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.

0 1 ln( )P X

1

1( )XP f X

X XP

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“IMPERFECT” INSTRUMENTAL VARIABLES (NEVO & ROSEN, 2010)

X: endogenous variable; Z: instrumental variable

(IV)

“perfect” IV: and

“imperfect” IV :

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0XU ZU

0ZX 0ZU

We allow correlation between IV and error (unobserved components of preferences!

Z is “perfect”:

Z is “imperfect”: is bounded by and

IV

OLS IV

Proposition (Nevo & Rosen, 2010):

Suppose both and

1-SIDED AND 2-SIDED BOUNDS

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cov( , )X U cov( , ) 0Z U

IV OLS cov( , ) 0Z X

min{ , }OLS IV cov( , ) 0Z X

Case 1: If , then

Case 2: If , then

cov( , )

var( )

cov( , )

cov( , )

OLS

IV

X U

X

Z U

Z X

“IMPERFECT” IVS 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 !

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PARTIAL IDENTIFICATION OF MARSHALLIAN CONSUMER SURPLUS (MCS)

Bounds on β Bounds on MCS Suppose we obtain a 2-sided bound:ˆ ˆ

L U

(slope = )ˆL

MCSl

(slope = )ˆU

MCS2

XP

X0X 1X

XP

X0X 1X6

PARTIAL IDENTIFICATION OF MCS

(slope = )ˆU

(slope = )ˆL

x

xp

x0x 1x

PARTIAL IDENTIFICATION OF MCS

Suppose we obtain a 1-sided bound: ˆU

(slope = )ˆU

S

X

XP

X0X1X

(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.

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TWO-STAGE HEDONIC MODEL

1st stage: Estimate hedonic price function (market-specific)

implicit price of water clarity:

2nd Stage: Estimate demand function parameters (pooled)

0 1 2 3 4

5 6 7

im m m im m im m im m im

m im m im m im im

P BARE SQFT LOT HEAT

FULLBATH FF WQ

ln( )WQ LAKESIZE WT

7WT imim m

im

LAKESIZEP

WT

0 1 2 3 4 5

6 7 8

(

)

WTi i i i i i i

i i i i

P WT SQFT FF AGE INC RETIRED

KIDS VISIT FRIEND U

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Table . Demand Estimation with Pooled Data

OLS M M*INC Bounds

Water Quality

-710*** -2,253*** -2,975*** (-∞, -2,975]

[0, $2,732]

(-∞, -$22,911]

0 12.1, 4.7, 5.4X X X

1( )MCS X X

0( )MCS X X

Boyle et al. (1999)’s point estimates fall into our bounds !

116287; ( ) $1270.36MCS X X

State Home Price Percent Effect

Maine $71,536 3.81.8

New Hampshire $159,299 1.7

Vermont $99,034 2.8

CONCLUSIONS 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.

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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

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VARIABLES

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

RESULTS

Variables Estimates

CUL 0.147**(0.007)

CURBGUTTER 0.074***(0.016)

STW20 0.032**(0.016)

STW25 0.040***(0.014)

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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.

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