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Nonparametric IV estimation of shape-invariant Engel curves

Blundell, R.; Chen, X.; Kristensen, D.; (2003) Nonparametric IV estimation of shape-invariant Engel curves. (cemmap Working Papers CWP15/). Institute for Fiscal Studies: London, UK. Green open access

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Abstract

This paper concerns the identification and estimation of a shape-invariant Engel curve system with endogenous total expenditure. The shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of Engel curves. Our focus is on the identification and estimation of both the nonparametric shape of the Engel curve and the parametric specification of the demographic scaling parameters. We present a new identification condition, closely related to the concept of bounded completeness in statistics. The estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric IV regression when the endogenous regressor has unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of ‘low-level’ sufficient conditions. Monte Carlo simulations shed lights on the choice of smoothing parameters and demonstrate that the sieve IV estimator performs well. An application is made to the estimation of Engel curves using the UK Family Expenditure Survey and shows the importance of adjusting for endogeneity in terms of both the curvature and demographic parameters of systems of Engel curves.

Type: Working / discussion paper
Title: Nonparametric IV estimation of shape-invariant Engel curves
Open access status: An open access version is available from UCL Discovery
Publisher version: http://www.cemmap.ac.uk/publications.php?publicati...
Language: English
Keywords: Consumer demands, nonparametric IV, bounded completeness, sieve minimum distance, measure of ill-posedness, nonparametric convergence rate, root-n semiparametric efficiency
UCL classification: UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of S&HS > Dept of Economics
URI: https://discovery.ucl.ac.uk/id/eprint/14697
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