NONLINEAR PANEL DATA MODELS WITH DISTRIBUTION-FREE CORRELATED RANDOM EFFECTS
提出一种无需对相关随机效应分布做参数假设的估计方法，通过傅里叶变换恢复未观测异质性分布，构建半参数平均似然函数并设计筛子最大似然估计，适用于静态和动态非线性面板数据模型。
Under a Mundlak-type correlated random effect (CRE) specification, we first show that the average likelihood of a parametric nonlinear panel data model is the convolution of the conditional distribution of the model and the distribution of the unobserved heterogeneity. Hence, the distribution of the unobserved heterogeneity can be recovered by means of a Fourier transformation without imposing a distributional assumption on the CRE specification. We subsequently construct a semiparametric family of average likelihood functions of observables by combining the conditional distribution of the model and the recovered distribution of the unobserved heterogeneity, and show that the parameters in the nonlinear panel data model and in the CRE specification are identifiable. Based on the identification result, we propose a sieve maximum likelihood estimator. Compared with the conventional parametric CRE approaches, the advantage of our method is that it is not subject to misspecification on the distribution of the CRE. Furthermore, we show that the average partial effects are identifiable and extend our results to dynamic nonlinear panel data models.