Essays On Weak Instruments And Finite Population Inference
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Essays on Weak Instruments and Finite Population Inference
The first chapter examines a linear regression model with a binary endogenous explanatory variable (EEV) and weak instruments. By estimating a binary response model via maximum likelihood in the first step, the nonlinear fitted probability can be constructed as an alternative instrument for the binary EEV. I show that this two-step instrumental variables (IV) estimation procedure produces a consistent and asymptotically normal IV estimator, even though the alternate linear two stage least squares estimator is inconsistent with nonstandard asymptotics. Results are illustrated in an application evaluating the effects of electrification on employment growth.The remaining two chapters study statistical inference when the population is treated as finite. When the sample is a relatively large proportion of the population, finite population inference serves as a more appealing alternative to the usual infinite population approach. Nevertheless, the finite population inference methods that are currently available only cover the difference-in-means estimator or independent observations. Consequently, these methods cannot be applied to the many branches of empirical research that use linear or nonlinear models where dependence due to clustering needs to be accounted for in computing the standard errors. The second and third chapters fill in these gaps in the existing literature by extending the seminal work of Abadie, Athey, Imbens, and Wooldridge (2020).In the second chapter, I derive the finite population asymptotic variance for M-estimators with both smooth and nonsmooth objective functions, where observations are independent. I also find that the usual robust "sandwich" form standard error is conservative as it has been shown in the linear case. The proposed asymptotic variance of M-estimators accounts for two sources of variation. In addition to the usual sampling-based uncertainty arising from (possibly) not observing the entire population, there is also design-based uncertainty, which is usually ignored in the common inference method, resulting from lack of knowledge of the counterfactuals. Under this alternative framework, we can obtain smaller standard errors of M-estimators when the population is considered as finite.In the third chapter, I establish asymptotic properties of M-estimators under finite populations with clustered data, allowing for unbalanced and unbounded cluster sizes in the limit. I distinguish between two situations that justify computing clustered standard errors: i) cluster sampling induced by random sampling of groups of units, and ii) cluster assignment caused by the correlated assignment of "treatment" within the same group. I show that one should only adjust the standard errors for clustering when there is cluster sampling, cluster assignment, or both, for a general class of linear and nonlinear estimators. I also find the finite population cluster-robust asymptotic variance (CRAV) is no larger than the usual infinite population CRAV, in the matrix sense. The methods are applied to an empirical study evaluating the effect of tenure clock stopping policies on tenure rates.
Essays in Honor of M. Hashem Pesaran
Author: Alexander Chudik
language: en
Publisher: Emerald Group Publishing
Release Date: 2022-01-18
The collection of chapters in Volume 43 Part B of Advances in Econometrics serves as a tribute to one of the most innovative, influential, and productive econometricians of his generation, Professor M. Hashem Pesaran.
Identification and Inference for Econometric Models
Author: Donald W. K. Andrews
language: en
Publisher: Cambridge University Press
Release Date: 2005-07-04
This 2005 volume contains the papers presented in honor of the lifelong achievements of Thomas J. Rothenberg on the occasion of his retirement. The authors of the chapters include many of the leading econometricians of our day, and the chapters address topics of current research significance in econometric theory. The chapters cover four themes: identification and efficient estimation in econometrics, asymptotic approximations to the distributions of econometric estimators and tests, inference involving potentially nonstationary time series, such as processes that might have a unit autoregressive root, and nonparametric and semiparametric inference. Several of the chapters provide overviews and treatments of basic conceptual issues, while others advance our understanding of the properties of existing econometric procedures and/or propose others. Specific topics include identification in nonlinear models, inference with weak instruments, tests for nonstationary in time series and panel data, generalized empirical likelihood estimation, and the bootstrap.