PARTIAL IDENTIFICATION OF HEDONIC DEMAND FUNCTIONS Congwen Zhang

PARTIAL IDENTIFICATION OF HEDONIC DEMAND FUNCTIONS Congwen Zhang (Virginia Tech) Nicolai Kuminoff (Arizona State University) Kevin Boyle (Virginia Tech) 10/23/2011

ENDOGENEITY PROBLEM WITH HEDONIC DEMAND ESTIMATION Endogeneity arises because people choose prices and quantities/qualities simultaneously. Example: we are interested in X, an environmental good. Hedonic price function: (non-linear in X ) Implicit price of X: ( is function of X ) Choice of X no based on an exogenous price. Why worry? Most policies result in nonmarginal changes in X. 2

“IMPERFECT” INSTRUMENTAL VARIABLES (NEVO & ROSEN, 2010) X: endogenous variable; Z: instrumental variable (IV) “perfect” IV: and “imperfect” IV : We allow correlation between IV and error (unobserved components of preferences! Z is “perfect”: Z is “imperfect”: is bounded by and 3

1 -SIDED AND 2 -SIDED BOUNDS Proposition (Nevo & Rosen, 2010): Suppose both and Case 1: If , then Case 2: If , then 4

“IMPERFECT” IVS IN DEMAND ESTIMATION Potential “imperfect” IVs: IV 1. market indicator (M) IV 2. interaction between M and income (M*INC) Why “imperfect” ? 1. sorting across markets 2. uncertainty about the spatial extent of a market Correlation Direction: cov(X, U)>0, cov(M, X)>0 cov(X, U)>0, cov(M*INC, X)>0 both IVs give us one-sided bound ! 5

PARTIAL IDENTIFICATION OF MARSHALLIAN CONSUMER SURPLUS (MCS) Bounds on β Bounds on MCS Suppose we obtain a 2 -sided bound: (slope = MCSl (slope = ) ) MCS 2 6

PARTIAL IDENTIFICATION OF MCS (slope = )

PARTIAL IDENTIFICATION OF MCS Suppose we obtain a 1 -sided bound: S (slope = ) ) 8

AN EMPIRICAL DEMONSTRATION Water quality in markets for lakefront properties. Data description: (1) House transactions: from multiple markets in VT, ME, and NH. (2) Water clarity data: associated w/ each house. (3) Demographic data: associated w/ each home owner. Important features: (1) Each state includes data from multiple markets. (2) The spatial extent of a market is difficult to determine with certainty. 9

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TWO-STAGE HEDONIC MODEL 1 st stage: Estimate hedonic price function (market-specific) implicit price of water clarity: 2 nd Stage: Estimate demand function parameters (pooled) 11

Table. Demand Estimation with Pooled Data OLS Water Quality M M*INC Bounds -710*** -2, 253*** -2, 975*** (-∞, -2, 975] (-∞, -$22, 911] Boyle et al. (1999)’s point estimates fall into our bounds ! State Maine New Hampshire Vermont Home Price Percent Effect $71, 536 3. 8 1. 8 $159, 299 1. 7 $99, 034 2. 8 12 [0, $2, 732]

CONCLUSIONS AND FUTURE RESEARCH Partial identification provides a more credible way to estimate demand welfare. Provides approach to uncertainty analysis. How big can the injuries or benefits be? One-side bounds not always helpful. Partial identification logic can be a robustness check on point estimates. Implicit prices are plausible. 13

PREFERENCES FOR STORMWATER CONTROL IN RESIDENTIAL DEVELOPMENTS Jessica Boatright Kurt Stephenson Kevin J. Boyle Sara Nienow Virginia Tech 11/1/2011

APPLICATION Subdivision infrastructure that affects stormwater runoff. Hanover County, Virginia Residential home sales between 1995 -1996 Mean sales price = $148, 950 15

VARIABLES CUL = 1 if cul-de-sac and 0 otherwise CURBGUTTER = 1 if curb-and-gutters and 0 otherwise STW 20 = 1 if street width 20 feet or less and 0 otherwise STW 25 = 1 if street width 20 to 30 ft and 0 otherwise street width greater than 30 ft is omitted category 16

RESULTS Variables CUL CURBGUTTER STW 20 STW 25 Estimates 0. 147** (0. 007) 0. 074*** (0. 016) 0. 032** (0. 016) 0. 040*** (0. 014) 17

IMPLICATIONS Cul-de-sacs and curb and gutters channel and rapidly transport stormwater, which can exacerbate nonpoint-source pollution of surface waters. Narrower streets mean less impervious surface, which can reduce some of the residential stormwater effects, but the benefits to home owners are less that being on a cul-de-sac or having a curb and gutter on their street. 18