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Essays on Statistical Inference in Econometrics.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Essays on Statistical Inference in Econometrics./
Author:	Kim, Deborah.
Description:	1 online resource (186 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
Contained By:	Dissertations Abstracts International85-11B.
Subject:	Statistics. -
Online resource:	click for full text (PQDT)
ISBN:	9798382763125

Essays on Statistical Inference in Econometrics.
Kim, Deborah.

Essays on Statistical Inference in Econometrics. - 1 online resource (186 pages)

Source: Dissertations Abstracts International, Volume: 85-11, Section: B.

Thesis (Ph.D.)--Northwestern University, 2024.

Includes bibliographical references

This dissertation consists of three essays covering statistical inference problems in econometrics. The initial two chapters concerns testing moment inequalities, specifically testing the agreement of signs among finite means and testing the non-positivity of finite means. The final chapter studies constructing confidence intervals using approximate randomization test.In the first chapter, I consider the problem of testing sign agreement of a finite number of means. This problem naturally emerge in numerous empirical contexts including detecting sign-opposing average treatment effects across subgroups in randomized controlled trials, testing external validity of local average treatment effects (LATE) across distinct subpopulations, and examining the testable implication of assumptions for LATE. For the null hypothesis that the means are all non-negative or all non-positive, I propose two novel statistical tests: the Least Favorable and the Hybrid tests. Both tests are the first to accommodate arbitrary dependence among estimators for any finite number of means and first to provide nonparametric bootstrap critical values. I show that both tests control their asymptotic sizes uniformly over a large class of nonparametric distributions. Results from simulation studies in finite samples, indicate that rejection probabilities of both tests reach the nominal level under the null hypothesis. The Hybrid test exhibits higher power than the Least Favorable test when there are more than three means; this relationship reverses when considering only two means. I demonstrate the utility of both tests in an application inspired by Angelucci, Karlan, and Zinman (2015), in which I study the impacts of microloans on various groups and outcomes.The second chapter analyzes the theoretical properties of the hybrid test for superior predictive ability proposed by Song (2012). A simple example reveals that the test may not be size-controlled at common significance levels with rejection rates exceeding 11% at a 5% nominal level. Generalizing this observation, the main results show the pointwise asymptotic invalidity of the hybrid test under reasonable conditions. Monte Carlo simulations support these theoretical findings. The size distortion of the hybrid test stems from misspecification of the least favorable configuration of the symmetrized test statistic--namely, the parameter values that satisfy the null hypothesis and stochastically maximize the test statistic. The first chapter investigates the correct specification of this test statistic's least favorable configuration under a different, yet related, null hypothesis.The final chapter is co-authored with Yong Cai, Ivan Canay, and Azeem Shaikh. This chapter provides a user's guide to the general theory of approximate randomization tests developed in Canay, Romano, and Shaikh (2017) when specialized to linear regressions with clustered data. An important feature of the methodology is that it applies to settings in which the number of clusters is small -- even as small as five. We provide a step-by-step algorithmic description of how to implement the test and construct confidence intervals for the parameter of interest. In doing so, we additionally present three novel results concerning the methodology: we show that the method admits an equivalent implementation based on weighted scores; we show the test and confidence intervals are invariant to whether the test statistic is studentized or not; and we prove convexity of the confidence intervals for scalar parameters. We also articulate the main requirements underlying the test, emphasizing in particular common pitfalls that researchers may encounter. Finally, we illustrate the use of the methodology with two applications that further illuminate these points: one to a linear regression with clustered data based on Meng, Qian, and Yared (2015) and a second to a linear regression with temporally dependent data based on Munyo and Rossi (2015).

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798382763125Subjects--Topical Terms:

556824
Statistics.
Subjects--Index Terms:

Approximate randomization testIndex Terms--Genre/Form:

554714
Electronic books.

Essays on Statistical Inference in Econometrics.
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520 $a This dissertation consists of three essays covering statistical inference problems in econometrics. The initial two chapters concerns testing moment inequalities, specifically testing the agreement of signs among finite means and testing the non-positivity of finite means. The final chapter studies constructing confidence intervals using approximate randomization test.In the first chapter, I consider the problem of testing sign agreement of a finite number of means. This problem naturally emerge in numerous empirical contexts including detecting sign-opposing average treatment effects across subgroups in randomized controlled trials, testing external validity of local average treatment effects (LATE) across distinct subpopulations, and examining the testable implication of assumptions for LATE. For the null hypothesis that the means are all non-negative or all non-positive, I propose two novel statistical tests: the Least Favorable and the Hybrid tests. Both tests are the first to accommodate arbitrary dependence among estimators for any finite number of means and first to provide nonparametric bootstrap critical values. I show that both tests control their asymptotic sizes uniformly over a large class of nonparametric distributions. Results from simulation studies in finite samples, indicate that rejection probabilities of both tests reach the nominal level under the null hypothesis. The Hybrid test exhibits higher power than the Least Favorable test when there are more than three means; this relationship reverses when considering only two means. I demonstrate the utility of both tests in an application inspired by Angelucci, Karlan, and Zinman (2015), in which I study the impacts of microloans on various groups and outcomes.The second chapter analyzes the theoretical properties of the hybrid test for superior predictive ability proposed by Song (2012). A simple example reveals that the test may not be size-controlled at common significance levels with rejection rates exceeding 11% at a 5% nominal level. Generalizing this observation, the main results show the pointwise asymptotic invalidity of the hybrid test under reasonable conditions. Monte Carlo simulations support these theoretical findings. The size distortion of the hybrid test stems from misspecification of the least favorable configuration of the symmetrized test statistic--namely, the parameter values that satisfy the null hypothesis and stochastically maximize the test statistic. The first chapter investigates the correct specification of this test statistic's least favorable configuration under a different, yet related, null hypothesis.The final chapter is co-authored with Yong Cai, Ivan Canay, and Azeem Shaikh. This chapter provides a user's guide to the general theory of approximate randomization tests developed in Canay, Romano, and Shaikh (2017) when specialized to linear regressions with clustered data. An important feature of the methodology is that it applies to settings in which the number of clusters is small -- even as small as five. We provide a step-by-step algorithmic description of how to implement the test and construct confidence intervals for the parameter of interest. In doing so, we additionally present three novel results concerning the methodology: we show that the method admits an equivalent implementation based on weighted scores; we show the test and confidence intervals are invariant to whether the test statistic is studentized or not; and we prove convexity of the confidence intervals for scalar parameters. We also articulate the main requirements underlying the test, emphasizing in particular common pitfalls that researchers may encounter. Finally, we illustrate the use of the methodology with two applications that further illuminate these points: one to a linear regression with clustered data based on Meng, Qian, and Yared (2015) and a second to a linear regression with temporally dependent data based on Munyo and Rossi (2015).
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