Combining cross-sectional and time-series data is a long and well-established practice in empirical economics. We develop a central limit theory that explicitly accounts for possible dependence between the two datasets. We focus on common factors as the mechanism behind this dependence. Using our central limit theorem (CLT), we establish the asymptotic properties of parameter estimates of a general class of models based on a combination of cross-sectional and time-series data, recognizing the interdependence between the two data sources in the presence of aggregate shocks. Despite the complicated nature of the analysis required to formulate the joint CLT, it is straightforward to implement the resulting parameter limiting distributions due to a formal similarity of our approximations with Murphy and Topel’s (1985, Journal of Business and Economic Statistics 3, 370–379) formula.

In this paper, we complement joint time-series and cross-section convergence results derived in a companion paper Hahn, Kuersteiner, and Mazzocco (2016, Central Limit Theory for Combined Cross-Section and Time Series) by allowing for serial correlation in the time-series sample. The implications of our analysis are limiting distributions that have a well-known form of long-run variances for the time-series limit. We obtain these results at the cost of imposing strict stationarity for the time-series model and conditional independence between the time-series and cross-section samples. Our results can be applied to estimators that combine time-series and cross-section data in the presence of aggregate uncertainty in models with rationally forward-looking agents.

The fixed effects estimator of panel models can be severely biased because of well-known incidental parameter problems. It is shown that this bias can be reduced in nonlinear dynamic panel models. We consider asymptotics where n and T grow at the same rate as an approximation that facilitates comparison of bias properties. Under these asymptotics, the bias-corrected estimators we propose are centered at the truth, whereas fixed effects estimators are not. We discuss several examples and provide Monte Carlo evidence for the small sample performance of our procedure.

Infinite order vector autoregressive (VAR) models have been used in a number of applications ranging from spectral density estimation, impulse response analysis, and tests for cointegration and unit roots, to forecasting. For estimation of such models it is necessary to approximate the infinite order lag structure by finite order VARs. In practice, the order of approximation is often selected by information criteria or by general-to-specific specification tests. Unlike in the finite order VAR case these selection rules are not consistent in the usual sense, and the asymptotic properties of parameter estimates of the infinite order VAR do not follow as easily as in the finite order case. In this paper it is shown that the parameter estimates of the infinite order VAR are asymptotically normal with zero mean when the model is approximated by a finite order VAR with a data dependent lag length. The requirement for the result to hold is that the selected lag length satisfies certain rate conditions with probability tending to one. Two examples of selection rules satisfying these requirements are discussed. Uniform rates of convergence for the parameters of the infinite order VAR are also established.Very helpful comments by the editor and two referees led to a substantial improvement of the manuscript. I am particularly indebted to one of the referees for pointing out an error in the proofs. All remaining errors are my own. Financial support from NSF grant SES−0095132 is gratefully acknowledged.

This paper analyzes autoregressive time series models where the errors are assumed to be martingale difference sequences that satisfy an additional symmetry condition on their fourth-order moments. Under these conditions quasi maximum likelihood estimators of the autoregressive parameters are no longer efficient in the generalized method of moments (GMM) sense. The main result of the paper is the construction of efficient semiparametric instrumental variables estimators for the autoregressive parameters. The optimal instruments are linear functions of the innovation sequence.

It is shown that a frequency domain approximation of the optimal instruments leads to an estimator that only depends on the data periodogram and an unknown linear filter. Semiparametric methods to estimate the optimal filter are proposed.

The procedure is equivalent to GMM estimators where lagged observations are used as instruments. As a result of the additional symmetry assumption on the fourth moments the number of instruments is allowed to grow at the same rate as the sample. No lag truncation parameters are needed to implement the estimator, which makes it particularly appealing from an applied point of view.