Economics

Inference in models where the parameter is defined by moment inequalities is of interest in many areas of economics. This paper develops a new method for improving the performance of generalized moment selection (GMS) testing procedures in finite-samples. The method modifies GMS tests by tilting the empirical distribution in its moment selection step by an amount that maximizes the empirical likelihood subject to the restrictions of the null hypothesis. We characterize sets of population distributions on which a modified GMS test is (i) asymptotically equivalent to its non-modified version to first-order, and (ii) superior to its non-modified version according to local power when the sample size is large enough. An important feature of the proposed modification is that it remains computationally feasible even when the number of moment inequalities is large. We report simulation results that show the modified tests control size well, and have markedly improved local power over their non-modified counterparts.

We consider inference for high-dimensional exchangeable arrays where the dimension may be much larger than the cluster sizes. Specifically, we consider separately and jointly exchangeable arrays that correspond to multiway clustered and polyadic data, respectively. Such exchangeable arrays have seen a surge of applications in empirical economics. However, both exchangeability concepts induce highly complicated dependence structures, which poses a significant challenge for inference in high dimensions. In this paper, we first derive high-dimensional central limit theorems (CLTs) over the rectangles for the exchangeable arrays. Building on the high-dimensional CLTs, we develop novel multiplier bootstraps for the exchangeable arrays and derive their finite sample error bounds in high dimensions. The derivations of these theoretical results rely on new technical tools such as Hoeffding-type decomposition and maximal inequalities for the degenerate components in the Hoeffiding-type decomposition for the exchangeable arrays. We illustrate applications of our bootstrap methods to robust inference in demand analysis, robust inference in extended gravity analysis, uniform confidence bands for density estimation with network data, and penalty choice for ℓ 1 -penalized regression under multiway cluster sampling.

Vector autoregressive (VAR) models assume linearity between the endogenous variables and their lags. This assumption might be overly restrictive and could have a deleterious impact on forecasting accuracy. As a solution, we propose combining VAR with Bayesian additive regression tree (BART) models. The resulting Bayesian additive vector autoregressive tree (BAVART) model is capable of capturing arbitrary non-linear relations between the endogenous variables and the covariates without much input from the researcher. Since controlling for heteroscedasticity is key for producing precise density forecasts, our model allows for stochastic volatility in the errors. We apply our model to two datasets. The first application shows that the BAVART model yields highly competitive forecasts of the US term structure of interest rates. In a second application, we estimate our model using a moderately sized Eurozone dataset to investigate the dynamic effects of uncertainty on the economy.

We consider the problem of inference in Difference-in-Differences (DID) models when there are few treated units and errors are spatially correlated. We first show that, when there is a single treated unit, existing inference methods designed for settings with few treated and many control units remain asymptotically valid when errors are strongly mixing. However, these methods are invalid with more than one treated unit. We propose asymptotically valid, though generally conservative, inference methods for settings with more than one treated unit. These alternative inference methods are valid even when the relevant distance metric across units is unavailable. Moreover, they may be relevant alternatives even for settings in which the number of treated units is usually considered as large enough to rely on cluster-robust standard errors. We also present an empirical application that highlights some common misunderstandings in the use of randomization inference in DID applications, and illustrates how our results can be used to provide proper inference.

We analyze the conditions in which ignoring spatial correlation is problematic for inference in differences-in-differences models. We show that the relevance of spatial correlation for inference (when it is ignored) depends on the amount of spatial correlation that remains after we control for the time- and group-invariant unobservables. As a consequence, details such as the time frame used in the estimation, and the choice of the estimator, will be key determinants on the degree of distortions we should expect when spatial correlation is ignored. Simulations with real datasets corroborate these conclusions. These findings provide a better understanding on when spatial correlation should be more problematic, and provide important guidelines on how to minimize inference problems due to spatial correlation.

We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical version of the latter, we derive a Kolmogorov-Smirnov statistic for Choquet capacity functionals, which we use to construct our test. We derive the limiting distribution of our test statistic under the null, and show that our test is consistent against certain classes of alternatives. When the model is given in parametric form, the test can be inverted to yield confidence regions for the identified parameter set. The approach can be applied to the estimation of models with sample selection, censored observables and to games with multiple equilibria.

Nonparametric series regression often involves specification search over the tuning parameter, i.e., evaluating estimates and confidence intervals with a different number of series terms. This paper develops pointwise and uniform inferences for conditional mean functions in nonparametric series estimations that are uniform in the number of series terms. As a result, this paper constructs confidence intervals and confidence bands with possibly data-dependent series terms that have valid asymptotic coverage probabilities. This paper also considers a partially linear model setup and develops inference methods for the parametric part uniform in the number of series terms. The finite sample performance of the proposed methods is investigated in various simulation setups as well as in an illustrative example, i.e., the nonparametric estimation of the wage elasticity of the expected labor supply from Blomquist and Newey (2002).

We provide an inference procedure for the sharp regression discontinuity design (RDD) under monotonicity, with possibly multiple running variables. Specifically, we consider the case where the true regression function is monotone with respect to (all or some of) the running variables and assumed to lie in a Lipschitz smoothness class. Such a monotonicity condition is natural in many empirical contexts, and the Lipschitz constant has an intuitive interpretation. We propose a minimax two-sided confidence interval (CI) and an adaptive one-sided CI. For the two-sided CI, the researcher is required to choose a Lipschitz constant where she believes the true regression function to lie in. This is the only tuning parameter, and the resulting CI has uniform coverage and obtains the minimax optimal length. The one-sided CI can be constructed to maintain coverage over all monotone functions, providing maximum credibility in terms of the choice of the Lipschitz constant. Moreover, the monotonicity makes it possible for the (excess) length of the CI to adapt to the true Lipschitz constant of the unknown regression function. Overall, the proposed procedures make it easy to see under what conditions on the underlying regression function the given estimates are significant, which can add more transparency to research using RDD methods.

In this article, we study the limiting behavior of Bai (2009)'s interactive fixed effects estimator in the presence of randomly missing data. In extensive simulation experiments, we show that the inferential theory derived by Bai (2009) and Moon and Weidner (2017) approximates the behavior of the estimator fairly well. However, we find that the fraction and pattern of randomly missing data affect the performance of the estimator. Additionally, we use the interactive fixed effects estimator to reassess the baseline analysis of Acemoglu et al. (2019). Allowing for a more general form of unobserved heterogeneity as the authors, we confirm significant effects of democratization on growth.

This paper analyzes the properties of the Maximum Likelihood Estimator for mixed causal and noncausal models when the error term follows a Student's t-distribution. In particular, we compare several existing methods to compute the expected Fisher information matrix and show that they cannot be applied in the heavy-tail framework. For this purpose, we propose a new approach to make inference on causal and noncausal parameters in finite sample sizes. It is based on the empirical variance computed on the generalized Student's t, even when the population variance is not finite. Monte Carlo simulations show the good performances of our new estimator for fat tail series. We illustrate how the different approaches lead to different standard errors in four time series: annual debt to GDP for Canada, the variation of daily Covid-19 deaths in Belgium, the monthly wheat prices and the monthly inflation rate in Brazil.