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Advances in Econometrics

Paper Session

Friday, Jan. 6, 2017 1:00 PM – 3:00 PM

Hyatt Regency Chicago, Water Tower
Hosted By: Econometric Society
  • Chair: Vitor Augusto Possebom, EESP-Getulio Vargas Foundation

Synthetic Control Estimator: A Generalized Inference Procedure and Confidence Sets

Vitor Augusto Possebom
,
EESP-Getulio Vargas Foundation
Sergio Firpo
,
Insper Institute of Education and Research-Brazil

Abstract

The Synthetic Control Method (SCM) was proposed to answer questions involving counterfactuals when only one treated unit and a few control units are observed. Although this method was applied in many empirical works, the formal theory behind its inference procedure is still an open question. In order to fulfill this lacuna, we make clear the sufficient hypotheses that guarantee the adequacy of Fisher's Exact Hypothesis Testing Procedure for panel data, allowing us to test any sharp null hypothesis and, consequently, to propose a new way to estimate Confidence Sets for the SCM by inverting a test statistic, the first confidence set when we have access only to finite sample, aggregate level data whose cross-sectional dimension may be larger than its time dimension. Moreover, we analyze the size and the power of the proposed test with a Monte Carlo experiment and find that test statistics that use the SCM outperforms test statistics commonly used in the evaluation literature. We also extend our framework for the cases when we observe more than one outcome of interest or more than one treated unit and when heteroskedasticity is present. Furthermore, we propose a sensitivity analysis that allows the researcher to verify the robustness of his or her empirical conclusions to one of our inference procedure's underlying assumptions. Finally, we apply our theoretical developments to reevaluate economic impact of ETA's terrorism on the Basque Country.

Uniform Confidence Bands: Characterization and Optimality

Joachim Freyberger
,
University of Wisconsin-Madison

Abstract

This paper characterizes optimal uniform confidence bands for functions in a general class of models. A uniform confidence band for a function g(x,b_0), where b_0 is an unknown parameter, consists of upper and lower bound functions gu(x) and gl(x), such that g(x,b_0) is contained in [gl(x), gu(x)] for all x with probability 1-a. While there are many different 1-a confidence bands for the same function, not all 1-a confidence bands are taut in the sense that it might be possible to weakly decrease the width of the interval for all x and to strictly decrease it for some x. In this paper, we provide a simple characterization of a general class of taut 1-a confidence bands, allowing for both nonlinear and nonparametric functions. Specifically, we show that all taut bands can be obtained from projections on confidence sets for b_0 and we characterize the class of confidence sets which yield taut bands. Given our simple and constructive characterization of these sets, we are then able to present a computational method for selecting an approximately optimal confidence band for a given objective function, such as minimizing the weighted area. We illustrate the wide applicability of these results in two numerical applications.

Inference with Many Instruments and Heterogeneous Treatment Effects

Kirill Evdokimov
,
Princeton University
Michal Kolesar
,
Princeton University

Abstract

This paper studies estimation and inference in an instrumental variables model
with heterogeneous treatment effects and possibly many instruments and/or %exogenous controls. When the treatment effects are heterogeneous, two-step estimators such as two-stage least squares (TSLS) or versions of the jackknife instrumental variables estimator (JIVE) estimate a particular weighted average of local average treatment effects. The weights in these estimands depend on the first-stage coefficients, and either the sample or population distribution of the the covariates and instruments, depending on whether they are treated as fixed or random. The usual confidence intervals based on Wald statistics as well as the recently proposed confidence intervals robust to weak instruments fail to achieve proper coverage for these estimands. We derive new asymptotic variance formulas for the TSLS and JIVE estimands. Compared to the case with homogeneous treatment effects, the variance expression contains an additional term reflecting variability of the local average treatment effects that is quantitatively important. We derive feasible estimators for the asymptotic variance. We also show that the additional variance term has important implications for instrument selection. A Monte Carlo study supports the conclusions from the asymptotic theory, and shows that the variance estimators perform well. We also illustrate our results in an empirical application.

Identifying Heterogenous Marginal Effects Using Covariates

Carolina Caetano
,
University of Rochester
Juan Carlos Escanciano
,
Indiana University

Abstract

This paper proposes a new strategy for the identification of the marginal
effects of an endogenous variable of interest in the presence of covariates. The identification is robust in two different ways: (i) to nuisance parameters (e.g. endogeneity of covariates); and (ii) to certain classic rank identification failures. Identification is achieved by exploiting heterogeneity of the \textquotedblleft first stage\textquotedblright\ in covariates through a new rank condition that we term covariance completeness. Following the identification strategy, this paper also proposes parametric and nonparametric Two-Stage Least Squares (TSLS) estimators which are simple to implement, discusses their asymptotic properties, and shows that the estimators have satisfactory performance in moderate samples sizes. Finally, we apply our methods to the problem of estimating the effect of air quality on house prices, based on Chay and Greenstone (2005).
JEL Classifications
  • C0 - General