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
X
P

f
(
X
)


P
Implicit price of 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
3
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 }
4
“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 !
5
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
6
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
8
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.
9
10
TWO-STAGE HEDONIC MODEL

1st stage: Estimate hedonic price function (market-specific)
Pim  0m  1m BAREim  2m SQFTim  3m LOTim  4 m HEATim
5m FULLBATHim  6 m FFim  7 mWQim   im
WQ  LAKESIZE  ln(WT )
implicit price of water clarity: PimWT  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, X1  5.4

[0, $2,732]
(-∞, -$22,911]
Boyle et al. (1999)’s point estimates fall into our bounds !
  16287; MCS ( X  X1 )  $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  X1 )
MCS ( X  X 0 )
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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