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.

中文翻译：

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具有无分布相关随机效应的非线性面板数据模型

在 Mundlak 型相关随机效应 (CRE) 规范下，我们首先表明参数非线性面板数据模型的平均似然是模型的条件分布和未观察到的异质性分布的卷积。因此，未观察到的异质性的分布可以通过傅里叶变换来恢复，而不会对 CRE 规范施加分布假设。随后，我们通过结合模型的条件分布和未观察到的异质性的恢复分布，构建了可观察值的平均似然函数的半参数族，并表明非线性面板数据模型和 CRE 规范中的参数是可识别的。根据识别结果，我们提出了一个筛子最大似然估计器。与传统的参数化 CRE 方法相比，我们的方法的优点是它不会对 CRE 的分布进行错误指定。此外，我们表明平均部分效应是可识别的，并将我们的结果扩展到动态非线性面板数据模型。