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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