Figure 1. Share of LEP Population in the U.S.

Notes: This fgure plots the share of LEP people, the share of LEP Hispanics, and the share

of LEP Chinese at the county level. The statistics come from the American Community

Survey 2015-2019.

47
Figure 2. Estimated Diferences between LEP and non-LEP Borrowers

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval.

The outcomes are indicators for whether the borrowers was familiar with four things about

the mortgage market in panel A, indicators for whether the borrower thought four factors

were important when choosing the mortgage lender in panel B, indicators for whether

the borrower had four problems in the process of getting the mortgage in panel C, and

indicators for whether the borrower knew about four alternative features of the mortgage in

panel D. All regressions include origination quarter fxed efects and census tract type fxed

efects. Demographic controls include race, ethnicity, gender, age and its squared, marital

status, education, and household income. Risk fxed efects are the full pairwise interactions

between LTV bins and FICO score bins, following the Loan-Level Price Adjustment Grid

of Fannie Mae. Loan controls include loan purpose, property type, and occupancy status.

All regressions are weighted by the analysis weight in NSMO. The 95% confdence intervals

are based on robust standard errors.

48
Figure 3. Google Trends

Notes: This fgure plots monthly Google Trends data for “mortgage” and “mortgage translation” from July 2018 to December 2019. Each series is separately normalized relative to

its value in July 2018. The shaded areas represent the approximate time of adding Spanish

translations and Chinese translations to the Mortgage Translations Clearinghouse.

49
Figure 4. Triple-Diferences Raw Comparison: Redo Paperwork

Notes: This fgure plots the pre-policy (in red) and post-policy (in blue) proportion of

borrowers who redid mortgage paperwork for 4 types of borrowers: LEP and Hispanic

in panel A, non-LEP and Hispanic in panel B, LEP and non-Hispanic in panel C, and

non-LEP and non-Hispanic in panel D. The number in the bar represents the proportion

(e.g., 33% of LEP Hispanic borrowers redid their paperwork before the policy change).

The p-values are associated with the null hypothesis that the post-pre diference is larger

than -0.05.

50
Figure 5. Triple-Diferences Raw Comparison: Interest Rate

Notes: This fgure plots the pre-policy (in red) and post-policy (in blue) average conditional

interest rate in basis points for 4 types of borrowers: LEP and Hispanic in panel A, nonLEP and Hispanic in panel B, LEP and non-Hispanic in panel C, and non-LEP and nonHispanic in panel D. Conditional interest rate is the mean of raw interest rate plus the

residual after regressing raw interest rate on origination quarter fxed efects, census tract

type fxed efects, loan type, loan term, loan purpose, property tpye, occupancy type, and

interest type. The p-values are associated with the null hypothesis that the pre-policy

mean is equal to the post-policy mean.

51
Figure 6. Triple-Diferences Raw Comparison: Number of Lenders Seriously

Considered

Notes: This fgure plots the distribution of the number of lenders seriously considered for 4

types of borrowers: LEP and Hispanic in panel A, non-LEP and Hispanic in panel B, LEP

and non-Hispanic in panel C, and non-LEP and non-Hispanic in panel D. The pre-policy

distribution is represented by red bars, and the post-policy distribution is represented by

blue frames. The number of lenders seriously considered is capped at 4. The p-values

are associated with a Kolmogorov-Smirnov test of the equality of the pre-policy and postpolicy distribution.

52
Figure 7. Flexible Diference-in-Diferences Estimates of the Efect on Mortgage

Credit Access of Conventional Purchase Loans

Notes: This fgure plots the estimates of βτ in Equation (4). The dependent variables in

panels A to D are the number of mortgage applications (in ten thousands), the share of

incomplete applications, the application denial rate, and the number of originations (in

ten thousands), respectively. I use the sample of conventional purchase loans in HMDA

to calculate these outcomes. The coefcient for 2017 is normalized to zero, so that all

estimates can be interpreted as the change in the outcome relative to the year prior to

when the policy change went into efect, which is marked by the vertically dashed gray

line. All regressions include total population, median household income, the proportion of

black people, Asians, and Hispanics, county fxed efects, and state-year fxed efects. The

95% confdence intervals are based on standard errors that are clustered at the state level.

53
Figure 8. Heterogeneous Efect on Mortgage Credit Access by Social Capital

Notes: This fgure plots the diference-in-diferences estimates of the policy efect on mortgage credit access of conventional purchase loans and the corresponding 90% confdence

intervals. I split the sample based on a county-level community health index (U.S. Congress

Joint Economic Committee, 2018). The dependent variables in panels A to D are the number of mortgage applications (in ten thousands), the share of incomplete applications, the

application denial rate, and the number of originations (in ten thousands), respectively.

The coefcients are obtained by regressing the specifcations in Panel A of Table 8.

54
Figure 9. Heterogeneous Efect on Interest Rate by Social Capital

Notes: This fgure plots the triple-diference estimates of the policy efect on interest rate

and the corresponding 95% confdence intervals. I split the sample based on a county-level

community health index (U.S. Congress Joint Economic Committee, 2018). The dependent

variables in panels A to D are the number of mortgage applications (in thousands), the

share of incomplete applications, the application denial rate, and the number of originations, respectively. The coefcients are obtained by regressing the specifcations in Panel

A of Table 8.

55
Table 1. Summary Statistics of NSMO

Sample All borrowers LEP Non-LEP

(1) (2) (3)

Panel A. Demographic characteristics

Female 0.435 0.454 0.432

(0.496) (0.498) (0.495)

Married 0.666 0.644 0.669

(0.472) (0.479) (0.471)

Age 46.214 46.487 46.182

(13.854) (13.817) (13.858)

College education 0.645 0.534 0.658

(0.479) (0.499) (0.475)

Income<$50K 0.151 0.218 0.143

(0.358) (0.413) (0.350)

FICO score 732.164 722.015 733.330

(65.924) (66.552) (65.752)

Panel B. Mortgage characteristics

Conventional loan 0.735 0.670 0.742

(0.441) (0.470) (0.437)

Loan amount<$200K 0.510 0.530 0.507

(0.500) (0.499) (0.500)

Loan to value ratio 78.070 79.230 77.937

(19.462) (19.285) (19.478)

Debt to income ratio 36.193 38.396 35.940

(12.273) (12.952) (12.167)

Interest rate 4.029 4.090 4.022

(0.678) (0.669) (0.678)

90-day delinquency 0.015 0.020 0.014

(0.121) (0.141) (0.119)

Observations 37,720 3,793 33,927

Notes: This table reports summary statistics of demographic characteristics (panel A) and

mortgage characteristics (panel B) in NSMO. All table entries represent sample means and

standard deviations in parentheses, weighted by the analysis weight in NSMO. Summary

statistics are presented for all observations in column 1 as well as separately for LEP

(column 2) and non-LEP borrowers (column 3).

56
Table 2. LEP Status and Concern about Qualifying for a Mortgage

Dependent variable 1(concern about qualifying for a mortgage)

(1) (2) (3) (4) (5)

LEP 0.102*** 0.100*** 0.064*** 0.058*** 0.059***

(0.009) (0.009) (0.008) (0.008) (0.008)

No college degree 0.062*** 0.029*** 0.029***

(0.005) (0.005) (0.005)

D.V. mean (LEP) 0.243

D.V. mean (non-LEP) 0.141

Observations 37,720 37,720 37,720 37,720 37,720

Quarter FEs No Yes Yes Yes Yes

Tract type FEs No Yes Yes Yes Yes

Race and ethnicity No No Yes Yes Yes

Gender No No Yes Yes Yes

Education No No Yes Yes Yes

Additional controls No No Yes Yes Yes

Risk FEs No No No Yes Yes

Loan controls No No No No Yes

Notes: This table reports the relationship between LEP status and an indicator for whether

the borrower was concerned about qualifying for a mortgage. There are three types of

census tracts: metropolitan CRA LMI tract, metropolitan CRA non-LMI tract, and nonmetropolitan tract. Additional controls include age and its squared, marital status, and

household income. Risk fxed efects are the full pairwise interactions between LTV bins

and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. Robust standard errors are reported in

parentheses. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

57
Table 3. LEP Status and Search Behavior

Dependent variable Number of lenders Why apply to multiple lenders?

seriously fnd better concern over learn applied to considered loan terms qualifcation information

(1) (2) (3) (4) (5)

LEP -0.065*** -0.024** 0.016 0.105*** 0.075***

(0.015) (0.012) (0.017) (0.020) (0.021)

D.V. mean (LEP) 1.643 1.296 0.821 0.407 0.425

D.V. mean (non-LEP) 1.719 1.303 0.822 0.270 0.319

Observations 37,720 37,720 8,569 8,569 8,569

Quarter FEs Yes Yes Yes Yes Yes

Tract type FEs Yes Yes Yes Yes Yes

Race and ethnicity Yes Yes Yes Yes Yes

Gender Yes Yes Yes Yes Yes

Education Yes Yes Yes Yes Yes

Additional controls Yes Yes Yes Yes Yes

Risk FEs Yes Yes Yes Yes Yes

Loan controls Yes Yes Yes Yes Yes

Notes: This table reports the relationship between LEP status and borrowers’ search

behavior. The dependent variables in the frst two columns are the number of lenders

people seriously considered and the number of lenders people fnally applied to. The

dependent variables in columns 3 to 5 are three dummy variables indicating the reason

of applying to multiple lenders. All regressions control for race, ethnicity, gender, and

education, as well as origination quarter fxed efects and census tract type fxed efects.

Additional controls include age and its squared, marital status, and household income.

Risk fxed efects are the full pairwise interactions between LTV bins and FICO score bins,

following the Loan-Level Price Adjustment Grid of Fannie Mae. Loan controls include loan

purpose, property type, and occupancy status. All regressions are weighted by the analysis

weight in NSMO. Robust standard errors are reported in parentheses. Signifcance levels

10%, 5%, 1% are denoted by *, **, and ***, respectively.

58
Table 4. LEP Status, Interest Rate, and 90-Day Delinquency

(1) (2) (3) (4)

Panel A. Interest rate

LEP 0.032***

(0.010)

0.029***

(0.010)

0.029***

(0.010)

0.021**

(0.010)

Panel B. 90-Day delinquency

LEP 0.003

(0.003)

0.002

(0.003)

0.002

(0.003)

0.002

(0.003)

Observations

Quarter FEs

Tract type FEs

Risk FEs

Loan controls

Race and ethnicity

Gender

Education

37,720

Yes

Yes

Yes

Yes

No

No

No

37,720

Yes

Yes

Yes

Yes

Yes

No

No

37,720

Yes

Yes

Yes

Yes

Yes

Yes

No

37,720

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the relationship between LEP status and interest rate (panel A)

and 90-day mortgage delinquency (panel B). Interest rate is winsorized at 1% and 99% level.

Column 1 uses the full sample. All regressions include origination quarter fxed efects and

census tract type fxed efects. Risk fxed efects are the full pairwise interactions between

LTV bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie

Mae. Loan controls include loan type, loan purpose, loan term, interest type, property

type, and occupancy status. All regressions are weighted by the analysis weight in NSMO.

Robust standard errors are reported in parentheses. Signifcance levels 10%, 5%, 1% are

denoted by *, **, and ***, respectively.

59
Table 5. Efect on Perceptions and Experiences

(1) (2) (3) (4)

Panel A. Dependent variable: 1(encounter ... in the application process)

Resolve credit Request more Have more Redo

report error income info. appraisals paperwork

LEP × Hispanic × Post -0.163*** -0.162** -0.125*** -0.137**

(0.060) (0.071) (0.048) (0.054)

Pre-policy treated mean 0.339 0.642 0.218 0.326

Panel B. Dependent variable: 1(do not know if my own mortgage has ...)

Adjustable Prepayment Escrow Balloon

rate penalty account payment

LEP × Hispanic × Post -0.083* 0.025 -0.069 -0.164***

(0.047) (0.063) (0.048) (0.057)

Pre-policy treated mean 0.109 0.296 0.206 0.380

Observations 35,553 35,553 35,553 35,553

Quarter FEs Yes Yes Yes Yes

Demographic controls Yes Yes Yes Yes

Post × Tract type FEs Yes Yes Yes Yes

Post × Risk FEs Yes Yes Yes Yes

Post × Loan controls Yes Yes Yes Yes

Notes: This table reports the triple-diference estimates of the policy efect on perceptions

and experiences in the mortgage market. The dependent variables in panel A are indicators

for whether the borrower encountered additional problems in the process of getting the

mortgage. The dependent variables in panel B are indicators for whether the borrower

knew about alternative features of the mortgage. Post equals one if the mortgage was

originated after June 2018. All regressions include origination quarter fxed efects and

census tract type fxed efects. Demographic controls include race, ethnicity, gender, age

and its squared, marital status, education, and household income. Risk fxed efects are the

full pairwise interactions between LTV bins and FICO score bins, following the Loan-Level

Price Adjustment Grid of Fannie Mae. Loan controls include loan purpose, property type,

occupancy status, and loan type. All regressions are weighted by the analysis weight in

NSMO. Robust standard errors are reported in parentheses. Signifcance levels 10%, 5%,

1% are denoted by *, **, and ***, respectively.

60
Table 6. Efect on Interest Rate and 90-Day Delinquency

Sample All

(1)

Purchase

(2)

Refnance

(3)

First-time

borrowers

(4)

Repeat

borrowers

(5)

Panel A. Interest rate

LEP × Hispanic × Post -0.149**

(0.074)

-0.165*

(0.096)

-0.082

(0.121)

-0.221*

(0.125)

-0.145

(0.093)

Panel B. 90-Day delinquency

LEP × Hispanic × Post -0.016

(0.015)

-0.022

(0.020)

-0.022

(0.024)

-0.009

(0.029)

-0.012

(0.017)

Observations

Quarter FEs

Demographic controls

Post × Tract type FEs

Post × Risk FEs

Post × Loan controls

35,553

Yes

Yes

Yes

Yes

Yes

18,118

Yes

Yes

Yes

Yes

Yes

15,977

Yes

Yes

Yes

Yes

Yes

6,739

Yes

Yes

Yes

Yes

Yes

28,807

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the triple-diference estimates of the policy efect on interest

rate (winsorized at 1% and 99% level) and 90-day delinquency. Column 1 uses the full

sample. Columns 2 and 3 use the sample of purchase and refnance loans, respectively.

Columns 4 and 5 use the sample of loans borrowed by frst-time borrowers and repeat

borrowers, respectively. Post equals one if the mortgage was originated after June 2018.

All regressions include origination quarter fxed efects and census tract type fxed efects.

Demographic controls include race, ethnicity, gender, age and its squared, marital status,

education, and household income. Risk fxed efects are the full pairwise interactions

between LTV bins and FICO score bins, following the Loan-Level Price Adjustment Grid

of Fannie Mae. Loan controls include loan type, loan purpose, loan term, interest rate

type, property type, and occupancy status. All regressions are weighted by the analysis

weight in NSMO. Robust standard errors are reported in parentheses. Signifcance levels

10%, 5%, 1% are denoted by *, **, and ***, respectively.

61
Table 7. Efect on Search Behavior

Dependent variable Search intensity Why apply to multiple lenders?

1(consider

multi. lenders)

# lenders

considered

fnd better

loan terms

concern over

qualifcation

learn

information

(1) (2) (3) (4) (5)

LEP × Hispanic × Post 0.162** 0.202* 0.058 -0.154 -0.269**

(0.073) (0.112) (0.097) (0.125) (0.135)

Observations 35,553 35,553 8,001 8,001 8,001

Quarter FEs Yes Yes Yes Yes Yes

Demographic controls Yes Yes Yes Yes Yes

Post × Tract type FEs Yes Yes Yes Yes Yes

Post × Risk FEs Yes Yes Yes Yes Yes

Post × Loan controls Yes Yes Yes Yes Yes

Notes: This table reports the triple-diference estimates of the policy efect on search

behavior. The dependent variable in column 1 is a dummy variable, indicating that the

borrower seriously considered more than one lender. The dependent variable in column 2 is

the number of lenders seriously considered, capped at 4. In columns 3 to 5, the dependent

variable is an indicator for each of the three reasons why the borrower applied to multiple

lenders. Post equals one if the mortgage was originated after June 2018. All regressions

include origination quarter fxed efects and census tract type fxed efects. Demographic

controls include race, ethnicity, gender, age and its squared, marital status, education,

and household income. Risk fxed efects are the full pairwise interactions between LTV

bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. Robust standard errors are reported in

parentheses. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

62
Table 8. Efect on Mortgage Credit Access

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

Panel A. Conventional purchase loans

LEP share × Post 0.121**

(0.060)

-0.062***

(0.022)

-0.155***

(0.041)

0.089**

(0.044)

Observations 25,225 25,225 25,225 25,225

Panel B. FHA purchase loans

LEP share × Post -0.088*

(0.048)

-0.113***

(0.021)

-0.088**

(0.035)

-0.048

(0.030)

Observations 25,059 25,059 25,059 25,059

County FEs

Year × State FEs

Additional controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the diference-in-diferences estimates of the policy efect on

mortgage credit access of conventional purchase loans (panel A) and FHA purchase loans

(panel B). The dependent variables in columns 1 to 4 are the number of mortgage applications (in ten thousands), the share of incomplete applications, the application denial rate,

and the number of originations (in ten thousands), respectively. LEP share is the share

of LEP Hispanic people before 2019, and the share of LEP Hispanics and Chinese in 2019.

Post equals one after 2017. All specifcations include county fxed efects, state-year fxed

efects, and additional controls, which include median household income, total population,

and the proportion of Hispanics, Asians, and black people. Standard errors are reported

in parentheses and are clustered at the state level. Signifcance levels 10%, 5%, 1% are

denoted by *, **, and ***, respectively.

63
Table 9. Efect on Mortgage Rate and Risk of GSE Loans

Sample All Purchase Refnance First-time

borrowers

Repeat

borrowers

Channel:

retail

Channel:

broker

(1) (2) (3) (4) (5) (6) (7)

Panel A. Average conditional interest rate

LEP share × Post -0.127** -0.154*** -0.115 -0.152* -0.120* -0.108** -0.044

(0.060) (0.053) (0.100) (0.078) (0.069) (0.053) (0.079)

Panel B. Average conditional 90-day delinquency rate

LEP share × Post 0.021 0.029 0.018 0.039 0.016 0.015 0.011

(0.016) (0.020) (0.016) (0.024) (0.014) (0.018) (0.029)

Panel C. Average FICO scores

LEP share × Post 7.744*** 8.846*** 7.065*** 8.986*** 6.883*** 5.458*** 8.234***

(1.702) (1.060) (1.694) (2.394) (1.777) (1.910) (2.809)

Observations 52,435 52,088 52,160 51,234 52,382 52,341 44,854

ZIP3 code FEs Yes Yes Yes Yes Yes Yes Yes

Month FEs Yes Yes Yes Yes Yes Yes Yes

Additional controls Yes Yes Yes Yes Yes Yes Yes

Notes: This table reports the diference-in-diferences estimates of the policy efect on

average conditional interest rate (Panel A), average conditional 90-day delinquency rate

(Panel B), and average FICO scores (Panel C) of GSE loans. The dependent variables are

at the 3-digit ZIP code-month level. The conditional outcome is obtained by averaging

the residuals after regressing the raw interest rate (90-day delinquency) on origination

month fxed efects, lender fxed efects, LTV × FICO score grids, loan purpose, loan

term, property type, and occupancy status. Column 1 uses the full sample. Columns 2

and 3 use the sample of purchase and refnance loans, respectively. Columns 4 and 5 use

the sample of loans borrowed by frst-time borrowers and repeat borrowers, respectively.

Columns 6 and 7 use the sample of loans originated through retail lenders and brokers,

respectively. LEP share is the share of LEP Hispanics before July 2019, and the share of

LEP Hispanics and Chinese starting from July 2019. Post equals one after June 2018. All

specifcations include 3-digit ZIP code fxed efects, origination month fxed efects, and

additional controls, which include median household income, total population, and the

proportion of Hispanics, Asians, and black people at the 3-digit ZIP code level. Standard

errors are reported in parentheses and are clustered at the state level. Signifcance levels

10%, 5%, 1% are denoted by *, **, and ***, respectively.

64
Table 10. Efect on Lender Competition

Dependent variable Number of Lenders HHI

application origination application origination

(1) (2) (3) (4)

Panel A. Markets of Hispanic and Asian borrowers

LEP share × Post 17.759* 21.983** -0.120* -0.263**

(9.809) (9.270) (0.070) (0.102)

Panel B. Markets of all borrowers

LEP share × Post -24.805 -17.327 -0.001 -0.055*

(16.586) (14.581) (0.024) (0.030)

Observations 25,225 25,225 25,225 25,225

County FEs Yes Yes Yes Yes

Year × State FEs Yes Yes Yes Yes

Additional controls Yes Yes Yes Yes

Notes: This table reports the diference-in-diferences estimates of the efect of language

help on lender competition in the conventional purchase mortgage market. LEP share

is the share of LEP Hispanic people before 2019, and the share of LEP Hispanics and

Chinese in 2019. Post equals one after 2017. The dependent variables in columns 1

to 4 are the number of lenders that received applications, the number of lenders that

originated mortgages, the Herfndahl-Hirschman Index (HHI) of applications, and the HHI

of originations, respectively. Panel A uses Hispanic and Asian borrowers to calculate the

outcomes, while panel B uses all borrowers. All specifcations include county fxed efects,

state-year fxed efects, and additional controls, which include median household income,

total population, and the proportion of Hispanics, Asians, and black people. Standard

errors are reported in parentheses and are clustered at the state level. Signifcance levels

10%, 5%, 1% are denoted by *, **, and ***, respectively.

65
Table 11. Efect on Interest Rate, Discount Points, and Delinquency (HMDA+)

Sample Purchase

(1)

First-time

borrowers

(2)

Repeat

borrowers

(3)

Channel:

retail

(4)

Channel:

broker

(5)

Panel A. Interest rate

LEP × Hispanic × Post

Implied lower bound

-0.035***

(0.009)

-0.049

-0.052***

(0.011)

-0.072

-0.004

(0.012)

-0.006

-0.041***

(0.011)

-0.057

-0.023*

(0.013)

-0.032

Observations 3,877,813 1,680,325 2,196,946 2,513,026 1,364,024

Panel B. Discount points (% of loan amount)

LEP × Hispanic × Post

Implied lower bound

0.006

(0.018)

0.008

0.035

(0.023)

0.049

-0.052*

(0.031)

-0.072

0.004

(0.025)

0.006

0.035

(0.025)

0.049

Observations 1,713,458 780,230 932,503 1,095,149 617,429

Panel C. 90-Day delinquency

LEP × Hispanic × Post

Implied lower bound

-0.013

(0.008)

-0.018

-0.013

(0.012)

-0.018

-0.008

(0.011)

-0.011

-0.014

(0.011)

-0.019

-0.012

(0.012)

-0.017

Observations 3,877,813 1,680,325 2,196,946 2,513,026 1,364,024

Month FEs

Demographic controls

Post × County FEs

Post × Risk FEs

Post × Lender FEs

Post × Loan controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the triple-diferences estimates and the implied lower bound of

the efect of language help on the interest rate (panel A), discount points (panel B), and

90-day delinquency (panel C). Post equals one if the mortgage was originated after June

2018. Column 1 uses all purchase loans in the HMDA+ sample. Columns 2 and 3 use

the sample of loans borrowed by frst-time borrowers and repeat borrowers, respectively.

Columns 4 and 5 use the sample of loans originated through retail lenders and brokers,

respectively. All regressions include origination month fxed efects, Post-county fxed

efects, and Post-lender fxed efects. Risk fxed efects are the full pairwise interaction

between LTV bins and FICO score bins. LTV bins and FICO score bins follow the LoanLevel Price Adjustment Grid of Fannie Mae. Loan controls include loan type, loan term,

property type, and occupancy status. All regressions are weighted by the analysis weight in

the HMDA+ sample. Standard errors are reported in parentheses and are clustered at the

county level. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

66
Language Frictions in Consumer Credit

Online Appendix

A Data 2

1 NSMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 FHA Snapshot+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 HMDA+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

B LEP Borrowers in the Mortgage Market 10

1 Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

C Robustness Checks 25

1 UAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2 NSMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 HMDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

D Machine Learning 37

1 Training Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2 Training Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3 Discussion on Prediction Performance . . . . . . . . . . . . . . . . . 38

E Triple-diference Model with Treatment Status Misclassifcation 43

1 Derivation of Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2 Lower Bound of the ATT . . . . . . . . . . . . . . . . . . . . . . . . 47

F Additional Figures and Tables 50

1 Additional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

2 Additional Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

1
A Data

1 NSMO

I clean the National Survey of Mortgage Originations (NSMO) using a number of

steps:

1. Drop survey respondents who are not the mortgage borrowers.

2. Drop survey respondents who have negative FICO scores.

3. Drop properties that are units in a partly commercial structure or land only.

4. Drop properties that are used as homes for other relatives.

5. Keep mortgages with a loan term of 5, 10, 15, 20, and 30 years.

6. Winsorize mortgage rate at the 1st and 99th percentile.

7. Winsorize the number of lenders seriously considered and the number of lenders

applied to more than 4.

8. Generate risk fxed efects that are the full pairwise interaction of LTV bins and

FICO score bins, following the Loan-Level Price Adjustment (LLPA) Grid of

Fannie Mae.1

I use the data set following these steps to conduct the descriptive analysis in Section II. Summary statistics of this sample are reported in Table 1. I further drop Asian

borrowers in this sample for the causal analysis in Section IV. This is because I can

only observe borrowers’ race (e.g., Asian) rather than borrowers’ primary language

(e.g., Chinese and Tagalog), which makes it difcult to precisely defne the treatment

group after the introduction of Chinese translations in 2019. Summary statistics of

this subsample are reported in Table A1.

2 FHA Snapshot+

The most granular geographical level in Ginnie Mae data is the state level, so I

match FHA Snapshot data with Ginnie Mae data to supplement detailed location

variables.

1See https://singlefamily.fanniemae.com/media/9391/display.

2
I frst select fxed rate, purchase or refnance FHA loans that were originated after

2015 from Ginnie Mae data. I merge two data sets based on a set of overlapping

variables: state, loan purpose, origination year and month, lender, loan size, and

interest rate. Specifcally, I allow a 2% diference in loan amount and a 3-month

diference in origination month in the frst round of fuzzy matching. For each one-tomany match, I keep the match with the smallest size and time diference. To ensure

the highest-quality match, I exclude all matches with duplicate observations. The

origination time in FHA Snapshot is systematically later than that in Ginnie Mae

data. Therefore, I select unmatched mortgages that were originated in the fourth

quarter after the frst round of matching in Ginnie Mae data, and then I merge them

with next year’s FHA Snapshot data. I further drop mortgages with missing FICO

scores or LTV ratios, and only keep mortgages with a loan term of 120 months, 180

months, 240 months, or 360 months. Following the above steps, the fnal data set

contains 1,783,367 FHA loans originated from 2015 to 2019. Figure A1 shows that

the FHA Snapshot+ data set covers about 32% of all FHA loans and 65% of FHA

loans sold to Ginnie Mae in HMDA data.

To make this sample representative, I use the reciprocal of the likelihood of being

sampled from HMDA data as the analysis weight. This assumes that each mortgage

in the FHA Snapshot+ data set is randomly sampled from the corresponding stratum

in the HMDA data of FHA loans. I separate all FHA loans in HMDA into diferent

strata based on property county, loan size, loan purpose, and origination year. In

other words, the analysis weight indicates how many FHA loans of a certain type in

the mortgage market are represented by a given loan in the FHA Snapshot+ sample.

Table A2 shows that the mortgage characteristics in the FHA Snapshot+ are very

similar as those in Ginnie Mae data.

3 HMDA+

The NSMO data ofer rich and unique information about borrowers’ mortgage

market experiences, but its small sample size could restrict the precision of my estimation. Another concern is that the NSMO data set does not contain location or

lender information. To address these concerns, I construct a novel loan-level data

set, HMDA+, which contains the most detailed loan-level information of borrowers, lenders, mortgages, and properties. Compared to existing eforts (Saadi, 2020;

Bartlett et al., 2022), my HMDA+ data set has three advantages. First, I only use

publicly available mortgage data to assemble the fnal sample. Second, I exploit

3
lenders’ names in the matching step to achieve a higher matching rate. Third, analysis weights are developed to represent the population of originated mortgages in

HMDA data.

To construct this data set, I frst merge Fannie Mae data with HMDA data. I

pick one to four-family mortgages sold to Fannie Mae in HMDA data for match. I

merge these loans with Fannie Mae data based on loan amount, MSA, 3-digit ZIP

code, state, lender, loan purpose, occupancy status, and the number of borrowers.

As HMDA started to disclose mortgage rate after 2018, I also use this variable as

a match key. To accommodate for rounding diferences, I allow a 2% diference

in loan amount. For each one-to-many match, I keep the matched pair with the

smallest loan size diference. To ensure the highest-quality match, I further exclude

all matches with duplicate observations. Because only large lenders are identifed

in Fannie Mae data, a large amount of Fannie Mae loans will not be matched after

the above steps. Therefore, I match the leftover mortgages in both data sets without

lender identifcation. Similarly, I repeat the above steps for mortgages sold to Freddie

Mac in HMDA. The fnal data set contains 8,154,065 GSE loans originated from 2015

to 2019, which covers about 59% of GSE loans in HMDA data. Figure A2 shows that

the matching rate increases when interest rate is used for matching.

The second step is to merge FHA Snapshot+ with HMDA. I select one to fourfamily FHA loans in HMDA for match. I merge two data sets based on county,

5-digit ZIP code, loan purpose, origination year, loan amount, and lender. Interest

rate is used as an additional match key after 2018. To accommodate for rounding

diferences between the two data sets, I allow loan amount to difer by 2% and interest

rate to difer by 2 basis point. For each one-to-many match, I keep the match with

the smallest size and interest rate diference. To ensure the highest-quality match, I

further exclude all matches with duplicate observations. Using this approach, the fnal

data set contains 1,376,241 FHA loans originated from 2015 to 2019, which covers

roughly 25% of FHA loans in HMDA data during the same period. The matching

rate is lower than that for GSE loans because the baseline data set, FHA Snapshot+,

only covers about 32% of all FHA loans. Overall, the HMDA+ data set includes

nearly half of GSE and FHA loans in the 2015-19 HMDA data.

To make the HMDA+ sample representative, I add an analysis weight for each

observation, using the reciprocal of the likelihood of being sampled from the HMDA

data. The sampling procedure assumes a random sampling within the corresponding

stratum. I separate all originated loans in HMDA data into diferent strata based on

4
property county, loan type, loan size, loan purpose, and origination year. As shown

in Table A3, the HMDA+ data set represents the whole mortgage market quite well.

Figure A1. FHA Snapshot+ Matching Rate

Notes: This fgure plots the matching rates between the FHA Snapshot+ dataset and

Ginnie Mae data, FHA Snapshot data, FHA loans in HMDA, and FHA loans sold to

Ginnie Mae in HMDA.

5
Figure A2. HMDA+ Matching Rate

Notes: This fgure plots the matching rates between the HMDA+ dataset and Ginnie Mae

data, FHA Snapshot data, FHA loans in HMDA, and FHA loans sold to Ginnie Mae in

HMDA.

6
Table A1. Summary Statistics of NSMO (excluding Asian borrowers)

Sample All Borrowers LEP Non-LEP

(1) (2) (3)

Panel A. Demographic Characteristics

Female 0.439 0.459 0.437

(0.496) (0.498) (0.496)

Married 0.660 0.635 0.663

(0.474) (0.481) (0.473)

Age 46.445 46.711 46.416

(13.970) (13.965) (13.971)

College education 0.632 0.519 0.645

(0.482) (0.500) (0.479)

Income<$50K 0.155 0.222 0.147

(0.362) (0.415) (0.354)

FICO score 730.823 719.668 732.079

(66.294) (66.562) (66.148)

Panel B. Mortgage Characteristics

Conventional loan 0.725 0.653 0.733

(0.447) (0.476) (0.442)

Loan amount<$200K 0.524 0.551 0.521

(0.499) (0.497) (0.500)

Loan to value ratio 78.419 79.899 78.252

(19.474) (19.243) (19.493)

Debt to income ratio 36.213 38.452 35.961

(12.323) (13.008) (12.218)

Interest rate 4.040 4.110 4.032

(0.676) (0.665) (0.676)

90-Day delinquency 0.016 0.021 0.015

(0.124) (0.145) (0.121)

Observations 35,553 3,489 32,064

Notes: This table reports summary statistics of demographic characteristics (panel A) and

mortgage characteristics (panel B) in NSMO excluding Asian borrowers. All table entries

represent sample means and standard deviations in parentheses, weighted by the analysis

weight in NSMO. Summary statistics are presented for all observations in column 1 as well

as separately for LEP (column 2) and non-LEP borrowers (column 3).

7
Table A2. Summary Statistics of the FHA Snapshot+ Sample

Sample FHA Snapshot+

(1)

Ginnie Mae

(2)

Purchase 0.753 0.745

Interest rate

(0.431)

4.159

(0.436)

4.176

Loan amount($1K)

LTV

(0.586)

209.186

(104.120)

92.956

(0.590)

205.926

(103.770)

93.100

DTI

(9.370)

42.016

(9.150)

41.962

FICO scores

(9.417)

671.276

(9.288)

676.082

(50.038) (49.031)

Observations 1,783,367 5,298,341

Notes: This table reports descriptive statistics of the FHA Snapshot+ dataset (column 1)

and the Ginnie Mae dataset (column 2). All table entries represent sample means and

standard deviations in parentheses. Summary statistics in column 1 are weighted by the

the reciprocal of the likelihood of being sampled from the HMDA data of FHA loans.

8
Table A3. Summary Statistics of the HMDA+ Sample

Sample HMDA+ HMDA

(1) (2)

GSE loans 0.726 0.714

(0.446) (0.452)

Purchase loans 0.581 0.581

(0.493) (0.493)

Owner occupied 0.905 0.914

(0.293) (0.281)

Loan amount 230.351 228.073

(118.585) (135.285)

Female 0.339 0.340

(0.473) (0.474)

Black 0.073 0.072

(0.261) (0.259)

Asian 0.070 0.067

(0.255) (0.249)

Hispanic 0.122 0.126

(0.328) (0.331)

Income 101.351 100.722

(85.129) (444.782)

Observations 9,530,306 19,449,814

Notes: This table reports descriptive statistics of the HMDA+ dataset (column 1) and the

HMDA dataset (column 2). All table entries represent sample means and standard deviations in parentheses. Summary statistics in column 1 are weighted by the the reciprocal

of the likelihood of being sampled from HMDA data.

9
B LEP Borrowers in the Mortgage Market

1 Additional Figures

Figure B1. Share of LEP Mortgage Borrowers

Notes: This fgure plots the share of LEP mortgage borrowers from 2013 to 2019 in the

NSMO sample.

10
Figure B2. Comparison of Demographic Characteristics

Notes: This fgure plots the distribution of selected demographic characteristics for LEP

and non-LEP borrowers in the NSMO sample. The demographic characteristics are educational level (panel A), the age of taking out the current mortgage (panel B), annual

household income (panel C), and borrower’s FICO score (panel D).

11
Figure B3. Perceptions and Experiences of LEP and non-LEP Borrowers

Notes: Panel A of this fgure plots the proportion of LEP and non-LEP borrowers who was

familiar with each of four things about the mortgage market. Panel B plots the proportion

of LEP and non-LEP borrowers who thought each of four factors were important when

choosing the mortgage lender. Panel C plots the proportion of LEP and non-LEP borrowers

who had each of four problems in the process of getting the mortgage. Panel D plots

the proportion of LEP and non-LEP borrowers who knew about each of four alternative

features of the mortgage. All statistics are weighted by the analysis weight in NSMO.

12
Figure B4. LEP Status and Ability to Explain Concepts about Mortgages

Notes: Panel A of this fgure plots the proportion of LEP and non-LEP borrowers who can

each explain four subtle concepts about mortgage to others very well. Panel B plots the

corresponding estimate of β in Equation (1) and its 95% confdence interval. All regressions

include origination quarter fxed efects and census tract type fxed efects. Demographic

controls include race, ethnicity, gender, age and its squared, marital status, education,

and household income. Risk fxed efects are the full pairwise interactions between LTV

bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. The 95% confdence intervals are based on

robust standard errors.

13
Figure B5. Estimated Diferences between LEP and non-LEP Borrowers (Hispanic

Borrowers)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of Hispanic borrowers. The outcomes are indicators for whether the

borrowers was familiar with four things about the mortgage market in panel A, indicators

for whether the borrower thought four factors were important when choosing the mortgage

lender in panel B, indicators for whether the borrower had four problems in the process

of getting the mortgage in panel C, and indicators for whether the borrower knew about

four alternative features of the mortgage in panel D. All regressions include origination

quarter fxed efects and census tract type fxed efects. Demographic controls include race,

ethnicity, gender, age and its squared, marital status, education, and household income.

Risk fxed efects are the full pairwise interactions between LTV bins and FICO score bins,

following the Loan-Level Price Adjustment Grid of Fannie Mae. Loan controls include loan

purpose, property type, and occupancy status. All regressions are weighted by the analysis

weight in NSMO. The 95% confdence intervals are based on robust standard errors.

14
Figure B6. Estimated Diferences between LEP and non-LEP Borrowers (Asian

Borrowers)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of Asian borrowers. The outcomes are indicators for whether the borrowers was familiar with four things about the mortgage market in panel A, indicators for

whether the borrower thought four factors were important when choosing the mortgage

lender in panel B, indicators for whether the borrower had four problems in the process of

getting the mortgage in panel C, and indicators for whether the borrower knew about four

alternative features of the mortgage in panel D. All regressions include origination quarter fxed efects and census tract type fxed efects. Demographic controls include race,

ethnicity, gender, age and its squared, marital status, education, and household income.

Risk fxed efects are the full pairwise interactions between LTV bins and FICO score bins,

following the Loan-Level Price Adjustment Grid of Fannie Mae. Loan controls include loan

purpose, property type, and occupancy status. All regressions are weighted by the analysis

weight in NSMO. The 95% confdence intervals are based on robust standard errors.

15
Figure B7. Estimated Diferences between LEP and non-LEP Borrowers (College

Graduates)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of college graduates. The outcomes are indicators for whether the borrowers was familiar with four things about the mortgage market in panel A, indicators for

whether the borrower thought four factors were important when choosing the mortgage

lender in panel B, indicators for whether the borrower had four problems in the process of

getting the mortgage in panel C, and indicators for whether the borrower knew about four

alternative features of the mortgage in panel D. All regressions include origination quarter fxed efects and census tract type fxed efects. Demographic controls include race,

ethnicity, gender, age and its squared, marital status, education, and household income.

Risk fxed efects are the full pairwise interactions between LTV bins and FICO score bins,

following the Loan-Level Price Adjustment Grid of Fannie Mae. Loan controls include loan

purpose, property type, and occupancy status. All regressions are weighted by the analysis

weight in NSMO. The 95% confdence intervals are based on robust standard errors.

16
Figure B8. Estimated Diferences between LEP and non-LEP Borrowers

(Non-College Graduates)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of borrowers without a bachelor’s degree or higher. The outcomes are

indicators for whether the borrowers was familiar with four things about the mortgage

market in panel A, indicators for whether the borrower thought four factors were important

when choosing the mortgage lender in panel B, indicators for whether the borrower had four

problems in the process of getting the mortgage in panel C, and indicators for whether the

borrower knew about four alternative features of the mortgage in panel D. All regressions

include origination quarter fxed efects and census tract type fxed efects. Demographic

controls include race, ethnicity, gender, age and its squared, marital status, education,

and household income. Risk fxed efects are the full pairwise interactions between LTV

bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. The 95% confdence intervals are based on

robust standard errors.

17
Figure B9. Estimated Diferences between LEP and non-LEP Borrowers (High

Income)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of borrowers with household incomes exceeding $100,000. The outcomes

are indicators for whether the borrowers was familiar with four things about the mortgage

market in panel A, indicators for whether the borrower thought four factors were important

when choosing the mortgage lender in panel B, indicators for whether the borrower had four

problems in the process of getting the mortgage in panel C, and indicators for whether the

borrower knew about four alternative features of the mortgage in panel D. All regressions

include origination quarter fxed efects and census tract type fxed efects. Demographic

controls include race, ethnicity, gender, age and its squared, marital status, education,

and household income. Risk fxed efects are the full pairwise interactions between LTV

bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. The 95% confdence intervals are based on

robust standard errors.

18
Figure B10. Estimated Diferences between LEP and non-LEP Borrowers (Low

Income)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of borrowers with household incomes less than $100,000. The outcomes

are indicators for whether the borrowers was familiar with four things about the mortgage

market in panel A, indicators for whether the borrower thought four factors were important

when choosing the mortgage lender in panel B, indicators for whether the borrower had four

problems in the process of getting the mortgage in panel C, and indicators for whether the

borrower knew about four alternative features of the mortgage in panel D. All regressions

include origination quarter fxed efects and census tract type fxed efects. Demographic

controls include race, ethnicity, gender, age and its squared, marital status, education,

and household income. Risk fxed efects are the full pairwise interactions between LTV

bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. The 95% confdence intervals are based on

robust standard errors.

19
Figure B11. Estimated Diferences between LEP and non-LEP Borrowers (Through

Brokers)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of borrowers who applied through mortgage brokers. The outcomes

are indicators for whether the borrowers was familiar with four things about the mortgage

market in panel A, indicators for whether the borrower thought four factors were important

when choosing the mortgage lender in panel B, indicators for whether the borrower had four

problems in the process of getting the mortgage in panel C, and indicators for whether the

borrower knew about four alternative features of the mortgage in panel D. All regressions

include origination quarter fxed efects and census tract type fxed efects. Demographic

controls include race, ethnicity, gender, age and its squared, marital status, education,

and household income. Risk fxed efects are the full pairwise interactions between LTV

bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. The 95% confdence intervals are based on

robust standard errors.

20
Figure B12. Estimated Diferences between LEP and non-LEP Borrowers (Through

Lenders)

Notes: This fgure plots the estimate of β in Equation (1) and its 95% confdence interval,

using the sample of borrowers who applied directly to lenders. The outcomes are indicators

for whether the borrowers was familiar with four things about the mortgage market in

panel A, indicators for whether the borrower thought four factors were important when

choosing the mortgage lender in panel B, indicators for whether the borrower had four

problems in the process of getting the mortgage in panel C, and indicators for whether the

borrower knew about four alternative features of the mortgage in panel D. All regressions

include origination quarter fxed efects and census tract type fxed efects. Demographic

controls include race, ethnicity, gender, age and its squared, marital status, education,

and household income. Risk fxed efects are the full pairwise interactions between LTV

bins and FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae.

Loan controls include loan purpose, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. The 95% confdence intervals are based on

robust standard errors.

21
Figure B13. Comparison of Mortgage Characteristics

Notes: This fgure plots the distribution of selected mortgage characteristics for LEP and

non-LEP borrowers in the NSMO sample. The mortgage characteristics are loan amount

in $100K (panel A), loan-to-value ratio (panel B), debt-to-income ratio (panel C), and

interest rate (panel D).

22
2 Additional Tables

Table B1. LEP Status and Search Behavior

Dependent variable Number of lenders Why apply to multiple lenders?

seriously

considered

(1)

applied to

(2)

fnd better

loan terms

(3)

concern over

qualifcation

(4)

learn

information

(5)

LEP -0.065*** -0.024** 0.016 0.105*** 0.075***

Hispanic

Asian

(0.015)

0.049***

(0.018)

0.110***

(0.012)

0.065***

(0.015)

0.058***

(0.017)

0.012

(0.016)

0.005

(0.020)

0.043**

(0.019)

0.117***

(0.021)

0.098***

(0.021)

0.133***

Black

(0.021)

0.110***

(0.017)

0.116***

(0.017)

0.007

(0.022)

0.006

(0.024)

0.041*

(0.021) (0.017) (0.018) (0.021) (0.022)

D.V. mean (LEP)

D.V. mean (non-LEP)

1.643

1.719

1.296

1.303

0.821

0.822

0.407

0.270

0.425

0.319

Observations

Quarter FEs

Tract type FEs

Demographic controls

Risk FEs

37,720

Yes

Yes

Yes

Yes

37,720

Yes

Yes

Yes

Yes

8,569

Yes

Yes

Yes

Yes

8,569

Yes

Yes

Yes

Yes

8,569

Yes

Yes

Yes

Yes

Loan controls Yes Yes Yes Yes Yes

Notes: This table reports the relationship between LEP status and borrowers’ search

behavior. The dependent variables in the frst two columns are the number of lenders

people seriously considered and the number of lenders people fnally applied to. The

dependent variables in columns 3 to 5 are three dummy variables indicating the reason

of applying to multiple lenders. All regressions include origination quarter fxed efects

and census tract type fxed efects. Demographic controls include gender, age and its

squared, marital status, education, and household income. Risk fxed efects are the full

pairwise interactions between LTV bins and FICO score bins, following the Loan-Level

Price Adjustment Grid of Fannie Mae. Loan controls include loan purpose, property type,

and occupancy status. All regressions are weighted by the analysis weight in NSMO.

Robust standard errors are reported in parentheses. Signifcance levels 10%, 5%, 1% are

denoted by *, **, and ***, respectively.

23
Table B2. LEP Status, Interest Rate, and 90-Day Delinquency

Sample All Purchase Refnance First-time

borrowers

Repeat

borrowers

(1) (2) (3) (4) (5)

Panel A. Interest rate

LEP 0.032*** 0.027** 0.034** 0.038* 0.028***

(0.010) (0.014) (0.013) (0.021) (0.010)

Panel B. 90-Day delinquency

LEP 0.003 0.005 0.0002 0.005 0.001

(0.003) (0.004) (0.004) (0.007) (0.003)

Observations 37,720 19,268 16,937 7,338 30,382

Quarter FEs Yes Yes Yes Yes Yes

Tract type FEs Yes Yes Yes Yes Yes

Risk FEs Yes Yes Yes Yes Yes

Loan controls Yes Yes Yes Yes Yes

Notes: This table reports the relationship between LEP status and interest rate (panel

A) and 90-day mortgage delinquency (panel B). Interest rate is winsorized at 1% and

99% level. Column 1 uses the full sample. Columns 2 and 3 use the sample of purchase

and refnance loans, respectively. Columns 4 and 5 use the sample of loans borrowed by

frst-time borrowers and repeat borrowers, respectively. All regressions include origination

quarter fxed efects and census tract type fxed efects. Risk fxed efects are the full

pairwise interactions between LTV bins and FICO score bins, following the Loan-Level

Price Adjustment Grid of Fannie Mae. Loan controls include loan type, loan purpose, loan

term, interest type, property type, and occupancy status. All regressions are weighted

by the analysis weight in NSMO. Robust standard errors are reported in parentheses.

Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

24
C Robustness Checks

1 UAD

The triple-diference estimates using NSMO have implied that reducing language

frictions could streamline LEP Hispanic borrowers’ application process. In line with

this, I estimate a diference-in-diferences model below to present suggestive evidence

of the positive policy impact on LEP borrowers’ experience with property appraisals.

The outcome of interest is the fraction of home appraisals receiving a lower price

than the contract price. When this unexpected type of appraisal occurs, the mortgage

amount will be capped because lenders base the loan on the appraisal. This could

delay or even derail the mortgage closing. A common solution to this problem is to

schedule another home appraisal in the hopes of obtaining a higher appraised value.

Therefore, I use this ratio as a measure of how troublesome the mortgage application

is at the county level. The data come from the Uniform Appraisal Dataset (UAD)

Aggregate Statistics Data File, which aggregates Enterprise single family appraisal

records at the county-quarter level.2

My diference-in-diferences results from estimating Equation (3) at the countyquarter level demonstrate a positive efect on LEP borrowers’ appraisal experience.

Column 1 of Table C1 shows that the probability of the appraised price below the contract price decreased by about 16.1 percentage points for treated borrowers following

the policy shock. This result echoes the triple-diference estimate reported in Table 5,

where I fnd that the probability of having more than one home appraisal decreased

by 12.5 percentage points for LEP Hispanic borrowers. Interestingly, the magnitudes

of two estimates are quite close, suggesting that the share of low-priced appraisals can

be used as a proxy for the inconvenience of getting a mortgage. Columns 2 to 4 of

this table show that the 25th percentile, median, and 75th percentile of the appraised

value did not change much after the policy shock. These results suggest that the

FHFA Language Access Plan had little impact on the local housing market, which is

consistent with the intention and content of this policy.

2The UAD appraisal records only include loans requiring traditional appraisals. For each property, it keeps the fnal appraisal record. Therefore, I use the proportion instead of the count of

appraisals to study if borrowers encounter more than one home appraisal.

25
Table C1. Efect on Home Appraisals

Dependent variable

Share of

appraisal

< ofer

(1)

Appraised

value

(p25)

(2)

Appraised

value

(p50)

(3)

Appraised

value

(p75)

(4)

LEP share × Post -0.161*** 0.062 -0.051 0.015

(0.026) (0.055) (0.074) (0.126)

Observations

County FEs

Quarter FEs

Additional controls

36,216

Yes

Yes

Yes

36,216

Yes

Yes

Yes

36,216

Yes

Yes

Yes

36,216

Yes

Yes

Yes

Notes: This table reports the diference-in-diferences estimates of the policy efect on

home appraisals. The dependent variables in columns 1 to 4 are the share of appraisals

with a value lower than the contract price, the 25th percentile appraised value, the median

appraised value, and the 75th percentile appraised value, respectively. LEP share is the

share of LEP Hispanic people before July 2019, and the share of LEP Hispanics and

Chinese starting from July 2019. Post equals one after June 2018. All specifcations

include county fxed efects, quarter fxed efects, and additional controls, which include

median household income, total population, and the proportion of Hispanics, Asians, and

black people. Standard errors are reported in parentheses and are clustered at the state

level. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

26
2 NSMO

Table C2. Efect on Mortgage Performance: Robustness

Sample All

(1)

Purchase

(2)

Refnance

(3)

First-time

borrowers

(4)

Repeat

borrowers

(5)

Panel A. 60-Day delinquency

LEP × Hispanic × Post -0.009

(0.026)

0.002

(0.043)

-0.041

(0.028)

0.013

(0.053)

-0.032

(0.021)

Panel B. Default

LEP × Hispanic × Post -0.003

(0.008)

-0.003

(0.012)

-0.004

(0.008)

0.002

(0.016)

-0.000

(0.004)

Observations

Quarter FEs

Demographic controls

Post × Tract type FEs

Post × Risk FEs

Post × Loan controls

35,553

Yes

Yes

Yes

Yes

Yes

18,118

Yes

Yes

Yes

Yes

Yes

15,977

Yes

Yes

Yes

Yes

Yes

6,739

Yes

Yes

Yes

Yes

Yes

28,807

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the triple-diference estimates of the policy efect on 60-day

delinquency and default. Column 1 uses the full sample. Columns 2 and 3 use the sample

of purchase and refnance loans, respectively. Columns 4 and 5 use the sample of loans

borrowed by frst-time borrowers and repeat borrowers, respectively. Post equals one if the

mortgage was originated after June 2018. All regressions include origination quarter fxed

efects and census tract type fxed efects. Demographic controls include race, ethnicity,

gender, age and its squared, marital status, education, and household income. Risk fxed

efects are the full pairwise interactions between LTV bins and FICO score bins, following

the Loan-Level Price Adjustment Grid of Fannie Mae. Loan controls include loan type,

loan purpose, loan term, interest rate type, property type, and occupancy status. All

regressions are weighted by the analysis weight in NSMO. Robust standard errors are

reported in parentheses. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***,

respectively.

27
Table C3. Robustness Test: Drop Mortgages Originated after June 2019

Dependent variable Redo

paperwork

Balloon

payment

Interest

rate

Consider

multi. lenders

(1) (2) (3) (4)

LEP × Hispanic × Post -0.148** -0.208*** -0.091 0.143

(0.064) (0.067) (0.088) (0.088)

Observations 34,871 34,871 34,871 34,871

Quarter FEs Yes Yes Yes Yes

Demographic controls Yes Yes Yes Yes

Post × Tract type FEs Yes Yes Yes Yes

Post × Risk FEs Yes Yes Yes Yes

Post × Loan controls Yes Yes Yes Yes

Notes: This table reports the triple-diference estimates in the NSMO sample that excludes

mortgages originated after June 2019. Post equals one if the mortgage was originated after

June 2018. Column 1 uses the same specifcation as column 4 in Panel B of Table 5. Column

2 uses the same specifcation as column 4 in Panel C of Table 5. Column 3 uses the same

specifcation as column 1 in Panel A of Table 6. Column 4 uses the same specifcation as

column 1 in Table 7.

28
Table C4. Robustness Tests: Diference-in-Diferences

Dependent variable Redo

paperwork

(1)

Balloon

payment

(2)

Interest

rate

(3)

Consider

multi. lenders

(4)

Panel A. Sample of Hispanic borrowers

LEP × Post -0.117**

(0.054)

-0.133**

(0.054)

-0.106*

(0.064)

0.128*

(0.070)

Observations 2,933 2,933 2,933 2,933

Panel B. Sample of LEP borrowers

Hispanic × Post -0.157***

(0.051)

-0.135***

(0.051)

-0.095

(0.066)

0.174***

(0.066)

Observations 3,485 3,485 3,484 3,485

Panel C. Sample of non-Asian borrowers

Treated × Post -0.124***

(0.045)

-0.164***

(0.048)

-0.142**

(0.061)

0.175***

(0.062)

Observations 35,553 35,553 35,553 35,553

Quarter FEs

Demographic controls

Post × Tract type FEs

Post × Risk FEs

Post × Loan controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports three diference-in-diferences estimates using NSMO. In panel A,

the sample only includes Hispanic borrowers, so the triple-diference model degenerates to

a diference-in-diferences model where treatment status is determined by LEP status. In

panel B, the sample only includes LEP borrowers, so the triple-diference model degenerates

to a diference-in-diferences model where treatment status is determined by ethnicity. In

panel C, the sample excludes Asian borrowers, and I compare LEP Hispanic borrowers

with other borrowers. For outcomes and control variables, column 1 is same as column 4

in panel B of Table 5, column 2 is same as column 4 in panel C of Table 5, column 3 is

same as column 1 in panel A of Table 6, and column 4 is same as column 1 in Table 7.

29
Figure C1. Flexible Diference-in-Diferences Estimates of the Efect on LEP

Hispanic Borrowers

Notes: This fgure plots the dynamic policy impact estimated from a fexible diferencein-diferences regression where I compare LEP Hispanic borrowers with other borrowers

(excluding Asian borrowers). The policy impact can vary every six months, and the coeffcient for the frst half of 2018 is normalized to zero. Panel A uses the same specifcation

as column 4 in panel B of Table 5. Panel B uses the same specifcation as column 4 in

panel C of Table 5. Panel C uses the same specifcation as column 1 in panel A of Table

6. Panel D uses the same specifcation as column 1 in Table 7.

30
Table C5. Placebo Tests

Dependent variable Redo

paperwork

(1)

Balloon

payment

(2)

Interest

rate

(3)

Consider

multi. lenders

(4)

Panel A. Change Postt

LEP × Hispanic × Post -0.064

(0.060)

0.038

(0.060)

0.069

(0.064)

-0.027

(0.067)

Observations 30,645 30,645 30,645 30,645

Panel B. Change Hispanici

LEP × Asian × Post -0.044

(0.061)

0.032

(0.086)

0.005

(0.089)

0.022

(0.097)

Observations 34,748 34,748 34,748 34,748

Quarter FEs

Demographic controls

Post × Tract type FEs

Post × Risk FEs

Post × Loan controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports two triple-diference placebo tests using NSMO. In panel A, I

assume that the policy change happened in July 2016. The sample includes mortgages

originated before July 2018. Post equals one if the mortgage was originated after June

2016. In panel B, I assume that the initial translated documents were in Asian languages

instead of Spanish. Post equals one if the mortgage was originated after June 2018.

31
Figure C2. Placebo Test: Randomly Assigned LEP Status

Notes: This fgure plots the distribution of the triple-diference coefcients from 1000

placebo tests. In each iteration, I randomly select a group of observations and assume

that they are LEP borrowers. To preserve the true market share of LEP borrowers, this

simulated NSMO has the same number of LEP borrowers as the real NSMO. I then estimate

Equation (2) using the simulated NSMO and get one placebo coefcient βˆ5. The vertical

red line represents the estimated triple-diference coefcient using the true LEP status

in NSMO. Empirical p-value is calculated as the number of iterations when the placebo

estimated efect is larger than the true estimated efect divided by 1000. Panel A uses the

same specifcation as column 4 in panel B of Table 5. Panel B uses the same specifcation

as column 4 in panel C of Table 5. Panel C uses the same specifcation as column 1 in

panel A of Table 6. Panel D uses the same specifcation as column 1 in Table 7.

32
3 HMDA

Table C6. TWFE Estimation with Heterogeneous Treatment Efects

Dependent variable # Applications

(10K)

(1)

Incomplete

share

(2)

Denial

rate

(3)

# Originations

(10K)

(4)

Dct 0.201***

(0.037)

-0.686**

(0.277)

-1.118***

(0.320)

0.065***

(0.022)

No. of switchers

County FEs

Year × State FEs

1,902

Yes

Yes

1,902

Yes

Yes

1,902

Yes

Yes

1,902

Yes

Yes

Additional controls Yes Yes Yes Yes

Notes: This table reports the TWFE estimation results following De Chaisemartin and

d’Haultfoeuille (2020). The dependent variables in columns 1 to 4 are the number of mortgage applications (in ten thousands), the share of incomplete applications, the application

denial rate, and the number of originations (in ten thousands), respectively. Dct is the

share of potential treated LEP people in county c in year t. The estimation uses counties

whose treatment level changed in absolute value by less than 0.5% as control groups. All

specifcations include county fxed efects, state-year fxed efects, and additional controls,

which include median household income, total population, and the proportion of Hispanics,

Asians, and black people. Standard errors are reported in parentheses and are clustered at

the state level. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

33
Table C7. Falsifcation Tests

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

Panel A. Change Postt

LEP share × Post 0.011

(0.061)

0.015

(0.037)

-0.013

(0.034)

0.015

(0.048)

Observations 19,623 19,623 19,623 19,623

Panel B. Asian borrowers

LEP share × Post 0.018

(0.014)

-0.039

(0.038)

-0.067*

(0.037)

0.016

(0.012)

Observations 12,936 12,936 12,936 12,936

County FEs

Year × State FEs

Additional controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports two falsifcation tests of the diference-in-diferences estimates

of the policy efects on mortgage credit access of conventional purchase loans. In Panel

A, I assume that the policy change happened in 2016 and use HMDA data from 2011 to

2017. In Panel B, I use the sample of Asian borrowers to calculate the dependent variables.

The dependent variables in columns 1 to 4 are the number of mortgage applications (in

ten thousands), the share of incomplete applications, the application denial rate, and the

number of originations (in ten thousands), respectively. LEP share is the share of LEP

Hispanic people. Post equals one after 2015 and 2017 in Panels A and B, respectively. All

specifcations include county fxed efects, state-year fxed efects, and additional controls,

which include median household income, total population, and the proportion of Hispanics,

Asians, and black people. Standard errors are reported in parentheses and are clustered at

the state level. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

34
Table C8. Efect on Accessing Mortgage Credit: Hispanic Borrowers

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

LEP × Post 0.169*** -0.074*** -0.183*** 0.114***

(0.050) (0.021) (0.064) (0.037)

Observations

County FEs

Year × State FEs

17,147

Yes

Yes

17,147

Yes

Yes

17,147

Yes

Yes

17,147

Yes

Yes

Additional controls Yes Yes Yes Yes

Notes: This table reports the diference-in-diferences estimates of the policy efect on mortgage credit access of conventional purchase loans for Hispanic borrowers. The dependent

variables in columns 1 to 4 are the number of mortgage applications (in ten thousands),

the share of incomplete applications, the application denial rate, and the number of originations (in ten thousands), respectively. LEP share is the share of LEP Hispanic people.

Post equals one after 2017. All specifcations include county fxed efects, state-year fxed

efects, and additional controls, which include median household income, total population,

and the proportion of Hispanics, Asians, and black people. Standard errors are reported

in parentheses and are clustered at the state level. Signifcance levels 10%, 5%, 1% are

denoted by *, **, and ***, respectively.

35
Figure C3. Placebo Test: Randomly Assigned LEP Share

Notes: This fgure plots the distribution of the diference-in-diferences estimates from 1000

placebo tests. In each iteration, I randomly assign the share of LEP Hispanics and LEP

Chinese at the county level within each state and then run the diference-in-diferences

regressions. The underlying regressions use the same specifcation as Panel A in Table 8.

The vertical red line represents the estimated diference-in-diferences coefcient using the

real data. Empirical p-value is calculated as the number of iterations when the placebo

estimated efect is larger than the true estimated efect divided by 1000.

36
D Machine Learning

1 Training Sample

I use the micro-level 2015-19 American Community Survey (ACS) to construct

the training sample as follows:

1. Keep household heads who are older than 18.

2. Keep household heads in contiguous states.

3. Keep household heads who have mortgages or purchase contracts.

4. Keep household heads who moved into the dwelling unit within 12 months or

less.

5. Use person weights (PERWT) to expand the sample.3

This training sample tries to represent home buyers between 2015 and 2019. The

summary statistics of this sample are reported in Table D1.

2 Training Procedure

First, I randomly select 80% of the ACS sample as the training set, and the

remaining 20% of the sample will be used as a test set to prevent overftting. Useful

features should exist in both the training sample and the prediction sample, so I

select household income, ethnicity, race (a Black indicator, an Asian indicator, and

a white indicator), gender, and a series of state-year fxed efects. In total, there are

251 features used for prediction.

I specify objective and eval metric to set the learning task as a logistic regression for binary classifcation. TO fne-tune the model, I use GridSearchCV to pick

the optimal set of the following hyperparameters.4 reg lambda is the L2 regularization term on weights. Increasing this value will make model more conservative.

learning rate (η) is the step size shrinkage used in update to prevent overftting.

gamma is the minimum loss reduction required to make a further partition on a leaf

node of the tree. The larger gamma is, the more conservative the algorithm will be.

3PERWT indicates how many persons in the U.S. population are represented by a given person

in an IPUMS sample.

4GridSearchCV is the process of performing hyperparameter tuning in order to determine the

optimal values for a given model.

37
max depth is the maximum depth of a tree. Increasing this value will make the

model more complex and more likely to overft. scale pos weight controls the balance of positive and negative weights. colsample bytree is the subsample ratio of

columns when constructing each tree. subsample is set to be 0.8, which means that

XGBoost would randomly sample 80% of the training data prior to growing trees.

n estimators is the number of trees.

I train two classifers for the full sample and the sample of Hispanics, separately.

For Hispanic borrowers, they are classifed as LEP if any classifer predicts a positive

class. The machine learning algorithm, XGBOOST, is capable of predicting a probability of being LEP. The mapping from this continuous variable to a crisp class label

is achieved by using a threshold, where all values equal or greater than the default

threshold (0.5) are mapped to LEP, and all other values are mapped to non-LEP. After applying threshold-moving to tune these parameters that generate the best overall

performance in the test set, I set the thresholds at 0.5 for the full model and 0.9 for

the Hispanic model, respectively.

For performance comparison, I use a traditional Logit model as the benchmark.

The Logit model for the full sample and the Hispanic sample both include an L1

penalty term, C.

5 Similarly, I use GridSearchCV to pick the optimal regularization

parameter C. The fnal results are reported in Table D2. The Logit model tends to

predict every observation as non-LEP. As a result, the model has a very low recall

rate for LEP people. By contrast, my XGBoost model has higher precision, recall,

and overall accuracy than the Logit model.

3 Discussion on Prediction Performance

The machine learning model predicts that 3.3% of all and 11.6% of Hispanic

people are LEP borrowers in the HMDA+ sample. Table D3 compares several key

characteristics between LEP and non-LEP borrowers, based on the machine learning

prediction. Consistent with the NSMO sample, a typical LEP borrower has a lower

income, credit score, and mortgage amount but a higher DTI, mortgage rate, and

delinquency rate. This suggests that the prediction is defnitely better than a random

guess.

However, about 4.9% of all and 22% of Hispanic household heads are LEP borrowers in the training sample. Therefore, the machine learning model under-predicts

LEP borrowers in both the full and the Hispanic sample. This is probably because

5C is the inverse of regularization strength. Smaller values specify stronger regularization.

38
the training sample and the prediction sample have diferent distributions in some

aspects. Comparing the frst column in Table D1 and Table D3, the training sample

has a larger fraction of minority borrowers. Figure D1 plots the income distribution

of Hispanic households (truncated at $150K) in both samples. The HMDA+ sample

has a much smaller share of households with incomes lower than $50K. Because minorities and low-income people are more likely to be LEP, the share of LEP people

in the prediction sample may be smaller than that in the training sample.

Figure D1. Income Distribution of Hispanic Households

Notes: This fgure plots the income distribution of Hispanic households (truncated at

$150K) in the ACS sample and the HMDA+ sample.

39
Table D1. Summary Statistics of the ACS Sample

Sample All

(1)

LEP

(2)

Non-LEP

(3)

Female 0.458 0.384 0.462

Minority

Age

Married

(0.498)

0.251

(0.434)

41.824

(13.789)

0.612

(0.486)

0.864

(0.343)

43.547

(12.241)

0.714

(0.499)

0.220

(0.414)

41.736

(13.857)

0.607

College

Income<$50K

(0.487)

0.504

(0.500)

0.194

(0.452)

0.290

(0.454)

0.350

(0.488)

0.515

(0.500)

0.186

(0.396) (0.477) (0.389)

Observations 3,687,402 178,928 3,508,474

Notes: This table reports descriptive statistics of the training set for machine learning.

The data come from the micro-level ACS 2015-2019. I select adult household heads who

own their homes with mortgages and moved into the current residence within 12 months

or less. The sample is expanded based on the individual weights in ACS. All table entries

represent sample means and standard deviations in parentheses. Summary statistics are

presented for all observations in column 1 as well as separately for LEP (column 2) and

non-LEP borrowers (column 3).

40
Table D2. Machine Learning Model Performance

Model

(1)

Class

(2)

Precision

(3)

Recall

(4)

Accuracy

(5)

Panel A. Full sample

Logit 0

1

0.952

0.542

0.999

0.005 0.952

XGBoost 0

1

0.989

0.886

0.995

0.787 0.985

Panel B. Hispanics sample

Logit 0

1

0.786

0.657

0.997

0.023 0.785

XGBoost 0

1

0.954

0.882

0.969

0.831 0.939

Notes: This table reports the performance of a benchmark Logit model and the XGBoost

model in the full test sample (panel A) and the test sample of Hispanics (panel B). See

Appendix D for details of the models. Class 1 stands for LEP and class 0 stands for

non-LEP. For each class, precision is the fraction of relevant instances among the retrieved

instances, and recall is the fraction of relevant instances that are retrieved. Accuracy is

the ratio of correct predictions of two classes to all instances.

41
Table D3. Summary Statistics of the HMDA+ Dataset (Purchase Loans)

Sample All LEP Non-LEP

(1) (2) (3)

Female 0.344 0.292 0.345

(0.475) (0.455) (0.476)

Minority 0.159 0.488 0.147

(0.366) (0.500) (0.354)

Income<$50K 0.201 0.316 0.196

(0.401) (0.465) (0.397)

FICO score 722.537 715.904 722.783

(59.982) (58.146) (60.036)

Conventional loan 0.641 0.577 0.643

(0.480) (0.494) (0.479)

LTV 85.353 85.296 85.355

(14.479) (14.943) (14.462)

DTI 37.667 40.612 37.557

(10.100) (10.157) (10.082)

Interest rate 4.220 4.229 4.220

(0.559) (0.563) (0.558)

90-Day delinquency 0.099 0.131 0.098

(0.299) (0.337) (0.297)

Observations 4,349,661 144,371 4,205,290

Notes: This table reports descriptive statistics of the prediction sample (purchase loans in

the HMDA+ dataset) for machine learning. LEP status is based on the prediction made by

the XGBoost machine learning model (see Appendix D). All table entries represent sample

means and standard deviations in parentheses. Summary statistics are presented for all

observations in column 1 as well as separately for LEP (column 2) and non-LEP borrowers

(column 3).

42
E Triple-diference Model with Treatment Status

Misclassifcation

1 Derivation of Bias

I abstract away from control variables and fxed efects and rewrite the triplediference model in simpler notation as:

Yt = α+β0L+β1H +β2P +β3L×H +β4L×P +β5H ×P +β6L×H ×P +εt. (E.1)

This is a canonical triple-diference model with a 2 × 2 × 2 setup. There are two time

periods, namely pre- and post-implementation of the FHFA Language Access Plan,

denoted as t = 0 and t = 1. P is a dummy variable indicating the post-policy period

(t = 1). L equals one if the borrower has limited English profciency in the data, and

H equals one if the borrower is Hispanic. However, the LEP status in the data, L,

is a misclassifed version of the true LEP status, L∗, which is unobservable. I use a

latent variable, ρ, as an indicator for misclassifcation. When ρ = 0, L = L∗. When

ρ = 1, L = 1 − L∗. The treatment status D is also a dummy variable, which takes

the value of one only when P = 1, L∗ = 1, and H = 1. Let Yt and Yt(D) represent

the observed outcome and the potential outcome in period t if the treatment status is

D. I am interested in identifying the average treatment efect on the treated (ATT)

that can be written as:

ATT = E[Y1(1) − Y1(0) | L∗ = 1, H = 1].

Under the assumption that E(εt|L, H, P) = 0, the standard triple-diference estimator

can be defned as:

θDDD =(E[Y1 | L = 1, H = 1] − E[Y0 | L = 1, H = 1])

− (E[Y1 | L = 1, H = 0) − E[Y0 | L = 1, H = 0]) (E.2) − (E[Y1 | L = 0, H = 1) − E[Y0 | L = 0, H = 1])

+ (E[Y1 | L = 0, H = 0) − E[Y0 | L = 0, H = 0]).

Before presenting the main result, I state the parallel trends assumption in this

triple-diference model with treatment misclassifcation.

43
Assumption E.1. (Parallel Trends)

(E [Y1(0) | L = 1, H = 1] − E [Y0(0) | L = 1, H = 1])

− (E [Y1(0) | L = 1, H = 0] − E [Y0(0) | L = 1, H = 0])

=

(E [Y1(0) | L = 0, H = 1] − E [Y0(0) | L = 0, H = 1])

− (E [Y1(0) | L = 0, H = 0] − E [Y0(0) | L = 0, H = 0]).

Note that this parallel trends assumption is based on the observed LEP status instead

of the true one. This is because when I run triple-diference regressions using the

HMDA+ data set, I implicitly proceed with this assumption instead of the assumption

stated in terms of L∗. If there is no misclassifcation of L∗, then Assumption E.1 helps

to identify the ATT (Olden and Møen, 2022). However, as L is not always equal to

L∗, the following lemma reveals that the triple-diference estimator cannot recover the

ATT and is a weighted average of the ATT for the correctly classifed and misclassifed

treatment groups.

Lemma E.1. In a 2 × 2 × 2 canonical triple diferences design with treatment status misclassifcation, if Assumption E.1 holds, then the triple-diference estimator

(defned as Equation (E.2)) can be written as:

θDDD = E [Y1(1) − Y1(0) | ρ = 0, L∗ = 1, H = 1] P(ρ = 0 | L = 1, H = 1)

− E [Y1(1) − Y1(0) | ρ = 1, L∗ = 1, H = 1] P(ρ = 1 | L = 0, H = 1)

Proof. Using the notation of potential outcome framework and treatment misclassifcation, I have:

E[Y1 | L = 1, H = 1] = E[Y1(1)L∗ + Y1(0)(1 − L∗

) | L = 1, H = 1]

= E[(Y1(1) − Y1(0))L∗ | L = 1, H = 1] + E[Y1(0) | L = 1, H = 1].

The frst equality refects that some people with L = 1 are actually not treated because

they are misclassifed. Similarly, other terms in the triple-diference estimator can be

written as:

E[Y0 | L = 1, H = 1] = E[Y0(0) | L = 1, H = 1],

E[Y1 | L = 1, H = 0] = E[Y1(0) | L = 1, H = 0],

44
E[Y0 | L = 1, H = 0] = E[Y0(0) | L = 1, H = 0],

E[Y1 | L = 0, H = 1] = E[Y1(1)L∗ + Y1(0)(1 − L∗

) | L = 0, H = 1]

= E[(Y1(1) − Y1(0))L∗ | L = 0, H = 1] + E[Y1(0) | L = 0, H = 1],

E[Y0 | L = 0, H = 1] = E[Y0(0) | L = 0, H = 1],

E[Y1 | L = 0, H = 0] = E[Y1(0) | L = 0, H = 0],

E[Y0 | L = 0, H = 0] = E[Y0(0) | L = 0, H = 0].

The fourth term shows that although some people have L = 0 in the data set, they

are actually treated because their true LEP status is L∗ = 1. In other cases, the

misclassifcation of L∗ does not afect potential outcomes, because either H = 0 or

T = 0. Substituting these terms into Equation (E.2), I get

θDDD = E[(Y1(1) − Y1(0))L∗ | L = 1, H = 1] − E[(Y1(1) − Y1(0))L∗ | L = 0, H = 1].

Therefore,

θDDD = E [Y1(1) − Y1(0) | ρ = 0, L∗ = 1, H = 1] P(ρ = 0 | L = 1, H = 1)

− E [Y1(1) − Y1(0) | ρ = 1, L∗ = 1, H = 1] P(ρ = 1 | L = 0, H = 1)

as L∗ = 1, L = 1 is equivalent to ρ = 0, L∗ = 1 or ρ = 0, L = 1, and L∗ = 1, L = 0 is

equivalent to ρ = 1, L∗ = 1 or ρ = 1, L = 0.

This lemma shows that the bias direction of the triple-diference estimator is

ambiguous. To see this, I rewrite the ATT as:

ATT = E[Y1(1) − Y1(0) | L∗ = 1, H = 1, ρ = 1]P(ρ = 1 | L∗ = 1, H = 1)

+ E[Y1(1) − Y1(0) | L∗ = 1, H = 1, ρ = 0]P(ρ = 0 | L∗ = 1, H = 1).

When E[Y1(1) − Y1(0) | L∗ = 1, H = 1, ρ = 1] and E[Y1(1) − Y1(0) | L∗ = 1, H =

1, ρ = 0] are both positive, the ATT is positive. However, it is possible that θDDD

is negative in this case, because the relationship between P(ρ = 0 | L = 1, H = 1)

and P(ρ = 1 | L = 0, H = 1) is undetermined. The misclassifcation in this lemma

is arbitrary, which leads to this pessimistic result. I then show that a reasonable

assumption on the of structure of misclassifcation can help to identify both the

direction and magnitude of the bias.

45
⊥

Assumption E.2. (Non-diferential Misclassifcation)

ρ ⊥ (Y1(1), Y1(0)) | L∗

, H

This assumption states that misclassifcation is not correlated to potential outcomes conditional on the true treatment status. This assumption is likely to hold in

my context, because the misclassifcation mechanically comes from a pure statistics

exercise. Then the following proposition holds.

Proposition E.1. Under Assumptions E.1 and E.2, the triple-diference estimator

can be written as:

θDDD = ATT(P(ρ = 0 | L = 1, H = 1) + P(ρ = 0 | L = 0, H = 1) − 1).

If 1 − P(ρ = 1 | L = 1, H = 1) − P(ρ = 1 | L = 0, H = 1) ∈ (0, 1], then the

triple-diference estimator has attenuation bias.

Proof. Assumption E.2 implies that

E[Y1(1) − Y1(0) | ρ, L∗

, H] = E[Y1(1) − Y1(0) | L∗, H]

Thus,

θDDD = E[Y1(1) − Y1(0) | L∗ = 1, H = 1](P(ρ = 0 | L = 1, H = 1) − P(ρ = 1 | L = 0, H = 1))

= ATT(P(ρ = 0 | L = 1, H = 1) + P(ρ = 0 | L = 0, H = 1) − 1)

= ATT(1 − P(ρ = 1 | L = 1, H = 1) − P(ρ = 1 | L = 0, H = 1)).

If 1 − P(ρ = 1 | L = 1, H = 1) − P(ρ = 1 | L = 0, H = 1) ∈ (0, 1], then θDDD is

downward biased compared to the true ATT.

Proposition E.1 shows that the triple-diference estimate is smaller than the true

ATT when the misclassifcation problem is not too severe. Because non-Hispanic

people are always untreated, the bias is only determined by the precision in the

Hispanic sample.

46
2 Lower Bound of the ATT

Proposition E.1 links the performance of machine learning models to the bias

magnitude. However, the true LEP status is not observable in the prediction sample,

so I cannot evaluate the prediction performance in this sample. To convert the triplediference estimate to the ATT, I impose two additional assumptions that allow me

to pin down the range of the precision in the prediction sample.

Assumption E.3. The fraction of LEP people among Hispanic borrowers in the

prediction sample is lower than that in the training sample.

Figure D1 provides supporting evidence for Assumption 3, as it shows that the

training sample has a larger fraction of low-income Hispanic households than the

prediction sample. Given this assumption, because about 22% of Hispanic household

heads in the ACS sample are LEP, there will be at most 94,194 LEP Hispanic borrowers in the HMDA+ sample. If I know the number of true positive instances that

my machine learning model predicts, I can evaluate the prediction performance. I

state another assumption needed to achieve this.

Assumption E.4. The machine learning model does not perform better in the prediction sample than in the test sample.

Then Assumption 4 also stands because the prediction sample does not represent

the test sample perfectly. Under these two assumptions, I can calculate a lower

bound of the ATT. Table E1 presents the confusion matrix of Hispanic borrowers in

the HMDA+ data set. Each element of this matrix, as well as the precision and recall

metrics, can be expressed by two unknowns: the number of true positive instances

(denoted as x) and the number of LEP Hispanic borrowers in reality (denoted as y).

Assumption E.3 implies that y ≤ 94194. Assumption E.4 implies that the precision

and recall metrics in the prediction sample are smaller than those reported in Panel

B of Table D2. Therefore, fnding the lower bound of the ATT is equivalent to solving

47
the following constrained maximization problem:

x 381634 − y + x

max +

x, y 49857 381634

s.t. y ≤ 94194,

x

precision1 = ≤ 0.882, 49857

x

recall1 = ≤ 0.831, y

381634 − y + x

precision0 = ≤ 0.954, 381634

381634 − y + x

recall0 = ≤ 0.969 431491 − y

Solving this system, I obtain the maximum value of 1.72 for the sum of prediction

precision for two classes (i.e., P(ρ = 0 | L = 1, H = 1) + P(ρ = 0 | L = 0, H = 1)).

This is achieved when the number of LEP Hispanic borrowers is 55,765 and the

number of true positive instances is 38,210. Therefore, according to Proposition E.1,

the ATT in this case is the triple-diference coefcient multiplied by 1.39.

Notice that this is the lower bound of the ATT. Given the same triple-diference

coefcient, any deviation of the actual number of LEP Hispanic borrowers or the

machine learning performance from the value that achieves the maximum of the

precision sum will generate a larger ATT. For example, if the fraction of LEP people

among Hispanic borrowers is the same in the training sample and the prediction

sample (i.e., y = 94194), x will be smaller than 39401. Furthermore, the sum of

the precision of two classes is smaller than 1.65, and then ATT = θDDD × 1.54. If

y = 45179 and x = 29914, then ATT = θDDD × 5. In this case, the magnitude of the

triple-diference estimates in the HMDA+ sample is comparable to that of the NSMO

sample.

48
Table E1. Confusion Matrix of the Prediction Sample

Data

0 1

0 381,634 Prediction 1 49,857TN=381,634-y+x FN=y-x

FP=49,857-x TP=x

431,491-y y

Notes: This table is the confusion matrix of the Hispanic prediction sample. Class 0

stands for non-LEP, and class 1 stands for LEP. Each row represents the classifcation of

the model, and each column represents the classifcation of the data. All data points can

be separated into four groups based on the data and the prediction: true negative, false

negative, false positive, and true positive. Since the the number of true positive instances

(T P = x) and the actual number of LEP Hispanic borrowers (y) are unknown, each cell

in this confusion matrix is expressed in terms of x and y.

49
F Additional Figures and Tables

1 Additional Figures

Figure F1. Language Translation Disclosure

Notes: This fgure shows the English version and Spanish version of Language Translation

Disclosure.

50
Figure F2. Snapshot of Mortgage Translations Clearinghouse

(a) Translated Documents

(b) Glossary

Notes: This fgure is the snapshot of Mortgage Translations Clearinghouse website in

January 2019, which is retrieved from Wayback Machine (https://archive.org/web/).

51
Figure F3. Triple-Diferences Raw Comparison

(a) resolve credit report errors

(b) answer further request for income or asset information

52
Figure F3. Triple-Diferences Raw Comparison (cont.)

(c) have more than one appraisal

(d) do not know if it is an ARM

53
Figure F3. Triple-Diferences Raw Comparison (cont.)

(e) do not know if it has a balloon payment

Notes: This fgure plots the raw triple-diference comparison for fve outcomes: the share of

borrowers who resolved credit report errors, the share of borrowers who answered further

request for income or asset information, the share of borrowers who had more than one

home appraisal, the share of borrowers who did not know if the mortgage has an adjustable

interest rate, and the share of borrowers who did not know if the mortgage has a balloon

payment. Each panel plots for a certain type of borrowers: LEP and Hispanic in Panel

A, non-LEP and Hispanic in Panel B, LEP and non-Hispanic in Panel C, and non-LEP

and non-Hispanic in Panel D. The pre-policy shares are denoted by red bars, and the postpolicy shares are denoted by blue bars. The number in the bar represents the corresponding

share.

54
Figure F4. Consumer Search and Realized Mortgage Rates

Notes: This fgure plots the relationship between the number of lenders seriously considered

and realized mortgage rates. I estimate the following specifcation:

X rit = α + βs1 {si = s} + γXi + δt + εit

s≥2

where the dependent variable rit is the mortgage rate of borrower i who took out the

mortgage at time t. The independent variable of interest, si, is the number of lenders that

a borrower seriously considered (capped at 4) before taking up a mortgage. This fgure

plots the coefcients βs for 4 types of borrowers: all borrowers in panel A, LEP borrowers

in panel B, prime LEP borrowers in panel C, and subprime borrowers in panel D. Subprime

borrowers have a FICO score lower than 640.

55
2 Additional Tables

Table F1. Efect on Debt-to-Income Ratio

Sample All Purchase Refnance First-time

borrowers

Repeat

borrowers

(1) (2) (3) (4) (5)

LEP × Hispanic × Post -2.816** -2.854* -4.842** -3.220 -2.933*

(1.345) (1.686) (2.348) (2.133) (1.777)

Observations 35,553 18,118 15,977 6,739 28,807

Quarter FEs Yes Yes Yes Yes Yes

Demographic controls Yes Yes Yes Yes Yes

Post × Tract type FEs Yes Yes Yes Yes Yes

Post × Risk FEs Yes Yes Yes Yes Yes

Post × Loan controls Yes Yes Yes Yes Yes

Notes: This table reports the triple-diference estimates of the policy efect on debt-toincome ratio. Column 1 uses the full sample. Columns 2 and 3 use the sample of purchase

and refnance loans, respectively. Columns 4 and 5 use the sample of loans borrowed by

frst-time borrowers and repeat borrowers, respectively. Post equals one if the mortgage

was originated after June 2018. All regressions include origination quarter fxed efects

and census tract type fxed efects. Demographic controls include race, ethnicity, gender,

age and its squared, marital status, education, and household income. Risk fxed efects

are the full pairwise interactions between LTV bins and FICO score bins, following the

Loan-Level Price Adjustment Grid of Fannie Mae. Loan controls include loan type, loan

purpose, loan term, interest rate type, property type, and occupancy status. All regressions

are weighted by the analysis weight in NSMO. Robust standard errors are reported in

parentheses. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

56
Table F2. Efect on Financial Literacy

Dependent variable: Mortgage Down Credit Market

1(familiar with ...) types payment history rate

(1) (2) (3) (4)

LEP × Hispanic × Post -0.043 -0.054 -0.038 0.007

(0.068) (0.070) (0.067) (0.067)

Pre-policy treated mean 0.319 0.425 0.706 0.421

Observations 35,553 35,553 35,553 35,553

Quarter FEs Yes Yes Yes Yes

Demographic controls Yes Yes Yes Yes

Post × Tract type FEs Yes Yes Yes Yes

Post × Risk FEs Yes Yes Yes Yes

Post × Loan controls Yes Yes Yes Yes

Notes: This table reports the triple-diference estimates of the policy efect on borrowers’

fnancial literacy about the mortgage market. The dependent variables are indicators for

whether the borrower was familiar with the market when they started their application.

Post equals one if the mortgage was originated after June 2018. All regressions include

origination quarter fxed efects and census tract type fxed efects. Demographic controls

include race, ethnicity, gender, age and its squared, marital status, education, and household income. Risk fxed efects are the full pairwise interactions between LTV bins and

FICO score bins, following the Loan-Level Price Adjustment Grid of Fannie Mae. Loan

controls include loan purpose, property type, and occupancy status. All regressions are

weighted by the analysis weight in NSMO. Robust standard errors are reported in parentheses. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

57
Table F3. Efect on Accessing Mortgage Credit: Conventional Refnance Loans

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

LEP share × Post -0.445* 0.002 0.020 -0.211

(0.240) (0.020) (0.026) (0.145)

Observations

County FEs

Year × State FEs

25,253

Yes

Yes

25,253

Yes

Yes

25,253

Yes

Yes

25,253

Yes

Yes

Additional controls Yes Yes Yes Yes

Notes: This table reports the diference-in-diferences estimates of the policy efect on

the credit access of conventional refnance loans. The dependent variables in columns 1

to 4 are the number of mortgage applications (in ten thousands), the share of incomplete

applications, the application denial rate, and the number of originations (in ten thousands),

respectively. LEP share is the share of LEP Hispanic people before 2018, and the share of

LEP Hispanics and Chinese in 2019. Post equals one after 2017. All specifcations include

county fxed efects, state-year fxed efects, and additional controls, which include median

household income, total population, and the proportion of Hispanics, Asians, and black

people. Standard errors are reported in parentheses and are clustered at the state level.

Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

58
Table F4. Efect on Accessing Mortgage Credit: All Purchase Loans

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

LEP share × Post 0.014 -0.082*** -0.106*** 0.026

(0.061) (0.012) (0.032) (0.046)

Observations

County FEs

Year × State FEs

25,255

Yes

Yes

25,255

Yes

Yes

25,255

Yes

Yes

25,255

Yes

Yes

Additional controls Yes Yes Yes Yes

Notes: This table reports the diference-in-diferences estimates of the policy efect on the

credit access of all purchase loans. The dependent variables in columns 1 to 4 are the

number of mortgage applications (in ten thousands), the share of incomplete applications,

the application denial rate, and the number of originations (in ten thousands), respectively. LEP share is the share of LEP Hispanic people before 2019, and the share of LEP

Hispanics and Chinese in 2019. Post equals one after 2017. All specifcations include

county fxed efects, state-year fxed efects, and additional controls, which include median

household income, total population, and the proportion of Hispanics, Asians, and black

people. Standard errors are reported in parentheses and are clustered at the state level.

Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

59
Table F5. Heterogeneous Efect on Accessing Mortgage Credit by Share of

Hispanics and Chinese

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

Panel A. Small share of Hispanics and Chinese

LEP × Post 0.791***

(0.243)

-1.001***

(0.335)

-2.172**

(1.046)

0.550***

(0.167)

Observations 12,558 12,558 12,558 12,558

Panel B. Large share of Hispanics and Chinese

LEP × Post 0.086

(0.053)

-0.037*

(0.022)

-0.090*

(0.046)

0.065

(0.039)

Observations 12,649 12,649 12,649 12,649

County FEs

Year × State FEs

Additional controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the diference-in-diferences estimates of the heterogeneous efect

of language help on mortgage credit access across racial composition. The sample is split

based on the share of Hispanic and Chinese people. LEP share is the share of LEP Hispanic

people before 2019, and the share of LEP Hispanics and Chinese in 2019. Post equals

one after 2017. The dependent variables in columns 1 to 4 are the number of mortgage

applications (in ten thousands), the share of incomplete applications, the application denial

rate, and the number of originations (in ten thousands), respectively. All specifcations

include county fxed efects, state-year fxed efects, and additional controls, which include

median household income, total population, and the proportion of Hispanics, Asians, and

black people. Standard errors are reported in parentheses and are clustered at the state

level. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

60
Table F6. Heterogeneous Efect on Accessing Mortgage Credit by Lender

Competition

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

Panel A. Low HHI

LEP × Post 0.248**

(0.098)

-0.104***

(0.024)

-0.181***

(0.054)

0.173**

(0.073)

Observations 12,246 12,246 12,246 12,246

Panel B. High HHI

LEP × Post -0.007

(0.009)

-0.016

(0.034)

-0.120**

(0.054)

0.0003

(0.005)

Observations 12,979 12,979 12,979 12,979

County FEs

Year × State FEs

Additional controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the diference-in-diferences estimates of the heterogeneous effect of language help on mortgage credit access across lender competition. The sample is

split based on the HHI of conventional purchase loan originations for Hispanic and Asian

borrowers in 2017. LEP share is the share of LEP Hispanic people before 2019, and the

share of LEP Hispanics and Chinese in 2019. Post equals one after 2017. The dependent

variables in columns 1 to 4 are the number of mortgage applications (in ten thousands),

the share of incomplete applications, the application denial rate, and the number of originations (in ten thousands), respectively. All specifcations include county fxed efects,

state-year fxed efects, and additional controls, which include median household income,

total population, and the proportion of Hispanics, Asians, and black people. Standard

errors are reported in parentheses and are clustered at the state level. Signifcance levels

10%, 5%, 1% are denoted by *, **, and ***, respectively.

61
Table F7. Heterogeneous Efect on Accessing Mortgage Credit by LEP Share

Dependent variable # Applications

(10K)

(1)

Share of

incomplete app.

(2)

Denial rate

(3)

# Originations

(10K)

(4)

Panel A. Low LEP share

LEP share × Post 1.507***

(0.321)

-1.349***

(0.380)

-3.781***

(1.260)

0.998***

(0.227)

Observations 12,607 12,607 12,607 12,607

Panel B. High LEP share

LEP share × Post 0.081

(0.054)

-0.038*

(0.020)

-0.094*

(0.048)

0.063

(0.040)

Observations 12,478 12,478 12,478 12,478

County FEs

Year × State FEs

Additional controls

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Notes: This table reports the diference-in-diferences estimates of the heterogeneous efect

of language help on mortgage credit access across treatment level. The sample is split

based on the LEP share at the level of 1%. The dependent variables in columns 1 to

4 are the number of mortgage applications (in ten thousands), the share of incomplete

applications, the application denial rate, and the number of originations (in ten thousands),

respectively. LEP share is the share of LEP Hispanic people before 2019, and the share of

LEP Hispanics and Chinese in 2019. Post equals one after 2017. All specifcations include

county fxed efects, state-year fxed efects, and additional controls, which include median

household income, total population, and the proportion of Hispanics, Asians, and black

people. Standard errors are reported in parentheses and are clustered at the state level.

Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

62
Table F8. Efect on Overall Mortgage Performance

Panel A. County level

Dependent variable 90–day delinquency rate

(1)

30-89 delinquency rate

(2)

LEP share × Post -0.193 -0.502

(0.587) (0.303)

Observations

County fxed efects

Month fxed efects

33,624

Yes

Yes

33,624

Yes

Yes

Additional controls Yes Yes

Panel B. CBSA level

Dependent variable 90–day delinquency rate

(1)

30-89 delinquency rate

(2)

LEP share × Post 0.122

(0.568)

0.251

(0.335)

Observations

CBSA fxed efects

Month fxed efects

Additional controls

12,924

Yes

Yes

Yes

12,924

Yes

Yes

Yes

Notes: This table reports the diference-in-diferences estimates of the efect of language

help on the overall mortgage performance. LEP share is the share of LEP Hispanics

before July 2019, and the share of LEP Hispanics and Chinese starting from July 2019.

Post equals one after June 2018. The dependent variables are the 90–day delinquency rate

and the 30-89 delinquency rate in columns 1 and 2, respectively. The data come from the

National Mortgage Database (NMDB) and provided by Consumer Financial Protection

Bureau (CFPB). All specifcations include location fxed efects (county in panel A and

CBSA in panel B), month fxed efects, and additional controls, which include median

household income, total population, and the proportion of Hispanics, Asians, and black

people. All regressions are weighted by total population. Standard errors are reported in

parentheses and are clustered at the state level in panel A and at the CBSA level in panel

B. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

63
Table F9. Efect on Mortgage Rate and Risk of FHA Loans

Sample All Purchase Refnance First-time

borrowers

Repeat

borrowers

Channel:

retail

Channel:

broker

(1) (2) (3) (4) (5) (6) (7)

Panel A. Average conditional interest rate

LEP share × Post -0.133*** -0.163*** -0.051*** -0.159*** -0.099*** -0.144*** -0.122***

(0.019) (0.022) (0.019) (0.023) (0.023) (0.022) (0.033)

Observations 592,464 479,204 338,413 400,288 438,232 509,430 251,743

Panel B. Average conditional 90-day delinquency rate

LEP share × Post 0.015 -0.003 0.044* -0.008 0.029 -0.015 0.023

(0.015) (0.018) (0.024) (0.017) (0.037) (0.013) (0.025)

Observations 592,464 479,201 338,291 400,286 217,651 509,399 251,735

Panel C. Average FICO scores

LEP share × Post 17.876*** 22.277*** 6.096 21.257*** 11.155*** 11.180*** 21.195***

(2.087) (2.970) (4.330) (3.003) (3.902) (2.770) (4.044)

Observations 592,464 479,204 338,415 400,289 438,233 509,431 251,747

ZIP5 code FEs Yes Yes Yes Yes Yes Yes Yes

Month FEs Yes Yes Yes Yes Yes Yes Yes

Additional controls Yes Yes Yes Yes Yes Yes Yes

Notes: This table reports the diference-in-diferences estimates of the policy efect on

average conditional interest rate (Panel A), average conditional 90-day delinquency rate

(Panel B), and average FICO scores (Panel C) of FHA loans. The dependent variables are

at the 5-digit ZIP code-month level. The conditional outcome is obtained by averaging the

residuals after regressing the raw interest rate (90-day delinquency) on origination month

fxed efects, lender fxed efects, LTV × FICO score grids, loan purpose, loan term, property type, and occupancy status. Column 1 uses the full sample. Columns 2 and 3 use

the sample of purchase and refnance loans, respectively. Columns 4 and 5 use the sample

of loans borrowed by frst-time borrowers and repeat borrowers, respectively. Columns 6

and 7 use the sample of loans originated through retail lenders and brokers, respectively.

LEP share is the share of LEP Hispanics before July 2019, and the share of LEP Hispanics

and Chinese starting from July 2019. Post equals one after June 2018. All specifcations

include 5-digit ZIP code fxed efects, origination month fxed efects, and additional controls, which include median household income, total population, and the proportion of

Hispanics, Asians, and black people at the 3-digit ZIP code level. Standard errors are

reported in parentheses and are clustered at the 3-digit ZIP code level. Signifcance levels

10%, 5%, 1% are denoted by *, **, and ***, respectively.

64
Table F10. Efect on Interest Rate: Adding Post × Lender × County FEs

Sample Purchase First-time

borrowers

Repeat

borrowers

Channel:

retail

Channel:

broker

(1) (2) (3) (4) (5)

LEP × Hispanic × Post -0.034*** -0.046*** -0.004 -0.043*** -0.017

(0.008) (0.011) (0.012) (0.011) (0.012)

Observations 3,779,493 1,616,120 2,111,259 2,428,526 1,325,020

Month FEs Yes Yes Yes Yes Yes

Demographic controls Yes Yes Yes Yes Yes

Post × Lender × County FEs Yes Yes Yes Yes Yes

Post × Risk FEs Yes Yes Yes Yes Yes

Post × Loan controls Yes Yes Yes Yes Yes

Notes: This table reports the triple-diferences estimates of the policy efect on interest rate.

Column 1 uses all purchase loans in the HMDA+ sample. Columns 2 and 3 use the sample

of loans borrowed by frst-time borrowers and repeat borrowers, respectively. Columns 4

and 5 use the sample of loans originated through retail lenders and brokers, respectively.

Post equals one if the mortgage was originated after June 2018. All regressions include

origination month fxed efects and Post-lender-county fxed efects. Risk fxed efects are

the full pairwise interaction between LTV bins and FICO score bins, following the LoanLevel Price Adjustment Grid of Fannie Mae. Loan controls include loan type, loan term,

property type, and occupancy status. All regressions are weighted by the analysis weight in

the HMDA+ sample. Standard errors are reported in parentheses and are clustered at the

county level. Signifcance levels 10%, 5%, 1% are denoted by *, **, and ***, respectively.

65