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Do Changes in Mortgage Credit Constraints
Explain the Housing Boom and Bust?
Andra C. Ghent
University of Wisconsin-Madison
ghent@wisc.edu
Preliminary and Incomplete
October 1, 2018
Abstract
This paper documents patterns in US mortgage debt and home ownership in recent decades and explores how well changes in mortgage credit constraints can explain these changes. The age-adjusted home ownership rate declined slightly between
2000 and 2007, but the real stock of residential mortgage debt doubled. Since 2007,
age-adjusted home ownership rates have trended down significantly as has the real
stock of residential mortgage debt. The paper builds an equilibrium life-cycle model
of tenure and mortgage choice that shows that a relaxation of the Loan-to-Value (LTV)
constraint increases the homeownership rate for young, high-income households.
1
Introduction
The last two decades have featured dramatic changes in the availability and use of
mortgage credit. The first part of this paper summarizes data and literature on the mortgage credit landscape in the last two decades. I use this data to generate facts that a theory
of the boom and bust in the housing market needs to explain. Most strikingly, any theory of the boom period of 2000-2007 needs to reconcile 1) no increase in the age-adjusted
home ownership rate, and 2) a dramatic increase in the real stock of mortgage debt relative to real home prices. The bust period, in contrast, features significant declines in
age-adjusted home ownership rates for all ages but especially those under the age of 55.
I then build an equilibrium life cycle model based on Ghent (2015) to study how well
changes in credit constraints can explain the boom and bust. In particular, I look at how
changes in the maximum loan-to-value (LTV) on a low down payment (LDP) mortgage
affect the stock of mortgage debt and home ownership rates by age. I show that the main
effect of such a relaxation of the LTV constraint is an increase in the age-adjusted home
ownership rate, particularly the home ownership rate of high-income young households.
The findings in this paper indicate that we need to look to other changes in the mortgage landscape to explain increasing levels of mortgage debt with no change in the home
ownership rate during the boom. While optimism in home price expectations is likely a
necessary ingredient, a promising further candidate is a decrease in the cost of extracting equity. Our findings also suggest that the tightening of mortgage credit constraints
during the bust period, in part due to more regulation, is decreasing home ownership
consistent with the empirical evidence in Gete and Reher (forthcoming).
1
2
Trends in Housing Finance
2.1
Homeownership
The top panel of Figure 1 plots the aggregate US home ownership rate as well as
the home ownership rate for those above and below the median income. The overall
rate rises by 5% (3.3 percentage points) between 1994 and 2000, from 64.2% to 67.5%.
Home ownership rises for both low- and high-income American households but the rise is
sharper for low-income Americans. The home ownership rate for those below the median
income rose by 6.6% while the rise for households above the median income level was
only 3.6%.
The aggregate home ownership rate peaks at 69.2% in 2004. It stays close to that level
until 2007 when it begins a steady decline that levels out at about 64% in 2014. Looking
specifically at the 2000 to 2007 period, which is commonly considered to be the boom
period for housing prices and nonprime mortgage originations, the increase is just 0.3
percentage points or 0.4%. The home ownership rate for low-income Americans actually
declines slightly over this period from 51.8% to 50.9%.
The small increase in the aggregate home ownership rate over the 2000-2007 housing
boom is, however, partly due to the aging of the US population. The bottom panel of
Figure 1 shows the home ownership rate by broad age category for 1995, 2001, 2007, 2013,
and 2016. The home ownership rate in 2001 is higher for every age category than in
1995. However, the home ownership rates within an age category actually decline slightly
between 2001 and 2017. Home ownership rates by age category fall significantly between
2007 and 2013 for all ages except senior citizens with a slight further decline between 2013
2
Figure 1: US Homeownership, 1994-2017
(a) By Income Group
(b) By Age Category
Source: U.S. Census Bureau, Current Population Survey / Housing Vacancy Survey, July 26, 2018.
3
and 2016.
The decline in home ownership in the bust period is of a similar magnitude for low
and high income Americans. For households above the median income, home ownership
peaks at 84.6% in 2004 and reaches a trough of 78% in 2016, a total decline of 6.6 percentage points or almost 7.8%. Home ownership for households below the median income
declines from 53.1% to 49% or about 7.7%.
2.2
Mortgage Credit
Although the age-adjusted home ownership rate did not increase during the boom, the
real stock of residential mortgage debt almost doubled over this period as Figure 2 shows.
Some of the increase in mortgage debt was likely to finance more expensive homes rather
than a deliberate decision by borrowers and lenders to increase leverage. Indeed Adelino
et al. (2018) find that the increase in mortgage credit was most pronounced in areas with
the fastest increase in home prices. Nevertheless, the increase in the FHFA home price
index was only 40% during the boom period.
While very high by historical standards, such growth can account for less than half
of the growth in the stock of mortgage debt as Table 1 illustrates. Table 1 shows how a
growth rate in home prices of 40% would affect a typical US household’s mortgage debt
with no change in the household’s ability to generate a down payment. For a household
that could initially come up with a 20% down payment, the growth in mortgage debt
from the increase in home prices would be 50%. For a household that could initially
come up with only a 10% down payment, the growth is 44% while the growth is 40% for
4
Figure 2: US Real Residential Mortgage Debt and Home Prices
Sources: Federal Reserve Financial Accounts of the United States, FHFA, and BLS.
households with no initial down payment.
Thus, most of the growth in mortgage debt between 2000 and 2007 came along the intensive margin with home owners taking on higher relative mortgage burdens. However,
Adelino et al. (2018) find no discernible trend in combined LTVs (CLTVs) at origination.
Thus, it seems more likely that much of the increase in mortgage debt during the boom is
due to home equity extraction, a channel emphasized by Greenspan and Kennedy (2008).
Lee et al. (2013) find that the majority of second liens are taken out subsequent to origination, a finding that can reconcile significant growth in mortgage debt along the intensive
5
Table 1: Hypothetical Change in Mortgage Debt for Home Price Growth of 40%
Home Price
LTV
Mortgage Debt
Down Payment
LTV
Mortgage Debt
Down Payment
LTV
Mortgage Debt
Down Payment
2000
2006
Growth
$ 300,000 $ 420,000
40%
80%
86%
$ 240,000 $ 360,000
50%
$ 60,000 $ 60,000
90%
$ 270,000 $ 390,000
44%
$ 30,000 $ 30,000
100%
$ 300,000 $ 420,000
40%
$$-
Notes: 1) Table shows hypothetical increase in mortgage debt generated by a 40%
increase in real home prices between 2000 and 2007. 2) Table assumes no growth in
household wealth between the two years such that any increase in home purchase price
must be financed. 3) Table shows an initial home price of $300,000 for exposition
purposes but growth rates are the same regardless of the initial home price.
margin with no change in CLTVs at origination.
Several recent papers explore how the growth of residential mortgage debt differed
across different income groups during the boom. These papers show that the growth in
mortgage credit was broad-based and occurred among all income groups rather than being concentrated among low-income borrowers. Figure 3, taken from Foote et al. (2016),
illustrates that the growth in mortgage debt during the boom was evenly distributed
across household income and neighborhood income quintiles. Foote et al. (2016) argue
that, although the growth rate was roughly evenly distributed across income groups, the
larger total amounts of debt held by high-income mortgage borrowers generate disproportionate shares of the increase. Adelino et al. (2018) similarly emphasize that both the
flow and stock of debt rose across all income groups.
The broad-based growth in mortgage credit was also not confined to borrowers with
6
low credit scores. Indeed, Albanesi et al. (2017) show that mortgage debt growth during
the boom was concentrated on borrowers in the upper half of the FICO score distribution. As such, they argue that subprime, at least using a definition of subprime based on
borrower credit scores, which are highly correlated with household income, is not a first
order factor in the boom.
None of these papers dispute the growth in the PLMBS market during this period.
Figure 4 illustrates the explosion in the issuance of PLMBS during the boom. It is worth
noting that many of the mortgages securitized in PLMBS were not made to low-income
borrowers, however. In their analysis of mortgages on property in California and Florida,
Ghent et al. (2015) show that the average borrower in a PLMBS pool had a stated household income of over $100,000. Rather than being a niche product originated to a set of
households historically excluded from the mortgage market, subprime was very much a
middle-class product.
3
The Model
I study an overlapping generations endowment economy similar to that in citetGhent2015.
Households live for at most J periods of which JRET < J are spent “working”. Each period, the household makes decisions regarding its tenure, assets, and mortgage choice. If
the household chooses to rent, it must rent a home of quality h1 . If a household chooses
to own its home, it chooses what quality of home to buy, and selects a mortgage (when
given a choice). The mortgage rate for each mortgage type is computed as the rate that
makes the expected present value of the mortgage equal to the mortgage balance at orig7
Figure 3: Cross-Sectional Distribution of Mortgage Debt
Source: Foote et al. (2016).
8
Figure 4: US MBS Issuance by Year, USD Billions
Source: SIFMA.
ination. There are a small number of home qualities; a small number of home qualities
reduces the computation required to solve the model.
The price of a unit of housing (in terms of the non-housing consumption good) is
exogenous. Households face idiosyncratic income and home quality risk.1 I represent
stochastic home values by assuming the home will decrease or increase in quality with
exogenously given probability; the home quality follows a Markov chain. As in other
models with mortgage choice and foreclosure, I model home prices as exogenous to focus on modeling mortgage contracts and mortgage default in more detail. If a financial
intermediary is forced to foreclose on a borrower, it incurs a cost χ (a percentage of the
home value at the time of foreclosure) to rehabilitate the home to the quality it was at the
time of foreclosure.
1 See,
among others, Case and Shiller (1989), Goetzmann (1993), Quigley and Van Order (1995), Deng
et al. (2000), and Flavin and Yamashita (2002) for evidence that a substantial portion of the variation in
home values is idiosyncratic.
9
Similar to Campbell and Cocco (2015) and Corbae and Quintin (2015), there is no option to refinance to keep the model computationally tractable. Prepayment in the model
thus corresponds to a sale of the home. When the household wishes to sell its home, it
must pay a fixed cost that is a percent of the value of the home. The sale of the home may
be viewed as a particular kind of refinancing: the household may refinance into the same
value of home with a new mortgage if it pays the fixed moving cost. Viewed this way, the
moving cost is akin to a prepayment penalty. The moving cost is what makes the home a
commitment device for saving. Because the household cannot easily change its housing
investment decision, taking on a mortgage commits the household to a particular savings
path.
To fit the home ownership rate patterns of older households in the data, I assume a
bequest motive on the part of the household. I model the bequest motive similarly to
Campbell and Cocco (2003), Cocco (2005), and Cocco et al. (2005). When a household
dies, a newly born household that begins life with no assets immediately replaces it.
At the beginning of each period, the household learns its income for that period and, if
it is an owner, whether its home has appreciated or depreciated in value. The household
then makes its tenure, housing, mortgage termination, mortgage product, and consumption decisions. If the household chooses to enter into a new mortgage contract, it makes
the down payment at the start of the period. At the end of the period, the household
receives its income, consumes, and makes rent or mortgage payments. Mortgages are
non-recourse in the sense that the lender cannot seize assets other than the house if the
borrower defaults on the mortgage.
10
3.1
Households
Households that choose to own a home take on a T period mortgage. The household’s
state vector is { j, a, H, h, n, hO , κ, y} where j ∈ {0, ..., J − 1} represents the household’s age,
a represents the household’s assets, H ∈ {0, 1} is the household’s tenure, h ∈ { h1 , h2 , h3 }
is the home quality, n ∈ {0, ..., T } is the number of periods the household has remaining
on in its current mortgage, and hO ∈ {h2 , h3 } denotes the home quality that the household
chose at origination. As in Gervais (2002) and Corbae and Quintin (2015), the poorest
quality home a household can buy is h2 rather than h1 . Income, y, is exogenous and
follows a Markov process. κ ∈ { TRAD, LDP} represents the household’s mortgage type.
A TRAD mortgage is a traditional mortgage that requires a down payment of νTRAD
percent, full amortization over the term of T periods, and carries a constant interest rate
of r TRAD . A LDP mortgage is a mortgage that requires a down payment of νLDP , is fully
amortizing over T periods, and carries a constant interest rate of r LDP .
The household aged j that enters the period with assets a, tenure H, home quality h,
n periods remaining on its mortgage, mortgage type κ, and income y thus chooses its
tenure, housing, mortgage, and assets to maximize
0
u c, h0 , H 0 + βπ j EV j + 1, a0 , H 0 , h0 , n0 , hO
, κ 0 , y0 + β 1 − π j E ln W
where
n0 =
(1 − 1S − 1 D ) max (0, n − 1) + 1 B ( T − 1) i f H 0 = 1
0 if
11
H0
=0
,
(1)
The indicator function 1 B takes on a value of one if the household buys a new home
in that period, and hence takes on a new mortgage, and 0 otherwise. The indicator 1 D
takes on a value of 1 if the household chooses to default in that period, 0 otherwise. The
indicator 1S takes a value of 1 if the household chooses to sell its home, 0 otherwise. π j is
the probability that a household that has survived to age j survives to age j + 1.
W represents net worth in equation (1) and V (·) is defined by
V ( j, a, H, h, n, hO , κ, y) = max
u (c, h0 , H 0 ) +
0 , κ 0 , y0
βπ j EV j + 1, a0 , H 0 , h0 , n0 , hO
+ β 1 − π j E ln W
.
In computing expected net worth, I assume that when a household dies the housing position is liquidated and the financial intermediary is repaid the debt if the house value is
adequate or receives the house value.
For a household that starts the period as a renter ( H = 0), the constraint on (1) is
c + a0 = y + (1 + r ) a − H 0 ν (κ ) qh0 − H 0 p T (κ ) + δh0 − 1 − H 0 Rh1
(2)
where q is the price per unit of housing, pn (κ ) is the payment due on a mortgage of type
κ with n periods remaining, δ is the depreciation rate, and R is the rental rate.
If the household starts the period as an owner ( H = 1), it decides whether to default
on its mortgage and whether to sell its home. If the household decides to default, H 0 = 0.
12
The constraints on (1) if H = 1 are thus
c + a0 = y + (1 + r ) a + 1S [q (1 − σ ) h − bn (κ )] − H 0 1 B ν (κ ) qh0
− H 0 (1 − 1 B ) pn (κ ) + 1 B p T κ 0 + δh0 − 1 − H 0 Rh1 ,
H 0 ≡ 0 i f 1 D = 1,
∈ { TRAD, LDP} i f 1 B = 1
κ0
= κ i f 1S ∪ 1 D = 0
= ∅ i f H0 = 0
(3)
, and
(4)
0
hO
≡ hO i f 1 B = 0.
(5)
where σ represents the transactions cost of selling a home and bn (κ ) is the outstanding
balance on a mortgage of type κ with n periods remaining on its term.
The interpretation of (3) is that if the household chooses to default on its mortgage,
it must rent for that period. Equations (4) and (5) represent the fact that the household
cannot refinance. Equation (4) says that the household can only enter into a new mortgage contract when it buys a new home and κ is null if the household chooses to rent.
Households in the model choose between TRAD and LDP. Equation (5) is mechanical: it
says merely that the household’s state variable for the home quality at origination does
not change if the household does not buy a new home.
The Benefits of Home Ownership
In this framework, there are two potential benefits of owning a home relative to renting. First a premium for owning relative to renting is built into the felicity function
13
through its dependence on tenure chosen in that period, H 0 . In this respect, I follow
Hu (2005), Chu (2014), and Corbae and Quintin (2015). Arguably, the owner-occupied
utility premium captures the benefit from a household being able to customize an owneroccupied home (e.g., paint the kitchen purple or install carpeting instead of wood floors)
and any psychic benefit from owning relative to renting.
Second, households can only rent a home of quality h1 ; if a household wants to consume housing services associated with a home of quality h2 or h3 , it must be a home
owner. I follow Corbae and Quintin (2015) in this respect. These assumptions are important to generate home ownership rates similar to what we observe in the data. The
assumption that all rental homes are of quality h1 also implies that the housing share of
expenditure is declining in income. The assumptions are also important for understanding the results regarding welfare.
3.2
Financial Intermediary
As in Corbae and Quintin (2015), the financial intermediary is an infinitely lived company that accepts household savings and makes mortgage loans. It earns the exogenously
given rate r on savings. Each period, it pays a servicing cost φ, a percent of the value of
the mortgage, on each mortgage it holds. It also holds a stock of housing capital which it
can rent out at rate R per unit or sell to households as owner-occupied housing. It incurs
the maintenance cost δ on its housing stock and a cost χqh of rehabilitating housing units
it acquires through foreclosure. In equilibrium, it must make zero profits. Since the value
of a home must be equal to the present value of future rents, in equilibrium each unit of
14
housing rents at rate R = rq + δ where q is the price per unit of housing.
3.3
Home Values
As in Corbae and Quintin (2015), stochastic house prices are captured by households
facing an exogenously given probability that their house changes in quality and, hence,
value. In particular, a home owner that currently owns a home of quality h2 faces a
probability λ that the home will increase to quality h3 and a probability λ that the home
will decrease to quality h1 . A home owner that currently owns a home of quality h3 faces
a probability λ that the home will depreciate to quality h2 . A home owner that owns a
home of quality h1 faces a probability λ that the home will increase to a home of quality
h2 . Rental units, all of which are of quality h1 , do not change in quality.
3.4
Steady State Equilibrium and Computation
In equilibrium, lenders make zero profits. This implies that the contract rates, r TRAD
and r LDP are the rates that equate the expected present value of the mortgage to the loan
balance at origination. The equilibrium concept in this paper is the same as that Athreya
(2002): the equilibrium is a pooling equilibrium where the financial intermediary offers
the same interest rate to all borrowers in a particular product category. In Corbae and
Quintin (2015), the mortgage interest rate is specific to a single household’s asset, income,
and housing combination such that it represents financial intermediaries assessing the
risk of individual households. Introducing interest rates specific to each individual is
unlikely to qualitatively change the predictions of the model regarding how credit con-
15
straints affect different age groups and substantially increases the computational cost of
solving the model. The opportunity cost of the lender’s funds is the riskless interest rate,
r; it costs lenders φ to service the mortgage rate. Lenders thus compute the present value
of the mortgage rate by discounting the expected cash flows by r + φ. An equilibrium is
thus a set of interest rates, {r TRAD , r LDP }, such that the average present value of a mortgage contract κ is equal to the size of the mortgage at origination.
The solution algorithm consists of two loops. In an inner loop, I solve the household’s
problem using grid search over each of the choice variables for a given pair of interest
rates, r TRAD and r LDP . I simulate the model over 20,000 households for 1,000 periods for
each mortgage rate or rates. I drop the first 100 periods as burn-in iterations.
The outer loop solves for the mortgage rate or rates. After solving the household’s
problem and simulating the model based on the solution to the household’s problem, I
compute the average present value of a mortgage contract of type κ. With a large enough
number of households and periods, the average present value of the mortgage contract
will also be the expected present value of the mortgage contract. Thus, if the difference
between the average present value of a mortgage contract and the loan balance at origination is sufficiently small, the mortgage rates constitute an equilibrium.
4
Benchmark Parameterization
Table 2 summarizes the benchmark parameterization. Several of the parameters are
fixed based on empirical estimates. The remaining parameters are chosen to ensure that
the model matches certain moments in the data.
16
Table 2: Benchmark Parameterization
Parameter
β
νTRAD
r
ψ
θ
h1
h2
h3
q
λ
φ
χ
δ
ρ
T
J
J ret
4.1
Description
3-Yr Discount Factor
Down Payment Share for TRADs
3-Yr Real Risk-Free Rate
Non-housing Consumption Share
Owner-occupied Premium
Small House Size
Mid-Size House Size
Large House Size
Relative Price of Housing
House Price Shock Probability
Servicing Cost
Foreclosure Discount
Housing Depreciation
Selling Costs
Mortgage Contract Term
Maximum Life Span
Retirement Age
Value
0.857
20%
0.12
0.76
0.0
29,390
45,421
66,795
1.0
0.15
0.02
0.25
0.04
0.08
10
20
13
Fixed or Calibrated
Fixed
Fixed
Fixed
Fixed based on Davis and Ortalo-Magné (2011)
Calibrated
Calibrated
Calibrated
Calibrated
Calibrated
Calibrated
Calibrated
Fixed based on Campbell et al. (2011)
Calibrated
Fixed
Fixed (30 years)
Fixed
Fixed
Preferences
The felicity function is
u (c, h, H ) = ψ ln c + (1 − ψ) ln h + θ1h>h1 .
I set ψ to 0.76 implying that renters spend 24% of their consumption expenditure on housing based on the estimates in Davis and Ortalo-Magné (2011). There are no good estimates
for θ such that I use θ to calibrate the model to match certain characteristics of the data.
4.2
Demographics
A period in the model corresponds to 3 years. The household is born at age 25, such
that j = 0 corresponds to a chronological age of 25. The household lives until at most
85 years of age corresponding to J = 20. The age at which the household retires, J RET ,
17
is 13 such that the household retires at a chronological age of 64. I take the survival
probabilities, π j
4.3
J −1
,
j =0
from Arias et al. (2008).
Income
I assume that the income process during working years follows an AR(1) process with
a quadratic polynomial in age. That is, the process for income is
yt = ρyt−1 + γ1 aget + γ2 age2t + ε t
(6)
where ε t has variance σε2 . I estimate the parameters of (6) using triennial PSID data on
earnings from 1967 to 1992. I estimate the model using all heads of households between
the ages of 25 and 64 that have positive labor income in the year prior to the survey, that
have only high school degrees, and that are not part of the Survey of Economic Opportunities sample. The measure of income is all labor income. I convert income for all years
into 1983$ prior to estimation using the CPI (all items). This estimation procedure yields
ρ̂ = 0.76, and σ̂ε2 = 8817. After removing the age-specific mean of income, I then approximate (6) with a three state Markov chain using the approach of Tauchen and Hussey
(1991). After retirement, labor income is set to 60% of income in the last working year
following Cocco et al. (2005) and Yao and Zhang (2005).
18
The transition probability matrix that governs the transitions between states is
0.7049 0.2877 0.0073
0.1667 0.6667 0.1667 .
0.0073 0.2877 0.7049
For example, a household that is a low income earner in period t has a 70.5% chance of
being a low income earner in period t + 1, a 28.8% of being a medium income earner in
period t + 1, and a 0.007% chance of being a high-income earner in period t + 1. The
ergodic distribution associated with this Markov chain is such that, in the steady state,
26.85% of households have low income, 46.3% of households have medium income, and
26.85% of households have high income. In the simulations, income at birth is randomly
allocated to match the ergodic distribution.
4.4
Housing Costs
Based on the estimates of Campbell et al. (2011), I set χ, the foreclosure discount, to
0.25. I choose λ, the probability of an idiosyncratic home value shock, the home qualities,
h1 , h2 , and h3 , the relative price of housing, q, and the mortgage servicing cost, φ, to
calibrate the model to match the key moments in the data. The calibration implies that the
price of the homes in 1983$ (the same units as income) are $29, 390, $45, 421, and $66, 795.
By comparison, the median home price in the 1980 US census was $54, 022 in 1983$. I
set T, the mortgage term, to 10 such that mortgages have 30 year terms. For TRADs,
households must make a 20% down payment such that ν = 0.2. The three-year risk-free
19
rate, r, is 12%. Selling costs, ρ, are 8% of the value of the home as in Cocco (2005). I use
δ, the per period depreciation rate on housing, to calibrate the model to match particular
moments in the data.
5
Results
Table 3 presents equilibrium statistics regarding the model when there is no LDP op-
tion, when νLDP = 10%, and when νLDP = 0%. There is a unique equilibrium with positive home ownership in all three cases. I present moments from the data for comparison.
For all three parameterizations, the home ownership rate is increasing in household income consistent with the data. Going from no LDP option to an option with νLDP = 10%
increase the home ownership rate slightly, from 71.3% to 71.5%. The increase in home
ownership in this case is quite slight because only a small fraction (2%) of home owners
choose the LDP mortgage because of its higher rate. For the parameterization chosen, it
just does not help many individuals become home owners.
20
Table 3: Steady State Equilibria
21
Moment
Home Ownership Rate
Low Income
Mid Income
High Income
Under 35
35-44
45-54
55-65
65+
Loan-to-Income
Rent-to-Income
Share of Home
Owners Using LDPs
Ann. TRAD Mtg Rate
Ann. NDP Mtg Rate
Average Real 30-year
Mtg Rate
Foreclosure Rate
1995
65.1%
2001
68.0%
Data
2007
67.8%
2013
65.2%
2016
63.7%
39%
66%
75%
80%
79%
171%
36.3%
42%
68%
76%
81%
81%
182%
35.2%
41%
67%
75%
80%
80%
241%
34.6%
37%
61%
71%
77%
81%
246%
38.4%
35%
59%
70%
75%
80%
230%
37.0%
5.93%
4.97%
4.34%
1.98%
1.65%
no LDP
71.3%
30%
83%
92%
31%
70%
81%
86%
76%
208%
32.3%
-
Model
νLDP = 0.1
71.5%
30%
83%
92%
31%
71%
81%
86%
76%
207%
32.9%
2.2%
νLDP = 0.0
72.5%
30%
83%
98%
37%
70%
81%
86%
76%
199%
34.2%
12.0%
5.27%
5.27%
5.27%
5.93%
5.28%
5.27%
7.08%
5.33%
1.29%
1.31%
1.41%
Notes: 1) Data sources are US Census CPS / Housing Vacancy Survey, Federal Reserve Consumer Finance Survey, and
Federal Reserve Bank of St. Louis. 2) In columns (2)-(6) I subtract 2% from the nominal mortgage rate for expected inflation
to make the mortgage rates comparable to the model.
Introducing the option of νLDP = 0% increases the home ownership rate more substantially as 12% of home owners finance home ownership with no down payment mortgages
when that option is available. This raises the aggregate home ownership rate to 72.5%.
The increase in home ownership from no down payment mortgages is almost exclusively
because young households can become home owners earlier. The home ownership rate
for those under age 35 is 37% when νLDP = 0% while it is only 31% in the other two
versions of the model. In contrast, the home ownership rates for other age categories are
unaffected. In fact, virtually the only households that take out an LDP when νLD = 0%
are those below age 35; the share of originations using LDPs are all under 0.5% for households above the age of 34.
Looking at differences across income, the home ownership rate rises only for high
income households when I introduce no down payment mortgages into the economy.
The reason is that only young households that expect to have high future income, but
do not currently have the assets for a down payment, avail themselves of the option to
become home owners while young. Because income has a strong persistent component,
young high income earners smooth their consumption over the life cycle by becoming
home owners earlier.
The finding that tightening credit constraints decreases the home ownership rate and
especially that of younger households is consistent with the empirical evidence in Duca
and Rosenthal (1994) from prior to 1995. The predictions of the model are also consistent
with the empirical evidence of Gete and Reher (forthcoming) using US data from the
bust. However, the change in the home ownership rate from relaxing the LTV constraint
is inconsistent with the 2001 to 2007 data. Not only does the overall age-adjusted home
22
ownership rate fall between 2001 and 2007, it falls for the youngest age group.
Perhaps surprisingly, overall debt-to-income ratios actually fall slightly in this economy. The main reason for the slight decline is that relaxing the LTV constraint introduces
high income young households into the home ownership pool. Because they still have
low assets, having yet to have worked long enough to accumulate substantial net worth,
they buy small houses relative to their incomes and thus have lower loan to income ratios
than most home owners. This lowers the aggregate debt to income ratio. This fact, too, is
inconsistent with the sharp rise in the debt-to-income ratio over the boom period.
6
Conclusions
This paper has explored how well a model of tenure and mortgage choice with binding
LTV constraints can fit US home ownership and mortgage debt patterns over the last two
decades. The main finding is that a relaxation of the LTV constraint raises the home
ownership rate primarily for high income, young households. This is inconsistent with
static to declining age-adjusted US home ownership but increasing debt levels over the
2000 to 2007 housing boom. The effects of the LTV constraint in the model are, however,
consistent with tightening LTV constraints since 2007 having reduced home ownership,
particularly for high income Americans.
The empirical facts regarding home ownership and debt levels appear consistent with
a significant decline in the costs of equity extraction, particularly for home owners staying
in their current home, during the housing boom of the 2000s. A fruitful direction for
future research is explicitly modeling the effect of declines in the costs of home equity
23
extraction in a life cycle model with housing decisions.
An important limitation of the model is its assumption of exogenous home prices. Previous research has shown that collateral constraints can meaningfully affect home prices
in life cycle models.2 A useful further direction of research would thus be to endogenize
home prices in a life-cycle model with mortgage and tenure choice.
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