Recently, the co-authored paper Identification and inference for semiparametric single index transformation models by Assistant Professor Lin Yingqian from the Department of Econometrics, School of Economics, Shanghai University of Finance and Economics, has been formally published in Journal of Econometrics, a top-tier international economics journal.
Abstract
This paper considers a semiparametric single index model in which the dependent variable is subject to a nonparametric transformation. The model has the form G₀(Y)=g₀(Xᵀθ₀)+e, where X is a random vector of regressors, Y is the dependent variable and e is the random noise, the monotonic function G₀, the smooth function g₀ and the index vector θ₀ are all unknown. This model is quite general in the sense that it nests many popular regression models as special cases. We first propose identification strategies for the three unknown quantities, based on which estimators are then constructed. The kernel density weighted average derivative estimator of δ (proportional to θ₀) has a V-statistic representation and its asymptotical normality is established under the small bandwidth asymptotics. The kernel estimator of the transformation function G₀ is a functional of the conditional distribution estimator of Y given Xᵀθ₀ and is shown to be √n-consistent and asymptotically normal. The sieve estimator of g₀ is shown to enjoy the standard nonparametric asymptotic properties. A specification test for the single index structure and extension to allow for endogenous regressors are also developed. In addition, data-driven choices of the smoothing parameters are discussed. Simulation results illustrate the nice finite sample performance of the proposed estimators and specification test. An empirical application to studying the impact of family income on child achievement demonstrates the practical merits of the proposed model.
About the Author
Lin Yingqian is an Assistant Professor at the School of Economics, Shanghai University of Finance and Economics, and holds a PhD in Economics from Peking University. Her research fields include nonparametric statistics and time series analysis. She has published multiple academic papers in journals such as Journal of Econometrics, Economics Letters and Advances in Econometrics. She presides over the Youth Project of the National Natural Science Foundation of China and the Shanghai Chenguang Program, and is a recipient of the Shanghai Higher Education Talent Attraction and Retention Initiative.
