We derive uniform convergence results of lag-window spectral density estimates for a general class of multivariate stationary processes represented by an arbitrary measurable function of iid innovations. Optimal rates of convergence, that hold as both the time series and the cross section dimensions diverge, are obtained under mild and easily verifiable conditions. Our theory complements earlier results, most of which are univariate, which primarily concern in-probability, weak or distributional convergence, yet under a much stronger set of regularity conditions, such as linearity in iid innovations. Based on cross spectral density functions, we then propose a new test for independence between two stationary time series. We also explain the extent to which our results provide the foundation to derive the double asymptotic results for estimation of generalized dynamic factor models.

We propose nonparametric estimators for conditional value-at-risk (CVaR) and conditional expected shortfall (CES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning covariates, which may include lagged returns and other exogenous variables, are assumed to be strong mixing and follow a nonparametric conditional location-scale model. First stage nonparametric estimators for location and scale are combined with a generalized Pareto approximation for distribution tails proposed by Pickands (1975, Annals of Statistics 3, 119–131) to give final estimators for CVaR and CES. We provide consistency and asymptotic normality of the proposed estimators under suitable normalization. We also present the results of a Monte Carlo study that sheds light on their finite sample performance. Empirical viability of the model and estimators is investigated through a backtesting exercise using returns on future contracts for five agricultural commodities.

This paper examines the ordinary least squares (OLS) estimator of the structural parameters in a simple macroeconomic model in which agents are boundedly rational and use an adaptive learning rule to form expectations of the endogenous variable. The popularity of learning models has recently increased amongst applied economists and policy makers who seek to estimate them empirically. Yet the econometrics of learning models is largely uncharted territory. We consider two prominent learning algorithms, namely constant gain and decreasing gain learning. For each of the two learning rules, our analysis proceeds in two stages. First, the paper derives the asymptotic properties of agents’ expectations. At the second stage, the paper derives the asymptotics of OLS in the structural model, taking the first stage learning dynamics as given. In the case of constant gain learning, the structural model effectively amounts to a stationary, cointegrating, or co-explosiveness regression. With decreasing gain learning, the regressors are asymptotically collinear such that OLS does not satisfy, in general, the Grenander conditions for consistent estimability. Nevertheless, this paper shows that the OLS estimator remains consistent in all models considered. It also shows, however, that its asymptotic distribution, and hence any inference based upon it, may be nonstandard.

In this paper we study doubly robust estimators of various average and quantile treatment effects under unconfoundedness; we also consider an application to a setting with an instrumental variable. We unify and extend much of the recent literature by providing a very general identification result which covers binary and multi-valued treatments; unnormalized and normalized weighting; and both inverse-probability weighted (IPW) and doubly robust estimators. We also allow for subpopulation-specific average treatment effects where subpopulations can be based on covariate values in an arbitrary way. Similar to Wooldridge (2007), we then discuss estimation of the conditional mean using quasi-log likelihoods (QLL) from the linear exponential family.

This paper studies linear factor models that have arbitrarily dependent factors. Assuming that the coefficients are known and that their matrix representation satisfies rank conditions, we identify the nonparametric joint distribution of the unobserved factors using first and then second-order partial derivatives of the log characteristic function of the observed variables. In conjunction with these identification strategies the mean and variance of the vector of factors are identified. The main result provides necessary and sufficient conditions for identification of the joint distribution of the factors. In an illustrative example, we show identification of an earnings dynamics model with a subset of arbitrarily dependent income shocks. Closed-form formulas lead to estimators that converge uniformly and despite being based on inverse Fourier transforms have tight confidence bands around their theoretical counterparts in Monte Carlo simulations.

Proxies for unobserved skills and technologies are increasingly available in empirical data. For dynamic discrete choice models of forward-looking agents where a continuous state variable is unobserved but its proxy is available, we derive closed-form identification of the structure by explicitly solving integral equations. In the first step, we derive closed-form identification of Markov components, including the conditional choice probabilities and the law of state transition. In the second step, we plug in these first-step identifying formulas to obtain primitive structural parameters of dynamically optimizing agents.

Many economic models yield conditional moment inequalities that can be used for inference on parameters of these models. In this paper, I construct new tests of parameter hypotheses in conditional moment inequality models based on studentized kernel estimates of moment functions. The tests automatically adapt to the unknown smoothness of the moment functions, have uniformly correct asymptotic size, and are rate-optimal against certain classes of alternatives. Some existing tests have nontrivial power against n−1/2-local alternatives of a certain type whereas my methods only allow for nontrivial testing against (n / log n)−1/2-local alternatives of this type. There exist, however, large classes of sequences of well-behaved alternatives against which the tests developed in this paper are consistent and those tests are not.

Using a simplified approach developed by Severini and Tripathi (2001), we calculate the semiparametric efficiency bound for the finite-dimensional parameters of censored linear regression models with heteroskedastic errors. Under an additional identification at infinity type assumption, we propose an efficient estimator based on a novel result from Lewbel and Linton (2002). An extension to censored partially linear single-index models is also presented.