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Working Paper
Tests of Conditional Predictive Ability: A Comment
We investigate a test of equal predictive ability delineated in Giacomini and White (2006; Econometrica). In contrast to a claim made in the paper, we show that their test statistic need not be asymptotically Normal when a fixed window of observations is used to estimate model parameters. An example is provided in which, instead, the test statistic diverges with probability one under the null. Simulations reinforce our analytical results.
Working Paper
Tests of Conditional Predictive Ability: Existence, Size, and Power
We investigate a test of conditional predictive ability described in Giacomini and White (2006; Econometrica). Our main goal is simply to demonstrate existence of the null hypothesis and, in doing so, clarify just how unlikely it is for this hypothesis to hold. We do so using a simple example of point forecasting under quadratic loss. We then provide simulation evidence on the size and power of the test. While the test can be accurately sized we find that power is typically low.
Working Paper
Local Projections
A central question in applied research is to estimate the effect of an exogenous intervention or shock on an outcome. The intervention can affect the outcome and controls on impact and over time. Moreover, there can be subsequent feedback between outcomes, controls and the intervention. Many of these interactions can be untangled using local projections. This method’s simplicity makes it a convenient and versatile tool in the empiricist’s kit, one that is generalizable to complex settings. This article reviews the state-of-the art for the practitioner, discusses best practices and ...
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Micro Responses to Macro Shocks
We study panel data regression models when the shocks of interest are aggregate and possibly small relative to idiosyncratic noise. This speaks to a large empirical literature that targets impulse responses via panel local projections. We show how to interpret the estimated coefficients when units have heterogeneous responses and how to obtain valid standard errors and confidence intervals. A simple recipe leads to robust inference: including lags as controls and then clustering at the time level. This strategy is valid under general error dynamics and uniformly over the degree of ...
Working Paper
Bootstrapping out-of-sample predictability tests with real-time data
In this paper we develop a block bootstrap approach to out-of-sample inference when real-time data are used to produce forecasts. In particular, we establish its first-order asymptotic validity for West-type (1996) tests of predictive ability in the presence of regular data revisions. This allows the user to conduct asymptotically valid inference without having to estimate the asymptotic variances derived in Clark and McCracken’s (2009) extension of West (1996) when data are subject to revision. Monte Carlo experiments indicate that the bootstrap can provide satisfactory finite sample size ...
Working Paper
Local Projections Bootstrap Inference
Bootstrap procedures for local projections typically rely on assuming that the data generating process (DGP) is a finite order vector autoregression (VAR), often taken to be that implied by the local projection at horizon 1. Although convenient, it is well documented that a VAR can be a poor approximation to impulse dynamics at horizons beyond its lag length. In this paper we assume instead that the precise form of the parametric model generating the data is not known. If one is willing to assume that the DGP is perhaps an infinite order process, a larger class of models can be accommodated ...
Working Paper
Impulse Response Diagnostics for Priors on Parameters in Structural Vector Autoregressions
Structural impulse response functions may be estimated based on priors about the parameters of the structural VAR presentation. Even when such priors appear seemingly reasonable, they may imply an unintentionally informative prior for the structural impulse responses. Rather than pretending that the posterior of the impulse responses does not depend on this prior, the proposal in this paper is to verify that the prior distribution of the vector of impulse responses of interest is not unintentionally informative. Moreover, if the impulse response prior is intentionally informative, this point ...
Working Paper
Simpler Bootstrap Estimation of the Asymptotic Variance of U-statistic Based Estimators
The bootstrap is a popular and useful tool for estimating the asymptotic variance of complicated estimators. Ironically, the fact that the estimators are complicated can make the standard bootstrap computationally burdensome because it requires repeated re-calculation of the estimator. In Honor and Hu (2015), we propose a computationally simpler bootstrap procedure based on repeated re-calculation of one-dimensional estimators. The applicability of that approach is quite general. In this paper, we propose an alternative method which is specific to extremum estimators based on U-statistics. ...
Working Paper
Tests of Conditional Predictive Ability: Some Simulation Evidence
In this note we provide simulation evidence on the size and power of tests of predictive ability described in Giacomini and White (2006). Our goals are modest but non-trivial. First, we establish that there exist data generating processes that satisfy the null hypotheses of equal finite-sample (un)conditional predictive ability. We then consider various parameterizations of these DGPs as a means of evaluating the size and power properties of the proposed tests. While some of our results reinforce those in Giacomini and White (2006), others do not. We recommend against using the fixed scheme ...
Working Paper
Mean Group Distributed Lag Estimation of Impulse Response Functions in Large Panels
This paper develops Mean Group Distributed Lag (MGDL) estimation of impulse responses in large panels with one or two cross-section dimensions. Sufficient conditions for asymptotic consistency and asymptotic normality are derived, and satisfactory small sample performance is documented using Monte Carlo experiments. MGDL estimators are used to estimate the effects of crude oil price increases on U.S. city- and product-level retail prices.