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Federal Reserve Bank of Chicago

Rushing into the American Dream?
House Prices Growth and the
Timing of Homeownership
Sumit Agarwal, Luojia Hu, and Xing Huang

REVISED
May 2016
WP 2013-13

Rushing into the American Dream? House Prices Growth and the
Timing of Homeownership*
Sumit Agarwal†, Luojia Hu‡, Xing HuangS
Abstract
We use the New York Fed Consumer Credit Panel dataset to empirically examine how past house
price growth influences the timing of homeownership. We find that the median individual in metropolitan
areas with the highest quartile house price growth becomes a homeowner 5 years earlier than that in areas
with the lowest quartile house price growth. The result is consistent with a life-cycle housing-demand
model in which high past price growth increases expectations of future price growth thus accelerating
home purchases at young ages. We show that extrapolative expectations formed by home-buyers are a
necessary channel to explain the result.
Keywords: Housing, Homeownership, Consumer Finance, Credit Constraints, Life Cycle
JEL Classification: R21, D12, D91, D14

* The authors would like to thank Anna Neumann and Ashley Wong for excellent research assistance. We also benefited from
conversations and comments from Zahi Ben-David, Souphala Chomsisengphet, Bo Honore, Amit Seru, seminar participants
and discussants at Chicago Fed, Dallas Fed Housing, Stability and the Macroeconomy conference, AAEA, and IBEFA. The
views expressed in this research are those of the authors and do not necessarily represent the policies or positions of the Federal
Reserve Board or the Federal Reserve Bank of Chicago.
† National university of Singapore - Departments of Economics, Finance and Real Estate
‡ Federal Reserve Bank of Chicago
S Michigan State University - Department of Finance

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1.

Introduction
Homeownership is often said to be an integral part of the American dream. However, modeling the

demand for housing is complicated. Houses provide utility and serve as collateral for additional credit needs.
They may bring investment benefits as well. These features suggest that homeownership may vary over the
life cycle and among different cohorts. Past literatures have focused on the impact of demographics (such
as marriage), income, and credit constraints on homeownership. However, these factors cannot explain the
sharp rise in homeownership leading up to the crisis.
In this paper, we investigate the influence of house price growth on the demand for homeownership over
the lifecycle.1 We focus on first home purchases, because they account for 40% of home sales over the past 30
years and more than 50% in 2009, according to the National Association of Realtors. First home purchases
may also matter for the long-term dynamics of the housing market, because first home purchases affect the
demand for trade-up homes in the future housing market.
In a life-cycle model, there may be two offsetting effects of house price growth on housing demand. On
the one hand, if the price recently increased by a large amount, the individual may face a high level of house
price. She has to sacrifice more consumption to pay the down payment if she wants to buy it when she is
young. When she is financially constrained and her preference for owning a home varies over the life cycle,
she will prefer to postpone the home purchase until middle age. Hence, house price growth decreases the
probability of individuals buying first homes at early ages, which we call the liquidity constraint channel
hypothesis. On the other hand, individuals may extrapolate future house price growth from past house price
growth. These people are more likely to buy a house early in their life cycle if they expect the house prices
to rise fast.2 In this case, house price growth increases the probability of individuals buying their first homes
earlier through investment and/or hedging incentives, which we call the expectation channel hypothesis.
In this paper, we lay out a simple conceptual model to illustrate the two different channels through which
housing price could affect demand for homeownership over the life cycle. We then empirically test which
effects dominate in the data. We exploit a large panel of individuals from the Federal Reserve Bank of New
York’s Consumer Credit Panel (CCP) data set. We follow each individual from 1999 to 2012 and study
the homeownership timing decision as a function of house price changes across CBSAs controlling for other
demand and supply factors. This data set is truly unique and well suited for our line of inquiry because of the
following three reasons: (i) The data are a long panel of quarterly information about limited demographics
1 Other related papers studying the impact of house prices have focused on the feedback effect on current home owner’s
home equity-based borrowing (Mian and Sufi, 2011), the impact on local demand and retail prices (Stroebel and Vavra, 2015),
or the timing of selling (Qian, 2013).
2 Survey evidence from the Michigan Survey of Consumers also suggests that a significant portion of respondents, around
30%, explicitly mention house prices to justify their views on whether the present is a “good time to buy [housing] for investment”
(Piazzesi and Schneider, 2009).

2

and risk measures that are time varying with little measurement errors (unlike the survey data sets that
can be potentially biased, e.g., the Survey of Consumer Finance); (ii) the data have detailed geographic
information up to the zip code level; and (iii) unlike survey data sets, this is a panel of the entire population
that is active in the credit markets, so our estimates are reasonably precise. The strength of the data allows
us to exploit the time-varying, cross-regional variation in house price growth and its impact on the timing
of homeownership.
Despite the long panel nature of the data set, 13 years is not sufficient to study life-cycle decisions. For
instance, it is possible that even after 13 years many individuals may not have made a decision to buy a
house, so as econometricians, we face a right censoring problem. To explicitly account for the censoring
issue, we estimate the transition into homeownership using a discrete time survival model. This also allows
us to study the entire age distribution of potential home buyers (as some will never buy a home).
Our main variable of interest is the past three-year house price changes at the metropolitan area (CBSA)
level. There could be confounding factors that could explain the timing of the homeownership decision. To
deal with this, we have CBSA-fixed effects to control for the level of house prices across CBSAs and the
credit supply that is not time varying. These effects also control for some demographic and other market
conditions. We also have time-fixed effects that control for the variation in demand and supply of credit
and house prices at the aggregate level. We have CBSA-specific time-varying control variables such as the
unemployment rate, the growth rate of the number of businesses, and wages. We also control for individualspecific time-varying credit risk by each person’s credit risk score (this measures the individual’s ability and
willingness to pay credit).
To fix ideas, let us explain the thought experiment that we have in mind. We take two random people
and assign them to the highest and lowest house price growth CBSA quartiles and assume that they do not
move between CBSAs. Then we study if the house price growth in the quartiles affects the timing of their
first home purchase. We show that the probability of buying a house is accelerated in CBSAs in the highest
quartile of house price growth relative to that in CBSAs with the lowest quartile of house price growth.
Specifically, we find that the age at which the median individual becomes a homeowner is 5 years younger
for people in the highest house price growth quartile compared with those in the lowest house price growth
quartile. This magnitude is similar to what is found in Fetter (2013) — the median individual becomes a
home owner about 5 years earlier if the Veteran Affairs (VA) benefits were extended to all individuals (about
a 10 percentage point reduction in down payment).
One might still be concerned about the potential endogeneity of housing price growth if the controls
in the model do not capture all the unobservables that affect the local housing demand through changes
in fundamentals (such as demographics or economic conditions). To partially address this issue, we also
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instrument local house prices with national house prices interacted with local house supply elasticity (Saiz,
2010), and we still find the accelerating effect of house price growth.
The results show the effects of the expectation channel dominate. According to a survey of U.S. home
buyers from 2003 through 2012 conducted by Case et al. (2012), home buyers’ expectations of high future
home prices are substantially affected by recent experience. We also provide supportive evidence that for
the four counties documented in the survey, the expectations are positively correlated with the house price
growth measure used in our paper. In the region with high house price appreciation, individuals are more
likely to form expectations of high future house prices and become homeowners at young ages, despite their
needing to sacrifice consumption to afford large down payment.
The extrapolative expectations may apply not only to home buyers but also to credit suppliers, who
could have relaxed buyers’ borrowing constraints by lowering lending standards or payments if they also
have expectations of high future price growth. The relaxation of borrowing constraints may be confounded
with the accelerating effect of extrapolative expectations from home buyers. To separate these two effects
(mortgage-supply explanations vs house-demand explanations), we first extend our sample back to the 1990s
when the mortgage supply varied little across different regions and find that the accelerating effect still
exists. Then, we repeat our main analysis on the non-subprime borrowers, a group that was less likely to
be much affected by the credit supply change during the recent housing cycle. Specifically, we look at a
subsample of borrowers with credit scores above 660 (Keys et al., 2010) when they enter our sample. The
results are largely unchanged. Furthermore, using a new merged data set between the Equifax and the Loan
Performance Services (LPS), we examine how house size and down payment vary with past house price
growth, and compare the changes between young and old buyers. We find that in areas with faster house
price growth, young buyers tend to purchase smaller houses and, for houses of same size, they also pay
higher (rather than lower) down payment. The evidence on these two dimensions can not be explained if the
mortgage-supply explanation were the only force for the accelerating effect. The house-demand channel is a
necessary mechanism for one to explain all evidence documented in the paper. We want to emphasize that
the mortgage supply-side explanation and the housing demand-side explanation are not mutually exclusive,
and we view the house-demand side story as complementary, rather than alternative, to the mortgage-supply
side explanations.
Our paper is most closely related to Landvoigt (2011), in the sense that he also studies the role of credit
constraints and house price expectations on the decision to purchase and the size of home purchased. However, there are some key differences between the two studies. First, we focus on the timing of homeownership
as opposed to decision to buy a house. Second, we proxy for expectations of future house prices using past
house price changes and investigate the effects of expectations. Differently, Landvoigt (2011) aims to infer
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house price expectations from observed household choices. Furthermore, we use an administrative panel
data set with little measurement error of individuals, with detailed geographic information that allows us to
exploit the geographical variation in house price growth.
Our paper is related to the large literature that studies housing demand over the life cycle. Ortalo-Magne
and Rady (2006) study a life-cycle model of the housing market with a property ladder and a credit constraint.
Rather than emphasizing on the link between income shock and house prices like they do, our paper focuses
on the influence of house price expectations on the behavior of first time home buyers. Attanasio et al. (2012)
also construct a life-cycle model and incorporate some realistic features, but this model still lacks one feature
considered in our paper: the possibility that individuals extract time-varying utility from homeownership.
Sinai and Souleles (2005) model the demand for homeownership as the trade-off between rent risk and the
asset price risk. They relate the demand for homeownership to local rent volatility and individuals’ expected
horizon. Han (2010) identifies two effects of price risk on housing demand: a financial risk effect and a
hedging effect against future housing costs. The author studies the timing and size of house purchases by
existing homeowners. Our paper differs by studying the timing of the purchases by marginal first time home
buyers.
The paper proceeds as follows. In Section 2, we lay out a conceptual model highlighting the different
channels through which housing prices could affect demand for homeownership over the life cycle. In Section
3, we describe the data sets we use and present some summary statistics. In Section 4, we empirically
examine the impact of house price growth on the timing of first home purchases. We discuss and test some
alternative explanations (such as expansion of mortgage supply) in Section 5. And Section 6 concludes.

2.

A Conceptual Model
To illustrate how housing prices could affect individuals’ demand for homeownership over the life cycle,

we consider a simple model in which an individual maximizes her lifetime utility by choosing an optimal
path for nondurable consumption, an optimal time to purchase a house, and an optimal level of debt/saving.
2.1

MODEL SETUP
Preferences. We model the timing of house purchases and consumption choices of the individuals who

live for T periods. For the simplified case, T is equal to 2. The individual decides whether to purchase a
house in each period. If the individual buys the house at time 𝜏 , 𝑂𝑡 equals to 1 for all 𝑡 ≥ 𝜏 , meaning that
the individual owns the house. For the sake of simplicity, all the houses are of the same size. An individual’s
choice of house size is not considered here. In each period 𝑡, the individual also needs to optimize nondurable
consumption 𝐶𝑡 .
Individuals derive utility from both housing and nondurable goods for each period before period T, as
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well as from bequeathing terminal wealth, 𝑊𝑇 . We assume individuals are indifferent to owning versus
renting a house at 𝑡 = 0, but individuals could get a huge extra utility from owning a house rather than
renting a house at 𝑡 = 1. Therefore, to normalize the utility from renting a house as 0, the lifetime utility
could be described as:
𝑈0 = 𝑙𝑜𝑔𝐶0 + 𝑙𝑜𝑔𝐶1 + 𝑙𝑜𝑔𝑊2 + 𝑚𝑂1
where 𝑚 is the extra utility an individual could obtain if she owns a house at 𝑡 = 1. Note that there is
no extra utility if she owns a house at 𝑡 = 0. Let’s assume 𝑚 is extremely large, so that if she could ever
afford the down payment, she will purchase a house, either at time 0 or time 1.
Housing. The individual can rent or own a house in which to live. To simplify an individual’s choice and
emphasize the timing problem, all the houses are assumed to be the same size. If the individual purchases a
house at period 𝜏 , 𝑏𝜏 = 1. And for all the other periods, 𝑏𝑡 = 0 (𝑡 ̸= 𝜏 ). The purchase price of the house at
period 𝑡 is denoted as 𝑃𝑡 . The perceived future house price will affect the individual’s decision. We’ll discuss
the details about perceived future house price later. If the individual rents a house to live, she needs to pay
a fixed rent, 𝑁 , for each period. For the simplified case, we normalize 𝑁 = 0.
Borrowing Constraint. The individual could borrow against the value of the house to buy the house
at a fixed rate 𝑅𝐷 , which is normalized to zero for the simplified case. Let 𝐷𝑡 denote the dollar amount the
investor owns in mortgages at period 𝑡. Following Cocco (2004), we assume that the investor is allowed in
every period to costlessly renegotiate the desired level of debt (for example, with penalty-free prepayment).
A down payment is required to buy a house. Specifically, the individual has to pay up at least a proportion
(𝑑) of the value of the house (𝑃𝑡 ). In other words, the mortgage value will be less than the remaining portion
of the value of the house after the down payment:

0 ≤ 𝐷{𝑡} ≤ (1 − 𝑑) 𝑃𝑡 , ∀ 𝑡

Beliefs of Future House Price. At this point, we want to keep things simple to focus only on the
effects of the borrowing constraint under the assumption of a preference shift of housing in middle age; hence,
we will assume the price is deterministic in order to factor out the effects of house price risk. Assuming
individuals believe that house prices will increase by rate 𝜆 at 𝑡 = 1, i.e., 𝑃0 = 𝑃, 𝑃1 = 𝑃2 = (1 + 𝜆)𝑃 , we
will consider three simple cases: (1) stable house prices (𝜆 = 0); (2) downward house prices (𝜆 < 0); (3)
upward house prices (𝜆 > 0).
Labor Income. The individual earns labor income for 𝑡 = 0 and 𝑡 = 1. To avoid the influence of labor
income risk and the shape of income in the life cycle, we will assume for both periods, the individual earns

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the same certain amount,

𝑌
2

, i.e., 𝑌0 = 𝑌1 =

𝑌
2

.

Budget Constraint. The individual could save beforehand at the risk-free rate, 𝑅𝑓 . For the simplified
case, let 𝑅𝑓 = 0. Let 𝑆𝑡 denote the saving of the household. The liquid wealth at period 𝑡 (𝑡 > 1) is
𝐿𝑊𝑡 = 𝑆𝑡−1 − 𝐷𝑡−1 . Following Cocco (2004), Deaton (1991) and Carroll (1997), we calculate cash on hand
by adding period 𝑡 liquid wealth to period 𝑡 labor income 𝐿𝑊𝑡 + 𝑌𝑡 . In each period, the individual needs
to choose the nondurable consumption level and decide whether to buy or continue renting a house. The
budget constraint at period 𝑡 is given by

𝑆𝑡 = 𝐿𝑊𝑡 + 𝑌𝑡 − 𝐶𝑡 + 𝐷𝑡 − 𝑏𝑡 𝑃𝑡

with 𝑆𝑡 ≥ 0. The last period wealth is given by 𝑊𝑇 = 𝐿𝑊𝑇 + 𝑃𝑇 .
Optimization Problem. The individual maximizes lifetime utility by choosing the optimal nondurable
consumption ({𝐶𝑡 }𝑡=0,1 ), the optimal time for purchasing a house ({𝑏𝑡 }𝑡=0,1 ), and the optimal level of debt
({𝐷𝑡 }𝑡=0,1 ). In the simplified case, since both borrowing and saving rates are normalized to zero, households
do not have preferences between savings and debts. To make it convenient for discussion, we can let the
debt level always be (1 − 𝑑) 𝑃𝑡 after the individual buys a house. In Appendix A, we discuss in detail the
optimal consumption choice and the best timing for buying a house under three cases.
2.2

PREDICTIONS
As described before, we assume individuals’ preferences for owning a house vary over the life cycle. An

individual could obtain huge extra consumption utilities from homeownership at middle age relative to at a
young age. In this model, house price growth could affect the housing demand through two channels.
Proposition 1. All else being equal, the probability of buying a home at time 0, Pr(𝜏 * = 0), decreases with
the current price 𝑃 , and increases with price expectation parameter 𝜆.
Proof. In Appendix A.

Q.E.D.

The first channel is house price expectations. Specifically, individuals are more likely to buy a house
early in their life cycle if they expect house prices to rise faster. The intuition is as follows. When there are
expectations of low future house prices, the individual would prefer to postpone her purchase of a first home.
Otherwise, she has to sacrifice her consumptions at a young age for the down payment without experiencing
as much utility from homeownership as in middle age. In contrast, when there are expectations of high future
house prices, the individual would make the first home purchase earlier. There are two incentives to do so.
The first incentive is investing. The individual might obtain potential capital gain from the house purchase.
The second incentive is hedging. The individual can hedge against the possibility that she may not be able
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to afford the down payment in middle age (thus, losing out on the extra utility from homeownership) if the
price reaches sky high. Through this channel, house price growth increases the probability of individuals
buying a first home earlier.
The second channel is liquidity constraints. If house prices recently increased by a large amount, the
individual may face a high level of house price. As the price increases, all else being equal, she has to
sacrifice more consumption to pay the down payment if she wants to buy it at a young age. When she is
financially constrained, she will prefer to postpone the home purchase to middle age. Hence, house price
growth decreases the probability of individuals buying a first home at early ages.
One caveat is that our model only illustrates the decision-making of individuals and abstracts away
from the action of mortgage credit suppliers. Specifically, we assume a fixed minimum down payment ratio,
which may vary with market conditions in a general equilibrium setting. If instead we assume mortgage
credit suppliers would relax borrowing constraints given expectations of high future house prices, there will
be two scenarios: (1) if home buyers have negative or zero price growth expectations, they will prefer to
wait to buy at time 1 or be indifferent about when the purchase is made (at time 0 or time 1). In this
case, relaxing borrowing constraints does not influence the timing of individual’s first home purchases; (2)
if home buyers share similar positive expectations of house price growth as the credit suppliers, relaxing
borrowing constraints will then amplify the accelerating effect of homebuyer price growth expectations on
first home purchases. Later in the paper, we’ll test both mortgage-supply explanation and housing-demand
explanation for the accelerating effect of housing price growth expectations on first home purchases. These
two explanations are not mutually exclusive. We find that mortgage-supply alone could not explain the
accelerating effect, and the housing demand explanation plays an important role.3

3.

Data

3.1

FRBNY (EQUIFAX) CONSUMER CREDIT PANEL
The main data set we use for the empirical analysis is from the Federal Reserve Bank of New York’s

(FRBNY) Consumer Credit Panel (CCP). This is a panel data set collected by the credit bureau (Equifax)
each quarter starting from the first quarter of 1999. Individuals in the panel are selected randomly from
the U.S. population based on the last two digits of their Social Security number (SSN). Then the FRBNY
collects credit bureau data for these individuals, including mortgage and non-mortgage debt, collection
agency records, and personal background information.
Individuals can only be selected into the sample if they have a credit record on file that includes their
SSN. This means that as soon as a young adult with a randomly selected SSN opens the first line of credit
3 Details

are illustrated in Appendix A.

8

(often around age 18), that person will be added to the Equifax data set. Deceased individuals are dropped
from the data set. This sampling methodology ensures that the 5% random sample reflects the current
demography of the U.S. population with a credit history and SSN.4
In this paper, we use the 1% sample of the primary-individual data over the period 1999-2012 and only
include individuals aged 18-60. Credit files for the very young and the very old are often small or incomplete.
In particular, elderly individuals may have already paid off their mortgage in the past so that it no longer
appears in their credit file,5 which would make it impossible to identify the time of their first home purchase.
So we exclude them from our analysis.
The main variables we select from the Equifax data set are a person’s age, address, credit score, and
mortgage history. Panel A of Table I reports summary statistics. In the sample, after all the individual-year
observations are pooled, the average age is about 40 and the average credit score is 667.6
For our study, the key variable of interest is each person’s oldest mortgage account, which we use to infer
their first home purchase. Since we want to analyze home purchase decisions at a yearly frequency, we select
each person’s age, credit score and address at the beginning of each year (usually Q1, unless an individual
enters the data set mid-year). We then look to see if they purchased their first home at any point during
that calendar year. As Panel A of Table I shows, the average age to purchase the first home is 35.4 in our
sample.
We exclude observations with missing birth years, which are about 5% of individuals in the Equifax
sample. To the extent that birth years are missing from the data randomly, this should not affect our
analysis. For individuals with inconsistent values of the age of the oldest mortgage, we take the age of the
oldest mortgage from the earliest survey response where a person had reported having ever taken out a
mortgage, and then replace any subsequent oldest mortgage values, if different, to match the oldest nonmissing survey response.
Besides mortgages, the Equifax data also has extensive information on non-mortgage debts and their
repayment status, which we will exploit in the second part of the empirical analysis. Panel A of Table 1 also
presents summary statistics for the balances and the delinquency status for different credit accounts.

4 See

Lee and van der Klaauw (2010) for an excellent introduction to the data set.
to the FRBNY staff report (Lee and van der Klaauw, 2010), closed accounts remain on credit reports for up
to 7 to 10 years after their closing. Therefore, our panel includes those with no recent credit activity, such as in the past 24
months, but with credit activity in the past 10 years (footnote 4, p.2, Lee and van der Klaauw (2010)). However, detailed
information on specific accounts (such as a mortgage) must be updated by an individuals creditors in the past 3 months in
order to be included in the Equifax dataset for a given quarter: While records will be included in our panel for all individuals
with some credit activity on their credit reports over the past 7 years or so, records will only include information on recently
updated accounts (footnote 14, p.10, Lee and van der Klaauw (2010)).
6 The risk score in the Equifax data ranges between 280 and 850.
5 According

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3.2

CORELOGIC HOME PRICE INDEX
We use CoreLogic home price index (HPI) data to compare housing price growth in different regions, as

a measure of expected growth in future housing prices. CoreLogic home price indices are calculated using
weighted repeat sales methodology on a monthly frequency, with January 2000 as the base month. For our
analysis we select data only for single family combined homes (including distressed sales). For these homes,
we use HPI data calculated at the metropolitan area (CBSA level) to capture variation in price growth
between different metropolitan areas across the country.
Specifically, we first calculate the average HPI at year 𝑡 in city 𝑐 as the 12-month average of the monthly
HPI from CoreLogic. We then compute the annual growth rate of HPI from year 𝑡 − 1 to year 𝑡 as:7

𝛾𝑐,𝑡 =

𝑝𝑐,𝑡 − 𝑝𝑐,𝑡−1
𝑝𝑐,𝑡−1

We then smooth the house price growth by taking the average of HPI growth over the most recent three
years:
2

𝛿𝑐,𝑡 =

1 ∑︁
𝛾𝑐,𝑡−𝑘
3
𝑘=0

Over the sample period and across all CBSAs, the average annual HPI growth rate is about 3% a year
(Table I, Panel B). There is variation both across cities and over time. We also compute the range of the
HPI growth over the sample period (taking the difference between the highest and the lowest growth rate)
for each CBSA. According to Table I, Panel B, within a given CBSA, HPI growth varies over time — the
average range of HPI growth across all CBSAs is 21 percentage points. More importantly, this range also
varies quite a bit across CBSAs. For example, while the annual HPI growth rate changed by no more than
13 percentage points over the period in the quarter of cities with lowest HPI growth rate, it swung by 25
percentage points or more in the quarter of cities with highest HPI growth rate.
3.3

BLS: EMPLOYMENT AND WAGE DATA
To capture local business and labor market conditions, we use regional employment and wage data from

the Quarterly Census of Employment and Wages (QCEW), compiled by the U.S. Bureau of Labor Statistics
(BLS). This is a near-census of business establishments across the country. At the county level, we select
annual average employment levels, weekly wages, and the number of establishments, and then calculate
growth rates for the each of these variables.
In addition to the QCEW data, we use county-level unemployment rates from the Local Area Unemploy7 For

the sake of robustness, we also exploit the growth rate from quarter 4 of year 𝑡 − 1 to quarter 4 of year 𝑡, and the
results remain the same.

10

ment Statistics published on the BLS website for 1999-2012.
Since these variables are given at the county-level, we map each county to its corresponding CBSA in
order to link it with the housing price data. If a CBSA includes more than one county, we take an average
for each of these four macroeconomic indicators across all counties within a given CBSA. The summary
statistics are reported in Table 1, Panel C.
[ Insert Table I ]
3.4

LOAN PERFORMANCE SERVICES (LPS) DATASET
To further test the housing-demand from the mortgage-supply explanations, we also merge the Equifax

dataset with the Loan Performance Services (LPS) dataset to obtain information about loan characteristics
such as loan-to-value (LTV) ratio and downpayment, etc.
The Equifax Credit Risk Insight Servicing McDash (CRISM) database links individuals in the Equifax
Consumer Credit Panel to the mortgage-level McDash servicing data (LPS) using a confidential and proprietary matching process. Using the unique consumer identifier, we find each first-time homebuyer in our
original sample in the 2005-2012 CRISM dataset in order to obtain mortgage characteristics provided by
LPS for their first home.
As recommended by Equifax, we only consider the individuals with an Equifax-provided match confidence
score of at least 0.8. To identify the loan that corresponds to the first home purchase (oldest first mortgage)
referred to in the consumer credit panel, we identify the oldest first mortgage loan on record by origination
year for each matched individual in the CRISM dataset. We eliminate loans that have large discrepancies
between origination date and first payment date; loans with payment dates prior to origination dates are
dropped as well as loans with first payment dates over two years after the origination date. We then compare
the year of first home purchase in the consumer credit panel with the origination year of the oldest loan on
record for the matched individual. We drop all loans with over a two year difference between the year of first
home purchase and the origination year of the oldest loan record in CRISM. Because the CRISM dataset
begins in 2005, we can only observe loans that are still active in 2005 if they originated prior to 2005.
As a result, not all individuals with a match in the CRISM dataset will be linked to a mortgage account
in the LPS data. Of the 15,872 homebuyers in the original sample from the consumer credit panel, we are
able to find mortgage characteristics for 7,437 individuals about 47% of the homebuyers.

4.

House Prices and the Timing of First Home Purchase
In this section, we empirically examine how house price growth affects the housing demand over the life

cycle using micro-level data.

11

4.1

HOMEOWNERSHIP RATE
The Equifax data do not explicitly measure whether an individual owns a home at the survey date or

when an individual bought his or her first home. It does, however, record the age of the individual’s oldest
mortgage account. Based on this information, we derive a measure for whether or not individuals ever owned
a home in a given year, and among those who did, the age at which they bought their first home.
For the purpose of this paper, we consider an individual to be a homeowner in a given year 𝑡 if that
person purchased a home in year 𝑡 or earlier. Accordingly, we define the homeownership rate in year 𝑡 as
the fraction of individuals in year 𝑡 who have ever purchased a home by year 𝑡. Specifically, let 𝐵𝑡 denote
the total number of individuals who bought a home in year 𝑡 or earlier, and 𝑁𝑡 denote the total number of
individuals at year 𝑡. Then the home ownership rate in each year, 𝐻𝑡 , can be calculated as follows:

𝐻𝑡 =

𝐵𝑡
𝑁𝑡

We calculate the homeownership rate by age in a similar fashion. Specifically, let 𝐵𝑎𝑡 denote the total
number of individuals in age group 𝑎 at year 𝑡 who purchased a home in year 𝑡 or earlier, and 𝑁𝑎𝑡 denote
the total number of individuals in age group 𝑎 at year 𝑡. Then the homeownership rate for age group 𝑎 in
each year, 𝐻𝑎𝑡 , can be calculated as follows:

𝐻𝑎𝑡 =

𝐵𝑎𝑡
𝑁𝑎𝑡

Figure 1(a) plots the aggregate homeownership rate 𝐻𝑡 over the time period 1999-2012. Over the sample
period between 1999 and 2012, the fraction of homeowners varies between 44% and 47%, with an average of
around 46%. The magnitude is similar to Mian and Sufi (2011) — they use the same Equifax data but with
a slightly different definition for homeownership rate and find that the homeownership rate to be around
40%.8
Figures 1(b)-(d) plot the home ownership rates for three age groups (age 25-34, 35-44, and 45-60) over
the sample period9 . Two things are worth noting. First, the fraction of individuals ever owning a home for
the young group (25-34) is lower in level than that for the two older age groups (35-44 and 45-60). Second,
8 Both

magnitudes are, however, lower than the homeownership rate measured using other data (such as the U.S. Census,
Current Population Survey (CPS) or American Housing Survey (AHS)). For example, Fisher and Gervais (2011) use the Census
data to examine homeownership trends and find that over 1996-2007, the homeownership rate for households headed by owners
of age 25+ rose from roughly 65% to 68%. There are two main reasons for the discrepancy. First, our homeownership rate is
based on individual-level data, while the homeownership constructed by Census data is at the household level. Second, Fisher
and Gervais (2011) count homeownership for households with owner heads aged 25 and older, while we consider all individuals
between age 18 and 60. By including people younger than 25 (who do not usually own homes) and excluding the elderly (who
often do), our sample would have a lower fraction of homeowners.
9 The group for age 18-24 is not included because its average homeownership (round 5%) is generally much lower than that
of the other groups

12

homeownership varies over time and the variation is greater for the young group than for the older groups.
For example, after steadily increasing in the early 2000s across all ages, the ownership rate trended down
for the young group in the second half of the decade while it remained relatively stable among the two older
groups. Over this period, housing prices also varied greatly. In the next section, we examine whether and
how (expected) house prices affect people’s decisions about when to enter the housing market.
[ Insert Figure 1 ]
4.2

HAZARD RATE OF FIRST HOME PURCHASE BY AGE AND HOUSING PRICE GROWTH
For our paper, the key concept to examine is the hazard rate of the first home purchase. In other words,

what is the probability that an individual will buy a home in a given year, conditional on the fact that she
never bought a home in a previous year? Using cross sections from the data, we can compute this conditional
probability (the hazard rate) of the first home purchase at a given age by year and geographic area. Let
˜ 𝑐𝑡 (𝑎) denote the total number of individuals of age 𝑎 living in area 𝑐 at year 𝑡 who purchased their first
𝐻
˜ 𝑐𝑡 (𝑎) denote the total number of individuals of age 𝑎 living in area 𝑐 at year 𝑡 who
home in year 𝑡, and 𝑅
have never bought a home before year 𝑡, then the hazard rate is given by:

ℎ̃𝑐𝑡 (𝑎) =

˜ 𝑐𝑡 (𝑎)
𝐻
˜
𝑅𝑐𝑡 (𝑎)

We initially compute the hazard rate of first home purchase by age for each city-year cell as described
before. Then we group the city-year cells into four groups based on HPI growth, and compute the average
hazard rate across city-year cells within each group, weighted by the cell size (i.e., the number of people in
the city-year cell). Figure 2 presents the average hazard rate for each of the four groups, ranging from the
lowest- to the highest-quartile of housing price growth.
Figure 2 shows that the hazard rate of home purchase over the life cycle is hump-shaped: It increases
sharply after the mid-20s, peaks in the early 30s, and declines afterwards.
The figure also shows that at a given age, the hazard rate of home purchase in cities during periods of
faster house price growth is generally higher than that in cities during periods of low price growth. Moreover,
the gap widens at ages between the mid-20s and the early 30s, and stays roughly constant afterward. This
suggests that people tend to purchase their first home at young ages, when they live in cities during periods
of fast price appreciation.
To look more directly at the house price effect on the distribution of age-at-purchase, we can use the
estimated hazard rate to compute and compare the counterfactual cumulative distribution functions (CDFs)
under the assumption that an individual always lives in the low- versus the high-house price growth area.

13

First, note that with the estimated the hazard rate (conditional probability) of home purchase for each
age, we can also compute the corresponding unconditional probability of purchasing a home at or before a
given age (i.e., the cumulative distribution function). Specifically, for each age (𝑗) from 18 through 60, we
calculate the probability that an individual would purchase a home at or before that age as:

𝐹˜𝑗 = 1 − Π𝑗18 (1 − ℎ̃𝑗 )

Based on this, we first compute the CDF by city-year cell and then take the (weighted) average across all
cities and years within each of the four HPI growth groups. Figure 3 presents the resulting (counterfactual)
CDFs.
Figure 3 shows that the distribution of age at first home purchase for the high HPI growth city-year
groups lies uniformly above and to the left of the distribution for the low HPI growth city-year groups. In
other words, the former distribution stochastically dominates the latter. Figures 2 and 3 suggest that people
living in cities during periods of high house price growth are generally more likely to purchase their first
home at a younger age than those living in places with low house price growth. The result is consistent with
the notion that the accelerating effect of rising house prices through the house price expectation channel
more than offsets their decelerating effect through the liquidity constraints channel.
Note that so far our comparisons are made between city-year groups with high versus low housing price
growth and use only the aggregate cross-section data. As such, we cannot distinguish whether the differences
in home purchases by age come from variations in price growth across cities in a given year or from variations
over time within a city. To sort these out (and to also take into account other factors that might affect an
individual’s decision to purchase a home), we turn to multivariate analyses using individual-level panel data
in the next section.
4.3

ESTIMATION OF HAZARD RATE – MULTIVARIATE ANALYSIS
We use a simple discrete-time hazard specification to model the probability of first home purchase, with

the Equifax individual-level data. Specifically, we use a Probit model for the binary outcome of home
purchase (conditional on never previously owning a home). The latent variable is

*
′
′
𝑦𝑖𝑎𝑐𝑡
= 𝛽1 · Δ𝐻𝑃 𝐼𝑐𝑡 + 𝛽2 · 𝐴𝑔𝑒𝑎 + 𝑌 𝑒𝑎𝑟𝑡 + 𝐶𝐵𝑆𝐴𝑐 + 𝑋𝑖𝑎𝑐𝑡
𝜂1 + 𝑀𝑐𝑡
𝜂2 + 𝜀𝑖𝑎𝑐𝑡

where 𝑖 indexes individual, 𝑎 indexes age, 𝑐 indexes CBSA, and 𝑡 indexes year. The model includes the
average HPI growth rate over the past recent years Δ𝐻𝑃 𝐼𝑐𝑡 , year- and CBSA-fixed effects, single-year age
′
dummies, the individual-level time-varying variable 𝑋𝑖𝑎𝑐𝑡
(risk-score), and variables proxying local economic

14

′
conditions 𝑀𝑐𝑡
(e.g., growth rates of the number of businesses, employment and wage, and the unemployment

rate). The hazard rate for an individual’s first home purchase is then

ℎ𝑖𝑐𝑡 (𝑎)

=

𝑃 𝑟(𝐵𝑢𝑦𝑖𝑎𝑐𝑡 = 1|𝐵𝑢𝑦𝑖𝑎𝑐𝜏 = 0, 𝜏 < 𝑡)

=

*
𝑃 𝑟(𝑦𝑖𝑎𝑐𝑡
> 0)

=

′
′
Φ(𝛽1 · Δ𝐻𝑃 𝐼𝑐𝑡 + 𝛽2 · 𝐴𝑔𝑒𝑎 + 𝑌 𝑒𝑎𝑟𝑡 + 𝐶𝐵𝑆𝐴𝑐 + 𝑋𝑖𝑎𝑐𝑡
𝜂1 + 𝑀𝑐𝑡
𝜂2 )

where Φ(·) is the CDF of a standard normal distribution.
Table II reports the estimates from the full sample of CBSAs over the period 1999-2012. Our main
result can be found in Column 1. The coefficient on HPI growth is positive and significant. If we assume
individuals form their expectations of future house prices based on recent housing price growth, the result
suggests that all else being equal, at a given age, individuals who live in cities with expected high future
house price appreciations are more likely to buy a first home than their counterparts in areas with expected
low future housing prices.
[ Insert Table II ]
There is distinct life-cycle pattern in the hazard rate of first home purchase. The coefficients on the age
dummies (not reported here) exhibit a skewed hump-shaped age profile that is similar to what we saw before
(in Figure 2 — the hazard rises sharply from the late 20s, peaks around 30, and then declines gradually
afterward). Given this pattern, house price expectations might have a differential impact on the likelihood
of first home purchase at different ages.
There are many other factors that could affect whether an individual is willing and/or able to buy a
home. For example, since most home purchases are financed by a mortgage and having a good credit score
is crucial for obtaining a loan, we would expect credit scores to have an important effect on home purchases.
And this is exactly what we found. The risk score variable enters the model positively and with strong
statistical significance.
Our hypothesis is based on the assumption that we can interpret the recent house price growth as a
proxy to future house price growth. One potential problem is that housing price growth might also be
correlated with other economic conditions that affect housing demand, regardless of the expectations of
future prices. For example, cities that experienced rapid house price appreciation might also have had fast
growing local economies with more jobs and increasing wages. Higher incomes, in turn, could make a house
more affordable and thus lead to more and earlier entrants into the housing market. To address this concern,
we added some CBSA-level controls to capture the time-varying local economic conditions. Specifically, we
include the growth rates of employment, wages, and business establishments, as well as the unemployment
15

rate. Columns 2 and 3 show that while local employment, wage, and business growth seem to have little
additional impact on the likelihood of an individual’s first home purchase, the local unemployment rate has
a negative impact on the likelihood of first home purchase. While the effect of HPI growth on the hazard
rate is reduced somewhat with the addition of each variable, it remains statistically significant even in the
full model (Column 3).
We also experiment with a specification that relaxes the linearity functional form assumption on the
housing price variable. Specifically, we replace the continuous variable, HPI growth, by a set of dummies
that represents the quartiles of its distribution. The results in Column 4 show that generally the hazard rate
of home purchase indeed increases monotonically with HPI growth.
Since 3-year HPI growth might also reflect growth between 𝑡 − 1 and 𝑡, this period may be when the first
home purchases occur. One concern is that increases in home purchases may cause house prices to go up
during year 𝑡, leading to reverse causality. To alleviate this concern, we also use another measure: 2-year
HPI growth from year 𝑡 − 3 to 𝑡 − 1, which does not include the current year. The results (Column (5))
are largely unchanged. It suggests that our result is not driven by the effect of increasing house demand on
current house prices.
4.4

EVALUATE THE MAGNITUDE OF THE HPI EFFECT
While the estimated coefficients from the model show that HPI growth has a positive effect on the hazard

rate of an individual’s home purchase, the magnitude of this impact is not immediately clear since the model
is highly nonlinear. Moreover, since the hazard rate is only a conditional probability, it might not be the
final object of interest if, for example, one wants to answer questions such as the following: If house prices
increase by 10 percentage points, how big an increase would there be in the share of individuals who have
bought a home by age 30?
In this section, we conduct two counterfactual experiments. We consider two scenarios: (1) we assume
that individuals in our sample have always lived in the cities with the lowest HPI growth (the bottom
quartile) versus (2) we assume that individuals in our sample have always lived in cities with highest HPI
growth (the top quartile).
[ Insert Figure 4 ]
Under each scenario, we use the estimates from the probit model in Column 4 of Table II to predict
for each individual the hazard rate of home purchase at each age from 18 through 60. For each prediction,
we only vary the HPI growth and age variables at their hypothetical values and keep all other variables at
their actual values in the data. We then take the average of the predicted hazard rates across all individuals.
Figure 4, Panel (a) presents the average hazard for the top quartile and bottom quartile separately. Panel (b)

16

presents the proportional margional difference. The figure shows a V-shaped heterogeneous effect of house
price growth — when house price growth increases, the relative increase in the hazard rate of buying first
home is larger for young individuals than for the middle-age group. This result is consistent with our model’s
prediction that individuals have a higher probability to purchase home at a young age than at middle age.
Similarly, under each scenario, we also use the predicted hazard rates to estimate the CDF for each
individual at each age and then take the average across all individuals. Figure 4, Panel (c) presents the
average CDF from the experiment.
According to the counterfactual distributions in Panel (c) of Figure 4, the difference in the age at which
the median individual becomes a first-time home buyer (that is, the age by which half of the population has
bought a home) is about 5 years: First-time home buyers are 5 years younger under scenario 2 than under
scenario 1 (39 versus 44 years).
Note that as we only have estimates of the hazard and survivor functions for individuals up to 60 years
old, we can not reliably estimate the expected value (mean) of age-to-purchase for the entire population. The
reason is there are many people in the population who will never buy a home. However, with the available
estimates, we can still calculate some summary measures for the conditional distribution of age at purchase
among those who will have eventually bought a home by age 60.
Specifically, we can estimate for each individual 𝑖 the conditional distribution function as:

𝐹^ (𝑎𝑖 |𝑎𝑖 ≤ 60) =

𝐹^ (𝑎𝑖 )
^ 𝑖 (60)
1−𝐺

where
^ 𝑖 (𝑠))
𝐹^𝑖 (𝑡) = 1 − Π𝑡𝑠=18 (1 − ℎ
or equivalently
𝐹^𝑖 (𝑡) =

60
∑︁

^ 𝑖 (𝑠)𝐺
^ 𝑖 (𝑠 − 1)
ℎ

𝑠=18

Based on the estimated conditional CDF, we find that the median age at first home purchase among those
who have eventually bought a home by age 60 is about 1 year younger under scenario 2 than under scenario
1 (31 versus 32 years). Note the difference in the conditional median is smaller than the difference in the
unconditional median we estimated earlier.
4.5

ROBUSTNESS TESTS
One might still be concerned about the potential endogeneity of housing price growth if the controls in

the model do not capture all the unobservables that affect the local housing demand through changes in

17

fundamentals (such as demographics or economic conditions). To partially address this issue, we instrument
local house prices with national house prices interacted with local house supply elasticity (Saiz, 2010). The
rationale for the instrument is based on the intuition that when there is an aggregate shock to housing
demand (say, lower interest rates), house prices could rise by different degrees across areas depending on
the supply response. For a given increase in demand, prices might rise more in areas where the supply is
less elastic. Specifically, we create an instrument for our 3-year change in HPI growth variable by using
a national measure of house price growth (also taken from CoreLogic) multiplied by the elasticity of the
housing supply in each CBSA.10 We then estimate an ivprobit model for the hazard rate using a subsample
of CBSAs for which the supply elasticity information is available. The results for the first and second stage
are listed in Panel A of Table III, which continue to show a positive effect of housing price growth on the
likelihood of home purchase. In fact, the coefficient is larger in magnitude than the probit baseline (Column
1 of Panel A), although it is also less precisely estimated.
Furthermore, as our data on individual credit scores, addresses, etc., only goes back to 1999, we have
to limit the estimation to the years 1999-2012. This may cause a left censoring problem, since we cannot
observe past data for older individuals who have never bought a home when they enter our data in 1999.
We perform a robustness check by only keeping young individuals (18-25 years old when they enter our
data). Since this cut the sample size dramatically, we used a 5% primary random sample, rather than the
1% primary sample we use for the rest of our analysis. The results remain the same, as shown in Panel B of
Table III.
Another concern is the confounding effect of migration. Geographic patterns of industry agglomeration
(e.g., a Silicon Valley effect) may lead to spatial groupings of young people receiving unusually large incomes,
thereby fueling both rapid house price increases and sooner-than-average first home purchases. To address
this concern, we also restrict our sample to individuals who have been in the same CBSA for at least three
years prior to the purchase of the house. The results remain the same, as reported in Panel C of Table III.
[ Insert Table III ]
4.6

HOUSE PRICE GROWTH AND EXTRAPOLATIVE EXPECTATIONS
The results show that individuals purchase their first homes at young ages when they have lived in places

experiencing high house price growth in the past few years. The direction of the empirical relationship
between housing price and age at purchase runs contrary to the prediction from the liquidity constraint
hypothesis, but is consistent with the expectation channel hypothesis — rising past price growth leads to
expectations of higher future price growth and thus accelerates home purchases at early ages. Case et al.
10 Saiz

(2010) provides estimated elasticities for 95 of the largest CBSAs, so we estimate the model using data from these
CBSAs (which cover a little less than half of the observations in our survey data).

18

(2012) conducted an annual survey of US home-buyers in four metropolitan areas from 2003 through 2012.
The survey elicits quantitative estimates of expected future house price growth, specifically, homebuyers’
expectations of the change of the value of their homes in the next year and ten years. They show that
the expected change in home prices is positively correlated with actual lagged price changes based on the
S&P/Case-Shiller Home Price Index. Specifically, they run a simple regression of the reported expected oneyear change in house prices on one-year lagged price changes and find a statistically significant coefficient
of 0.23 and 𝑅2 = 0.73. Similarly, when we regress the reported expected one-year price change from their
survey on the actual average annual price change in the past three years based on the CoreLogic home price
index as used in our paper, we find a slope coefficient of 0.29 (with p-value<0.01) and 𝑅2 of 0.70, as shown
in Table IV. This provides additional supportive evidence that individuals form expectations of high future
price growth largely based on past price growth, and corroborates the expectation channel hypothesis that
links past price growth with individuals’ timing of homeownership.
[ Insert Table IV ]

5.

Mortgage-supply Explanation vs Housing-demand Explanation
It is, however, worth noting that the extrapolative expectation may apply not only to home buyers, but

also to credit suppliers (as discussed at the end of the conceptual model section). Given expectations of
high future price growth, credit suppliers may lower lending standards and thus relax buyers’ borrowing
constraints. The relaxation of borrowing constraints may be confounded with the accelerating effect of the
extrapolative expectation from the home buyers, because it could also lead to a larger increase in the hazard
rate of first home purchases for the young group than relative to the middle-age group, if the young group
is more financially constrained than the middle-age group, other things being equal. In this section, we
conduct some tests to separate these two competing effects. First, we show that the accelerating effect of
housing price growth on first home purchases still exists during a subperiod or for a subsample of individuals
for which there was less variation from the mortgage supply side. Next, we provide evidence related to
house size and down payment and show that the housing-demand story is a necessary and complementary
explanation to explain the evidence all together.
5.1

SUBPERIOD FROM 1991 TO 1999
To separate the housing demand versus mortgage supply explanations, we extend our sample back to the

1990s, the period when the mortgage supply side forces vary less across different regions. If the mortgagesupply side is the main force driving our results and the housing-demand plays very little role, we should
expect no accelerating effect of house price growth on first-home purchases in this period since mortgage
supply was unlikely to be dramatically different across regions.
19

Table V reports the results from reestimating our main specifications for the 90s sample. We are able
to extend the panel back to the 90s because we identify individual’s first home purchases by the person’s
oldest mortgage account. The sample is restricted to only observations from 1991 to 1999. Individuals exit
the sample after the year of their first home purchase. We include the same set of control variables as in our
main analysis, except the time-varying credit score, because the credit score from the 90s is not available in
the Equifax dataset.
The results remain the same—despite the mortgage supply remaining stable in the 90s, we still find that
the hazard rate of first-home purchase increases monotonically with HPI growth. The evidence corroborates
the hypothesis that home buyers develop extrapolative expectations on future house price growth, and
purchase house earlier in their life cycle when they witness experience high house price growth in the past
few years.
[ Insert Table V ]
5.2

NON-SUBPRIME INDIVIDUALS
To further test the two explanations, we also repeat our analysis on the non-subprime borrowers. It is

well documented that credit supply increases were mainly concentrated in the subprime areas (Mian and
Sufi, 2009). Dell’Ariccia et al. (2012) also document that the deterioration of lending standards was more
of a subprime market phenomenon, and much weaker or absent in the prime mortgage market.
Therefore, to isolate the housing-demand explanation for first home purchases at young ages in areas
with high house price growth, we focus our analysis on a subsample of non-subprime borrowers who were
less likely to be much affected by the credit supply change. Specifically, we look at a subsample of borrowers
with FICO scores above 660 (Keys et al., 2010) when they enter our sample.
The results, as shown in Table VI, are largely unchanged and deliver a similar pattern of V-shaped
heterogeneous effect of house price growth as previously seen in Panel (b) of Figure 4. The results provide
support for the housing-demand explanation, because the mortgage-supply explanation is less applicable for
the non-subprime individuals given the absence of the deterioration of lending standards.
[ Insert Table VI ]
5.3

EVIDENCE ON HOUSE SIZE AND DOWN PAYMENT
One might argue that the laxing of lending standards to include more risky borrowers is only part of

the story for the expansion of the mortgage supply. Given high expectations of future house price growth,
lenders may also be willing to ask for lower down payment (higher LTVs) which would relax borrowing
constraints for individuals, especially for young buyers. In that case, we would expect to see a positive effect
of house price growth on LTV, especially at the upper tail of the LTV distribution. To test this, we merge
20

the Equifax and the LPS datasets and run quantile regressions of LTV on past house price growth (both
level and quartile dummies).
The results are presented in Table VII. Column 1-2 and 3-4 are estimated separately for each conditional
quantile: 0.5 and 0.75. As the table shows, the coefficients are either insignificant or significantly negative,
indicating that the LTV does not increase with the past house price growth across the distribution, including
the upper tail, of LTV. The evidence is not consistent with the mortgage-supply side explanations, lenders
lower down payment given expectations of high future house price growth, since it would suggest a higher
rather than lower LTV ratio associated with higher past price growth.
[ Insert Table VII ]
Despite the evidence of unchanged or even lower LTV in areas with high house price growth, one might
still think that the required down payment is lowered (looser borrowing constraints) in those areas. In this
subsection, we provide further evidence related to house size and down payment and show that the morgagesupply explanation, though might be applicable, can not be the only story to explain the accelerating effect
of housing price growth on the first-home purchases.

5.3.1

Optimal House Size

If young buyers are financially constrained, when they form higher expectations about future house prices
and increase their demand for housing, they are likely to purchase a smaller home and enter the housing
market earlier. In contrast, if the mortgage supply-side explanation is the only story, young buyers borrowing
constraints are relaxed, and we would not expect them to reduce house sizes.
To test this hypothesis, we regress house size (proxied by the price of the purchased house deflated by
the house price growth) on house price growth, and then compare the response of house size to house price
growth between young buyers (age≤30) and old buyers (age>30). If the mortgage supply-side explanation is
the only channel, we would expect no reduction in the size of houses bought by either young or old buyers.
If anything, we would expect house sizes become larger in areas with higher house price growth, especially
for young buyers.
Table VIII present the results of regressing house size on quartile dummies of house price growth for
young and old buyers separately. The two age groups exhibit very different patterns. Young buyers tend
to choose smaller houses in areas with higher house price growth, whereas the house size chosen by older
buyers shows an increasing pattern with house price growth. The downsizing pattern of young buyers who
experienced high house price growth is more consistent with the demand-side explanation, and certainly
cannot be explained only by the mortgage supply-side story. The evidence also provides additional insight
that the accelerating effect of house price growth on first home purchases may have differential impact on

21

the market for houses of different sizes, with more amplification for smaller houses. For example, Agarwal
et al. (2014) show that the condominium loan market experienced a 15-fold increase in origination from 2001
to 2007. The differential impact on the housing market segments may enhance our understanding about the
recent financial crisis.
[ Insert Table VIII ]

5.3.2

Down Payment

Another dimension we examine is down payment. If the mortgage supply-side explanation is the only
story to explain the accelerating effect, young buyers (the more financially constrained group) are more likely
to purchase a house of the same size only if they could lower the total amount of down payment.
We regress down payment on past house price growth (controlling for house size) for the young and old
buyers separately. If the demand channel does not exist and the accelerating effect could be fully explained
by the mortgage supply-side story, we would expect that, holding house size constant, down payment will
decrease, especially for young buyers, as house price growth increases. However, as shown by Table IX, both
groups pay higher (rather than lower) down payment in areas with higher past house price growth. The
pattern of increasing down payment for a given house size, which likely come from the higher house prices,
rules out the possibility that the supply-side story alone could explain the accelerating effect documented in
our paper.
[ Insert Table IX ]
5.4

SUMMARY
To sum up, while we cannot completely rule out the mortgage supply-side explanation, there is strong

evidence that the housing demand explanation plays a crucial role in explaining the accelerating effect of
house price growth on first-home purchases. First, we find that the accelerating effect still appear during
the 90s when the mortgage supply varies little across different regions or for the non-subprime individuals
who were less likely to be much affected by the credit supply change. Furthermore, we find that the
mortgage-supply explanation alone can not explain the results related to house size and down payment. The
house-demand story is a necessary mechanism for one to explain all evidence documented in the paper. We
view the house-demand side story as complementary, rather than alternative, to the mortgage-supply side
explanations.

6.

Conclusion
In this paper we investigate how house price growth affects individuals’ timing of the first home purchase

over the life cycle. A priori, there might be two offsetting channels that lead to two opposite hypotheses.

22

The first one is the liquidity constraint channel hypothesis. Larger past price increase may lead to a higher
level of current house price. Higher current prices may postpone home purchases if individuals are financially
constrained and thus less likely to be able to meet the larger down payment requirement. The second one
is the expectation channel hypothesis. Higher recent price growth may also lead households to expect house
prices to rise faster in the near future. Expectations of higher future price may prompt individuals to prepone
first home purchases because of investment or hedging incentives.
We use a unique panel data set covering the period 1999-2012 that allows us to track the same individual
over these 13 years and observe her decision to buy a house. We show that when house prices are rising,
individuals tend to buy houses earlier in their life cycle, which is more consistent with the expectation
hypothesis, i.e., all else being equal, expectations of higher future house prices accelerate house purchase in
early ages. By exploiting the time-varying cross-sectional variations in house price growth across metropolitan
areas while controlling for other potentially confounding demand and supply factors, we find that individuals
accelerate their probability of buying a house in metropolitan areas with the highest quartile house price
growth relative to metropolitan areas with the lowest quartile house price growth. Specifically, we find
that the age at which the median individual becomes a first-time home buyer in the population goes down
(buying at an earlier age) by 5 years when we compare individuals who live in the highest house price growth
quartile with those who live in the lowest house price growth quartile. The accelerating effects are likely to
be driven by extrapolative expectations of both mortgage suppliers and home buyers. We provide evidence
that the accelerating effect exists even in cases when the mortgage-supply story is likely to be absent, and
the mortgage-supply story alone can not explain the evidence related to house size and down payment.
Therefore, the housing demand explanation plays a crucial role in explaining the accelerating effect of house
price growth on first-home purchases.
Our key contributions to the existing literature can be summarized as follows. First, we are the first to
use the FRBNY CCP data set to study housing demand over the life cycle. This data set is a large panel,
with little measurement error, following individuals over a fairly long time horizon with detailed geographical
information. We also use a survival type of analysis that explicitly accounts for censoring. This also allows
us to study the entire age distribution of potential home buyers (as some will never buy a home). Second, the
prior housing literature focuses mostly on the level of homeownership and not the timing of homeownership.
We show that the timing is impacted by local past house price growth — individuals prepone the first house
purchase when they live in places that have experienced high local house price growth in recent years. Besides
providing implications for the aggregate effect on the housing market, the shift in timing may also provide
additional insight about the differential impacts across various submarkets. For example, our evidence that,
when house price grows fast in recent years, individuals purchase their first houses earlier with smaller sizes,
23

suggests that the recent house price growth has a larger amplification effect on the market for smaller houses.

24

A

Appendix

A.1

CONCEPTUAL MODEL

A.1.1

Case 1: Stable house price (𝜆 = 0, i.e., 𝑃0 = 𝑃1 = 𝑃2 = 𝑃 )

In this case, individuals believe that house prices will stay at the same level for all periods. There is
no investment incentive to purchase a house. The benefit of buying a house comes only from the extra
utility of owning a house at time 1. Since buying a house requires a down payment and thus reduces current
consumption, households will not have incentives to buy houses when they are young (𝑡 = 0). Instead, they
will plan to purchase houses in their middle age (𝑡 = 1).
Without any constraints, individuals would choose the optimal consumption level as 𝐶0𝑁 𝐶 = 𝐶1𝑁 𝐶 =
𝑌
3

. But since individuals have to make a down payment for a house purchase, they may not achieve the

unconstrained optimum. Specifically,
1. If

𝑌
2

− 𝑑𝑃 ≥

𝑌
3

1
( 𝑑𝑝
𝑌 ≤ 6 ), individuals are affluent. Even during their young age, they could buy a house

and maintain unconstrained optimal consumption. Therefore, they will buy a house at either time 0
or time 1 (𝜏 * = 0 𝑜𝑟 𝜏 * = 1) and choose the unconstrained optimal consumption (𝐶0* = 𝐶1* =
2. If

𝑌
2

− 𝑑𝑃 <

𝑌
3

and

𝑌
3

− 𝑑𝑃 ≥ 0 ( 16 <

𝑑𝑃
𝑌

𝑌
3

).

≤ 13 ), individuals can afford the home at time 0, but if they

buy one, they will not be able to maintain consumption level 𝐶0𝑁 𝐶 . Hence, they will choose to delay
the house purchase and buy a home at time 1. Under this condition, since

𝑌
3

− 𝑑𝑃 ≥ 0, individuals will

still be able to keep both 𝐶0𝑁 𝐶 and 𝐶1𝑁 𝐶 . Therefore, individuals will buy a house at time 1 (𝜏 * = 1)
and choose unconstrained optimal consumption (𝐶0* = 𝐶1* =
3. If

𝑌
3

−𝑑𝑃 < 0 and

𝑌
2

−𝑑𝑃 ≥ 0 ( 13 <

𝑑𝑃
𝑌

𝑌
3

).

≤ 21 ), individuals still can afford a house at time 0, but similarly,

they will choose to buy the home at time 1 (𝜏 * = 1). But even they buy a house at time 1, they will
not be able to achieve the consumption levels of 𝐶0𝑁 𝐶 and 𝐶1𝑁 𝐶 . Instead, optimal consumption will
be 𝐶0* = 𝐶1* =
4. If

𝑌
2

𝑌
2

−

𝑑𝑃
2

.

− 𝑑𝑃 < 0 and 𝑌 − 𝑑𝑃 ≥ 0, individuals can not afford the down payment at time 0 any more, but

by saving money in the first period, they can still purchase the home at time 1. Therefore, the optimal
time of buying a home is time 1 (𝜏 * = 1) and 𝐶0* = 𝐶1* =

𝑌
2

−

𝑑𝑃
2

.

5. If 𝑌 − 𝑑𝑃 ≥ 0, lifetime income is too low to afford the down payment, so the individual will never buy
a home.
The results can be summarized in A.1 When households believe that house prices will be stable in the future,
they prefer to buy a house in their middle age.
25

[ Insert Figure A.1 ]

A.1.2

Case 2: Downward house price (𝜆 < 0)

In this case, at time 0, individuals expect that house prices will decrease in the next period. We can
easily show that buying homes at time 1 is always preferred to buying homes at time 0.
*
*
*
Let 𝐶0|𝜏
=0 , 𝐶1|𝜏 =0 , 𝑊2|𝜏 =0 denote the optimal consumption choices given that individuals buy homes at

time 0. Then these choices satisfy the conditions:
⎧
⎪
⎪
⎪
⎪
⎨

*
𝐶0|𝜏
=0 <

𝑌
2

− 𝑑𝑃

*
*
𝐶0|𝜏
=0 + 𝐶1|𝜏 =0 < 𝑌 − 𝑑𝑃
⎪
⎪
⎪
⎪
*
*
⎩ 𝑊*
2|𝜏 =0 = 𝑌 + 𝜆𝑃 − 𝐶0|𝜏 =0 − 𝐶1|𝜏 =0

Consider an alternative consumption bundle with buying homes at time 1 (𝐶0|𝜏 =1 , 𝐶1|𝜏 =1 , 𝑊2|𝜏 =1 ). If
*
we increase the consumption at time 0 by a small positive amount (i.e., 𝐶0|𝜏 =1 = 𝐶0|𝜏
=0 + 𝜖, 0 < 𝜖 <
*
𝑚𝑖𝑛(𝑑𝑃, −𝑑𝜆𝑃, −𝜆𝑃 )) and keep the consumption at time 1 the same (i.e., 𝐶1|𝜏 =1 = 𝐶1|𝜏
=0 ), we can show

that this alternative bundle is feasible, because
⎧
⎪
⎨

𝐶0|𝜏 =1 <

𝑌
2

⎪
⎩ 𝐶0|𝜏 =1 + 𝐶1|𝜏 =1 < 𝑌 − 𝑑(1 + 𝜆)𝑃
*
*
*
and is strongly preferred to (𝐶0|𝜏
=0 , 𝐶1|𝜏 =0 , 𝑊2|𝜏 =0 ), because

⎧
⎪
⎪
⎪
⎪
⎨

*
𝐶0|𝜏 =1 > 𝐶0|𝜏
=0

*
𝐶1|𝜏 =1 = 𝐶1|𝜏
=1
⎪
⎪
⎪
⎪
⎩ 𝑊2|𝜏 =0 = 𝑌 − 𝐶0|𝜏 =1 − 𝐶1|𝜏 =1 > 𝑊 *
2|𝜏 =0

Therefore, when individuals expect that house prices will go down in the future, they will always prefer
to delay home purchases to their middle age.

A.1.3

Case 3: Upward house price (𝜆>0)

In this case, at time 0, individuals expect that house prices will increase in the next period. They
may consider buying homes at a young age because (1) buying a home at time 0 could lead to investment
opportunities (investment motives for homeownership) and (2) some may not be able to afford the high house
price at time 1 if not buying at time 0 (consumption motives of homeownership). We will discuss individuals’
decisions in different regions of

𝜆𝑃
𝑌

and

𝑑𝑃
𝑌

in more detail. Then, to separate out the young-age home buying

induced by consumption motives, we will compare the results with the decisions under a baseline model
26

without middle-age extra utility of owning a house.
[ Insert Figure A.2 ]
1. If

𝑌
2

− 𝑑𝑃 < 0 and 𝑌 − 𝑑 (1 + 𝜆) 𝑃 < 0 (Area A in Figure A.2), individuals cannot afford a house in

either period. So they never buy houses.
2. If

𝑌
2

− 𝑑𝑃 < 0 and 𝑌 − 𝑑 (1 + 𝜆) 𝑃 ≥ 0 (Area B in Figure A.2), individuals cannot afford at time 0 but

can afford a house at time 1. So they buy houses at time 1.
3. If

𝑌
2

− 𝑑𝑃 ≥ 0 and 𝑌 − 𝑑 (1 + 𝜆) 𝑃 < 0 (Area C in Figure A.2), individuals can afford a house at time

0, but will not be able to afford one if they wait until time 1 to buy one. So they buy houses at time 0.
4. If

𝑌
2

− 𝑑𝑃 ≥ 0 and 𝑌 − 𝑑 (1 + 𝜆) 𝑃 ≥ 0 (Area D1-D5 in Figure A.2), individuals can afford a house

in both periods. We proceed as follows: (1) solve the optimal consumption plans given the individual
chooses to buy a home at time 0 and at time 1; and (2) compare the utilities based on the two
conditional optimized consumption plans and then decide which period is the best time to buy a home.
Given individuals buy a home at time 0, the unconstrained optimal consumption plan is as follows:
𝑁𝐶
1
𝑁𝐶
𝐶0|𝜏
=0 = 𝐶 1|𝜏 =0 = 3 (𝑌 + 𝜆𝑃 ).

(a) If

𝑌
2

− 𝑑𝑃 ≥

1
3 (𝑌

+ 𝜆𝑃 ) (Area D1 in Figure A.2), individuals can maintain the unconstrained

optimal consumption and at the same time buy a house at time 0. So their best choices are to
buy a house at time 0 (𝜏 * = 0) and consume 𝐶0* = 𝐶1* = 31 (𝑌 + 𝜆𝑃 ).
(b) If 0 ≤

𝑌
2

− 𝑑𝑃 < 31 (𝑌 + 𝜆𝑃 ) (Area D2-D5 in Figure A.2), individuals are not able to maintain

𝑁𝐶
𝐶0|𝜏
=0 if buying a house at time 0. So the corner solution gives that, at time 0, individuals
*
consume 𝐶0|𝜏
=0 =

- If 0 ≤

𝑌
2

𝑌
2

− 𝑑𝑃 . To further split the region, we do the following:

− 𝑑𝑃 < 𝜆𝑃 (Area D2 and D3 in Figure A.2), which means

𝑌
2

< (𝑑 + 𝜆) 𝑃 , the

income at time 1 is less than the final wealth after selling the house at time 2. Since the
individuals cannot borrow from the future other than buying a house in the simplified model,
they are not able to smooth consumption between time 1 and time 2. So they consume
*
𝐶1|𝜏
=0 =

𝑌
2

*
; hence, 𝑊2|𝜏
=0 = (𝑑 + 𝜆) 𝑃 . Let’s denote this non-smoothing consumption

bundle as C𝑁 𝑆 |𝜏 =0 = { 𝑌2 − 𝑑𝑃,

𝑌
2

, (𝑑 + 𝜆) 𝑃 }.

−𝑑𝑃 < 13 (𝑌 +𝜆𝑃 ) (Area D4 and D5 in Figure A.2), individuals will smooth the con(︀
)︀
1 𝑌
*
*
sumption between time 1 and time 2, so 𝐶1|𝜏
=0 = 𝑊2|𝜏 =0 = 2 2 + (𝑑 + 𝜆) 𝑃 . Let’s denote
(︀
)︀
(︀
)︀
this smoothing consumption bundle as C𝑆 |𝜏 =0 = { 𝑌2 −𝑑𝑃, 21 𝑌2 + (𝑑 + 𝜆) 𝑃 , 12 𝑌2 + (𝑑 + 𝜆) 𝑃 }.

- If 𝜆𝑃 ≤

𝑌
2

27

Given individuals buy a home at time 1, the unconstrained optimal consumption plan is as follows:
𝑁𝐶
𝑁𝐶
𝐶0|𝜏
=1 = 𝐶 1|𝜏 =1 =

(a) If

𝑌
3

𝑌
3

.

≥ 𝑑 (1 + 𝜆) 𝑃 (Area D2 and D4 in Figure A.2), even though individuals buy a house at

a high price, they can still maintain the unconstrained consumption level

𝑌
3

. Let’s denote this

smoothing consumption bundle as C𝑆 |𝜏 =1 = { 𝑌3 , 𝑌3 , 𝑌3 }.
(b) If

𝑌
3

< 𝑑 (1 + 𝜆) 𝑃 (Area D3 and D5 in Figure A.2), individuals cannot achieve the unconstrained

consumption level if they buy a house at time 1. So the corner solution gives the non-smoothing
consumption bundle as
C𝑁 𝑆 |𝜏 =1 = { 21 (𝑌 − 𝑑 (1 + 𝜆) 𝑃 ) , 21 (𝑌 − 𝑑 (1 + 𝜆) 𝑃 ) , 𝑑 (1 + 𝜆) 𝑃 }.
We then compare the conditional maximized utilities when buying a home at time 0 and buying a home at
time 1 in Area D2-D5. Through comparison, we can obtain the regions of optimal timing of house purchases
as shown in A.3. The horizontal line represents the special case of stable house prices (Case 1). The blue
lines separate the area into three regions. For notation convenience, we denote 𝐿 =

𝜆𝑃
𝑌

and 𝐾 =

𝑑𝑃
𝑌

. The

region (𝑅) where individuals choose to buy a house at time 0 could be described as
⎧
⎪
⎪
𝐿≥0
⎪
⎪
⎨
𝐿 ≥ 𝑆(𝐾), where 𝑆( 16 ) = 0, 𝑆( 12 ) =
⎪
⎪
⎪
⎪
⎩ 𝐿> 1
2𝑑

when 𝐾 ≤
1
2𝑑 ,

′

′′

𝑆 (𝐾) > 0, 𝑆 (𝐾) > 0

when

1
6

1
6

<𝐾≤

when 𝐾 =

1
2

1
2

When price expectation is higher than the threshold, individuals buy a home at their young age (time
0). They are willing to sacrifice their consumption at a young age to either profit from the investment
opportunity or hedge to assure they could become home owners during their middle age.

A.1.4

Testable Predictions

We assume the population of individuals is heterogeneous in their lifetime income 𝑌 with c.d.f. 𝐹 . The
following proposition outlines the testable prediction regarding the probability of buying a home at time 0
(𝑃 𝑟(𝜏 * = 0)).
Proposition 2. All else being equal, the probability of buying a home at time 0, Pr(𝜏 * = 0), decreases with
the current price 𝑃 , but increases with price expectation parameter 𝜆.
Proof. When 𝜆 ≤ 0, individuals always prefer to buy a house at time 1 or are indifferent about the timing
of the purchase (time 0 or time 1), so 𝑃 𝑟(𝜏 * = 0) = 0;
When 𝜆 > 0, the probability of buying a home at time 0 is 𝑃 𝑟(𝜏 * = 0) =

28

∫︀
(𝐿,𝐾)∈𝑅

𝑑𝐹 , which is greater

than zero. We discuss two cases 0 ≤ 𝜆 < 1 and 𝜆 ≥ 1. Let’s write the relationship between 𝐿 and 𝐾 as
𝐿(𝐾) = 𝜆𝑑 𝐾.
If 𝜆 < 1, then 𝐿( 12 ) < 𝑆( 12 ).We also know that 𝐿( 16 ) > 𝑆( 16 ). To compare 𝐿(𝐾) and 𝑆(𝐾) for
1
2,

1
6

<𝐾≤

we look at their difference 𝐹 (𝐾) = 𝐿(𝐾) − 𝑆(𝐾). So we have 𝐹 ( 12 ) > 0 and 𝐹 ( 16 ) < 0. We can easily get
′

that there is a unique solution𝐾 𝑐 ∈ ( 16 , 21 ] s.t. 𝐹 (𝐾 𝑐 ) = 0 and 𝐹 (𝐾 𝑐 ) < 0. It means that when
(i.e., 𝑌 𝑐 < 𝑌 < 6𝑑𝑃 , where

𝑑𝑃
𝑌𝑐

1
6

< 𝐾 < 𝐾𝑐

= 𝐾 𝑐 ), individuals choose to buy homes at time 0. When 0 < 𝐾 ≤

1
6

(i.e.

𝑌 ≥ 6𝑑𝑃 ), 𝐿(𝐾) = 𝜆𝑑 𝐾 ≥ 0, we have already known that individuals will also choose to buy homes at time
0.
Combining these two regions, we get that 𝑃 𝑟(𝜏 * = 0) =
𝑐

𝜕𝐹 (𝐾 )/𝜕𝑃
− 𝜕𝐹
(𝐾 𝑐 )/𝜕𝑌 𝑐 =

Therefore,

𝐹 ′ (𝐾 𝑐 )· 𝑑𝑐
− 𝐹 ′ (𝐾 𝑐 )·(−𝑌𝑑𝑃
)
𝑐2
*

𝜕 Pr(𝜏 =0)
𝜕𝑃

> 0,

𝑌

< 0,

𝑐

𝜕𝑌
𝜕𝜆

*

𝜕 Pr(𝜏 =0)
𝜕𝜆

∫︀ ∞
𝑌𝑐

𝑑𝐹 . We can further prove that

𝑐

𝑐

𝜕𝐹 (𝐾 )/𝜕𝜆
𝐾 /𝑑
= − 𝜕𝐹
(𝐾 𝑐 )/𝜕𝑌 𝑐 = − 𝐹 ′ (𝐾 𝑐 )·(−

𝑑𝑃
2

𝑌𝑐

)

𝜕𝑌 𝑐
𝜕𝑃

=

< 0.

> 0.

If 𝜆 ≥ 1,then 𝐿( 21 ) ≥ 𝑆( 12 ). Given 𝐿( 16 ) > 𝑆( 61 ), then for the whole region 𝐾 ∈ (0, 12 ], individuals choose
∫︀ ∞
*
*
=0)
to buy a home at time 0. So, Pr(𝜏 * = 0) = 2dP 𝑑𝐹 . Therefore, 𝜕 Pr(𝜏
< 0, 𝜕 Pr(𝜏𝜕𝜆=0) = 0.
𝜕𝑃
𝜕 Pr(𝜏 * =0)
𝜕𝑃

After combining the cases, we get

≤ 0,

𝜕 Pr(𝜏 * =0)
𝜕𝜆

≥ 0.

Q.E.D.

One caveat is that our model only illustrates the decision-making of individuals and abstracts away the
action of mortgage credit suppliers. Specifically, we assume a fixed minimum down payment ratio, which
may vary with market conditions in a general equilibrium setting. If instead we assume mortgage credit
suppliers would relax borrowing constraints (i.e., lower the down payment ratio 𝑑) given expectations of high
future house prices, there will be two scenarios:
(1) If home buyers have negative or zero price growth expectation (𝜆 ≤ 0), they will prefer to buy at
time 1 or be indifferent about when they buy (at time 0 and at time 1). In this case, relaxing borrowing
constraints does not influence the timing of individual’s first-home purchases.
(2) If home buyers share similar positive expectations of house price growth (𝜆 > 0) as the credit
∫︀ ∞
suppliers, there will be discuss two cases as shown above: When 0 < 𝜆 < 1, 𝑃 𝑟(𝜏 * = 0) = 𝑌 𝑐 𝑑𝐹 and
𝜕𝑌 𝑐
𝜕𝜆

𝑐

𝑐

𝜕𝐹 (𝐾 )/𝜕𝜆
𝐾 /𝑑
= − 𝜕𝐹
(𝐾 𝑐 )/𝜕𝑌 𝑐 = − 𝐹 ′ (𝐾 𝑐 )·(−

)

< 0. It’s easy to get that

𝜕𝑌 𝑐
𝜕𝜆

decreases when 𝑑 decreases. Therefore,
∫︀ ∞
𝑃 𝑟(𝜏 * = 0) increases when 𝑑 decreases. When 𝜆 ≥ 1, Pr(𝜏 * = 0) = 2dP 𝑑𝐹 , so 𝑃 𝑟(𝜏 * = 0) also increases
𝑑𝑃
2
𝑌𝑐

with 𝑑 decreases. To sum up, when 𝜆 > 0, relaxing borrowing constraints will then amplify the acceleration
effect of home buyers’ price growth expectation on first home purchases.

29

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30

Mian, A. and A. Sufi (2011). House prices, home equity-based borrowing, and the us household leverage
crisis. American Economic Review 101 (5), 2132–2156.
Ortalo-Magne, F. and S. Rady (2006). Housing market dynamics: On the contribution of income shocks and
credit constraints. Review of Economic Studies 73, 459–485.
Piazzesi, M. and M. Schneider (2009). Momentum traders in the housing market: Survey evidence and a
search model. American Economic Review Papers and Proceedings, 406–411.
Qian, W. (2013). Why do sellers hold out in the down market? an option-based explanation. Real Estate
Economics 41 (2), 384–417.
Saiz, A. (2010). The geographic determinants of housing supply. Quarterly Journal of Economics 125,
1253–1296.
Sinai, T. and N. S. Souleles (2005). Owner-occupied housing as a hedge against rent risk. Quarterly Journal
of Economics 120 (2), 763–789.
Stroebel, J. and J. Vavra (2015). House prices, local demand, and retail prices. Working Paper .

31

Figure 1: Probability of Homeownership (Full sample and by age group), 1999-2012
The figure presents the homeownership of the full sample and by three age groups (25-34, 35-44, 45-60) for
each year from 1999 through 2012. The homeownership rate in year 𝑡 is defined as the fraction of individuals
in year 𝑡 who have ever purchased a home by year 𝑡. The time individuals bought their first home is identified
by the age of their oldest mortgage account.

-

-

(a) Full Sample

0~

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2000 2002 2004 2006 2008 2010 2012

2000 2002 2004 2006 2008 2010 2012

Year

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(c) Age group: 35-44

(d) Age group: 45-60

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2000 2002 2004 2006 2008 2010 2012

Year

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2000 2002 2004 2006 2008 2010 2012

Year

32

Figure 2: Hazard Rate of Buying First Home by Age
The figure presents the average hazard rate of buying a first home for four city-year groups sorted by lagged
three-year CoreLogic Home Price Index (HPI) growth. For each city-year cell, the hazard rate is computed
as the total number of individuals of a given age within that city-year cell who purchase their first home
divided by the total number of individuals of that given age within that city-year cell who have never bought
a home before. The hazard rate is then averaged across city-year cells within each group sorted by lagged
three-year HPI growth, weighted by the number of people in the city-year cell.

-

· - • Top Quartile HPJ Growth
3rd Quartile HPJ Growth

• • ..... •
.·f\ :\
----·
.,; ..·.' I· \,·
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2nd Quartile HPJ Growth
Bottom Quartile HPJ Growth

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0

20

25

30

35

40

Age

33

45

50

55

60

Figure 3: Cumulative Distribution of Homeownership by Age
The figure presents the cumulative probability of purchasing a home at or before a given age for four groups
sorted by the lagged three-year HPI growth. The cumulative probability is first constructed by city-year
cell and then averaged across all city-year cells within each group, weighted by the number of people in the
city-year cell.

34

Figure 4: The HPI Effect by Age (Estimated by Probit Regression)
The figure presents the hazard rate of first home purchase at each age between 18 and 60 predicted by
the estimates from the probit model in Column (4) of Table II. For each prediction, the individuals are
assumed to have always lived in the cities with either the highest HPI growth (the top quartile) or the lowest
HPI growth (the bottom quartile), and only the HPI growth and age variables are allowed to vary at their
hypothetical values while all other variables are kept at their actual values in the data. The predicted hazard
is then averaged across all individuals within each group. Panel (a) presents the average predicted hazard
rate for the top quartile and bottom quartile separately. Panel (b) presents the difference of the average
predicted hazard rates between these two groups normalized by the sum of the hazard rates of these two
groups. Panel (c) presents the predicted cumulative probability.
(a) Hazard Rate of Buying First Home by Age

(b) Proportional Marginal Difference

(c) Cumulative Distribution of Homeownership by Age

35

Table I: Summary Statistics
Panel A reports the summary statistics for the 1% sample of the primary-individual data from the FRBNY (Equifax) Consumer Credit Panel
Dataset. Our sample covers the period from 1999 through 2012 and only include individuals with age between 18 and 60 years old. Panel B reports
the summary statistics for the house price growth constructed by CoreLogic Home Price Index (HPI). Panel C reports the summary statistics for
CBSA-level variables constructed by county-level data from the Quarterly Census of Employment and Wages (QCEW) compiled by the BLS.
Obs
A. FRBNY (Equifax) Consumer Credit Panel
Pooled individual-year obs:
Age
1184591
Credit Score
1096090
Individual obs:
Age at first-home purchase
16689
Credit score range for individuals over time (High-Low)
116128
Consumer credit:
Credit card balance
1182788
Auto loan balance
1182788
Delinquency Rate for accounts with nonzero balances (1 = 90+ days past due and severe derogatory or bankruptcy; 0 =
Credit card
793849
Auto loan
427830
Mortgage
104176

36

B. CoreLogic House Price Index
Pooled CBSA-year obs:
3-year average HPI growth (%)
CBSA obs:
HPI growth range for CBSA over time (High-Low) (%)
C. BLS: Employment and Wage Data
Annual average employment growth (%)
Annual average weekly wage growth (%)
Annual average quarterly growth in number of establishments (%)
Annual unemployment rate (%)

Mean

Std

25th

Median

75th

39.91
666.87

11.55
106.05

30.00
589.00

40.00
677.00

50.00
758.00

35.36
124.91

10.01
86.83

27.00
57.00

33.00
115.00

42.00
182.00

0.00
0.00

639.50
0.00

3557.75
6060.00

3763.15 9254.63
4643.74 9855.08
otherwise):
0.19
0.39
0.09
0.29
0.08
0.27

13351

2.90

6.05

-0.79

3.61

6.11

960

20.64

11.76

13.36

16.34

24.88

960
960
960
960

0.31
2.90
0.69
6.38

1.28
0.77
1.09
1.87

-0.40
2.49
-0.04
5.22

0.28
2.83
0.55
6.16

0.94
3.21
1.27
7.31

Table II: Hazard Rate of Buying the First Home (Probit Regression)
The table estimates the hazard rate of buying the first home using a probit binary choice model for first home purchase. The sample is based on the
1% sample of the primary-individual data from the FRBNY (Equifax) Consumer Credit Panel Dataset. Individuals exit the sample after they year
of their first home purchases. The main variable is the house price growth (HPI growth) and the quartile dummies sorted on the HPI growth among
the pooled CBSA-year observations. Control variables are the time-varying individual-level credit score, CBSA-level employment and wage variables,
year, age, and CBSA effects. Standard errors are clustered at the CBSA level and are shown below the coefficient estimates. * 10%, ** 5%, *** 1%
significance.

(1)
HPI growth measure:

HPI growth

(2)
(3)
3-year HPI growth from t-3 to t

0.342***
(0.108)

0.303***
(0.110)

3rd quartile HPI growth (CBSAs)

37

4th quartile HPI growth (CBSAs)
0.00274***
(0.000)

0.00274***
(0.000)
0.327
(0.239)
0.411
(0.253)
-0.126
(0.196)

Yes
Yes
Yes

Yes
Yes
Yes

0.00274***
(0.000)
0.184
(0.257)
0.390
(0.265)
-0.149
(0.194)
-1.165**
(0.584)
Yes
Yes
Yes

524,168

524,168

523,768

Annual average employment growth
Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate
Year dummies
Age dummies
CBSA dummies
Observations

(5)
Quartile
dummy for
2-year HPI
growth from
t-3 to t-1

0.0576***
(0.0180)
0.0505**
(0.0210)
0.0697***
(0.0216)
0.00274***
(0.000)
0.175
(0.256)
0.384
(0.264)
-0.115
(0.193)
-1.188**
(0.586)
Yes
Yes
Yes

0.0423**
(0.0177)
0.0574***
(0.0206)
0.0731***
(0.0202)
0.00274***
(0.000)
0.210
(0.258)
0.378
(0.266)
-0.137
(0.194)
-1.226**
(0.565)
Yes
Yes
Yes

523,768

523,768

0.202*
(0.116)

2nd quartile HPI growth (CBSAs)

Credit score (time-varying)

(4)
Quartile
dummy for
3-year HPI
growth from
t-3 to t

Table III: Robustness Tests for Hazard Rate of Buying the First Home
In Panel A, we instrument the 3-year local house price growth with national house price growth interacted with local house supply elasticity (Saiz,
2010). The sample only includes the CBSAs which could be matched with supply elasticities reported in Saiz (2010). For comparison, we feature
Column (1) reporting the hazard rate estimated by our baseline probit model for the same subsample. Panel B estimates the hazard rate of buying
the first home using a probit binary choice model for first home purchase. The sample is based on the 5% sample of the primary-individual data from
the FRBNY (Equifax) Consumer Credit Panel Data set, and only includes individuals who enter the sample between 18 and 25 years old. Individuals
exit the sample after the year of their first home purchase. The main variable is the quartile dummies sorted on the HPI growth among the pooled
CBSA-year observations. Control variables are the time-varying individual-level credit score, CBSA-level employment and wage variables, year, age,
and CBSA effects. Panel C restricts the sample to individuals who lived in the same CBSA for at least three years. Standard errors are all clustered
at the CBSA level and are shown below the coefficient estimates. * 10%, ** 5%, *** 1% significance.
Panel A: Instrumental Variable Estimation

Left-hand side variable:
HPI growth measure:
HPI growth
(Instrument = Elasticity x National HPI Growth)
Credit score (time-varying

38

Annual average employment growth
Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate
Constant
Year dummies
Age dummies
CBSA dummies
Wald test of exogeneity p-value
Observations

(1)
Probit (Subsample)
Hazard Rate

(2)
First Stage
3-year HPI growth from 𝑡 − 3 to 𝑡

(3)
IV Probit
Hazard Rate

3-year HPI growth
0.233
(0.162)
0.00280***
(0.000)
0.502
(0.443)
0.389
(0.415)
-0.0753
(0.266)
-0.413
(0.958)
-4.536***
(0.152)
Yes
Yes
Yes

-0.278***
(0.0318)
0.000
(0.000)
0.323**
(0.142)
0.0886
(0.0674)
0.142*
(0.0794)
-2.110***
(0.252)
0.142***
(0.0111)
Yes
Yes
Yes

Instrumented 3-year HPI growth
0.525*
(0.311)
0.00280***
(0.000)
0.408
(0.468)
0.354
(0.405)
-0.103
(0.262)
0.361
(1.163)
-4.571***
(0.156)
Yes
Yes
Yes

295,746

0.263
295,746

0.263
295,746

Panel B: Subsample for Individuals Who Enter the Sample Between 18 and 25 Years Old

HPI growth measure:
2nd quartile HPI growth CBSAs
3rd quartile HPI growth CBSAs
4th quartile HPI growth CBSAs
Credit score (time-varying
Annual average employment growth
Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate
Constant
Year dummies
Age dummies
CBSA dummies
Observations

39

(1)
3-year HPI growth
from 𝑡 − 3 to 𝑡

(2)
2-year HPI growth
from 𝑡 − 3 to 𝑡 − 1

0.0754***
(0.0208)
0.0462*
(0.0240)
0.0960***
(0.0259)
0.00307***
(0.000)
0.319
(0.249)
0.548**
(0.255)
-0.0701
(0.184)
-0.565
(0.545)
-4.959***
(0.0777)
Yes
Yes
Yes
650,687

0.0381*
(0.0220)
0.0294
(0.0260)
0.0772***
(0.0274)
0.00307***
(0.000)
0.387
(0.251)
0.548**
(0.255)
-0.0945
(0.184)
-0.702
(0.551)
-4.920***
(0.0800)
Yes
Yes
Yes
650,687

Panel C: Subsample restricted to individuals who lived in the same CBSA for at least three years

HPI growth measure:
2nd quartile HPI growth CBSAs
3rd quartile HPI growth CBSAs
4th quartile HPI growth CBSAs
Credit score (time-varying)
Annual average employment growth
Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate
Year dummies
Age dummies
CBSA dummies
Observations

40

(1)
3-year HPI growth
from t-3 to t

(2)
2-year HPI growth
from t-3 to t-1

0.0470**
(0.0219)
0.0377
(0.0237)
0.0511**
(0.0248)
0.00260***
(4.17e-05)
0.122
(0.267)
0.432
(0.270)
-0.235
(0.204)
-1.064*
(0.579)
Yes
Yes
Yes
519,116

0.0527**
(0.0230)
0.0618**
(0.0262)
0.0804***
(0.0251)
0.00260***
(4.17e-05)
0.146
(0.266)
0.403
(0.267)
-0.240
(0.204)
-0.880
(0.573)
Yes
Yes
Yes
519,116

Table IV: Regressions of the Expected One-Year Change in Home Prices on Lagged Actual Price Changes
The table reports the results of regressing the survey-reported expected one-year change in house prices on the 3-year lagged HPI growth. The
survey-reported house price growth expectation is from an annual survey of U.S. home buyers in four metropolitan areas from 2003 through 2012,
conducted by Case et al. (2012). Standard errors are shown below the coefficient estimates. * 10%, ** 5%, *** 1% significance.

(1)

Survey location:
3-year lagged HPI growth
Constant
Observations
R-squared
County FE

(2)
(3)
(4)
Dependent Variable: Price change expectations within 12 months
Alameda County
Middlesex County
Milwaukee County
Orange County
0.249***
(0.0560)
4.651***
(0.637)
10
0.712
No

0.353***
(0.0895)
2.505***
(0.492)
10
0.661
No

0.315***
(0.0477)
3.738***
(0.285)
10
0.845
No

0.313***
(0.0794)
2.820**
(1.041)
10
0.660
No

(5)

(6)

All

All

0.287***
(0.0348)
3.482***
(0.334)
40
0.642
No

0.292***
(0.0338)
2.611***
(0.624)
40
0.695
Yes

41

Table V: Hazard Rate of Buying the First Home (Subsample for 1991-1999)
The table estimates the hazard rate of buying the first home using a probit binary choice model for first home
purchase. The sample is based on the 1% sample of the primary-individual data from FRBNY (Equifax)
Consumer Credit Panel Dataset. We extended the panel dataset back to 1991 and restricted the sample
to only observations from 1991 to 1999. Individuals exit the sample after the year of their first home
purchase. The main variable is the quartile dummies sorted on the HPI growth among the pooled CBSAyear observations. Control variables are CBSA-level employment and wage variables, year, age, and CBSA
effects. Standard errors are clustered at the CBSA level and are shown below the coefficient estimates. * 10%,
**
5%, *** 1% significance.

HPI growth measure:
2nd quartile HPI growth CBSAs
3rd quartile HPI growth CBSAs
4th quartile HPI growth CBSAs
Annual average employment growth
Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate
Year dummies
Age dummies
CBSA dummies
Observations

42

(1)
3-year HPI growth
from t-3 to t
0.0105
(0.0131)
0.0322**
(0.0159)
0.0759***
(0.0179)
-0.164
(0.142)
-0.0745
(0.0912)
0.423**
(0.166)
0.418
(0.568)
Yes
Yes
Yes
486,274

(2)
2-year HPI growth
from t-3 to t-1
0.0191
(0.0118)
0.0412***
(0.0150)
0.0733***
(0.0169)
-0.113
(0.140)
-0.0510
(0.0924)
0.450***
(0.169)
0.264
(0.571)
Yes
Yes
Yes
486,274

Table VI: Hazard Rate of Buying the First Home (Subsample for Individuals Who Enter the Sample with
Credit Score ≥ 660)
The table estimates the hazard rate of buying the first home using a probit binary choice model for first
home purchase. The sample is based on the 5% sample of the primary-individual data from the FRBNY
(Equifax) Consumer Credit Panel Data set, and only includes individuals who enter the sample with credit
score greater than or equal to 660. Individuals exit the sample after the year of their first home purchases.
The main variable is the quartile dummies sorted on the HPI growth among the pooled CBSA-year observations. Control variables are the time-varying individual-level credit score, CBSA level employment and
wage variables, year, age, and CBSA effects. Standard errors are clustered at CBSA level and are shown
below the coefficient estimates. * 10%, ** 5%, *** 1% significance.

HPI growth measure:
2nd quartile HPI growth CBSAs
3rd quartile HPI growth CBSAs
4th quartile HPI growth CBSAs
Credit score (time-varying)
Annual average employment growth
Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate
Year dummies
Age dummies
CBSA dummies
Observations

43

(1)
3-year HPI growth
from 𝑡 − 3 to 𝑡
0.0746***
(0.0257)
0.0684**
(0.0325)
0.0916***
(0.0324)
-0.000416***
(0.000121)
0.170
(0.337)
0.591**
(0.302)
0.126
(0.248)
-0.914
(0.814)
Yes
Yes
Yes

(2)
2-year HPI growth
from 𝑡 − 3 to 𝑡 − 1
0.0561**
(0.0244)
0.0618**
(0.0287)
0.0817***
(0.0298)
-0.000415***
(0.000121)
0.209
(0.340)
0.596*
(0.305)
0.107
(0.252)
-1.043
(0.784)
Yes
Yes
Yes

209,009

209,009

Table VII: Quantile Regression of Loan-to-value (LTV) Ratio
The table reports the results of regressing the median and third quantile of loan-to-value (LTV) ratio on
lagged housing price growth using quantile regressions. The sample only includes homebuyers of the 1%
sample of the primary-individual data from FRBNY (Equifax) Consumer Credit Panel Dataset whose first
time home purchase mortgage can be matched to McDash mortgage servicing data using the Credit Risk
Insight Servicing McDash (CRISM) dataset. The main variables are 3-year lagged HPI growth and the
quartile dummies sorted on the HPI growth among the pooled CBSA-year observations. Control variables
are year and age effects. Standard errors are clustered at the CBSA level and are shown below the coefficient
estimates. * 10%, ** 5%, *** 1% significance.

(1)

2nd quartile HPI growth CBSAs
3rd quartile HPI growth CBSAs
4th quartile HPI growth CBSAs
3-year HPI growth from t-3 to t
Year dummies
Age dummies
Observations

(2)
(3)
(4)
Quantile Regression
50th LTV
75th LTV
0.767
-0.0300
(0.860)
(0.856)
-1.365
-0.230
(1.073)
(1.067)
-6.805***
-5.380***
(1.044)
(1.039)
-23.78***
-29.19***
(3.823)
(3.726)
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
7,248
7,248
7,248
7,248

44

Table VIII: Housing size and HPI growth
The table reports the results of regressing housing size (proxied by housing price in 2000 dollars) on quartile
dummies sorted on HPI growth among the pooled CBSA-year observations by age. Housing price in 2000
dollars is the appraisal amount (i.e. origination amount/LTV) deflated by CBSA-specific house price growth
to 2000 dollars. The sample only includes homebuyers of the 1% sample of the primary-individual data
from FRBNY (Equifax) Consumer Credit Panel Dataset whose first time home purchase mortgage can be
matched to McDash mortgage servicing data using the Credit Risk Insight Servicing McDash (CRISM)
dataset. Columns 1 and 2 reports the results of the regressions when the sample is restricted to homebuyers
whose age was less than 30 at time of home purchase. Columns 3 and 4 reports the results of homebuyers
whose age was greater than or equal to 30 at time of home purchase. The main variables are the quartile
dummies sorted on the HPI growth among the pooled CBSA-year observations. Control variables are the
individual-level credit score at time of home purchase, CBSA-level employment and wage variables, year,
age, and CBSA effects. Standard errors are clustered at the CBSA level and are shown below the coefficient
estimates. * 10%, ** 5%, *** 1% significance.

(1)

(2)

Dependent variable:
2nd quartile HPI growth CBSAs
3rd quartile HPI growth CBSAs
4th quartile HPI growth CBSAs
Credit score (time-varying)

Young

Young

Old

Old

3,111
(7,061)
9,842
(8,624)
20,541**
(9,713)
341.3***
(34.50)

99,020
(148,524)

-16,039**
(6,258)
-29,764***
(7,833)
-23,043***
(8,264)
225.1***
(26.84)
-1,163
(106,262)
40,893
(122,084)
-74,040
(92,697)
-191,941
(294,008)
117,244
(151,325)

-162,070***
(29,673)

2,562
(7,766)
9,575
(9,355)
20,926*
(11,102)
341.7***
(34.61)
124,024
(126,729)
119,530
(155,888)
-112,479
(79,744)
110,373
(231,691)
-173,117***
(31,406)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

0.332
2,807

0.332
2,805

0.303
4,508

0.303
4,506

Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate

Year dummies
Age dummies
CBSA dummies
R-squared
Observations

45

(4)

-14,473**
(6,369)
-27,675***
(7,929)
-20,665***
(7,826)
223.3***
(26.30)

Annual average employment growth

Constant

(3)
Housing Size

Table IX: Downpayment and HPI growth
The table reports the results of regressing home purchase downpayment on quartile dummies sorted on
HPI growth among the pooled CBSA-year observations by age. Downpayment is defined to be loan size
×(1-LTV)/LTV. The sample only includes homebuyers of the 1% sample of the primary-individual data
from FRBNY (Equifax) Consumer Credit Panel Dataset whose first time home purchase mortgage can be
matched to McDash mortgage servicing data using the Credit Risk Insight Servicing McDash (CRISM)
dataset. Columns 1 and 2 reports the results of the regressions when the sample is restricted to homebuyers
whose age was less than 30 at time of home purchase. Columns 3 and 4 reports the results of homebuyers
whose age was greater than or equal to 30 at time of home purchase. The main variables are the quartile
dummies sorted on the HPI growth among the pooled CBSA-year observations. Control variables are the
individual-level credit score at time of home purchase, house price in 2000 dollars, CBSA-level employment
and wage variables, year, age, and CBSA effects. Standard errors are clustered at the CBSA level and are
shown below the coefficient estimates. * 10%, ** 5%, *** 1% significance.

(1)
Dependent variable:

(2)

(3)

(4)

Downpayment

2nd quartile HPI growth CBSAs
3rd quartile HPI growth CBSAs
4th quartile HPI growth CBSAs
House Price (2000 Dollars)
Credit score (time-varying)

Young

Young

Old

Old

14,118*
(7,533)
22,697*
(12,084)
27,144***
(9,925)
0.901***
(0.314)
-36.38
(54.03)

17,383**
(7,942)
23,037***
(7,681)
26,100***
(6,560)
0.678***
(0.0476)
46.53***
(14.33)

-7,971
(51,040)

11,293
(6,912)
18,796*
(11,170)
20,988**
(8,784)
0.899***
(0.313)
-33.06
(52.16)
-126,063
(89,593)
22,647
(97,011)
-87,512
(81,874)
-593,074**
(242,264)
45,800
(38,306)

-102,327***
(16,778)

12,521
(7,700)
17,196**
(7,500)
16,857**
(7,387)
0.678***
(0.0479)
47.12***
(14.05)
-48,946
(88,919)
-184,646**
(93,374)
20,025
(59,621)
-757,369***
(156,631)
-77,943***
(14,511)

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

Yes
Yes
Yes

0.576
2,727

0.578
2,727

0.668
4,410

0.671
4,408

Annual average employment growth
Average weekly wage growth
Average quarterly growth in number of establishments
Unemployment rate
Constant
Year dummies
Age dummies
CBSA dummies
R-squared
Observations

46

Figure A.1: Regions of Opitimal Time of First Home Purchases and Optimal Consumption Plan (Case 1)

Figure A.2: Regions for Discussing Optimal Timing of First Home Purchases (Case 3)

47

Figure A.3: Regions of Optimal Timing of First Home Purchases (Case 3)

(3) Never

(I) '!"=0

(2) r-= 1

·..

""

·.

"'

.....,.,

48

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