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Under What Circumstances do First-time Homebuyers Overpay? – An Empirical Analysis Using Mortgage and Appraisal Data

Authors:
  • Federal Housing Finance Agency
  • Federal Housing Finance Agency

Abstract

We study whether first-time homebuyers overpay for their homes and whether the magnitude of the overpayment varies with the diligence of appraisers involved. We present a robust result that first-time homebuyers sort into smaller and cheaper houses, but that once observed and unobserved house characteristics are controlled for, they pay a premium compared to their more experienced counterparts. Our analysis additionally suggests that certain appraisals and appraisers might be able to mitigate this overpayment by inducing downward renegotiation. This research is among the first to contribute both theoretically and empirically to the literature on first-time homebuyers' sales transactions.
FHFA STAFF WORKING PAPER SERIES
J. Shui & S. Murthy — First-time Homebuyer Overpayment
Under What Circumstances do First-time Homebuyers Overpay?
– An Analysis Using Mortgage and Appraisal Data
Jessica Shui
Shriya Murthy
April 2018 (revised)
April 2017 (original)
Working Paper 17-03
FEDERAL HOUSING FINANCE AGENCY
Division of Housing Mission & Goals
Office of Policy Analysis & Research
400 7th Street SW
Washington, DC 20219, USA
Working Papers prepared by staff of the Federal Housing Finance Agency (FHFA) are preliminary
products circulated to stimulate discussion and critical comment. The analysis and conclusions
are those of the authors alone, and should not be represented or interpreted as conveying an official
FHFA position, policy, analysis, opinion, or endorsement. Any errors or omissions are the sole
responsibility of the authors. References to FHFA Working Papers (other than acknowledgment)
should be cleared with the authors to protect the tentative character of these papers.
Many thanks to Andy Leventis and members of FHFA’s Research Oversight Committee for their
support and comments that greatly improved this research. We thank Bob Witt for sharing his
expertise. We also thank Sam Frumkin and those participants of the ARES April 2017 Conference
who provided helpful suggestions.
FHFA Working Paper 17-03
2 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Under What Circumstances do First-time Homebuyers Overpay?
– An Empirical Analysis Using Mortgage and Appraisal Data
Jessica Shui and Shriya Murthy
FHFA Staff Working Paper 17-03
April 2018 (revised)
April 2017 (original)
Abstract
We study whether first-time homebuyers overpay for their homes and whether the
magnitude of overpayment varies with the diligence of appraisers involved. We
present a robust result that first-time homebuyers sort into smaller and cheaper houses,
but that once observed and unobserved house characteristics are controlled for, they
pay a premium compared to their more experienced counterparts. Our analysis
additionally suggests that certain appraisals and appraisers might be able to mitigate
this overpayment by inducing downward renegotiation. This research is among the
first to contribute both theoretically and empirically to the literature on first-time
homebuyers’ sales transactions.
Keywords: first-time homebuyer, overpayment, appraisal, appraiser, renegotiation,
repeat-sales approach
JEL Classification: C33 · D83 · G21 · G23 · L85 · R3
Jessica Shui
Federal Housing Finance Agency
Office of Policy Analysis & Research
400 7th Street SW
Washington, DC 20219, USA
jessica.shui@fhfa.gov
Shriya Murthy
Federal Housing Finance Agency
Office of Policy Analysis & Research
400 7th Street SW
Washington, DC 20219, USA
shriya.murthy@fhfa.gov

FHFA Working Paper 17-03
3 J. Shui & S. Murthy — First-time Homebuyer Overpayment
1 Introduction
According to the 2016 Profile of Home Buyers and Sellers by the National Association of Realtors
(NAR), 35 percent of buyers are first-time homebuyers (FTHBs). In November 2016, the FTHB
share stood at 43.6 percent and 81.8 percent of Government-sponsored Enterprise (GSE) purchase
loans1 and Federal Housing Administration loans respectively (Urban Institute Monthly Chartbook
(February, 2017). Given the importance of FTHBs to the U.S. economy2 and the importance of
homeownership in wealth accumulation (Herbert, McCue, and Sanchez-Moyano, 2013) and
consumption (Case, Quigley, and Shiller, 2005), numerous efforts have been made to help FTHBs.
Such efforts include providing FTHBs with tax credits as additional incentives for homeownership
through legislation.3 They also include the creation of a variety of free financial coaching
programs4 to strengthen FTHBs’ skills in assessing their own abilities to make mortgage payments
as well as of programs that provide FTHBs with access to better mortgage terms.5
Though extensive research has been conducted on FTHB mortgage choices and
consequences related to these policy maneuvers (Heath and Soll, 1996; Tong, 2005; Cheema and
Soman, 2006; Van Zandt and Rohe, 2006, 2011; Baker, 2012; Collins, Loibl, Moulton, and Samak,
2013; Dynan, Gayer, and Plotkin, 2013; Harris, Steuerle, and Eng, 2013; Moulton, 2013;
Patrabansh, 2013, 2015), little has been done on FTHBs and their real estate transaction outcomes.
In particular, the lack of data has resulted in little empirical research.
The purpose of this paper is to extend the literature by investigating the sales prices paid
by FTHBs in the residential real estate market. Building upon the existing search model, we
provide a theoretical framework in which FTHBs pay rent each period in addition to the search
cost. This allows us to analyze their search behavior and outcomes. We assume that houses differ
only in quantity and price per unit, both drawn independently and identically from two separate
uniform distributions. We derive that for any given quantity, the reservation price for FTHBs is
strictly greater than the reservation price for repeat buyers. Therefore we propose that for any
given quantity, FTHBs pay a higher average sales price than repeat buyers pay.

1 First-time homebuyer purchase loans constitute only about 5 percent of GSE mortgage loans overall (Patrabansh,
2013).
2 It is particularly important that FTHBs make up a significant share of homebuyers. First-time homebuyers form new
households; along with the net gain in the number of houses occupied, a home purchase by a first-time buyer starting
from scratch results in more supplementary purchases, such as of appliances or furniture.
3 Such legislations include but are not limited to the Housing and Economic Recovery Act, the American Recovery
and Reinvestment Act, and the Worker, Homeownership, and Business Assistance Act.
4 The GSEs in particular offer both online education, as well as expanded access to credit to those unable to make a
substantial down payment (such as 97% loan-to-value options). This, along with the fact that they buy loans from
lenders of all sizes, is what makes them especially relevant to FTHBs.
5 Such programs include the Home Affordable Modification Program, the Home Purchase Assistance Program, and
the Home Affordable Refinance Program.
FHFA Working Paper 17-03
4 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Using a novel dataset—one that contains appraisal information (including sales
concessions) associated with loan applications submitted to the Enterprises from the fourth quarter
of 2012 to the first quarter of 2016—we find supporting evidence for our proposition. Specifically,
we find that once we control for observed and unobserved house heterogeneity, FTHBs pay
significantly more than their more experienced counterparts.6 In other words, they “overpay,”7 on
average by 1.04 percent, which is not an inconsequential amount particularly when the size and
the FTHB share of the residential purchase-money mortgage market are considered. We further
include sales concession information and confirm the robustness of this result.8
We then investigate whether this overpayment can be mitigated. Once a buyer has applied
for a loan, an appraiser is tasked by the lender with valuing the property to determine whether it is
worthy collateral. The lender will divide the loan amount by the lesser of the contract price and
the appraised value to determine the loan-to-value (LTV) ratio, which will be used to accurately
price the loan. Therefore, if the appraiser determines that the appraised value equals or exceeds
the contract price, the transaction will move forward. If the appraiser determines that the appraised
value is lower than the contract price, the buyer/borrower has two options: increase the down
payment or attempt to renegotiate the contract price with the seller. If neither option works out,
the borrower will have to face elevated interest rate and mortgage insurance costs as a result of
departing the targeted LTV range, and the deal will likely fall through; the buyer may get his or
her earnest money back depending on whether there is a proper appraisal contingency in the
contract. Thus diligent appraisers—those appraisers who cultivate high accuracy standards—may
be able to bring about lower transaction prices by identifying overpayment and thereby possibly
inducing renegotiation.
We take two steps to test the above theory. First, we examine whether certain types of
appraisals and appraisers are associated with a higher propensity for downward renegotiation.
Second, we examine whether downward renegotiation has a strong influence on FTHB
overpayment.
In order to conduct our study, we construct a variety of appraisal- and appraiser-level
quality or diligence measures.9 For example, at the appraisal level, we use public records data to

6 We also provide evidence that at first glance, FTHBs pay less than repeat buyers, and that this is driven by the sorting
of FTHBs into smaller houses.
7 Throughout the paper, we use the term “overpay” to refer to cases where FTHBs pay more for the same house
compared to repeat buyers. We use the term “overpayment” to refer to the amount by which they overpay.
8 In fact, we incorporate sales concession information throughout our analyses and confirm the robustness of all results.
9 There are multiple factors that could influence appraiser diligence. For example, these include the amount of effort
appraisers put forth, the amount of skill they possess, whether they view themselves more as validators who are tasked
with confirming contract price than as evaluators who must provide objective analyses of the market value of subject
properties, and (given that they perceive themselves as objective evaluators) how constrained they are by professional
ethics concerns. Our main goal in this paper is not to separate these contributing factors in our quality or diligence
FHFA Working Paper 17-03
5 J. Shui & S. Murthy — First-time Homebuyer Overpayment
check whether the appraiser failed to flag that the subject property had sold within the three years
preceding the appraisal date. If there was such a failure, we flag the appraisal as “failed_to_find.”
Similarly, we flag an appraisal as “any_wrong if it contains mistakes in at least one of three fields
(the number of bathrooms, the number of bedrooms, and the square footage), and as “exactlyif
the appraisal value matches the contract price. In addition, for each appraisal record we calculate
the percentage deviation of the appraisal valuation from the contract price and define it as gap_p.”
To the extent that gap_p is greater than zero, it reflects the percentage by which the valuation
exceeds the contract price—this percentage we refer to as the percentage of “overvaluation.” For
the cases in which the valuation does not exceed the contract price by more than six percent, we
assign a flag “ne_super_over.”
Intuitively, flags for mistakes (failed_to_find and any_wrong) are direct quality measures
and to some extent may reflect the effort or skill of the appraiser. Contract price confirmation
(exactly) to some extent reflects a combination of effort and attitude because the confirmation of
contract price takes less cognitive effort and, for cases in which the real value is lower than the
contract price, imposes a higher ethical cost—appraisers are incentivized to confirm the contract
price because it increases the chances of the deal going through. Thus, “better” appraisers would
confirm the contract price with a lower frequency than do other appraisers and appraisals with
higher quality would be less likely to be associated with contract price confirmation. This variation
in appraisal quality in some cases might mean the difference between a FTHB overpaying and not
overpaying for a home.
We then collapse the data to the appraiser level and calculate the averages of these quality
measures for each appraiser. We assign flags where the averages exceed certain thresholds (e.g.,
often_failed_to_find equals one if the average of failed_to_find is greater than 0.02—i.e., if the
appraiser failed to find prior sales in more than two percent of cases) and attach an appraiser’s
averages and flags to each of her appraisal records; altogether we construct often_ff,
often_anywrong, often_exact and appraiser_avg_gap. Thus, in our primary analysis dataset, each
appraisal record includes house characteristics and appraisal quality flags, as well as appraiser
quality averages and flags.
Finally, we flag cases associated with downward renegotiation. We employ both public
and appraisal records and track changes in the contract price as well as the deviation of the final
contract price from the final sales price. Despite significant sorting—houses with higher contract
prices are more likely to experience downward renegotiation—we find that appraisers prone to
making mistakes, confirming the contract price, and/or generally overvaluing the property
significantly reduce the probability of downward renegotiation and thus the probability of the
buyer getting a better deal. However, though appraisal-level flags confirm, as we expected, that

measures but rather focus on quality/diligence overall. We use the term “quality” and “diligence” interchangeably
throughout the paper, often using “quality” at an appraisal level and “diligence” at an appraiser level.
FHFA Working Paper 17-03
6 J. Shui & S. Murthy — First-time Homebuyer Overpayment
diligent appraisers are associated with greater chances of downward renegotiation, we found
confounding results on the indicators of mistakes—higher quality at the appraisal level overall in
fact decreases the chances of downward renegotiation, whereas at the appraiser level it increases
the chances of the same (but insignificantly). Thus, we find only suggestive evidence that
appraisers less prone to mistakes, confirmation, and/or overvaluation can help induce a higher
probability of downward renegotiation.
We then predict whether downward renegotiation will take place for each transaction based
on appraisal and appraiser characteristics, house attributes, and controls for time and cross-
sectional effects. We test whether a significant negative relationship exists between this predicted
probability of downward renegotiation and the log(sales price), controlling for cross-sectional
differences, time trends, local house price appreciation, etc. We find that the predicted probability
of downward renegotiation is significantly correlated with lesser overpayment and that this
correlation does not differentiate between first-time and repeat homebuyers.
One caveat in our research lies in the factors that drive downward renegotiation. It is
possible that downward renegotiation is driven by factors that we do not observe in our dataset—
for example, differences in the skills and strategies of the associated real estate agents.
Measurement of any appraiser “effects” may be confounding if agent behavior is correlated with
the types of appraisers employed—if, for instance, more conservative appraisers (i.e., those more
prone to flagging overpayment) tend to be paired with less experienced agents (e.g., agents less
inclined to advise renegotiation). Because of this and other issues, further research on the channel
through which appraisers and appraisals may mitigate FTHB overpayment is certainly warranted.
Additional caveats in our research lie in the definition of “first-time homebuyer” and in the
fact that we do not observe cash transactions in our dataset. Regarding the former, as Patrabansh
(2013) points out, the GSEs define a FTHB as an individual who had no ownership interest in a
residential property in the three years preceding the purchase date. The data we rely on employ
the GSEs’ definition, which is obviously not ideal; optimally, we would flag someone as a FTHB
if this person has never purchased a house before. This leads to overestimates of the real FTHB
share as well as of the level of experience of the average FTHB. Regarding the latter, experienced
buyers may be wealthier and therefore more likely to finance their purchase through cash, which
yields a discount compared to financing through a mortgage. Since we do not observe cash
transactions, our results underestimate how much FTHBs overpay compared to repeat buyers in
the general population. Thus, due to the reasons mentioned above, all our estimates might be
viewed as lower-bound estimates of the actual statistical relationships.
It is also worth pointing out that our paper does not speak to asymmetric information in credit
markets, i.e., FTHB overpayment in our context only accounts for transaction overpayment and
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7 J. Shui & S. Murthy — First-time Homebuyer Overpayment
not overpayment in interest. To the extent that FTHBs overpay in credit markets as well, the
overpayment we estimate is a lower bound of the overall FTHB overpayment.
The remainder of this paper is organized as follows. In Section 2, we briefly review the
literature. We propose and analyze the model in Section 3 and introduce a unique dataset in
Section 4. In Section 5, we test the theoretical proposition that FTHBs overpay and present
empirical evidence. In Section 6, we investigate possible overpayment mitigation. Finally,
Section 7 provides our conclusions.
2 Literature Review
There is rich theoretical and empirical literature on the seller’s search. However, on the buyer’s
side, there is little theoretical research and even less empirical research due to the lack of data on
buyer’s search duration, let alone empirical research focusing on FTHBs. Only a few studies focus
on FTHBs, and most of these concentrate on their mortgage outcomes and on the effectiveness of
programs that promote homeownership.
We begin this section by reviewing studies related to FTHBs, with topics such as mortgage
outcomes, neighborhood choices, and the traits that separate these buyers from repeat buyers. We
then follow up a brief discussion of the research on homeownership-promotion programs with an
overview of the few general buyer search models upon which we base our model. Finally, though
we use appraisal data to study a topic that differs from the traditional topics in appraisal literature
(these include valuation, information loss, and appraiser compensation), we highlight the main
takeaways from these topics.
2.1 First-Time Homebuyers
First-time homebuyers are often low- and middle-income (LMI) homebuyers. Thus much of the
literature on LMI homebuyers is relevant for our purposes. Prior studies suggest that LMI
homebuyers are more myopic and less skilled with long-term financial decisions in that they often
overestimate their own borrowing capacities and underestimate their own mortgage debt (Heath
and Soll, 1996; Cheema and Soman, 2006; Van Zandt and Rohe, 2006, 2011). Collin, Loibl,
Moulton, and Samak (2013) use data collected from a field experiment of financial planning
interventions specifically for LMI FTHBs and find that they are generally overconfident about
their finances, which leads to significantly less take-up of financial coaching. They are likely to
underestimate their non-mortgage debt and consequently take out large mortgages relative to their
income.
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Van Zandt and Rohe (2006) employ survey data from the Neighborhood Reinvestment
Corporation’s Homeownership Pilot Program (which aimed to help first-time LMI buyers) to
assess whether such buyers are able to access better quality neighborhoods. Their results indicate
that LMI buyers tend to purchase in neighborhoods similar to those in which they rented, whereas
continuing renters tend to upgrade to neighborhoods with better quality. In addition, they found
that the neighborhoods to which LMI buyers relocate tend to experience slower quality
improvement overtime than do other neighborhoods.
First-time homebuyers are different from repeat buyers in many aspects aside from their
inflated perceptions of their own borrowing capacities and their conservative neighborhood
choices. In addition to lower incomes, FTHBs on average have lower credit scores and higher
LTV and debt-to-income (DTI) ratios. They are younger than repeat homebuyers are. The
properties they purchase are usually less costly than the properties purchased by repeat buyers
(Patrabansh (2013)). Research has found these differences in borrower characteristics to be good
explanations for the differences in the default probabilities between first-time and repeat
homebuyers (Patrabansh (2015)).
The focus of this study is different from those of previous studies on FTHBs in that we
study the relationship between FTHBs and sales price.
2.2 Homeownership Promotion Programs
Despite the debate on the causal relationship between homeownership and household wealth gain
(e.g., Engelhardt, 1995; Herbert, McCue, and Sanchez-Moyano, 2013), homeownership is widely
believed to be an effective way to increase household wealth and consumption (Case, Quigley,
and Shiller, 2005). This belief has led to a number of policy programs aiming to foster
homeownership with monetary incentives such as tax credits or mortgage interest rate reductions.
Many researchers have assessed such programs (especially tax credit programs) and have
developed disparate views of their effectiveness.
Tong (2005) analyzes the District of Columbia First-Time Homebuyer Individual Income
Tax Credit program and concludes that the program is effective in increasing homeownership for
the targeted population and broadens the District’s tax base. However, Baker (2012) argues that
the FTHB credit in the 2009 national stimulus package (the American Recovery and Reinvestment
Act) was launched when the housing bubble had not fully deflated, thus incentivizing people to
buy too early and therefore pay too much. The study further argues that the credit only temporarily
delayed the adjustment process and was merely a redistribution of loss from existing homeowners
and mortgage borrowers to their new counterparts and to the government. In the middle ground,
Dynan, Gayer, and Plotkin (2013) examine nation- and state-level homebuyer tax credit programs.
Their results indicate that the American Recovery and Reinvestment Act and Worker,
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Homeownership, and Business Assistance Act homebuyer tax credit programs provided a modest
but partially reversible boost to home sales and home prices.
Some researchers propose alternative policies and argue that these policies are at least as
theoretically well-founded and transparent as the current policy. Harris, Steuerle, and Eng (2013)
analyze the economic effects of three proposed tax reforms: a FTHB tax credit, a refundable tax
credit for property taxes paid, and an annual flat tax credit for homeowners. They find that these
reforms would provide greater incentives for wealth accumulation than the current policy does
through mortgage interest rate reductions. Moulton (2013) suggests that such programs should be
designed and tailored at state level, as evidenced by the better performance of state Housing
Finance Agency loans.
2.3 Buyer Search Literature
Despite the relative scarcity of empirical buyer-side search literature, a consensus exists that
FTHBs are relatively inexperienced, and that in real estate transactions, inexperienced consumers
tend to have higher search costs and end up paying a premium and/or search for longer.
Consistent with the theoretical literature (Yinger, 1981; Wheaton, 1990; Yavas, 1992;
Munneke and Yavas, 2001; Rutherford, Springer, and Yavas, 2005; Genesove and Han, 2012),
Lambson, McQueen, and Slade (2004) find that out-of-state buyers tend to pay a premium for real
estate compared to their in-state counterparts and that this premium is possibly driven by haste,
high search costs, and/or an anchoring effect. Lacking a better source, researchers generally use
survey data to study buyer search duration. Employing survey data described in Anglin (1994),
Anglin (1997) estimates buyer search duration in terms of time and number of houses and
concludes that though the results generally support the existence of a buyer trade-off between time
and sales price, many important variables are needed to refine the buyer search model and to
produce a better estimate. Baryla and Zumpano (1995) use a cross-section subsample from the
1987 National Association of Realtors (NAR) National Homebuyer Survey to examine buyer
search durations with and without brokers’ assistance. They find that on average, broker-assisted
searches takes less time than self-directed search for all types of buyers—first-time, repeat, or out-
of-town. On average, first-time and out-of-town buyers search longer than repeat and local buyers.
Baryla, Zumpano and Elder (2000) rely on NAR 1988, 1991, and 1993 survey data and find that
broker-assisted searches have a higher probability of resulting in a home being found compared to
self-conducted searches.
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2.4 Research on Appraisals and Appraisers
Because we employ GSE appraisal data as well as appraisal and appraiser attributes, it is
worthwhile to highlight briefly which topics have been studied in the area of residential real estate
appraisals and the main findings of these studies.
The use of appraisals in the residential lending process raises many concerns. One concern
is that the current institutional incentives (including inadequate appraisal regulation) feed biased
and self-serving appraisals (Lentz and Wang, 1998; Murray, 2010). Murray (2010) calls attention
to the practice of inflating appraisals, a key factor in the last two financial crises, and the reason
behind it: self-interested parties tend to use the insecurity of future business to pressure appraisers.
In addition, Diaz III (1989) studies the behavior of expert appraisers in particular, showing
that they deviate significantly from the prescribed appraisal processes, and that clients pressure
appraisers to validate the contract price rather than provide an objective opinion of the property’s
market value (Appraisal Institute, 1997; Smolen and Hambleton, 1997; Wolverton and Gallimore,
1999). Wolverton and Gallimore (1999) suggest that client feedback can significantly affect
appraisers’ perceptions of their own role in the loan underwriting process. They show that coercive
feedback reinforces appraisers’ perceptions of themselves as price validators, whereas reiteration
of “normative performance criterion” (appraisers’ normative goal of estimating market value
highlighted in formal training) reinforces appraisers’ perceptions of themselves as independent
evaluators. Baum et al. (2002) use qualitative interview survey evidence of leading U.K. property
managers and owners and their appraisers to show that a significant number of appraisals are
unable to reflect some price-sensitive information due to the lack of such information, the lack of
appraiser effort in searching for such information, and/or institutional stress that prevents
appraisers from searching. Their results show that appraisals are smooth and lag the true levels of
price.
Two recent papers expressed concerns about appraisal information loss and property
overvaluation. Calem, Lambie-Hanson, and Nakamura (2015) present evidence that appraisals
are subject to information loss and that such loss is more common at LTV notches and is associated
with higher mortgage default risk. They argue that appraisals sometimes are less informative than
automated valuation models and this leads to a lower likelihood of renegotiation and therefore to
buyers paying more than they need to pay. Fout and Yao (2016) employ Fannie Mae appraisal
data from September 2011 to August 2012 in order to show that a low appraisal dramatically
increases the probability of buyer renegotiation and only slightly increases the probability of the
contract being delayed or cancelled. They also show that low appraisals are associated with a lack
of available comparable properties, forcing the appraisers involved to rely on properties with
dissimilar characteristics and on distressed sales. They estimate that low appraisals on average
decreased home prices by 0.2 percent and transaction volume by 0.3 percent.
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Aside from doubting the objectivity of appraisals and questioning the underlying
institutional settings, researchers are dissatisfied with the current situation in which the comparable
sales approach remains central to the practice of appraising residential real estate (Jenkins et al.,
1999), when in fact many different valuation methods can be used (Pagourtzi, Assimakopoulos,
Hatzichristos, and French, 2003; Lins, Novaes, and Legey, 2005).
3 Baseline Model
We develop a standard discrete-time buyer-side search model, built upon the classic search-
theoretic models from the labor literature (Rogerson, Shimer, and Wright (2005) provide a detailed
review) and the real estate search literature (Yinger, 1981; Wheaton, 1990; Yavas, 1992; Munneke
and Yavas, 2001; Rutherford, Springer, and Yavas, 2005; Genesove and Han, 2012; Albrecht,
Gautier, and Vroman, 2016).
To keep the analysis simple, we assume that houses only differ in quantity and price per
unit, and that there are only two types of risk-neutral buyers,10 first-time and repeat. At the
beginning of each period, the buyer pays a fixed search cost 0 to visit a house with a price
per unit drawn independently and identically from distribution  and a quantity drawn
independently and identically from distribution. For the sake of simplicity, we assume
uniform distributions for both , and ,, respectively. The buyer decides whether she wants
to buy this house or continue to search. In the event that the buyer continues to search in the next
period, she will pay rent 0 in addition to the search cost if she is a FTHB; if she is a repeat
buyer, she continues to live in her home and does not pay any additional cost (0. This
assumption simplifies the model without changing the qualitative results.11
The buyer’s maximization problem can be represented with the following equations:
– (1)
and

∗,. (2)
where is the utility to the buyer if she buys the house at price ,
 is the discount
factor,  is concave and increasing in , and is the utility to the buyer if she decides to
search. The problem can also be rewritten as
, (3)

10 Note that the results would continue to hold for risk-averse buyers.
11 In reality, repeat buyers do pay maintenance fees and property taxes for their houses. Our results hold as long as
the rents for the FTHBs are higher than the fees and taxes for the repeat buyers.
FHFA Working Paper 17-03
12 J. Shui & S. Murthy — First-time Homebuyer Overpayment
and

∗,,. (4)
where  is the cumulative distribution function of based on and . There exists a
unique such that the buyer purchases the house if ,, and does not purchase the
house if ,. Equivalently, for any given, there exists a unique 
such
that the buyer purchases the house if , and does not purchase the house if .
The intuition is as follows. If houses are homogenous in and the buyer observes the
lowest possible price per unit (i.e., ) in the current period, the expected cost of continued search
is strictly larger than the expected gain even if the lowest possible price per unit will be drawn
again in the next period. Therefore the buyer should purchase immediately. Similarly, if the buyer
observes the highest possible price per unit (i.e., ) in the current period, the expected cost of
continued search is strictly smaller than the expected gain in the next period, given that is drawn
randomly and if  is low enough.
Lemma 1: If searching is more costly for FTHBs than it is for repeat buyers (i.e., 0),
for any given , the reservation price per unit for FTHBs is strictly greater than the reservation
price per unit for repeat buyers.
The Lemma implies the following proposition.
Proposition 1: For any given , the average sales price, 
, is higher for
FTHBs than it is for repeat buyers.
Proposition 1 implies that for a given property, a FTHB pays more than a repeat buyer
pays.
4 Data
The data used to study the relationship between FTHBs and transaction prices come from the
Uniform Appraisal Dataset, gathered by the Enterprises through the Uniform Collateral Data
Portal. The dataset consists of active appraisal records associated with loan applications submitted
to Fannie Mae from the last quarter of 2012 to the first quarter of 2016 and to Freddie Mac from
the second quarter of 2012 to the second quarter of 2016. For subject properties, the dataset
contains flags for short sales and foreclosures in addition to detailed information on the contract
FHFA Working Paper 17-03
13 J. Shui & S. Murthy — First-time Homebuyer Overpayment
(including on any sales concessions), the appraiser certification, and the neighborhood. For both
subject and comparable properties,12 it includes a wide range of house characteristics.
Though the focus of our analysis is on appraisals associated with mortgages used to buy
properties (known as purchase-money mortgages), at an early stage we employ Uniform Appraisal
Dataset records associated with both purchase-money and refinance mortgages to calculate
appraisal and appraiser characteristics. At a later stage, we exclude from the sample comparable
sales records as well as appraisal records associated with refinance mortgages.
In the following subsections, we briefly discuss our strategy for identifying purchase-
money mortgage-based appraisals, the approaches used to calculate appraisal and appraiser
characteristics, and the summary statistics.
4.1 Appraisal Process and Mortgage Outcome Data
We identify an appraisal record as pertaining to a purchase-money mortgage if its contract price is
not missing. This identification strategy is well-founded—the common practice in purchase-
money mortgage-based appraisals is for appraisers to receive the sales contract and document the
contract price,13 whereas this is not the case in refinance-based appraisals.
Employing a separate dataset of loan-level data obtained from the Enterprises, we attach
to each appraisal record loan outcomes information as well as various loan attributes, such as
FTHB status, the LTV ratio, and the borrower credit score. We also attach to each record Federal
Housing Finance Agency monthly ZIP Code-level House Price Indices (HPI), merging by
appraisal date and ZIP Code.

12 Comparable properties are chosen and documented by appraisers in the Sales Comparison Approach section of the
Uniform Residential Appraisal Report. In the Uniform Appraisal Dataset, for each comparable sale a record
containing its documentation is linked to its corresponding subject property record. In our sample there are on average
5.16 comparable sales for every subject record. Unless we specifically refer to comparable sales, we use the term
“appraisal record” to refer to the subject property record.
13 There is an ongoing debate on the prudence of the common practice in the appraisal industry for appraisers to receive
the property sales contract prior to appraisal. The main argument for this practice, supported by the Uniform
Residential Appraisal Report guidelines, is that the contract price and the sales concession associated with it reflect
the buyer’s willingness to pay and thus the property’s market price, conceivably important information for an appraiser
to take into account when conducting analysis. The main argument against providing the contract price to appraisers
is that knowledge of the contract price might bias the appraiser’s judgment and consequently the appraisal value of
the property.
FHFA Working Paper 17-03
14 J. Shui & S. Murthy — First-time Homebuyer Overpayment
4.2 Creating Appraisal and Appraiser “Quality” Flags
After restricting the sample to purchase money mortgage appraisals,14 we create multiple appraisal
quality flags. We briefly discuss the approaches used to create the flags in this subsection.
In the Uniform Residential Appraisal Report, appraisers are required to document property
attributes for subject and comparable properties, as well as appraisal approaches adopted. Our
mistake indicator, any_wrong, reflects whether the appraisal contains a mistake in property
features. We construct this indicator by tracking property attributes as documented for the same
property by various appraisals (including appraisals where the property is in the role of comparable
sale) over time and identifying typos and mistakes particularly in the fields of number of
bathrooms, number of bedrooms, and square footage. We set any_wrong to one if the appraisal
contains a mistake in any of these three fields.15
Appraisers are also required to answer specific questions about their research in the
appraisal report. Two such questions ask: 1) whether the appraiser has thoroughly researched the
history of the subject property and 2) whether she has found for the subject property any
transactions information pertaining to the three years prior to the appraisal. To determine whether
the appraisal contains a mistake in property history, we conduct an independent research of sales
history; our findings are reflected in the second mistake indicator, failed_to_find. For each
appraisal record, we attach the sales date (from public records) of the most recent previous
transaction of the same property. If this sales date lies within the three years preceding the
appraisal date, we flag the appraisal record. We then set failed_to_find to one for all appraisal
records that are flagged in this way and also possess a flag indicating that the appraiser did not
find any transactions information pertaining to the previous three years.
We create another two variables as additional appraisal quality measures: exactly_flag and
ne_super_over. These measures are used to analyze the appraised value in comparison with the
contract price. Specifically, they are functions of the percentage difference between the appraised
value and the contract price. If the percentage difference, gap_p,is zero (i.e., the appraised
value is equal to the contract price), then the exactly_flag variable is set equal to one. Otherwise,

14 We also exclude appraisals associated with short sales or purchases of foreclosed properties.
15 We compare the value for a given field to the values for that field in the appraisals associated with the directly
preceding and subsequent transactions of the subject property. For example, if the reported number of bathrooms for
a subject property is one, but preceding and subsequent appraisals indicated that the number exceeded one, we flag
the appraisal as having a mistake in the number of bathrooms. An older version of this paper used a less conservative
method to determine if a given field contains a mistake; the change does not materially affect our results.
FHFA Working Paper 17-03
15 J. Shui & S. Murthy — First-time Homebuyer Overpayment
it is equal to zero. The ne_super_over variable is an indicator that is set equal to one if the
appraised value is less than six percent or more above the contract price.16
To establish a crude measurement that might be indicative of appraiser “quality,” we then
collapse these data to the appraiser level. In particular, we construct appraiser_avg_gap, often_ff,
often_exact, and often_anywrong. We define an appraiser often_ff (“often fails to find”) if she
failed to find one or more prior sales within the three years preceding the appraisal date in more
than 2 percent of her average number of appraisals per year, often_exact (“often exact”) if she
confirmed the contract price for more 20 percent of these, and often_anywrong (“often has any
wrong”) if, in 2 percent or more of her average annual appraisals, she made a mistake in one or
more of the following property attributes: square footage, the number of bathrooms, and the
number of bedrooms. For each appraiser, we attach this set of quality indicators to each of her
appraisals.
4.3 Summary Statistics
Finally, we refine our sample of purchase-money mortgage-related appraisals by excluding records
with certain data anomalies and use this refined sample in conjunction with a set of historical
transaction records to construct the repeated sales transaction sample.17 We then restrict the
sample to observations with non-missing FTHB flags.18 We define this as the “full sample.” We
define a “main sample” that consists of the “full sample” restricted to records associated with
appraisers whose average number of appraisals per year exceeds 20. Because our sample only
includes Enterprise appraisals, the restriction puts a minimum on the number of Enterprise-
submitted appraisals per year. While the full sample includes part-time and full-time appraisers,
the main sample contains only appraisals done by full-time appraisers. We focus on full-time
appraisers so that we have a sufficient number of observations for a given appraiser to derive a
reliable measure of the work quality.
Exhibits 1.1 1.3 present the summary statistics for the main sample. Among all the
appraisals in the main sample, 41.19 percent are associated with FTHBs and 5.72 percent are linked
to downward renegotiation. There are 1.35 percent with a positive failed_to_find flag, indicating
that the appraiser failed to find one or more prior sales that took place within the three years

16 These quality measures even together may not comprehensively assess the quality of appraisals or appraisers—they
are not necessarily indicative of bad appraisals or appraisers. However, we believe they are at least suggestive of
quality failures.
17 We identify houses that have been sold at least twice and calculate their demeaned sales price by subtracting time
trends and time-invariant house attributes.
18 We employ county recorder data to find the relevant sales prices for appraisal records. In total, 63 percent of the
purchase-money mortgage appraisals in our sample result in a regular sale. The absence of a sales price does not
necessarily indicate that the appraisal did not result in a sale. To the extent that the data we employ are not
comprehensive (i.e., do not include every relevant transaction), the unmatched 37 percent is an overestimate of
appraisals that did not result in a sale.
FHFA Working Paper 17-03
16 J. Shui & S. Murthy — First-time Homebuyer Overpayment
preceding the appraisal date. About 1.66 percent have a positive any_wrong flag, indicating that
the appraiser submitted incorrect information on square footage or the number of bathrooms or
bedrooms. About 29 percent have a positive exactly_flag, indicating that the appraisal value
exactly equals the contract price and 98.7 percent have a valuation “not super over” the contract
price (i.e., no more than 6 percent above the contract price). Among all appraisal records, 37.67
percent are associated with positive sales concessions—as negative concessions are rare to the
extent of being negligible, appearing to be the result of errors in entry, the remaining records are
not associated with sales concessions. About 45 percent of the FTHBs in our sample are associated
with positive sales concessions, with an average of $5,020, compared to 32.65 percent of repeat
buyers with an average of $4,853. Exhibit 1.2 shows the summary statistics of house attributes,
transaction price, and borrower characteristics. The main sample comprises 1,743,309 appraisals.
The average appraised property in the sample is contracted for $275,187, appraised for $279,829,
and sold for $275,021. It is about 16 years old and has around 1,813 square feet, three bedrooms,
and two bathrooms. The typical borrower in the sample has a credit score of 749; the average
(original) LTV is 83 percent.
Next, we collapse the data to the appraiser level and present summary statistics across all
appraisers in Exhibit 1.3. The typical appraiser completes about 99 appraisals each year (taking
the full years of our sample, 2013 2015) and has completed in total 413 appraisals over all years
of the sample. She employs on average 5.2 comparable sales for each appraisal and tends to
appraise at 2.50 percent higher than the contract price. For every 100 appraised properties, she
appraises 11 properties at exactly their contract prices, fails to find prior sales information for one
of them, and for 25 submits incorrect information on at least one field among the number of
bathrooms, the number of bedrooms, and the square footage.
FHFA Working Paper 17-03
17 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Exhibit 1.1: Distribution of Loan-, Appraisal-, and Appraiser-Related Characteristics, Main Sample
Fthb Often_ff
First-time homebuyer (%) 41.19 Appraiser often fails to find (%) 17.80
Repeat buyer (%) 58.81 Appraiser does not often fail to find (%) 82.20
N 1,743,309 N 1,743,309
Failed_to_find Often_anywrong
Failed to find prior sale(s) (%) 1.35 Appraiser prone to mistakes (%) 14.71
Did not fail to find prior sale(s) (%) 98.65 Appraiser not prone to mistakes (%) 85.29
N 1,743,309 N 1,743,309
Often_exact
Any_wrong
Appraiser often confirms CP (%) 18.2
Mistakes in # of baths, bdrms, or sqft (%) 1.66 Appraiser does not often confirm CP (%) 81.8
No mistakes in any above category (%) 98.34 N 1,743,309
N 1,743,309
Appraiser_avg_gap (= avg((Val - CP)/CP))
Exactly_flag Quartile 1 (least overvaluation) (%) 25.10
Valuation at contract price (%) 28.97 Quartile 2 (%) 25.06
Valuation not at contract price (%) 71.03 Quartile 3 (%) 24.99
N 1,743,309 Quartile 4 (most overvaluation) (%) 24.85
Ne_super_over
N 1,743,309
Valuation Not > 6% above CP (%) 98.70 Concession
Valuation > 6% above CP (%) 1.30 Sales concession (%) 37.67
N 1,743,309 No sales concession (%) 62.33
N 1,743,309
Reneg_down Sales concession among FTHB (%) 44.84
Downward renegotiation (%) 5.72 Absence of sales concession among FTHB (%) 55.16
No downward renegotiation (%) 94.28 N 718,115
N 1,743,309 Sales concession among repeat buyers (%) 32.65
Absence of sales concession among repeat buyers (%) 67.35
N 1,025,194
Notes: Exhibit 1.1 reports the total counts and distributions of loan, appraiser-, and appraisal-related characteristics/quality
measures. Each observation corresponds to a single appraisal record in the main sample (which is restricted to appraisals
associated with appraisers who have performed at least 20 appraisals per year on average), or, in the case of sales concession,
in first-time and repeat buyer subsets of the main sample. Each characteristic is listed as a bolded categorical variable followed
by its values. For dummy variables, the positive cases are always listed first. “Val” represents appraisal value, “CP” stands
for contract price, and “FTHB” stands for first-time homebuyer.
FHFA Working Paper 17-03
18 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Exhibit 1.2: House Attributes, Prices, and Borrower Characteristics, Main Sample
Variables N Mean SD Min Max
Sales Price 1,743,309 275,021 158,506 13,800 999,999
Log(Sales Price) 1,743,309 12.4 0.565 9.53 13.8
Contract Price 1,743,309 275,187 158,641 50,000 1,150,000
Square Footage 1,743,309 1,813 680 500 9,811
Number of Bathrooms 1,743,309 1.88 0.64 0.1 6.3
Number of Bedrooms 1,743,309 3.177 0.750 1 10
Valuation 1,743,309 279,829 159,658 30,000 1,550,000
Age of the House 1,743,309 15.8 9.841 0 180
Credit Score 1,742,309 749 43.8 465 839
LTV 1,743,309 0.829 0.13 0 1.23
Non-zero Sales Concession 656,750 4,935 8,023 100 600,000
Non-zero Sales Concession for FTHBs 321,986 5,020 8,531 100 500,000
Non-zero Sales Concession for Repeat Buyers 334,764 4,853 7,501 100 600,000
Notes: Exhibit 1.2 reports the summary statistics of house attributes, borrower characteristics, and transaction outcomes.
Each observation corresponds to a single appraisal record in the main sample. “Valuation” indicates the appraisal value
derived using the comparable sales approach. Stats for all sales concession variables are constructed based on positive
sales concession amounts.
Exhibit 1.3: Appraiser Characteristics, Collapsed from the Main Sample
Variable Description N Mean SD Min Max
Avg_comps_id Average number of comparables employed 37,716 5.16 0.999 2.46 11.022
Avg_failed_to_f Average propensity for failing to find a prior sale of the property 37,716 0.011 0.015 0 0.242
Avg_exactly Average propensity for valuing property exactly at contract price 37,716 0.112 0.081 0 0.686
Avg_anywrong Average propensity for incorrectly documenting number of
bathrooms, bedrooms, or square footage
37,716 0.013 0.014 0 0.342
Avg_ne_super_over Average propensity for valuing property at less than 6% above
contract price
37,716 0.990 0.016 0.692 1
Avg_ann_apps Average number of appraisals performed per year, over the full
years 2013 – 2015
37,716 99.4 79.9 20 603
Often_ff Equal to 1 when average of appraiser's failed_to_find flags > 0.02 37,716 0.187 0.390 0 1
Often_exact Equal to 1 when average of appraiser's exactly_flag flags > 0.20 37,716 0.137 0.344 0 1
Often_anywrong Equal to 1 when average of appraiser's any_wrong flags > 0.02 37,716 0.180 0.384 0 1
Appraiser_avg_gap Average percentage gap between valuation of property and its
contract price [(Val - CP)/CP]
37,716 0.025 0.022 -0.250 0.437
Tot_appraisals Total number of appraisals performed in sample overall 37,716 413 349 20 3,273
Notes: Exhibit 1.3 reports the summary statistics of appraiser characteristics for appraisers who have performed at least
20 appraisals per year on average. Each observation corresponds to a single appraiser in the dataset that is collapsed
from the main sample to the appraiser level.

FHFA Working Paper 17-03
19 J. Shui & S. Murthy — First-time Homebuyer Overpayment
5 Empirical Analysis
In this section, we test the theoretical proposition derived from the model that FTHBs pay more
than repeat buyers for a given house. We first show that FTHBs, compared to repeat buyers, sort
into smaller houses. After controlling for sorting, we find strong evidence that FTHBs pay more
than repeat buyers. We use the main sample to derive benchmark results and we additionally
incorporate sales concession information in our analysis to confirm that our results are robust to
concessions.19
5.1 FTHB Sorting
We begin with a straightforward hedonic house price regression with a FTHB indicator variable.
The regression takes the following form:
 ∗
 (5)
where  is the log(sales price) of property in ZIP Code and year-quarter ;
 is the parameter of interest;  is the dummy variable indicating whether
house
in ZIP Code  was sold to a FTHB at time ;  is a set of basic house characteristics (the square
footage, the age of the house, and the number of bedrooms and bathrooms) attributed to property
; is a vector of coefficients corresponding to each house characteristic;  are ZIP Code-
year-quarter interacted fixed effects;  are the error terms; and is the constant term.

19 Because our results are indeed robust, we report only benchmark results in this paper.
FHFA Working Paper 17-03
20 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Exhibit 2: Housing Characteristics by Type of Homebuyer
(2.1) Average Number of Bathrooms
(2.2) Average Number of Bedrooms
11.5 22.5 3
Average Number of Bathrooms
Repeat Buyers First-time Homebuyers
2345
Average Number of Bedrooms
Repeat Buyers First-time Homebuyers
FHFA Working Paper 17-03
21 J. Shui & S. Murthy — First-time Homebuyer Overpayment
(2.3) Average Square Footage
Notes: Exhibits 2.1 2.3 plot average house characteristics for repeat and FTHBs. The lines show one standard
deviation from the average. As shown by the figures, FTHBs on average “consume” less of each of the house
characteristics.
Column 1 in Exhibit 3 shows that there is a significant negative correlation between FTHB
and log(sales price) that is driven by FTHBs sorting into smaller houses with fewer bedrooms and
bathrooms (Exhibits 2.1 2.3). To take sorting into account, we control for observed house
attributes and ZIP Code-year-quarter interacted fixed effects in Exhibit 3, columns 2 and 3. The
magnitude of sorting decreases but the effect persists. Thus, we find strong evidence that
compared to repeat buyers, FTHBs purchase smaller houses with fewer bedrooms and bathrooms.20

20 Consistent with our model, we rank all houses from better to worse based on the single dimension of size.
1000 1500 2000 2500 3000
Average Square Footage
Repeat Buyers First-time Homebuyers
FHFA Working Paper 17-03
22 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Exhibit 3: First-time Homebuyers and Sorting
Dependent Variable: Log(Sales Price)
(1) (2) (3)
Fthb -0.150*** -0.154*** -0.0538***
(0.000868) (0.00128) (0.000717)
Constant 12.42*** 12.43*** 12.13***
(0.000553) (0.000529) (0.00153)
Controls:
House Attributes X
Zip-Year-Quarter FE X X
Observations 1,743,309 1,743,309 1,743,309
R-squared 0.017 0.619 0.801
Adjusted R-squared 0.017 0.613 0.797
Notes: This table reports OLS regression results. Each observation corresponds to a single
appraisal record in the main sample. Column 2 controls for zip-year-quarter interacted fixed
effects. Column 3 additionally controls for house attributes (the number of bathrooms, the
number of bedrooms, the square footage, and the age of the house). A robustness check using
the sales price net of sales concessions can be found in Appendix Exhibit 1. Significance levels
at the 1%, 5%, and 10% are denoted respectively by ***, **, and *.
5.2 FTHB Overpayment
As the effect is conceivably due to sorting on unobserved time-invariant house characteristics, we
must control for house fixed effects. The regression takes the following form:
 ∗
   (6)
As our sample is quite large, for computational efficiency we take the within form
transformation (i.e., demean both house FEs and year-quarter FEs). Specifically, define the unit-
specific average for unit as


 , 

 , 

 ,


 ,

 , 

 , and ̅

 .
Then define the deviation from the unit-specific mean as

 
,

,

 
, 
 
, 
, 
 
, and ̅.
The within estimator after demeaning house FEs is based on the following regression:
FHFA Working Paper 17-03
23 J. Shui & S. Murthy — First-time Homebuyer Overpayment

 


(7)
Both the unit term  and the constant term disappear because 
 
0 and
̅0.
Similarly, define the time-specific average for year-quarter as


 , 

 , 

 ,
 , 


where is the number of units/properties transacted in year-quarter . Then define the
deviation from the year-quarter-specific mean as



,


,



,

, and 


,
The within estimator, after demeaning in both unit and time dimensions, is based on the
following regression:

 


(8)
The year-quarter term disappears because

0. In other words, 
is
the demeaned log(sales price),21 of property in ZIP Code and year-quarter , estimated using
property 's multiple transaction records. It reflects the deviation of  from what would
be expected given prior and subsequent sales of the same property and given the average house
price appreciation in year-quarter .
After taking the within form transformation, we estimate (8), equivalent to estimating (6),
and report our regression results in Exhibit 4.

21 In the previous version of this paper, we referred to this as the residual log(sales price), since it is what is left after
demeaning the logarithm of sales price.
FHFA Working Paper 17-03
24 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Exhibit 4: Relationship Between First-time Homebuyers and House Price Residuals
Dependent Variable: Log(Sales Price) Dep. Variable:
Log(Net Sales Price)
(1) (2) (3) (4) (5) (6)
Main
Sample
Main
Sample
Main
Sample
Main
Sample
Avg. Annual
Appraisals
≥ 30
Main
Sample
Fthb 0.00229*** 0.0258*** 0.00960*** 0.0104*** 0.0106*** Fthb 0.00870***
(0.000456) (0.000439) (0.000466) (0.000462) (0.000470) (0.000461)
Log(Contract Price) 0.157*** 0.107*** 0.110*** 0.110*** Log(Net Contract Price) 0.115***
(0.000382) (0.00134) (0.00135) (0.00136) (0.00134)
Constant 0.0685*** -1.879*** -1.264*** -1.233*** -1.235*** Constant -1.296***
(0.000293) (0.00476) (0.0166) (0.0171) (0.0172) (0.0169)
Controls:
ZIP-Year-Quarter FE
X X X X
ZIP-Monthly HPI X X X
Observations 1,743,309 1,743,309 1,743,309 1,743,309 1,693,612 1,743,308
R-squared 0.000 0.088 0.219 0.219 0.220 0.223
Adjusted R-squared 0.000 0.088 0.206 0.206 0.206 0.209
Notes: Columns 1 5 of this table report the OLS regression results from regressing Log(Sales Price) on Fthb after manually demeaning
both house and year-quarter fixed effects. Columns 2 5 use Log(Contract Price) to account for additional unobserved house characteristics
associated with upgrades and renovations, and Columns 3 5 additionally control for ZIP-year-quarter interacted fixed effects. Columns
4 5 further control for monthly house price appreciation at the ZIP Code level. Column 6 resembles Column 4 but, in order to incorporate
any sales concessions, we employ Log(Net Sales Price) instead of Log(Sales Price) and Log(Net Contract Price) instead of Log(Contract
Price). We define Net Sales (Contract) Price as Sales (Contract) Price less the concession amount. Columns 1 4 and 6 employ the main
sample, whereas the sample employed in Column 5 is further restricted to appraisals associated with appraisers who have performed at least
30 appraisals per year on average. Each observation in this table corresponds to a single appraisal record. Significance levels at the 1%,
5%, and 10% are denoted respectively by ***, **, and *.
FHFA Working Paper 17-03
25 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Column 1 in Exhibit 4 shows that there is a significant positive effect of FTHB on the
log(sales price), suggesting that a typical first-time homebuyer pays significantly more than a
repeat homebuyer does for the same house. In Column 2, we include log(contract price) to control
for two factors that might conceivably weaken the observed overpayment effect: potential
renovations and upgrades that could drive additional sorting of FTHBs into smaller houses22 and
the tendency of larger and potentially better houses to appreciate at a different rate than others.
Though general time trends are already subtracted in the process of deriving demeaned sales
prices, it is necessary to control for the cross-sectional heterogeneity in house price appreciation
that is largely driven by local economic factors orthogonal to FTHB. Thus we control for ZIP
Code-year-quarter interacted fixed effects in Column 3 and further account for monthly house
price appreciation at ZIP code level in Columns 4-6. The effect of FTHBs overpaying compared
to repeat buyers remains significant as controls are added (Columns 2 4), regardless of the sa mple
employed (Column 5). Specifically, a typical FTHB pays on average 1.04 percent more than a
repeat homebuyer does for the same house (Column 4). Given that the average sales price in the
main sample is $275,021, this translates to about $2,860 per transaction.
However, this might be an overestimation. If FTHBs on average receive more help (e.g.,
on closing costs) from sellers than repeat buyers receive, and if such help is documented in the
sales concession rather than in the sales price, then the magnitude of overpayment should be
smaller once we take into consideration the sales concession amount. Indeed, in our sample, we
observe that FTHBs are more likely to obtain help in sales concessions than are repeat buyers (45
percent versus 33 percent) and that among those who do obtain a concession, FTHBs on average
obtain a larger concession compared to repeat buyers ($5,020 versus $4,853). Thus, we define the
net sales (contract) price as sales (contract) price less the concession amount. In Column 6, we
regress the log(net sales price) on a similar set of variables and employ similar controls as in
Column 4 in order to check the robustness of our results. Our results remain robust with a small
decrease in the magnitude of the coefficient from 0.0104 to 0.0087, suggesting that FTHBs would
overpay by about $2,393 rather than by about $2,860 once we include concession amount.
As an additional robustness check, we further separate our sample by borrower LTV
thresholds and find consistent results that FTHBs overpay in each threshold. We find that a FTHB
with a higher LTV tends to overpay by more compared to one with a lower LTV.23

22 This is a valid concern given that there is a significant positive correlation between demeaned log(sales price) and
log(sales price). If a house was renovated in the early 2000s and therefore was sold at a premium during our sample
period, the constant quality assumption will be violated and there will be a positive correlation between the demeaned
log(sales price) and log(sales price). One plausible control variable for unobserved changes in house quality due to
renovation is the contract price, because the contract price is likely to reflect the overall quality of the house. We also
substitute log(contract price) for log(sales price) and the result is robust.
23 For detailed results, please refer to Appendix Exhibit 2.
FHFA Working Paper 17-03
26 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Overall, we find strong supporting evidence for our proposition that controlling for
observed and unobserved house characteristics, FTHBs pay significantly more for a house than
repeat buyers.
6 Mitigation of Overpayment
In the previous section, we found strong evidence that FTHBs overpay for houses compared to
repeat buyers. Now we consider whether certain types of appraisals and appraisers can help
mitigate that overpayment. We suspect that they may be able to do so if they have the ability to
induce downward renegotiation. For example, a “better” appraiser is more likely to submit an
unbiased value of the property, which (compared to a biased value) is more likely to be lower than
the contract price. If it is indeed lower, the borrower would need to either make a larger down
payment in order to approach her targeted LTV (which is the loan amount over the lower of
contract price and appraisal value) or renegotiate the contract price to lower the borrowing amount.
Hence, a chance for the price to be renegotiated downward.24
In order to verify our theory that certain types of appraisers can help mitigate overpayment,
we first test (a) whether certain types of appraisals and appraisers are associated with a higher
propensity for downward renegotiation, and then (b) whether downward renegotiation has a strong
influence on FTHB overpayment.
We identify downward renegotiations by tracking, for a given appraisal record, downward
changes in the contract price and/or a negative deviation of the final transaction price from the
contract price within a three-month period. Overall, 5.72 percent of our sample is associated with
downward renegotiation, a finding consistent with the existing literature (Fout and Yao, 2016;25
Calem, Lambie-Hanson, and Nakamura, 2016).26
Once we identify downward renegotiation, we test part (a) using the following
specification:  
  μ  (8)
where  is the dummy variable indicating whether
house transacted at time had been
renegotiated downward; is a set of basic house characteristics (the square footage, the age of

24 Similar logic follows for high-quality appraisals.
25 In Fout and Yao (2016), the authors find that 7 percent of the potential sales that eventually transacted were
associated with downward renegotiation.
26 Calem, Lambie-Hanson, and Nakamura (2016) find that 57 percent of the transactions associated with negative
appraisals in their dataset result in downward renegotiation, whereas only 2 percent associated with non-negative
appraisals are renegotiated for any reason.
FHFA Working Paper 17-03
27 J. Shui & S. Murthy — First-time Homebuyer Overpayment
the house, and the number of bedrooms and bathrooms) attributed to property in ZIP Code and
year-quarter ;  is the log(contract price) of property ; includes a series of appraisal- and/or
appraiser-level characteristics indicating the degree of effort, the level of attention to details, and
the level of diligence associated with each appraiser or pertaining to each appraisal;  includes
controls for local house price appreciation (monthly HPI at the ZIP Code level), and time
and cross-sectional effects (year-quarter and state fixed effects); μare the error terms; and
is the intercept.
Exhibit 5 presents the results. Column 1 shows that the more expensive a house is, the
higher the possibility of a downward price adjustment through renegotiation. In Columns 2 – 4,
we include appraisal and appraiser attributes. Column 2 tests the impact of appraisal-level
attributes on the presence of downward renegotiation, and indicates that a downward renegotiation
is more likely to happen if the property is not super-overvalued in the appraisal and if the appraiser
does not simply confirm the contract price. Mistakes captured by failed_to_find do not have a
significant impact on the likelihood of renegotiation, whereas mistakes captured by any_wrong in
fact lead to a higher likelihood of the same.
FHFA Working Paper 17-03
28 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Exhibit 5: Renegotiation and Appraisal/Appraiser Characteristics, Main Sample
Dependent Variable: Downward Renegotiation
Appraisal
Characteristics
Appraiser
Characteristics
Both Appraisal and
Appraiser
Characteristics
(1) (2) (3) (4)
Log(Contract Price) 0.351*** 0.450*** 0.290*** 0.370***
(0.00862) (0.00867) (0.00880) (0.00884)
Failed_to_find 0.0255 0.0311
(0.0292) (0.0294)
Any_wrong 0.0792** 0.0797**
(0.0254) (0.0255)
Ne_super_over 1.179*** 1.132***
(0.0441) (0.0442)
Exactly_flag -1.232*** -1.294***
(0.00987) (0.0101)
Often_ff -0.00407 -0.0107
(0.00894) (0.00905)
Often_anywrong -0.0109 -0.0148
(0.00990) (0.00998)
Often_exact
-0.351*** -0.126***
(0.00949) (0.00969)
Appraiser_avg_gap
2nd quartile
(less overvaluation)
-0.321*** -0.397***
(0.00913) (0.00921)
3rd quartile -0.389*** -0.497***
(0.00985) (0.00993)
4th quartile
(most overvaluation)
-0.500*** -0.644***
(0.0107) (0.0108)
Constant -5.470*** -7.512*** -4.383*** -6.102***
(0.125) (0.132) (0.127) (0.134)
Controls:
House Attributes X X X X
Zip-Monthly HPI X X X X
Year-Quarter FE X X X X
State FE X X X X
Observations 1,743,299 1,743,299 1,743,299 1,743,299
Notes: This table reports the logit regression results from regressing the probability of downward renegotiation
on appraisal and appraiser attributes when using the main sample, controlling for house characteristics,
monthly house price appreciation at the ZIP Code level, and year-quarter and state fixed effects. Each
observation corresponds to a single appraisal record. Overall, lower appraisal quality (reflected in
Exactly_flag in Columns 2 and 4) and lower appraiser diligence (Often_exact and Appraiser_avg_gap in
Columns 3 and 4) dampen the chance of downward renegotiation, and higher appraisal quality (reflected in
Ne_super_over in Columns 2 and 4) increases the chance of downward renegotiation. Greater appraiser
diligence captured by the indicator of mistakes Often_anywrong does not seem to have a significant impact
on the probability of downward renegotiation, but at the appraisal level the presence of mistakes in house
attributes, reflected in Any_wrong, does in fact have a significant impact in increasing the likelihood of
downward renegotiation. As mistakes in property history (reflected in Failed_to_find) have no significant
impact, our analysis is inconclusive as to whether mistakes in appraisals shrink buyers’ opportunities for better
deals. Significance levels at the 1%, 5%, and 10% are denoted respectively by ***, **, and *.
FHFA Working Paper 17-03
29 J. Shui & S. Murthy — First-time Homebuyer Overpayment
We then test whether the appraiser-level attributes have a similar impact. In Column 3, we
add the quartiles of appraiser_avg_gap to the basic regression in addition to often_ff,
often_anywrong, and often_exact. Appraiser_avg_gap is defined as the average percentage
difference of the appraisal value from the contract price for a given appraiser. Thus a higher
quartile of appraiser_avg_gap represents a greater propensity for overvaluation. Moving from the
second-lowest quartile (the median) to the highest quartile of appraiser_avg_gap, the monotonic
decrease in the regression coefficient in Column 3 reflects a significantly increasing negative effect
of overvaluation on the likelihood of downward renegotiation. In other words, the more prone an
appraiser is to overvalue a property, the less likely are downward price adjustments through
renegotiation for that property. The coefficient in front of often_anywrong suggests that appraisers
prone to mistakes seem to dampen the likelihood of downward renegotiation (although
insignificantly), an effect that is different from the one suggested by the coefficient in front of
any_wrong in Column 2. We further include appraisal and appraiser attributes in a consolidated
regression and report the results in Column 4. All of the effects persist and the effect of
overvaluation becomes more salient. We report in Exhibit 6 the marginal effect of the variables
in specification Exhibit 5 Column 4.
Exhibit 6: Marginal Effects on Downward Renegotiation
Variables Marginal Effects
Log_cp 0.0163***
(0.000387)
Often_ff -0.000470
(0.000398)
Often_anywrong -0.000651
(0.000439)
Often_exact -0.00552***
(0.000426)
Appraiser_avg_gap
2nd quartile -0.0175***
(less overvaluation) (0.000404)
3rd quartile -0.0219***
(0.000435)
4th quartile -0.0283***
(more overvaluation) (0.000474)
Failed_to_find 0.00137
(0.00129)
Any_wrong_avl 0.00350***
(0.00112)
Ne_super_over 0.0497***
(0.00193)
Exactly_flag -0.0569***
(0.000402)
Observations 1,743,299
Notes: In this table, we report the marginal effect of the variables in specification
Exhibit 5 Column 4. Standard errors are in parentheses. Significance levels at the
1%, 5%, and 10% are denoted respectively by ***, **, and *.
FHFA Working Paper 17-03
30 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Thus far, these results provide evidence that certain appraisals and appraisers might be able
to induce downward renegotiation. We now test part (b) of our theory, whether downward
renegotiation has a strong influence on FTHB overpayment.
We first calculate the predicted probability of downward renegotiation,
, based on the
regression results in Exhibit 5 Column 4. We then add the predicted probability and the interaction
term of FTHB and the predicted probability as independent variables to our main specification
(Equation 8; Exhibit 4 Column 4).
Exhibit 7 reports the regression results, with Column 1 employing Log(Sales Price) and
Column 2 employing Log(Net Sales Price) as the dependent variables. Confirming our previous
finding (in Exhibit 4), the results in both columns consistently demonstrate that FTHBs overpay.
Both columns also show that the predicted probability of downward renegotiation has a significant
impact on overpayment. Specifically, a 10 percent increase in the predicted probability of
downward renegotiation leads to a 0.7 percent reduction in the sales price. However, the
interaction term of FTHB and the predicted probability of downward renegotiation is significant
in neither column, indicating that the effect of downward renegotiation does not differentiate
between FTHBs and repeat buyers.
Overall, we find suggestive evidence that certain types of appraisals and appraisers can
induce downward renegotiation and that such downward renegotiation has a significant impact in
mitigating overpayment. However, this effect is not unique to FTHBs.
FHFA Working Paper 17-03
31 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Exhibit 7: Downward Renegotiation and Log(Sales Price), Main Sample
Dependent Variable:
Log(Sales Price) Dependent Variable:
Log(Net Sales Price)
(1) (2)
Predicted Reneg_down -0.0736*** Predicted Reneg_down -0.0723***
(0.00751) (0.00752)
Fthb 0.0104*** Fthb 0.00871***
(0.000462) (0.000461)
Fthb*Predicted Reneg_down -0.0117 Fthb*Predicted Reneg_down -0.0111
(0.0122) (0.0122)
Log(Contract Price) 0.110*** Log(Net Contract Price) 0.115***
(0.00135) (0.00134)
Constant -1.226*** Constant -1.289***
(0.0171) (0.0170)
Controls:
ZIP-Year-Quarter FE X X
ZIP-Monthly HPI X X
Observations 1,743,299 1,743,298
R-squared 0.219 0.223
Adjusted R-squared 0.206 0.209
Notes: This table reports OLS regression results from regressing Log(Sales Price) and Log(Net Sales Price) on the
predicted probability of downward renegotiation and its interaction term with FTHB after manually demeaning both
house and year-quarter fixed effects, and when employing the main sample. Each observation corresponds to a single
appraisal record. Both columns control for ZIP-year-quarter interacted fixed effects and monthly house price
appreciation at the ZIP Code level. Significance levels at the 1%, 5%, and 10% are denoted respectively by ***, **, and
*.
7 Conclusion
Homeownership is arguably key to fostering wealth and stabilizing neighborhoods and
communities. Helping creditworthy, low- and middle-income FTHBs by providing them access
to better mortgage terms and by increasing temporary monetary incentives has been a key U.S.
policy for decades. So does a typical FTHB pay more than her more experienced counterparts do?
Even though this topic is important both academically and for policy matters, prior research has
been somewhat limited.
This paper contributes to the literature by filling in the gap between theoretical and
empirical literature on FTHBs and their real estate transaction outcomes. We present a theoretical
framework in which FTHBs pay rent in addition to the search cost paid by all buyers in each search
period and in which quantity and price per unit are drawn i.i.d from a uniform distribution. We
propose that for a given house, FTHBs pay a higher average sales price compared to repeat buyers.
FHFA Working Paper 17-03
32 J. Shui & S. Murthy — First-time Homebuyer Overpayment
We assemble a novel dataset to test our proposition and find that FTHBs do indeed overpay
for houses compared to repeat buyers, and that this overpayment is 1.04 percent on average—a
substantial amount particularly when considering the size of the residential purchase-money
mortgage market and the FTHB share of it.27
We then examine whether certain types of appraisals and appraisers can mitigate this
overpayment. We find that certain appraisal and appraiser attributes increase the probability of
downward renegotiation, and that downward renegotiation is correlated with lesser overpayment,
but that this effect has no consistent discernible connection with FTHB status.
Our research speaks directly to housing affordability. First-time homebuyers are
inexperienced house hunters and are more likely to be marginal borrowers. The challenge for
policy makers is to help them gain access to sufficient credit while controlling their default risk.
However, FTHBs may experience handicaps before credit even comes into the picture. In this
paper, we present a robust result that FTHBs are overpaying for their houses28—possibly a result
of their inexperience. Our analysis also suggests that certain appraisals and appraisers might be
able to mitigate FTHB overpayment.

27 This 1.04 percent translates to roughly $2,860. Taking sales concessions into consideration, a typical FTHB
overpays by 0.87 percent, which is equivalent to $2,393, per transaction.
28 Without noticeably elevated default rates. In the context of risk management, we have conducted a brief analysis
to determine whether FTHB overpayment leads to increased mortgage risk. In other words, given the well-known
connection between the LTV ratio of a mortgage and its outcome, one might wonder whether, all else equal, the
slightly-higher prices paid by FTHBs lead to elevated default rates. Our empirical work, though not particularly
extensive, suggests no discernible increase in default probabilities.
FHFA Working Paper 17-03
33 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Appendix
Following the set-up in equations (3) and (4), there exists a unique such that the buyer
purchases the house if ,, and does not purchase the house if ,.
Equivalently, for any given, there exists a unique 
such that the buyer purchases
the house if , and does not purchase the house if .
1∗


 (9)


∗
∗





The left-hand side describes the cost of search, while the right-hand side describes the
expected gain from future search. Calculating the integrals in the final equation above and
rearranging the equation:

 Vq∗
∗∗ (10)
Substituting ∗for and simplifying the above equation:
∗
2∗ (11)
Rearranging equation (11),
2∗∗
0 (12)
Solving equation (12) for ,
∗∗∗
(13)
∗
where ∆∗∗
2
∗
2
FHFA Working Paper 17-03
34 J. Shui & S. Murthy — First-time Homebuyer Overpayment
The following conditions need to be satisfied such that there exists a unique solution of
that lies in ,]:
i) ∆0
1
; (14)
It is obvious that ∗. Therefore ∗
is the unique solution if the following two conditions are satisfied:
ii) ∗
<= Δ∗ substitute 
∗
forΔ
<= 
1 (15)
iii)∗
<= Δ∗1, substitute Δ with its expression
<= 

1
(16)
Summarizing the above conditions, (15) is a sufficient condition for (14) – other words, ii)
is a sufficient condition for i). Therefore, only (15) and (16) need to hold, leading to the following
Lemma.
Lemma 2: For any given, if1 and
1
, then there exists a unique 
, such that the buyer purchases the house if, and does not purchase the house if 
.
Proof for Lemma 1:
For any given , the left-hand side of equation (11) is fixed. The right-hand side of
equation (11), 2∗, is obviously monotonically increasing in
in,]. Therefore the solution for is greater when 0than when 0.
FHFA Working Paper 17-03
35 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Proof for Proposition 1:
Following Lemma 1 in the model section, for any given , the reservation price for
FTHBs, , is strictly greater than the reservation price for repeat buyers, .
Therefore, it is obvious that 

>

.
FHFA Working Paper 17-03
36 J. Shui & S. Murthy — First-time Homebuyer Overpayment
Appendix Exhibit 1: FTHBs and Sorting
Dependent Variable: Log(Net Sales Price)
(1) (2) (3)
Fthb -0.155*** -0.159*** -0.0581***
(0.000868) (0.00130) (0.000723)
Constant 12.42*** 12.43*** 12.13***
(0.000557) (0.000534) (0.00154)
Controls:
House Attributes X
Zip-Year-Quarter FE X X
Observations 1,743,309 1,743,309 1,743,309
R-squared 0.018 0.618 0.799
Adjusted R-squared 0.018 0.612 0.796
Notes: This table reports OLS regression results. Net sales price is the sales price minus the
concession amount. Each observation corresponds to a single appraisal record in the main
sample. Column 2 controls for Zip-year-quarter interacted fixed effects. Column 3 additionally
controls for house attributes (the number of bathrooms, the number of bedrooms, the square
footage, and the age of the house). Significance levels at the 1%, 5%, and 10% are denoted
respectively by ***, **, and *.
Appendix Exhibit 2: Relationship Between FTHBs and House Prices by LTV Range, Main Sample
Dependent Variable:
Log(Sales Price) Dependent Variable:
Log(Net Sales Price)
(1) (2) (3) (4) (5) (6)
LTV ≤ 80% 80% ≤ LTV ≤
90% 90% < LTV LTV ≤ 80% 80% ≤ LTV ≤
90% 90% < LTV
Fthb 0.00753*** 0.00849*** 0.0113*** Fthb 0.00455*** 0.00704*** 0.0104***
(0.00125) (0.000672) (0.000753) (0.00125) (0.000672) (0.000752)
Log(Contract Price) 0.108*** 0.111*** 0.114*** Log(Net Contract Price) 0.115*** 0.116*** 0.117***
(0.00199) (0.00154) (0.00179) (0.00198) (0.00153) (0.00177)
Constant -1.198*** -1.249*** -1.272*** Constant -1.281*** -1.310*** -1.322***
(0.0252) (0.0196) (0.0225) (0.0251) (0.0194) (0.0223)
Controls: Controls:
ZIP-Year-Quarter FE X X X Zip-Year-Quarter FE X X X
ZIP-Monthly HPI X X X ZIP-Monthly HPI X X X
Observations 366,622 811,783 564,904 Observations 366,621 811,783 564,904
R-squared 0.256 0.229 0.225 R-squared 0.258 0.231 0.227
Adjusted R-squared 0.209 0.203 0.19 Adjusted R-squared 0.212 0.205 0.192
Notes: This table reports the OLS regression results from regressing Log(Sales Price) and Log(Net Sales Price) on FTHB for different
LTV ranges, after manually demeaning both house and year-quarter fixed effects. Columns 1 – 3 share specifications with Exhibit 4
Column 4, while Columns 4 – 6 share specifications with Exhibit 4 Column 6; all columns control for ZIP-year-quarter interacted
fixed effects and monthly house price appreciation at the ZIP Code level. As in Exhibit 4, results show that FTHBs overpay. Results
also show that FTHBs in higher LTV ranges tend to overpay by more compared to those in lower LTV ranges. Significance levels at
the 1%, 5%, and 10% are denoted respectively by ***, **, and *.
FHFA Working Paper 17-03
37 J. Shui & S. Murthy — First-time Homebuyer Overpayment
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