Lecture 9: Housing - Princeton Universityerossi/Urban/Lecture_9_538.pdfDecomposing House Price...

Lecture 9: HousingWWS 582a

Esteban Rossi-Hansberg

Princeton University

ERH (Princeton University ) Lecture 9: Housing 1 / 31

Decomposing House Price Changes

Use the decomposition in Davis and Heathcote (JME, 2007)

Decompose the value of a house using according to

plt lt = pht ht − pSt St

where plt , pht , and p

St are quality adjusted prices of land, houses, and

structures, and lt , ht , and St the corresponding quantities.

Suppose a set of houses is observed in two periods t and t + 1, then

plt+1plt

=1

w lt

[pht+1pht

−(1− w lt

) pSt+1pSt

]

where w lt is the fraction of the market value of the set of houses accountedfor by land (plt lt/p

ht ht = 1− pSt St/pht ht )


Data

This equation can be used to decompose the evolution of house prices into itstwo components

I Importantly the land share includes all the value of location

pSt : use the price index for gross investment in new residential structuresproduced by the Bureau of Economic Analysis (BEA) within the NationalIncome and Product Accounts (NIPA)

pht : use the repeat-sales-based index produced by the Offi ce of FederalHousing Enterprise Oversight (OFHEO)

Use the BEA’s published series for the replacement cost to estimate the valueof structures, pSt StUse Decennial Census of Housing (DCH) and perpetual inventory system


Decomposition

Second, the value of land has increased faster than the value of structures, and thus landhas become an increasingly important component of aggregate wealth. Averaging overour sample period, residential land accounts for 36% of the value of the housing stock.There is evidence of an upward long-run trend in the share of the market value ofhousing accounted for by land (see Fig. 2) and since the mid-1990s the value of land hasbeen rising quickly. By the second quarter of 2006, residential land was valued at $11.6trillion, accounting for 46% of the value of the housing stock and 88% of GDP, recordsfor our sample.

ARTICLE IN PRESS

1

2

3

4

1975 1980 1985 1990 1995 2000 2005

Index (1975:1

= 1

.0)

Residential Land

Homes

Structures

Fig. 1. Real land, home, and structures prices (log scale).

20

25

30

35

40

45

50

1975 1980 1985 1990 1995 2000 2005

Perc

ent

Fig. 2. Land’s share of home value.

M.A. Davis, J. Heathcote / Journal of Monetary Economics 54 (2007) 2595–2620 2607


Land’s Share

Second, the value of land has increased faster than the value of structures, and thus landhas become an increasingly important component of aggregate wealth. Averaging overour sample period, residential land accounts for 36% of the value of the housing stock.There is evidence of an upward long-run trend in the share of the market value ofhousing accounted for by land (see Fig. 2) and since the mid-1990s the value of land hasbeen rising quickly. By the second quarter of 2006, residential land was valued at $11.6trillion, accounting for 46% of the value of the housing stock and 88% of GDP, recordsfor our sample.

ARTICLE IN PRESS

1

2

3

4

1975 1980 1985 1990 1995 2000 2005

Index (1975:1

= 1

.0)

Residential Land

Homes

Structures

Fig. 1. Real land, home, and structures prices (log scale).

20

25

30

35

40

45

50

1975 1980 1985 1990 1995 2000 2005

Perc

ent

Fig. 2. Land’s share of home value.

M.A. Davis, J. Heathcote / Journal of Monetary Economics 54 (2007) 2595–2620 2607


Growth Rates

Third, the real stock of land has increased quite slowly, and changes to the quantity ofthe real stock of housing have been accomplished primarily through the addition ofstructures. The average annual growth rate of the real housing stock is 1.80% per year,compared to a 1.57% growth rate in the number of households.26 The constant-qualitystock of residential land has grown at a pretty stable annualized rate of 0.67% since thefirst quarter of 1975 (see Fig. 3).27 The growth rate of the real stock of residential structuresis much faster, 2.41% per year on average, but also more volatile.

Fourth, Fig. 3 indicates that growth in the real stocks of land, structures and housingduring the boom that began in the mid-1990s was comparable to growth in the rest of thepost 1975 period. We conclude that increased demand must play an important role inaccounting for the run-up in prices over this period.

4.2. New versus existing homes

The land data also allow us to better understand intrinsic differences in the pricedynamics of new versus existing homes. Our analysis of land’s share of home valueprovides evidence that typical newly built homes and existing homes are quite differentgoods. First, while land now accounts for almost half of the value of the existing aggregatehousing stock, the cost of purchasing raw land for newly built houses is only around 11%of these houses’ market value. Put differently, our estimates suggest that in 2006 home-buyers are paying about 40% more on average for existing homes relative to newly built

ARTICLE IN PRESS

-1

0

1

2

3

4

5

1980 1985 1990 1995 2000 2005

Pe

rce

nt

Residential Land

Homes

Structures

Fig. 3. Year-on-year growth of real land, home, and structures quantities.

26The household-size data are from Table HH-4, ‘‘Households by Size: 1960 to Present,’’ of the Current

Population Survey (CPS) Reports, and are available at http://www.census.gov/population/www/socdemo/

hh-fam.html.27The fact that the real quantity of residential land has risen so slowly and smoothly over time means that

fluctuations in the value of the stock of land are almost entirely attributable to fluctuations in land prices.

M.A. Davis, J. Heathcote / Journal of Monetary Economics 54 (2007) 2595–26202608


Urban and Farm Land

Now focus on rows (1) and (4) of Table 3, the house price regressions. Recall that houseprices are a weighted average of land prices and structures costs. In each case, thecoefficients on variables in the house price regressions appear to be a weighted average ofthe coefficients from the structures regression and the land regression. For example,the near-zero coefficient estimate on interest rates in the house price regression isa mix of the insignificant positive estimate from the structures price regressions (rows 2 and5) and the significant negative estimate from the land price regressions (rows 3 and 6).However, since the connection between fundamentals and structures prices is notgrounded in theory, and appears statistically questionable in practice, one should becautious in interpreting the near-zero interest rate coefficient in the house price regressionas evidence that nominal interest rates do not impact house prices. Rather we concludethat it is difficult to properly assess the impact of fundamentals like income, interest rates,and inflation on the housing market if one fails to disentangle their impact on land andstructures prices separately.

4.5. Farm land versus residential land

Fig. 4 compares our land price series to the price-per-acre of farm land for the aggregateUnited States.30 This is the only other published aggregate price series for land in theUnited States of which we are aware. First, we note that the market value of residentialland dwarfs the value of farmland. In 2002 there were 938.3 million acres of farmland inthe United States (2002 Census of Agriculture, USDA). The average price per acre was

ARTICLE IN PRESS

1

2

3

4

1975 1980 1985 1990 1995 2000 2005

Index (1975:1

= 1

.0)

Residential Land

Farm Land

Fig. 4. Real residential land and farm land prices (log scale).

30The annual farm price-per-acre series is available from the United States Department of Agriculture web site,

http://www.ers.usda.gov/Briefing/LandUse/aglandvaluechapter.htm. We linearly interpolate the annual data to

generate a quarterly price-per-acre series.

M.A. Davis, J. Heathcote / Journal of Monetary Economics 54 (2007) 2595–26202612


What are the Key Determinants of Housing Values

Glaeser and Gyourko (2003) argues for the importance of zoning to determinethe appreciation of houses (and land in particular)

Key issue is that houses can always be replicated at construction costs

So if cost of the house is larger than the cost of land plus structure thenthere is an implicit "zoning tax"

I Calculated as house price over the cost of land plus the building cost of thestructure


House Prices and Construction Costs

24 The Impact of Building Restrictions on Housing Affordability

on construction costs include material costs, labor costs, and equipment costs for four different quality types of single-unit residences. No land costs are included.4

The Means data contain information on four quality types of homes—economy, average, custom, and luxury. The data are broken down further by the size of living area (ranging from 600 to 3,200 square feet), the number of stories in the unit, and a few other differentiators. We focus on costs for a one-story, economy house with an unfinished basement, with the mean cost associated with four possible types of siding and building frame, and with small (less than 1,550 square feet), medium (1,550 to 1,850 square feet), or large (1,850 to 2,500 square feet) living areas. Generally, our choices reflect low to modest construction costs. This strategy will tend to overestimate the true gap between housing prices and construction costs. If the relevant benchmark is an average-quality unit, not an economy-quality unit, construction costs should generally be increased by about 20 percent.

The housing price data used in this paper to create the relationship between home prices and construction costs come from the American Housing Survey. We focus on observations of single-unit residences that are owner-occupied and exclude condominiums and cooperative units in buildings with multiple units, even if they are owned.

Excluding apartments simplifies our analysis, but in some ways the connection between construction costs and home prices is easier with apartments. In general, the marginal construction cost of an apartment is the price of building up. For example, other data from R.S. Means show that the price per square foot of building in a typical high-rise of from eight to twenty-four stories was nearly $110 per square foot in New York City in 1999.5 This implies that the purely physical costs of construction for a new 1,500-square-foot unit in New York City are about $166,500. Anyone familiar with the New York housing market knows that a large number of Manhattan apartments trade at many multiples of this amount.

Because house price will be compared with construction costs, and the latter are reported on a square-foot basis, the house price data must be put in similar form. This is straightforward for the AHS, which contains the square footage of living areas. For every single unit reported in the 1999 or 1989 AHS, we can then compute the ratio of house value to construction costs (as long as it is in an area tracked in the Means data).6 From this, we can calculate the distribution of homes priced above and below construction costs and can do so for nearly forty cities in both 1989 and 1999. We look at two measures: the first is the share of housing in the area that costs at least 40 percent more than new construction. These are the homes in the area where land is actually a significant share of

new construction costs. If the appropriate benchmark is an economy home, then for these homes land is about 40 percent or more of the value. If the appropriate benchmark is an average home, then for these homes land is approximately 20 percent of the value of the home. Our view is that homes below this cutoff are sitting on relatively cheap land. We also calculate the share of homes with prices that are more than 10 percent below the cost of new construction.

Table 1 shows the distribution of homes—relative to construction costs—for the nation as a whole and for the four main census regions. These data highlight the point that at least half of the nation’s housing is less than 40 percent more expensive than economy-quality home construction costs, or no more than 20 percent more expensive than average-quality home construction costs. They also suggest that a large share of the nation’s housing has its price determined roughly by the physical costs of new construction, as most of the housing value is within 40 percent of physical construction costs. That said, the regional breakdowns reported in Table 1 emphasize that much land in Western cities looks to be relatively expensive.

Charts 1 and 2 give an overall impression of the underlying data. In Chart 1, for central cities, we have graphed the share of homes with prices that are more than 40 percent above construction costs in the 1999 American Housing Survey on the share of comparable homes in the 1989 AHS. The straight line in the chart is the 45-degree line. In Chart 2, we have repeated this procedure for the suburban parts of the metropolitan areas.

Table 1

Distribution of Single-Family House Prices Relative to Construction CostsAmerican Housing Survey Data: 1989 and 1999, Central-City Observations

1989 1999

Fraction of Units

Valued below 90 Percent ofConstruction

Costs

Fraction of Units

Valued above 140 Percent of Construction

Costs

Fraction of Units

Valued below 90 Percent of Construction

Costs

Fraction of Units

Valued above 140 Percent of Construction

Costs

Nation 0.17 0.46 0.17 0.50

Midwest 0.41 0.14 0.30 0.27

Northeast 0.12 0.58 0.37 0.34

South 0.11 0.50 0.13 0.46

West 0.05 0.69 0.04 0.77

Source: Authors’ calculations.


House Prices and Construction Costs


Chart 2

House Prices/Construction Costs over TimeSuburban Areas

Note: The x-axis (y-axis) denotes the share of homes in suburban areas with prices that are more than 40 percent above construction costs in the 1999 (1989) American Housing Survey.

0.2 0.4 0.6 0.8 1.00

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1989

1999

0.3 0.7 0.9

Detroit

Milwaukee

Pittsburgh

Columbus

MinneapolisHouston

Salt Lake City

Miami

Chicago

Tampa

Orlando

New Orleans

Fort Worth

Cleveland

Sacramento

Seattle

Newark

Atlanta

Rochester Albany

St. Louis

Baltimore

Fort Lauderdale

Riverside

Birmingham

Phoenix

New York City

Philadelphia

Oxnard

Cincinnati

San Diego

Los Angeles

AnaheimSan Francisco

0.5

1.0

Kansas City

Dallas

Boston

61 percent in 1989 and 63 percent in 1999. We suspect that one reason for the higher fractions of expensive housing is that suburban homes are newer and are likely to be of high quality. A second reason is that suburban homes have more land and suburban land is more expensive.

The data by local area are shown in Tables 2 and 3. These tables also report the share of the housing stock that is priced at least 10 percent below construction costs. Across the United

States, there are many areas with extremely cheap housing. However, in this sample, only Philadelphia and Detroit had extremely large values of this measure in 1999.7 We should note that our previous work using the 1990 census suggests that there is a greater amount of cheaper housing than is indicated by the AHS. Our suspicion is that the census is more representative, but we leave further examination of these discrepancies to future work.


Zoning and House Prices


Survey. This survey, which took place in 1989, covers jurisdictions in sixty metropolitan areas. Because of the limitations of our American Housing Survey data, we are forced to consider only observations on the central cities of forty-five metropolitan areas.

The variable we focus on here is a survey measure of the average length of time between an application for rezoning and the issuance of a building permit for a modest size, single-family subdivision of fewer than fifty units. This measure can take on values ranging from 1 to 5: a value of 1 indicates the permit issuance lag is less than three months, a value of 2 indicates the time frame is between three and six months, a value of 3 indicates a seven-to-twelve-month lag, a value of 4 indicates the lag is between one and two years, and 5 indicates a very long lag of more than two years. Before proceeding to a regression, we note that the correlation of the permit length variable with the fraction of housing stock priced more than 40 percent above the cost of new construction is fairly high at 0.43. The mean fraction of high-cost housing among the cities with permit waiting times of at least six months (that is, a value of 3 or more for this variable) is 0.75. Difficult zoning seems to be ubiquitous in high-cost areas.16

Table 6 reports regression results using the permit length variable. In the first column, we regress our housing cost

measure (again using the share of the city’s housing stock priced more than 40 percent above the cost of new construction) on the first zoning measure—the time required to get a permit issued for a rezoning request. We find a strong positive relationship, so that when the index increases by one, 15 percent more of the housing stock becomes quite expensive. This positive relationship also survives controlling for population growth during the 1980s and median income, as shown in the second column.17

In the final column of Table 6, we return to our implied zoning tax—T/L from above. This value is calculated using the data in Table 4. Specifically, we subtract the cost of land estimated in the nonlinear hedonic equation (that is, p from column 2 of Table 4) from the cost of land implied by sub-tracting structure cost from total home value (that is, p+T/L from column 3 of Table 4). We then regress this variable on our zoning measure. As the results show, the implied zoning tax is strongly increasing in the length of time it takes to get a permit issued for a subdivision. Increasing a single category in terms of permit issuance lag is associated with a nearly $7 per-square-foot increase in the implicit zoning tax. If the dependent variable is logged, the results imply that a one-unit increase in the index is associated with a 0.50-log-point increase in the implicit zoning tax.18

Table 6

Zoning Regulations and the Distribution of House Prices

Dependent Variable

Fraction of Units Valued at or above 140 Percent of Construction Costs

Fraction of Units Valued at or above140 Percent of Construction Costs

T/L from Table 4(Implied Zoning Tax)

Time to permit issuance for rezoning request 0.150 0.112 6.796

(0.051) (0.044) (3.048)

Log median family income, 1989 0.260

(0.255)

Percentage population growth, 1980-90 1.080

(0.411)

Intercept 0.111 -2.512 -3.527

(0.120) (2.634) (7.732)

0.16 0.40 0.15

Number of observations 40 40 22

Note: The independent zoning variable is a categorical measure of time lag between the application for rezoning and the issuance of a building permit for development of a modest size, single-family subdivision.

R2


Housing Prices and Urban Decline

Glaeser and Gyourko (2006) argue that housing prices have an importanteffect on urban growth and decline

Main story is simple the elasticity of housing supply is larger aboveconstruction costs than below

Why? Because housing is durable so even if prices fall below constructioncosts houses depreciate slowly

Implies that:I Cities grow more quickly than they declineI Urban decline is persistentI Positive shocks increase population but not housing pricesI Negative shocks decrease housing prices more than they decrease populationI Housing prices below construction costs indicate decline


The Basic Mechanism

urban decline and durable housing 347

Fig. 1.—The nature of housing supply and construction costs

among cities with at least 100,000 people at the beginning of the 1990s).Durable housing largely explains why decline typically is such a lengthyprocess. The eight consistently declining cities referenced above remainlarge places even after five consecutive decades of population loss.

As figure 1 suggests, a durable housing model predicts that increasesin population will be associated with small increases in prices, but de-creases in population will be associated with large decreases in prices.The data support this prediction. Durable housing also suggests thatexogenous forces predicting urban growth will have large effects onpopulation and small effects on prices. Conversely, exogenous forcesthat predict urban decline will have small effects on population and bigeffects on prices. Using the weather as a source of exogenous changesin the attractiveness of cities, we find support for these predictions.

Durability also implies that a negative shock to a city’s productivitywill continue to cause population declines over many subsequent dec-ades. This is consistent with our results, which show that the degree ofpersistence in population change among declining cities is double thatfor growing cities. Durability of housing also implies that the distributionof house prices should predict future growth, and not merely becausehigh house prices reflect future price appreciation. Population growthis indeed much lower in cities with larger fractions of their housingstocks valued below the cost of new construction. This is not a causal


The Evidence

Use the main equilibrium condition across cities

wages + amenities - housing costs = reservation utility

Can estimate the equation using median family income and Januarytemperature


Housing Prices and Fitted Values

Variation above and below construction costs in 2000: $97,794

Fig. 2.—Median price regression and construction costs. The dashed horizontal line represents the $97,974 construction costs (in 2000 dollars) fora modest-quality, 1,200–square foot single-family home estimated by R. S. Means (2000a). The observation for Honolulu is not plotted for ease ofpresentation.


Is the Response Skewed?

Run the following specification:

House P %∆ = α0 + α1PopLossit + α2PopGainit + α3 × δt + εit

α1 and α2 indicate the elasticity of price change with respect to populationchanges


Skewness Evidence

354 journal of political economy

TABLE 1Relationship between Price Changes and Population Changes from

Equation (3) (Part b of Proposition 1)

a1

(1)a2

(2)Test for a1 p a2

(3)

2R(4)

Results from pooleddecadal observations(N p 963)*

1.80(.20)

.23(.05)

F(1, 320) p 45.20Prob 1 F p .00

.19

Results from three-decade change (N p321)†

1.64(.19)

.09(.04)

F(1, 320) p 55.16Prob 1 F p .00

.15

Note.—Standard errors (in parentheses) are based on clustering at the city level. There are 321 city clusters in eachregression. Specifications are estimated using data on cities with at least 30,000 residents in 1970. There are 963observations on the pooled decadal changes and 321 observations on the 30-year changes. Population and house pricesare obtained from the decennial censuses. Decadal dummy coefficients and intercepts are suppressed throughout. Fullresults are available on request. See the text for added detail on the specification.

* Observations pertain to the 1970s, 1980s, and 1990s.† Observations pertain to 1970–2000.

our cities. If housing was not durable, we would expect to see muchmore of a quantity response in declining cities over longer time spans,reducing the asymmetry predicted by our model.

The second implication of proposition 1 is that price changes aremore sensitive to population changes when the changes are negative.While there obviously is no causal linkage implied here, a concave re-lationship between price appreciation and population growth is an im-portant testable hypothesis implied by our framework. To investigatethis issue, we regress the percentage growth in housing prices (all pricesare in 2000 dollars) on a transformation of its population growth asshown in equation (3) below. Population growth is entered in piecewiselinear form to allow for differential effects in expanding versus decliningcities. Thus the POPLOSSi,t variable takes on a value of zero if city i’spopulation grew during decade t and equals city i’s actual percentagedecline in population if the city lost population during the relevantdecade. Analogously, the POPGAINi,t variable equals zero if the city lostpopulation during time period t and equals the actual populationgrowth rate if the city gained population. Whenever observations arepooled across decades, we include time dummies (dt) to allow for dif-ferent intercepts across decades and correct for intertemporal corre-lation in the error terms associated with multiple observations on thesame city over time. The actual specification estimated is

house price appreciation rate (%) pi,t

a � a # POPLOSS � a # POPGAIN � a # d � e , (3)0 1 i,t 2 i,t 3 t i,t

where ei,t is the standard error term.The first row of table 1 reports results from a specification that pools

the 963 observations on decadal price and population growth that we


Use Weather as an Exogenous Shifter

Weather does not change across cities, but its impact will change therebychanging city amenities

This can act as an exogenous amenity shock for the city

Run the following two specifications:

Pop %∆ = α0 + α1Coldi + α2Warmi + α3 × δt + εit

House P %∆ = β0 + β1Coldi + β2Warmi + β3 × δt + γit

I Coldi takes on a value of zero if city i’s mean January temperature is greaterthan 29.1 degrees and equals the city’s actual mean January temperatureotherwise

I Warmi takes on a value of zero if city i’s mean January temperature is colderthan 29.1 degrees and equals the city’s actual mean January temperatureotherwise


Asymmetric Response to Positive and Negative Shocks

358 journal of political economy

TABLE 2Population and Price Growth and the Weather (Part c of Proposition 1)

A. Based on Equation (4)

a1

(1)a2

(2)Test for a1 p a2

(3)

2R(4)

Population growthresults

.0008(.0020)

.0069(.0012)

F(1, 261) p 4.79Prob 1 F p .03

.15

B. Based on Equation (5)

b1

(1)b2

(2)Test for b1 p b2

(3)

2R(4)

House price apprecia-tion results

.0060(.0016)

.0023(.0011)

F(1, 261) p 2.39Prob 1 F p .12

.11

Note.—Standard errors (in parentheses) are based on clustering at the metropolitan area level. There are 262metropolitan area clusters in each regression. Specifications are estimated using data on 321 cities with at least 30,000residents in 1970. There are 963 observations across the three decades of the 1970s, 1980s, and 1990s. Population andhouse prices are obtained from the decennial censuses. Mean January temperature is a 30-year average that was collectedfrom the 1992 County and City Data Book. This variable does not vary over time. Decadal dummy coefficients andintercepts are suppressed throughout. Full results are available on request. See the text for added detail on thespecifications.

here because there is no variation in reported temperature within ametropolitan area.

The first row of table 2 finds the strong convexity of populationchange with respect to weather shocks predicted by part c of proposition1. Among colder cities, there is no statistically or economically mean-ingful relationship between being more (or less) cold and populationgrowth. The result is quite different for warmer places. Among thesecities, being warmer is strongly associated with greater populationgrowth. The coefficient of 0.0069 implies that an increase of 16 degrees,which is the interquartile range of mean January temperatures forwarmer cities (from 36 to 52 degrees), is associated with a 10.8 percenthigher decade population growth rate. That is an economically mean-ingful effect, since the mean decadal increase in population for thewarm cities is 13.5 percent. The F-test results reported in column 3 showthat we can conclude with high confidence that the impacts of thesenegative and positive “weather shocks” on population growth aredifferent.

The next row of table 2 reports results for house price appreciation.As predicted by part c of proposition 1, there is a concave relationshipbetween price changes and weather shocks. A negative shock has agreater impact on price than a positive shock of equal magnitude.Among colder places, a 10-degree higher temperature is associated witha 6 percent greater rate of house price growth ( ),0.0060 # 10 p 0.06with the same increase among warmer cities being associated with onlya 2.3 percent higher rate of price appreciation ( ).0.0023 # 10 p 0.023


Persistence

Test for the prediction that population declines will be more persistent thatpopulation growth

Run the following specification:

Pop %∆ = α0 + α1PopLossit−1 + α2PopGainit−1 + α3 × δt + εit


Evidence of Persistence

urban decline and durable housing 359

TABLE 3Persistence of Population Decline Based on Equation (6)

(Part a of Proposition 2)

a1

(1)a2

(2)a1 p a2

(3)

2R(4)

Results from pooleddecadal observations

1.001(.076)

.455(.039)

F(1, 320) p 29.0Prob 1 F p .00

.51

Note.—Standard errors (in parentheses) are based on clustering at the city level. There are 321 city clusters. Spec-ifications are estimated using data on 321 cities with at least 30,000 residents in 1970. In this table, population growthrates from the 1980s and 1990s are regressed on transformed lags of their respective growth rates and a single decadaldummy as described in the text. There are 642 decadal observations. All population data were obtained from decennialcensuses. The time dummy coefficient and the intercept are suppressed throughout. All results are available on request.

While this is consistent with our model, the F-test results reported incolumn 3 show that the effects are different at only the 88 percent level.

Table 3 addresses part a of proposition 2 that housing durabilityshould make population decline especially persistent because it can takemany decades for negative shocks to be fully reflected in the size of thehousing stock and population. As in table 1, we allow the estimation ofdifferential effects of growth versus decline so that the POPLOSS andPOPGAIN variables are as defined as above. Because we are interestedin persistence, current-period population growth is regressed on laggedgrowth (where the subscript signifies the decade prior to t), andt � 1we estimate the following specification:

population growth rate (%) pi,t

a � a # POPLOSS � a # POPGAIN � a # d � e . (6)0 1 i,t�1 2 i,t�1 3 t i,t

The use of lags results in the loss of one decade of data (the 1970s)and reduces the number of observations to 642 as described in table 3.

The coefficient on past growth when growth was negative is twice thatwhen past growth was positive. Among cities that declined in the pre-vious decade, a 1 percent greater population loss is associated with a 1percent larger population decline this decade. The positive coefficientof about 0.46 on the lagged value of POPGAIN indicates that there issome persistence for cities that were growing, too. However, we cancomfortably reject the null hypothesis that these are the same effects(see col. 3 of table 3). These findings reflect the permanence of declineamong American Rust Belt cities especially. There were 39 U.S. citieswith at least 100,000 people in 1950 that lost population during the1950s. Of these, 33 declined in the 1960s, 37 declined in the 1970s, 22declined in the 1980s, and 23 declined in the 1990s.

The final implication of proposition 2 implies that cities with an abun-dance of cheap housing that is priced below current replacement costwill not tend to grow as much in the future. This connection is notcausal. Cities with relatively large fractions of housing priced below


The Consequences of Mortgage Credit Expansion: TheCrisis

Mian and Sufi (2009) argue that the sharp increase in mortgage defaults in2007 is significantly amplified in subprime ZIP codes

Prior to the crisis, these ZIP codes experience an unprecedented relativegrowth in mortgage credit even though relative income was declining

2002 to 2005 is the only period in which income and mortgage credit growthwere negatively correlated

Why? Securitization of subprime credit


The Basic Facts

1460 QUARTERLY JOURNAL OF ECONOMICS

TABLE IISUBPRIME VERSUS PRIME ZIP CODES

Prime SubprimeZIP codes ZIP codes

Measures of mortgage credit availabilityFraction of subprime borrowers in 1996 (under 660) 0.159 0.444∗∗Fraction of loans backed by FHA in 1996 0.041 0.239∗∗Fraction of mortgage applications denied, 1996 0.148 0.307∗∗Home ownership rate, 2000 0.812 0.557∗∗

Demographic variables from Census 2000Median household income ($000) 76.4 38.9∗∗Poverty rate 0.038 0.169∗∗Fraction with less than high school education 0.077 0.289∗∗Fraction unemployed 0.031 0.081∗∗Fraction nonwhite 0.079 0.415∗∗

Notes. This table presents characteristics of prime and subprime ZIP codes in our sample. Prime andsubprime ZIP codes are determined by splitting ZIP codes into four quartiles based on the national distributionof the fraction of subprime borrowers (credit score less than 660) as of 1996. Prime ZIP codes are the lowestquartile and subprime ZIP codes are the highest quartile.

∗∗ ,∗ Difference between prime and subprime statistically distinct from 0 at the 1% and 5% levels, respec-tively.

in the nation and subprime ZIP codes are in the highest quartilein the nation.

Subprime ZIP codes have reduced access to mortgage lend-ing before the subprime mortgage expansion. A higher fractionof mortgages in subprime ZIP codes as of 1996 are backed bythe Federal Housing Administration, and mortgage applicationdenial rates as of 1996 are significantly higher. Homeownershipdata from the 2000 census show a 25% lower homeownership ratein subprime ZIP codes. As of 2000, subprime ZIP codes have muchlower median household income, much higher poverty rates, muchlower levels of education, and much higher unemployment rates.They also have a significantly larger fraction of the populationthat is nonwhite.

III. SUBPRIME MORTGAGE EXPANSION: MOTIVATING FACTS

AND EMPIRICAL MODEL

III.A. Motivating Facts

We begin by providing motivating facts for our empiricalmodel through an examination of the subprime mortgage expan-sion and the subsequent default crisis. The top left-hand panelin Figure II plots the differential growth rate for the number of

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The Basic FactsC

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FIGURE IIMortgage Credit Growth and Default Rates: Subprime Relative to Prime ZIP Codes

This figure plots the growth in the number (top left-hand panel) and amount (top right-hand panel) of originated mortgages and themortgage default rate (bottom panel) for subprime relative to prime ZIP codes in the same county. Subprime and prime ZIP codes aredefined to be the highest and lowest quartile ZIP codes in the national distribution based on the fraction of residents with a credit scoreless than 660 as of 1991.

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Potential Explanations of the Expansion in Credit

Income-based hypothesis: Improvements in the creditworthiness of subprimeborrowers

I income might have increased in the early 2000’s

Supply-based hypothesis: Outward shift in the supply of mortgage credit bylenders

I greater diversification of risk, greater subsidization of risk throughgovernment-backed programs, or greater moral hazard on the part oforiginators due to securitization

Expectations-based hypothesis: increased expectations of future house pricegrowth


The Importance of Zip Code Data not MSA Data

Income-based hypothesis inconsistent with ZIP code data

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FIGURE IIncome Growth, Mortgage Credit Growth, and Subprime Population: Between- and Within-MSA Correlations

This figure presents correlations between income growth, mortgage credit growth, and the fraction of the population with a creditscore under 660. The top panels present between-MSA correlations for the top forty MSAs by population, and the bottom panels utilizeZIP code–level data to show the within-MSA correlations for the top forty MSAs. The bottom panels present data that are deviated fromMSA level means.



Falsification of the Income-Based Hypothesis

CONSEQUENCES OF MORTGAGE CREDIT EXPANSION 1467

TABLE IIICAN PRODUCTIVITY/INCOME GROWTH EXPLAIN SUBPRIME CREDIT EXPANSION

FROM 2002 TO 2005?

Mortgageorigination Income Employment Establishment

growth growth growth growth2002–2005 2002–2005 2002–2005 2002–2005

(1) (2) (3) (4)

Fraction subprime 0.469∗∗ −0.141∗∗ −0.074∗∗ −0.042∗∗borrowers, 1996 (0.029) (0.006) (0.011) (0.005)

N 2,946 2,946 2,946 2,946R2 .42 .35 .15 .33

Notes. This table presents the correlation across ZIP codes between measures of income growth, employ-ment growth, and business growth and the fraction of subprime borrowers. All regressions include countyfixed effects.

∗∗ ,∗Statistically distinct from 0 at the 1% and 5% levels, respectively.

(expectations-based hypothesis).15 The next three sections exploreeach of these potential causes.

IV. TESTING THE INCOME-BASED HYPOTHESIS

Figure II shows a rapid increase in credit growth to sub-prime ZIP codes from 2002 to 2005. This result is further con-firmed by column (1) of Table III. Using county fixed effects, itshows a statistically significant positive relation between mort-gage origination growth in a ZIP code from 2002 to 2005 andthe fraction of subprime borrowers as of 1996.16 The point esti-mate implies that a one-standard-deviation increase in the frac-tion of subprime borrowers (0.094) leads to a five–percentagepoint increase in the annualized growth rate of mortgage origi-nations from 2002 to 2005. This represents a 3/4–standard devi-ation change in the left-hand-side variable.17 As our theoretical

15. Strictly speaking, our model generates a positive βt (i.e., higher relativemortgage growth for subprime ZIP codes) under the house price appreciationhypothesis only if the house price expectations go up differentially for subprimeZIP codes. However, one can imagine that a level increase in house price growthexpectation helps subprime customers more because they have a higher probabilityof default, and hence a reduction in loss given default is more useful to them.

16. The inclusion of county fixed effects means that our measure of subprimeborrowers is deviated from county means in the regressions. An alternative specifi-cation is to use the absolute measure of the fraction of borrowers that are subprimewhile using deviations from county means for all other variables. In unreported re-sults, we find similar quantitative results when using this alternative specification.

17. Given the presence of county fixed effects in all specifications, we usewithin-county standard deviations when discussing economic magnitudes. Within-county standard deviations are reported in Table I.

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TABLE IVHISTORICAL MORTGAGE CREDIT GROWTH AND INCOME GROWTH CORRELATIONS

Dependent variable: Mortgage originations for home purchase growth, annualized

2002–2005 1991–1998 1998–2001 2001–2002 2002–2004 2004–2005 2005–2006 2006–2007(1) (2) (3) (4) (5) (6) (7) (8)

Income growth, −0.662∗∗ 0.537∗∗ 0.517∗∗ 0.425 −0.394∗∗ −0.383∗∗ 0.103 0.716∗∗annualized (0.089) (0.084) (0.092) (0.368) (0.122) (0.077) (0.078) (0.093)

N 3,014 2,809 3,014 3,014 3,014 3,014 3,014 3,014R2 .34 .55 .27 .44 .24 .39 .27 .26

Notes. This table presents the correlation across ZIP codes between mortgage origination for home purchase growth and income growth for different periods of our sample.Income growth and mortgage origination growth are measured for the exact same period for all specifications except the specification reported in column (7). We do not have incomedata available for 2007; as a result, in column (7) we examine the correlation between mortgage origination growth from 2006 to 2007 and income growth from 2005 to 2006. Allspecifications include county fixed effects.

∗∗ ,∗Coefficient estimate statistically distinct from 0 at the 1% and 5% levels, respectively.



Evidence for the Supply-Based Hypothesis1478

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FIGURE VRelaxation in Borrower Credit Constraints

The top left-hand panel shows the correlation across ZIP codes between the mortgage application denial rate and the fraction ofresidents with a credit score below 660, both as of 1996. The data are deviated from county means. The top right-hand panel shows thedenial rate for mortgage applications for prime relative to subprime ZIP codes in the same county. The bottom left-hand panel shows thefraction of all originated mortgages for home purchase that are sold to non-GSE investors, and the bottom right-hand panel shows therelative fraction sold to non-GSE investors for subprime versus prime ZIP codes in the same county. Subprime and prime ZIP codes aredefined to be the highest- and lowest-quartile ZIP codes in the national distribution based on the fraction of residents with a credit scorebelow 660 as of 1996.

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FIGURE VIHouse Price Growth

The top left-hand panel shows average annual house price growth across ZIP codes. The top right-hand panel shows relative houseprice growth for subprime versus prime ZIP codes in the same county. The bottom left-hand panel shows average annual house pricegrowth for the top-decile and bottom-decile housing supply–elasticity MSAs based on the elasticity measures of Saiz (2008). The bottomright-hand panel shows relative house price growth for subprime versus prime ZIP codes in the same MSA for elastic and inelastic MSAs.Subprime and prime ZIP codes are defined to be the highest- and lowest-quartile ZIP codes in the national distribution based on thefraction of residents with a credit score below 660 as of 1996.



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TABLE VIIMORTGAGE ORIGINATION GROWTH AND MORTGAGE DEFAULT RATE CHANGES FOR HIGH–HOUSING SUPPLY ELASTICITY MSAS

Change in Change infraction sold in fraction to

Income growth securitizations other financial Mortgage origination Change in mortgage2002–2005 2002–2005 firms 2002–2005 growth 2002–2005 default rate 2002–2005

With controls With controls

(1) (2) (3) (4) (5) (6) (7)

Fraction subprime borrowers, 1996 −0.069∗∗ 0.100∗∗ 0.061∗∗ 0.305∗∗ 0.413∗∗ 0.057∗∗ 0.056∗∗(0.010) (0.009) (0.014) (0.061) (0.069) (0.015) (0.018)

N 655 655 655 655 655 655 655R2 .17 .28 .43 .10 .12 .04 .05

Notes. This table examines relative income growth, securitization patterns, and mortgage origination growth from 2002 to 2005 and the relative change in mortgage defaultrates from 2005 to 2007 in high–subprime borrower share ZIP codes. The sample is limited to the top–decile MSAs by housing supply elasticity as measured by Saiz (2008). The tenhigh–housing supply elasticity MSAs are Dayton, OH; Fort Wayne, IN; Greenville, SC; Indianapolis, IN; Kansas City, MO; Little Rock, AR; McAllen, TX; Omaha, NE; Tulsa, OK;and Wichita, KS. The control variables in columns (5) and (7) are income growth, employment growth, and business establishment growth from 2002 to 2005. All growth rates areannualized, and all specifications include MSA fixed effects.

∗∗ ,∗ Coefficient estimate statistically distinct from 0 at the 1% and 5% levels, respectively.



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