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.

Time variation is a fundamental problem in statistical and econometric analysis of macroeconomic and financial data. Recently, there has been considerable focus on developing econometric modelling that enables stochastic structural change in model parameters and on model estimation by Bayesian or nonparametric kernel methods. In the context of the estimation of covariance matrices of large dimensional panels, such data requires taking into account time variation, possible dependence and heavy-tailed distributions. In this paper, we introduce a nonparametric version of regularization techniques for sparse large covariance matrices, developed by Bickel and Levina (2008) and others. We focus on the robustness of such a procedure to time variation, dependence and heavy-tailedness of distributions. The paper includes a set of results on Bernstein type inequalities for dependent unbounded variables which are expected to be applicable in econometric analysis beyond estimation of large covariance matrices. We discuss the utility of the robust thresholding method, comparing it with other estimators in simulations and an empirical application on the design of minimum variance portfolios.

We discuss the existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated into the dynamic. To this end, we consider the convergence of the backward iterations of dependent random maps. In particular, we give a new result when the classical condition of contraction on average is replaced with a contraction in conditional expectation. Under some conditions, we also discuss the dependence properties of these processes using the functional dependence measure of Wu (2005, Proceedings of the National Academy of Sciences 102, 14150–14154) that delivers a central limit theorem giving a wide range of applications. Our results are illustrated with conditional heteroscedastic autoregressive nonlinear models, Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) processes, count time series, binary choice models, and categorical time series for which we provide many extensions of existing results.

This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive regression. A new test for linear cointegration against nonlinear departures is developed based on a simple linearized pseudo-model that is very convenient for practical implementation and has standard normal limit theory in the strictly exogenous regressor case. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semimartingale structure and considerably extend existing limit theory, complementing other recent findings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that encompasses stochastically nonstationary time series and should be of wide applicability.

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p-value of the TET statistic can provide an accurate approximation to the p-value of an infeasible saddlepoint statistic, which admits a Lugannani–Rice style adjustment with relative errors of order $n^{-1}$ both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- and overidentified moment condition models. A limitation of our analysis is that the theoretical approximation results are exclusively for the infeasible saddlepoint statistic, and closeness of the p-values for the infeasible statistic to the ones for the feasible TET statistic is only numerically assessed.

We propose a multiplex interdependent durations model and study its empirical content. The model considers an empirical stopping game of multiple agents making optimal timing decisions with incomplete information. We characterize the unique Bayesian Nash equilibrium of the stopping game in a system of simultaneous equations involving the conditional distribution of each duration with a moderate strategic interaction condition. The system of nonlinear simultaneous equations allows us to obtain constructive identification results of the interaction effects and other nonparametric model primitives. We propose two consistent semiparametric estimation methods based on different parameterizations of modeling components with right-censored duration data.

This paper develops an asymptotic theory of nonlinear least squares estimation by establishing a new framework that can be easily applied to various nonlinear regression models with heteroscedasticity. As an illustration, we explore an application of the framework to nonlinear regression models with nonstationarity and heteroscedasticity. In addition to these main results, this paper provides a maximum inequality for a class of martingales, which is of interest in its own right.