Partial Identification of Hedonic Demand Function
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Transcript Partial Identification of Hedonic Demand Function
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: P 0 1 ln( X ) (non-linear in X )
1
X
P
f
(
X
)
Implicit price of X:
( P X is function of X )
1
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: ZX 0 and ZU 0
“imperfect” IV : XU ZU 0
We allow correlation between IV and
error (unobserved components of preferences!
Z is “perfect”:
IV
Z is “imperfect”: is bounded by OLS and IV
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1-SIDED AND 2-SIDED BOUNDS
cov( X , U )
var( X )
cov( Z , U )
cov( Z , X )
OLS
IV
Proposition (Nevo & Rosen, 2010):
Suppose both cov( X , U ) and cov( Z , U ) 0
Case 1: If cov( Z , X ) 0 , then IV OLS
Case 2: If cov( Z , X ) 0 , then min{ OLS , IV }
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“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: ˆL ˆU
PX
PX
(slope = ˆU )
(slope = ˆL )
MCSl
MCS2
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X0
X1
X
X0
X1
X
PARTIAL IDENTIFICATION OF MCS
px
(slope = ˆU )
(slope = ˆL )
x0
x
x1
x
PARTIAL IDENTIFICATION OF MCS
Suppose we obtain a 1-sided bound: ˆU
PX
S
(slope = ˆU )
(slope = - )
X0
X
X1
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X
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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10
TWO-STAGE HEDONIC MODEL
1st stage: Estimate hedonic price function (market-specific)
Pim 0 m 1m BAREim 2 m SQFTim 3m LOTim 4 m HEATim
5m FULLBATH im 6 m FFim 7 mWQim im
WQ LAKESIZE ln(WT )
implicit price of water clarity: P
WT
im
7 m
LAKESIZEim
WTim
2nd Stage: Estimate demand function parameters (pooled)
PiWT WTi ( 0 1SQFTi 2 FFi 3 AGEi 4 INCi 5 RETIREDi
6 KIDSi 7VISITi 8 FRIENDi ) U i
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Table . Demand Estimation with Pooled Data
Water Quality
OLS
M
M*INC
Bounds
-710***
-2,253***
-2,975***
(-∞, -2,975]
X 0 2.1, X 4.7, X 1 5.4
[0, $2,732]
MCS ( X X 0 )
(-∞, -$22,911]
Boyle et al. (1999)’s point estimates fall into our bounds !
16287; MCS ( X X 1 ) $1270.36
State
Maine
New Hampshire
Vermont
Home Price
Percent Effect
$71,536
3.8
1.8
$159,299
1.7
$99,034
2.8
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MCS ( X X 1 )
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
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RESULTS
Variables
CUL
CURBGUTTER
STW20
STW25
Estimates
0.147**
(0.007)
0.074***
(0.016)
0.032**
(0.016)
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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