Nonparametric estimation with nonlinear budget sets

59 Pages·1999·1.6 MB·English

by  Blomquist, Nils Sren

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http://www.archive.org/details/nonparametricestOOblom
DEWEV
HB31
.M415
working paper
department
economics
of
NONPARAMETRICESTIMATION WITH
NONLINEARBUDGETSETS
Soren Blomquist
Whitney K. Newey
July, 1999
massachusetts
institute of
technology
50 memorial drive
Cambridge, mass. 02139

WORKING PAPER
DEPARTMENT
OF ECONOMICS
NONPARAMETRICESTIMATION WITH
NONLINEARBUDGETSETS
Soren Blomquist
Whitney K. Newey
No. 99-03 July, 1999
MASSACHUSETTS
OF
INSTITUTE
TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASS. 02142

NONPARAMETRIC ESTIMATION WITH
NONLINEAR BUDGET SETS *
Soren Blomquist Uppsala University Sweden
MA
Whitney Newey MIT, E52-262D Cambridge, 02139
September, 1998
Revised, February 1999
Abstract
Choice models with nonlinear budget sets are important in econometrics. In
this paper we propose a nonparametric approach to estimation of choice models
with nonlinear budget sets. The basic idea is to think of the choice, in our case
hours oflabor supply, as beinga function oftheentire budget set. Then we can ac-
count nonparametrically for a nonlinear budget set by estimating a nonparametric
regression where the variable in the regression is the budget set. We reduce the
dimensionality of this problem by exploiting additive structure implied by utility
maximization with convex budget sets. This structure leads to a polynomial con-
vergence rate for the estimator. We give asymptotic normality results also. The
usefulness of the estimator is demonstrated in Monte Carlo and empirical work,
where we find it can have a large impact on estimated effects of tax changes.
JEL Classification: C14, C24
Keywords: Nonlinear budget sets, nonparametric estimation, additive models.
•Financial support from the Bank ofSweden Tercentenary Foundation is gratefully acknowl-
edged. WearegratefultoMatiasEklofforcompetentresearchassistance. Wethankparticipants
at the Harvard-MIT econometrics workshop and the NBER for helpful comments.