Lecture 3 Fall 2009. Referee Reports Housing Data

Lecture 3

Fall 2009

Referee Reports

Referee Reports

Housing Data

U.S. Housing Data

• Housing price movements unconditionally

Census data

Transaction/deed data (provided by government agencies or available via public records)

Household data (PSID, Survey of Consumer Finances, etc.)

Mortgage data (appraised value of the home)

• Repeat sales indices

OFHEO

Case-Shiller

Repeat Sales vs. Unconditional Data

• House prices can increase either because the value of the land under the home increases or because the value of the structure increases.

* Is home more expensive because the underlying land is worth more or because the home has a fancy kitchen.

• Often want to know the value of the land separate from the value of the structure.

• New homes often are of higher quality than existing homes.

• Repeat sales indices try to difference out “structure” fixed effects – isolating the effect of changing land prices.

* Assumes structure remains constant (hard to deal with home improvements).

OFHEO/FHFA Repeat Sales Index

• OFHEO – Office of Federal Housing Enterprise OversightFHFA – Federal Housing Finance Agency

Government agencies that oversee Fannie Mae and Freddie Mac

• Uses the stated transaction price from Fannie and Freddie mortgages to compute a repeat sales index. (The price is the actual transaction price and comes directly from the mortgage document)

• Includes all properties which are financed via a conventional mortgage (single family homes, condos, town homes, etc.)

• Excludes all properties financed with other types of mortgages (sub prime, jumbos, etc.)

• Nationally representative – creates separate indices for all 50 states and over 150 metro areas.

Case Shiller Repeat Sales Index

• Developed by Karl Case and Bob Shiller

• Uses the transaction price from deed records (obtained from public records)

• Includes all properties regardless of type of financing (conventional, sub primes, jumbos, etc.)

• Includes only single family homes (excludes condos, town homes, etc.)

• Limited geographic coverage – detailed coverage from only 30 metro areas. Not nationally representative (no coverage at all from 13 states – limited coverage from other states)

• Tries to account for the home improvements when creating repeat sales index (by down weighting properties that increase by a lot relative to others within an area).

OFHEO vs. Case Shiller: National Index

OFHEO vs. Case Shiller: L.A. Index

OFHEO vs. Case Shiller: Denver Index

OFHEO vs. Case Shiller: Chicago Index

OFHEO vs. Case Shiller: New York Index

Conclusion: OFHEO vs. Case - Shiller

• Aggregate indices are very different but MSA indices are nearly identical.

• Does not appear to be the result of different coverage of properties included.

• I think the difference has to do with the geographic coverage.

• If using MSA variation, does not matter much what index is used.

• If calibrating aggregate macro models, I would use OFHEO data instead of Case-Shiller – I think it is more representative of the U.S.

A Note on Census Data

• To assess long run trends in house prices (at low frequencies), there is nothing better than Census data.

• Very detailed geographic data (national, state, metro area, zip code, census tract).

• Goes back at least to the 1940 Census.

• Have very good details on the structure (age of structure, number of rooms, etc.).

• Can link to other Census data (income, demographics, etc.).

Housing Cycles

Average Annual Real Housing Price Growth By US State

State 1980-2000 2000-2007 State 1980-2000 2000-2007AK -0.001 0.041 MT 0.003 0.049AL 0.000 0.024 NC 0.008 0.022AR -0.009 0.023 ND -0.010 0.033AZ -0.002 0.061 NE -0.002 0.007CA 0.012 0.066 NH 0.014 0.041CO 0.012 0.012 NJ 0.015 0.058CT 0.012 0.044 NM -0.002 0.043DC 0.010 0.081 NV -0.005 0.060DE 0.011 0.053 NY 0.020 0.051FL -0.002 0.068 OH 0.003 -0.001GA 0.008 0.019 OK -0.019 0.019HI 0.004 0.074 OR 0.009 0.051IA -0.001 0.012 PA 0.008 0.042ID -0.001 0.047 RI 0.017 0.059IL 0.010 0.030 SC 0.007 0.025IN 0.002 0.020 SD 0.002 0.025

Average 0.011 0.03617

Typical “Local” Cycle

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Typical “Local” Cycle

19

20

Housing Prices and Housing Cycles (Hurst and Guerrieri (2009))

• Persistent housing price increases are ALWAYS followed by persistent housing price declines

Some statistics about U.S. metropolitan areas 1980 – 2000

• 44 MSAs had price appreciations of at least 15% over 3 years during this period.

• Average price increase over boom (consecutive periods of price increases): 55%

• Average price decline during bust (the following period of price declines): 30%

• Average length of bust: 26 quarters (i.e., 7 years)

• 40% of the price decline occurred in first 2 years of bust 21

Typical “Country” Cycle (US – OFHEO Data)

U.S. Nominal House Price Appreciation: 1976 - 2008

22

Typical “Country” Cycle (US – OFHEO Data)

U.S. Real House Price Appreciation: 1976 - 2008

23

Country 1970-1999 2000-2006 Country 1970-1999 2000-2006

U.S. 0.012 0.055 Netherlands 0.023 0.027Japan 0.010 -0.045 Belgium 0.019 0.064

Germany 0.001 -0.029 Sweden -0.002 0.059France 0.010 0.075 Switzerland 0.000 0.019

Great Britain 0.022 0.068 Denmark 0.011 0.065Italy 0.012 0.051 Norway 0.012 0.047

Canada 0.013 0.060 Finland 0.009 0.040Spain 0.019 0.081 New Zealand 0.014 0.080

Australia 0.015 0.065 Ireland 0.022 0.059

Average 1970-1999 0.0122000-2006 0.046

Average Annual Real Price Growth By OECD Country

24

Country Cycles – The U.S. is Not Alone

25


26


27

28

Do Supply Factors Explain 2000-2008 Cycle

Change in Total Housing Units Against Change in Housing PriceAdjusted for Population Changes (2000-2005, State Level)

29

AK

AL

AR

AZ CA

CO

CTDC

DEFL

GA

HI

IA

ID

IL

IN

KSKY

LA

MA

MD

ME

MI

MN

MO

MS

MT

NC

ND

NE

NHNJ

NM

NV

NY

OH

OK

OR

PA

RI

SC SD

TN

TX

UT

VA

VTWA

WI

WVWY

-.04

-.02

0.0

2.0

4

-.2 0 .2 .4 .6Residuals

Residuals Fitted values

Do Supply Factors Explain 2000-2008 Cycle

Change in Total Housing Units Against Change in Housing PriceAdjusted for Population Changes (2005-2009, State Level)

30

AK

AL

AR

AZ

CACO

CT

DC

DE

FL

GA

HI

IA

ID

IL

INKS

KY

LA

MA

MD

MEMI

MN

MO

MS

MT

NC

ND

NE

NH

NJ

NM

NV

NY

OH

OKORPA

RISC

SDTN

TX

UT

VA VTWA

WIWV

WY

-.03

-.02

-.01

0.0

1.0

2

-.6 -.4 -.2 0 .2Residuals

Residuals Fitted values

HomeworkWhy Do Housing Prices Cycle?

A Spatial Equilibrium Model

Part 1

Model Particulars (Baseline Model): The City• City is populated by N identical individuals.

• City is represented by the real line such that each point on the line (i) is a different location:

• : Measure of agents who live in i.• : Size of the house chosen by agents living in i.

• (market clearing condition)

• (maximum space in i is fixed and normalized to 1)

( , )i

( )tn i di N

( ) ( ) 1t tn i h i

33

( )tn i

( )th i

Household Preferences

Static model:

, ,

1

max ( ) ( ) > 0 and > 0

( ) ( ) ( ) normalize price of consumption to 1

Arbitrage implies:

1( ) ( ) ( )

1

t tc h i

t t

c i h i

c i R i h i Y

P i R i P ir

Construction

A continuum of competitive builders can always build a unit of housing

at constant marginal cost .

Profit maximization implies builders will build a unit of housing anytime:

P t

Demand Side of Economy

1

1

max ( ) ( ) [ ( ) ( ) ( )]

( ) ( )( ) ( ) (F.O.C. wrt c)

( )

( ) ( )( ) ( ) ( ) (F.O.C. wrt h)

( )

( ) ( ) 1

( ) ( ( ) ( )) ( )

c i h i Y c i R i h i

c i h ic i h i

c i

c i h ic i h i R i

h i

h i h i

c i Y R i h i R i

Housing and Consumption Demand Functions

1( )

( ) ( )

( )( )

h i YR i

c i Y

Spatial Equilibrium

Consider two locations i and i.

Spatial indifference implies that:

( ) ( ) ( ) ( )

1 1

( ) ( )

( ) ( ) for all and

c i h i c i h i

Y Y Y YR i R i

R i R i i i

%

% %

%

% %

Households have to be indifferent across locations:

Equilibrium

( ) ( )(1 )

Housing Demand Curve:

1 1( )= =

Housing Supply Curve:

P =

rR i P i

r

rh i h Y

r P

Graphical Equilibrium

ln(P)

ln(κ) =ln(P*)

ln(h)

hD(Y)

ln(h*)

Shock to Income (similar to shock to interest rate)

ln(P)

ln(κ) =ln(P*)

ln(h)

hD(Y)

ln(h*)

hD(Y1)

ln(h*1)

Shock to Income (with adjustment costs to supply)

ln(P)

ln(κ) =ln(P*)

ln(h)

hD(Y)

ln(h*)

hD(Y1)

ln(h*1)

Some Conclusions (Base Model)

• If supply is perfectly elastic in the long run (land is available and construction costs are fixed), then:

Prices will be fixed in the long run

Demand shocks will have no effect on prices in the long run.

Short run amplification of prices could be do to adjustment costs.

Model has “static” optimization. Similar results with dynamic optimization (and expectations – with some caveats)

• Notice – location – per se – is not important in this analysis. All locations are the same.

Equilibrium with Supply Constraints

Suppose city (area broadly) is of fixed size (2*I). For illustration, lets index the middle of the city as (0).

-I 0 I

Lets pick I such that all space is filled in the city with Y = Y and r = r.

2I = N (h(i)*)

1 12

1

2

rI N Y

r P

N rP Y

I r

Comparative Statics

What happens to equilibrium prices when there is a housing demand shock (Y increases or r falls).

Focus on income shock. Suppose Y increases from Y to Y1. What happens to prices?

With inelastic housing supply (I fixed), a 1% increase in income leads to a 1% increase in prices (given Cobb Douglas preferences)

1

2

1ln( ) ln ln( )

2

N rP Y

I r

N rP Y

I r

Shock to Income With Supply Constraints

The percentage change in income = the percentage change in price

ln(P1)

ln(κ) =ln(P)

ln(h)

hD(Y)

ln(h)=ln(h1)

hD(Y1)

Intermediate Case: Upward Sloping Supply

Cost of building in the city increases as “density” increases

ln(P1)

ln(κ) =ln(P)

ln(h)

hD(Y)

ln(h)=ln(h1)

hD(Y1)

Implication of Supply Constraints (base model)?

• The correlation between income changes and house price changes should be smaller (potentially zero) in places where density is low (N h(i)* < 2I).

• The correlation between income changes and house price changes should be higher (potentially one) in places where density is high.

• Similar for any demand shocks (i.e., decline in real interest rates).

Question: Can supply constraints explain the cross city differences in prices?

Topel and Rosen (1988)

“Housing Investment in the United States” (JPE)

• First paper to formally approach housing price dynamics.

• Uses aggregate data

• Finds that housing supply is relatively elastic in the long run

Long run elasticity is much higher than short run elasticity.

Long run was about “one year”

• Implication: Long run annual aggregate home price appreciation for the U.S. is small.

Comment 1: Cobb Douglas Preferences?

• Implication of Cobb Douglas Preferences:

0 1

1

(expenditure on housing)

Implication: Constant expenditure share on housing

Implication: Housing expenditure income elasticity = 1

ln(Rh) = l

h YR

Rh Y

1

n( )

Estimated should be 1

Y

Use CEX To Estimate Housing Income Elasticity

• Use individual level data from CEX to estimate “housing service” Engel curves and to estimate “housing service” (pseudo) demand systems.

Sample: NBER CEX files 1980 - 2003

Use extracts put together for “Deconstructing Lifecycle Expenditure” and “Conspicuous Consumption and Race”

Restrict sample to 25 to 55 year olds

Estimate:

(1) ln(ck) = α0 + α1 ln(tot. outlays) + β X + η (Engle Curve)

(2) sharek = δ0 + δ1 ln(tot. outlays) + γ X + λ P + ν (Demand)

* Use Individual Level Data

* Instrument total outlays with current income, education, and occupation.

* Total outlays include spending on durables and nondurables.

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Engel Curve Results (CEX)

Dependent Variable Coefficient S.E.

log rent (renters) 0.93 0.014

log rent (owners) 0.84 0.001

log rent (all) 0.940.007

* Note: Rent share for owners is “self reported” rental value of home

Selection of renting/home ownership appears to be important

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Demand System Results (CEX)


rent share (renters, mean = 0.242) -0.030 0.003

rent share (owners, mean = 0.275) -0.050 0.002

rent share (all, mean = 0.263) -0.0250.002



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Engel Curve Results (CEX)


log rent (renters) 0.93 0.014

log rent (owners) 0.84 0.001

log rent (all) 0.940.007



Other Expenditure Categories

log entertainment (all) 1.610.013

log food (all) 0.640.005

log clothing (all) 1.24 0.010

X controls include year dummies and one year age dummies

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Demand System Results (CEX)


rent share (renters, mean = 0.242) -0.030 0.003

rent share (owners, mean = 0.275) -0.050 0.002

rent share (all, mean = 0.263) -0.0250.002



Other Expenditure Categories

entertainment share (all, mean = 0.033) 0.0120.001

food share (all, mean = 0.182) -0.0730.001

clothing share (all, mean = 0.062) 0.008 0.001

X controls include year dummies and one year age dummies

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Comment 1: Conclusion

• Cannot reject constant income elasticity (estimates are pretty close to 1 for housing expenditure share).

• Consistent with macro evidence (expenditure shares from NIPA data are fairly constant over the last century).

• If constant returns to scale preferences (α+β = 1), β ≈ 0.3 (share of expenditure on housing out of total expenditure).

Comment 2: Cross City Differences

“On Local Housing Supply Elasticity” Albert Siaz (QJE Forthcoming)

• Estimates housing supply elasticities by city.

• Uses a measure of “developable” land in the city.

• What makes land “undevelopable”?

Gradient

Coverage of water

• Differences across cities changes the potential supply responsiveness across cities to a demand shock (some places are more supply elastic in the short run).

Comment 3: Are Housing Markets Efficient?

• Evidence is mixed

• Things to read:

“The Efficiency of the Market for Single-Family Homes” (Case and Shiller, AER 1989)

“There is a profitable trading rule for persons who are free to time the purchase of their homes. Still, overall, individual housing price changes are not very forecastable.”

Subsequent papers find mixed evidence: Transaction costs?

Comment 4: Can Supply Constraints Explain Cycles?

“Housing Dynamics” (working paper 2007) by Glaeser and Gyrouko

Calibrated spatial equilibrium model

Match data on construction (building permits) and housing prices using time series and cross MSA variation.

Find that supply constraints cannot explain housing price cycles.

Their explanation: Negatively serially correlated demand shocks.

What Could Be Missing?

• Add in reasons for agglomeration.

• Long literature looking at housing prices across areas with agglomeration.

• Most of these focus on “production” agglomerations.

• We will lay out one of the simplest models – Muth (1969), Alonzo (1964), Mills (1967)

• Locations are no longer identical. There is a center business district in the area where people work (indexed as point (0) for our analysis).

• Households who live (i) distance from center business district must pay additional transportation cost of τi.

Same Model As Before – Except Add in Transport Costs

Static model:

, ,max ( ) ( ) > 0 and > 0

( ) ( ) ( )

Still no supply constraints (unlimited areas)

t tc h ic i h i

c i R i h i Y i

Demand Side of Economy

1

1

max ( ) ( ) [ ( ) ( ) ( )]

( ) ( )( ) ( ) (F.O.C. wrt c)

( )

( ) ( )( ) ( ) ( ) (F.O.C. wrt h)

( )

( ) ( )

( ) ( ( )

c i h i Y i c i R i h i

c i h ic i h i

c i

c i h ic i h i R i

h i

h i h i

c i Y i R i

1

( )) ( )h i R i

Housing and Consumption Demand Functions

1( ) ( )

( ) ( )

( ) ( )( )

h i Y iR i

c i Y i

Spatial Equilibrium

Consider two locations i and i.

Spatial indifference implies that:

( ) ( ) ( ) ( )

( ) ( )

When i > i, R(i) < R(i)

c i h i c i h i

Y iR i R i

Y i

%

% %

%%

% %

Households have to be indifferent across locations:

EquilibriumEquilibrium Result:

All occuppied neighborhoods i will be contained in [-I,I].

Define R(I) and P(I) as the rent and price, respectively,

at the boundary of the city.

Given arbitrage, we know that:

R(I)

= ( )(1 ) (1 )

Y ir rR i

r rY I

Complete Equilibrium: Size of City (Solve for I)

0

Remember: h(i)n(i) = 1 and ( )

12

( )

1 1( ) ( )

i

I

i

n i di N

di Nh i

rh i Y I Y i

r

Some Algebra (if my algebra is correct…)

0

0

12

1 1( )

1 1( )

2

1 11 1

21( )

1 11

2

I

i

I

i

di Nr

Y I Y ir

N rY i di Y I

r

N rr

I YN r

r

Prices By Distance (Initial Level of Y = Y0)

P

κ

0 I0 i

Linearized only for graphical illustration

Prices fall with distance. Prices in essentially all locations exceed marginal cost.

Suppose Y increases from Y0 to Y1

P

κ

0 I0 I1 i

Even when supply is completely elastic, prices can rise permanently with a permanent demand shock.

A Quick Review of Spatial Equilibrium Models

• Cross city differences?

Long run price differences across cities with no differential supply constraints.

Strength of the center business district (size of τ) drives long run price appreciations across city.

• Is it big enough?

• Fall in τ will lead to bigger cities (suburbs) and lower prices in center city (i = 0).

Documents

Lecture 3 Fall 2009. Referee Reports Housing Data