Essays in Econometrics: Inference in Spatial Causal and Limited-Information Settings and Marginal Forecast Adjustment for Bayesian Vector Autoregressions

Abstract

I develop and characterize valid standard errors and inference for both spatial causal inference problems and limited-information calibration, as well as define a post-estimation procedure that adjusts Bayesian vector autoregression (BVAR) forecasts given additional information in a manner consistent with full re-estimation. Chapter 1 provides and justifies standard errors for causal inference settings with spatial assignment. I show how knowledge of and weak dependence in the assignment mechanism alone justify particular design-based standard errors and inference, avoiding restrictive assumptions on outcomes or the distribution of individual causal effects. I contrast these standard errors with common alternatives from the literature, demonstrating that these alternatives tend to exhibit overcoverage and power loss when individual treatment effects are positively spatially correlated. Finally, I extend the results to derive valid design-based standard errors and inference for a local average treatment effect (LATE) estimand under correlated treatment assignment. Chapter 2, coauthored with Mikkel Plagborg-Møller, demonstrates how to conduct inference for calibrated model parameters when the correlation structure of moments used in calibration are unknown. Existing standard error formulas require a consistent estimate of the correlation structure. However, using only the variances of empirical moments, we derive conservative standard errors, confidence intervals, and overidentification tests that are valid even under the worst-case correlation structure. We apply the methods empirically to a model of menu cost pricing for multi-product firms and to a heterogeneous agent New Keynesian model. Chapter 3 defines a procedure for adjusting the forecast distribution of a BVAR by exploiting additional information ex-post after estimation and states conditions under which the adjustment procedure is mean-equivalent to re-estimation of an expanded model. I show how one can apply the Frisch-Waugh-Lovell Theorem in a Bayesian context to extract the marginal information in additional predictors and use it to drive data-driven adjustments of the forecast distribution, under proper penalization as would occur under re-estimation. In an out-of-sample forecasting exerise, I compare performance of this simple adjustment procedure to a popular alternative of constructing and estimating individual, custom nowcast models for each outcome in the core BVAR. I demonstrate that the recommended procedure performs comparably for most variables.