Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves
研究具有内生总支出的形状不变恩格尔曲线系统，通过筛子最小距离估计识别非参数形状和人口统计参数，并证明估计量的收敛速度与渐近正态性，应用英国家庭支出调查数据表明调整内生性的重要性。
This paper studies a shape-invariant Engel curve system with endogenous total expenditure, in which the shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and 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 instrumental variable regression when the endogenous regressor could have unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of "low-level" sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves. Copyright The Econometric Society 2007.