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## Lecture 3

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**Lecture 3**Fall 2009**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 U.S. Housing 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). Repeat Sales vs. Unconditional Data**OFHEO – Office of Federal Housing Enterprise Oversight**• FHFA – 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. OFHEO/FHFA 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). Case Shiller Repeat Sales Index**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. Conclusion: OFHEO vs. Case - Shiller**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.). A Note on Census Data**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 Housing Prices and Housing Cycles (Hurst and Guerrieri (2009))**U.S. Nominal House Price Appreciation: 1976 - 2008**Typical “Country” Cycle (US – OFHEO Data)**U.S. Real House Price Appreciation: 1976 - 2008**Typical “Country” Cycle (US – OFHEO Data)**Change in Total Housing Units Against Change in Housing**Price Adjusted for Population Changes (2000-2005, State Level) Do Supply Factors Explain 2000-2008 Cycle**Change in Total Housing Units Against Change in Housing**Price Adjusted for Population Changes (2005-2009, State Level) Do Supply Factors Explain 2000-2008 Cycle**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)**Household Preferences**Static model:**Households have to be indifferent across locations:**Spatial Equilibrium**hD(Y)**ln(P) Graphical Equilibrium ln(κ) = ln(P*) ln(h*) ln(h)**hD(Y1)**hD(Y) ln(P) Shock to Income (similar to shock to interest rate) ln(κ) = ln(P*) ln(h*) ln(h*1) ln(h)**hD(Y1)**hD(Y) ln(P) Shock to Income (with adjustment costs to supply) ln(κ) = ln(P*) ln(h*) ln(h*1) ln(h)**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)*)**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)**ln(P1)**Shock to Income With Supply Constraints ln(κ) = ln(P) hD(Y1) hD(Y) ln(h)=ln(h1) ln(h) The percentage change in income = the percentage change in price**Intermediate Case: Upward Sloping Supply**ln(P1) ln(κ) = ln(P) hD(Y1) Cost of building in the city increases as “density” increases hD(Y) ln(h)=ln(h1) ln(h)**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: