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Partial Identification of Hedonic Demand Functions Congwen Zhang (Virginia Tech) Nicolai Kuminoff (Arizona State University) Kevin Boyle (Virginia Tech) 10/23/2011

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E NDOGENEITY 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

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I MPERFECT I NSTRUMENTAL V ARIABLES (N EVO & R OSEN, 2010) X : endogenous variable; Z : instrumental variable (IV) perfect IV: and imperfect IV : 3 We allow correlation between IV and error (unobserved components of preferences! Z is perfect: Z is imperfect: is bounded by and

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

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I MPERFECT IV S IN DEMAND ESTIMATION Potential imperfect IVs: IV1. market indicator ( M ) IV2. 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, U )>0, cov( M, X )>0 cov( X, U )>0, cov( M*INC, U )>0, cov( M*INC, X )>0 both IVs give us one-sided bound ! 5

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P ARTIAL I DENTIFICATION OF M ARSHALLIAN C ONSUMER S URPLUS (MCS) Bounds on β Bounds on MCS Suppose we obtain a 2-sided bound: (slope = ) MCS l (slope = ) MCS 2 6

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P ARTIAL I DENTIFICATION OF MCS (slope = )

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P ARTIAL I DENTIFICATION OF MCS Suppose we obtain a 1-sided bound: (slope = ) S 8

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A N E MPIRICAL D EMONSTRATION 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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T WO -S TAGE H EDONIC M ODEL 1 st stage: Estimate hedonic price function (market-specific) implicit price of water clarity: 2 nd Stage: Estimate demand function parameters (pooled) 11

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12 Table. Demand Estimation with Pooled Data OLSMM*INCBounds Water Quality -710***-2,253***-2,975***(-, -2,975] [0, $2,732] (-, -$22,911] Boyle et al. (1999)s point estimates fall into our bounds ! StateHome PricePercent Effect Maine $71,5363.8 1.8 New Hampshire$159,2991.7 Vermont $99,0342.8

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C ONCLUSIONS AND FUTURE RESEARCH Partial identification provides a more credible way to estimate demand and 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

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P REFERENCES FOR S TORMWATER C ONTROL IN R ESIDENTIAL D EVELOPMENTS Jessica Boatright Kurt Stephenson Kevin J. Boyle Sara Nienow Virginia Tech 11/1/2011

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

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V ARIABLES CUL = 1 if cul-de-sac and 0 otherwise CURBGUTTER = 1 if curb-and-gutters and 0 otherwise STW20 = 1 if street width 20 feet or less and 0 otherwise STW25 = 1 if street width 20 to 30 ft and 0 otherwise street width greater than 30 ft is omitted category 16

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R ESULTS VariablesEstimates CUL0.147** (0.007) CURBGUTTER 0.074*** (0.016) STW200.032** (0.016) STW25 0.040*** (0.014) 17

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I MPLICATIONS 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

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