Things to do with Hedonic Prices © Allen C. Goodman, 2009

Things to do … 1. Estimate them 2. Interpret them 3. Make price indices

Value v. # of Rooms

Interpret them (1) P =  0 +  1 Z 1 +  2 Z  t + , 1. Estimate price changes Coefficient on t term would provide “quality adjusted price.” Problems: a. Estimating it this way assumes that  terms are constant both absolutely and relatively. b.  terms may actually vary across areas.

Interpret them (2) P =  0 +  1 Z 1 +  2 Z  t + , 1. Use them for property assessment. Suppose we have a data base on all of the houses in an area. H1 = (6 rooms, 2000 sq.ft., sq. ft. lot, etc.) H2 = (5 rooms, 1000 sq.ft., 8000 sq. ft. lot, etc.) H3 = (7 rooms, 3000 sq.ft., sq. ft. lot, etc.) We estimate regression on house sales in the area and we get:

Problems Do current sales reflect all of the housing? Do we know enough about all of the houses to make them comparable?

Interpret them (3) – air pollution This is a logical succession to the discussions of hedonic price models. The arguments went something like this: If air pollution was bad, then people should be willing to pay less for property that was polluted. If this was the case, then this should give some measure of the benefits that occur from the alleviation of air pollution. It should also give you the increase in property values that might occur, if we have an alleviation of pollution.

Air pollution So we get: % of Clean Air Valuation 0100zizi  P/  z i Problems with this: 1. To measure benefits, you want to measure the area under a demand curve. We can see from the accom- panying diagram, that any particular hedonic price gives you only one point on the demand curve.

Air pollution So we get: % of Clean Air Valuation 0100zizi  P/  Z i Problems with this: 1. To measure benefits, you want to measure the area under a demand curve. We can see from the accom- panying diagram, that any particular hedonic price gives you only one point on the demand curve. Estimated True

Air pollution % of Clean Air Valuation 0100zizi  P/  Z i Problems with this: 2. As we mentioned earlier, we have a real problem with the "open city - closed city" question. If pollution abatement changes the supply of different types of land, the total land values might not change much. Estimated

Other problems … 3. We really don't know what effects pollution should really have on property values. Does twice as much pollution just look bad, is it twice as bad, or does it kill you? Ridker and Henning used census tract level data, for 1960, in St. Louis. They looked at median property value in the tract. Used a variety of explanatory variables -- for air pollution, they used sulfates. They found that a 1 unit fall in sulfates was correlated with a $245 rise in property value. This implies, they said, an increase in property values by approximately $83,000,000 (in $ multiply by 5 for current dollars --- > about $415,000,000). Then use the identity: V = R/i to determine annual gain. If i = 10%, then: 83,000,000 = R/0.1  R = 8,300,000.

Create Price Indices P =  0 +  1 Z 1 +  2 Z , Example: Suppose we have reason to believe that there are two submarkets. We estimate: P 1 =   1 1 Z 1 +  1 2 Z P 2 =   2 1 Z 1 +  2 2 Z Take a bundle with (Z 1 *, Z 2 *, …) and “move” it from submarket to submarket. It is presumably always the same house. P 1 * =   1 1 Z 1 * +  1 2 Z 2 * P 2 * =   2 1 Z 1 * +  2 2 Z 2 * Price index = P 1 * / P 2 *

Create Quantity Indices P 1 * =   1 1 Z 1 * +  1 2 Z 2 * P 2 * =   2 1 Z 1 * +  2 2 Z 2 * Price index = P 1 * / P 2 * Q 1 = P 1 /P 1 * So if a house has a price of $250,000, and the “index house” has P 1 * = 200,000. The particular house has 1.25 (= 250/200) units of “housing.”

Repeat Sale Indices P int =  + βX + γAge + Σj δ j D j + ε int Where D j is a set of year dummies for when houses were built. Error term ε is ε int = ρ n + κ t + λ age + μ int where ρ n is house specific κ t is year specific, λ age is related to house age and μ is uncorrelated

Repeat Sale (2) Resale method with one year lag nets out house-specific effects yielding: ΔP= P int – P int-1 = γ + (κ t – κ t-1 ) + (λ age+1 – λ age ). This makes several assumptions 1.β is constant year after year – critical assumption. 2.λ is homoskedastic (GT show otherwise). Case-Shiller and others don’t do single period lags only. They difference by various intervals and argue that the differences are heteroskedastic by length of interval.

GT Goodman-Thibodeau (1998) argue that for houses to have longer duration between sales, they have to be older. Show that you can have heteroskedasticity related BOTH to age and to time between sales. CS method ALSO throws away LOTS of data.

Modeling Heteroskedasticity or Take reciprocal as weight, and re-estimate hedonic. Iterate until convergence (usually 3 or 4 iterations) Davidian, Marie, and Raymond J. Carroll Variance Function Estimation, J. Am. Stat. Ass’n