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Nonstandard Inference Methods

Paper Session

Sunday, Jan. 6, 2019 1:00 PM - 3:00 PM

Atlanta Marriott Marquis, L503
Hosted By: Econometric Society
  • Chair: Federico Bugni, Duke University

Instrumental Variable Identification of Dynamic Variance Decompositions

Mikkel Plagborg-Moller
,
Princeton University
Christian Wolf
,
Princeton University

Abstract

Macroeconomists often estimate impulse response functions using external instruments (proxy variables) for the shocks of interest. However, existing methods do not answer the key question of how important the shocks are in driving macro aggregates. We provide tools for doing inference on variance decompositions in a general semiparametric moving average model, disciplined only by the availability of external instruments. The share of the variance that can be attributed to a shock is partially identified, albeit with informative bounds. Point identification of most parameters, including historical decompositions, can be achieved under much weaker assumptions than invertibility, a condition imposed in conventional Structural Vector Autoregressive (SVAR) analysis. In fact, external instruments make the invertibility assumption testable. To perform inference, we construct partial identification robust confidence intervals. We illustrate our methods using (i) a structural macro model and (ii) an empirical study of the importance of monetary policy shocks.

Inference on Winners

Isaiah Andrews
,
Harvard University
Toru Kitagawa
,
University College London
Adam McCloskey
,
University of Colorado

Abstract

Many questions in econometrics can be cast as inference on a parameter selected through optimization. For example, researchers may be interested in the effectiveness of the best policy found in a randomized trial, or the best-performing investment strategy based on historical data. Such settings give rise to a winner's curse, where conventional estimates are biased and conventional confidence intervals are unreliable. This paper develops optimal confidence sets and median-unbiased estimators that are valid conditional on the parameter selected and so overcome this winner's curse. For settings where we need validity only on average over target parameters that might have been selected, we develop procedures offering further performance gains that are attractive relative to existing alternatives.

On Optimal Inference in the Linear IV Regression Model

Donald Andrews
,
Yale University
Vadim Marmer
,
University of British Columbia
Zhengfei Yu
,
University of Tsukuba

Abstract

This paper considers tests and confidence sets (CS's) concerning the coefficient on the endogenous variable in the linear IV regression model with homoskedastic normal errors and one right-hand side endogenous variable. The paper derives a finite-sample lower bound function for the probability that a CS constructed using a two-sided invariant similar test has infinite length and shows numerically that the conditional likelihood ratio (CLR) CS of Moreira (2003) is not always very close to this lower bound function. This implies that the CLR test is not always very close to the two-sided asymptotically-efficient (AE) power envelope for invariant similar tests of Andrews, Moreira, and Stock (2006) (AMS). On the other hand, the paper establishes the finite-sample optimality of the CLR test when the correlation between the structural and reduced-form errors, or between the two reduced-form errors, goes to 1 or -1 and other parameters are held constant, where optimality means achievement of the two-sided AE power envelope of AMS. These results cover the full range of (non-zero) IV strength. The paper investigates in detail scenarios in which the CLR test is not on the two-sided AE power envelope of AMS.

Testing Continuity of a Density Via G-Order Statistics in the Regression Discontinuity Design

Federico Bugni
,
Duke University
Ivan Canay
,
Northwestern University

Abstract

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut-off, e.g., McCrary (2008). In this paper, we propose a new test for continuity of a density at a point based on the so-called g-order statistics and study its properties under a novel asymptotic framework. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of effective observations local to the cut-off is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cut-off as n diverges, our framework allows for the number q of observations local to the cut-off to be fixed as n diverges. The new test is easy to implement, asymptotically valid under weaker conditions than those used by competing methods, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties against certain alternatives. In a simulation study, we find that the new test controls size remarkably well across designs. We finally apply our test to the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.
JEL Classifications
  • C2 - Single Equation Models; Single Variables
  • C5 - Econometric Modeling