Nonparametric Inference via Bootstrapping the Debiased Estimator

In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a debiased estimator was recently employed by Calonico et al. (2018b) to construct a confidence interval of the density function (and regression function) at a given point by explicitly estimating stochastic variations. We extend their ideas of using the debiased estimator and further propose a bootstrap approach for constructing simultaneous confidence bands. This modified method has an advantage that we can easily choose the smoothing bandwidth from conventional bandwidth selectors and the confidence band will be asymptotically valid. We prove the validity of the bootstrap confidence band and generalize it to density level sets and inverse regression problems. Simulation studies confirm the validity of the proposed confidence bands/sets. We apply our approach to an Astronomy dataset to show its applicabilityComment: Accepted to the Electronic Journal of Statistics. 64 pages, 6 tables, 11 figure

Bootstrap Confidence Bands for Forecast Paths

The problem of forecasting from vector autoregressive models has attracted considerable attention in the literature. The most popular non-Bayesian approaches use large sample normal theory or the bootstrap to evaluate the uncertainty associated with the forecast. The literature has concentrated on the problem of assessing the uncertainty of the prediction for a single period. This paper considers the problem of how to assess the uncertainty when the forecasts are done for a succession of periods. It describes and evaluates bootstrap method for constructing confidence bands for forecast paths. The bands are constructed from forecast paths obtained in bootstrap replications with an optimisation procedure used to find the envelope of the most concentrated paths. The method is shown to have good coverage properties in a Monte Carlo study.vector autoregression, forecast path, bootstrapping, simultaneous statistical inference

Generic inference on quantile and quantile effect functions for discrete outcomes

Quantile and quantile effect functions are important tools for descriptive and inferential analysis due to their natural and intuitive interpretation. Existing inference methods for these functions do not apply to discrete random variables. This paper offers a simple, practical construction of simultaneous confidence bands for quantile and quantile effect functions of possibly discrete random variables. It is based on a natural transformation of simultaneous confidence bands for distribution functions, which are readily available for many problems. The construction is generic and does not depend on the nature of the underlying problem. It works in conjunction with parametric, semiparametric, and nonparametric modeling strategies and does not depend on the sampling scheme. We apply our method to characterize the distributional impact of insurance coverage on health care utilization and obtain the distributional decomposition of the racial test score gap. Our analysis generates new, interesting empirical findings, and complements previous analyses that focused on mean effects only. In both applications, the outcomes of interest are discrete rendering existing inference methods invalid for obtaining uniform confidence bands for quantile and quantile effects functions.https://arxiv.org/abs/1608.05142First author draf

Fiscal policy and growth

In the literature neither taxes, government spending nor deficits are robustly correlated with economic growth when evaluated individually. The lack of correlation may arise from the inability of any single budgetary component to fully capture the stance of fiscal policy. We use pair-wise combinations of fiscal indicators to assess the relationship between fiscal policy and U.S. growth. ; We develop a VAR methodology for evaluating simultaneous shocks to more than one variable and use it to examine the impulse responses for simultaneous, unexpected and equivalent structural shocks to pair-wise combinations of fiscal indicators. We also exploit the identity relationship between taxes, spending and deficits and follow Sims and Zha (1998) to evaluate an unexpected structural shock to one included fiscal indicator, holding constant the other included indicator. We find that an increase in the size of federal government leads to slower economic growth, that the deficit is an unreliable indicator of the stance of fiscal policy, and that tax revenues are the most consistent indicator of fiscal policy.Taxation