Advances in Econometrics
Friday, Jan. 6, 2017 1:00 PM – 3:00 PM
- Chair: Vitor Augusto Possebom, EESP-Getulio Vargas Foundation
Uniform Confidence Bands: Characterization and Optimality
AbstractThis 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
AbstractThis 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
AbstractThis 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).
- C0 - General