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Thursday, 14 December, 2023

Alena Skolkova: Essays on Model Uncertainty and Model Averaging

Dissertation Committee:

Štěpán Jurajda (CERGE-EI, chair)

Veronika Selezneva (Université Paris Dauphine)

Ctirad Slavík (CERGE-EI)

Defense Committee:

Nikolas Mittag (CERGE-EI, chair)

Jozef Baruník (Institute of Economic Studies FSS CU)

Michal Pešta (Faculty of Mathematics and Physics CU)

Referees:

prof. Anna Mikusheva, Ph.D. (Massachusetts Institute of Technology)

Lukáš Lafférs, Ph.D. (Univerzita Mateja Bela)

Link for online connection: https://call.lifesizecloud.com/19933043, passcode: 5659

Abstract:

In the first chapter of this dissertation I study the properties of a model averaging estimator with ridge regularization. I propose the ridge-regularized modifications of Mallows model averaging (Hansen, 2007, Econometrica}, 75) and heteroskedasticity-robust Mallows model averaging (Liu and Okui, 2013, The Econometrics Journal, 16) to leverage the capabilities of averaging and ridge regularization simultaneously. Via a simulation study, I examine the finite-sample improvements obtained by replacing least-squares with a ridge regression. Ridge-based model averaging is especially useful when one deals with sets of moderately to highly correlated predictors, because the underlying ridge regression accommodates correlated predictors without blowing up estimation variance. A two-model theoretical example shows that the relative reduction of mean squared error is increasing with the strength of the correlation. I also demonstrate the superiority of the ridge-regularized modifications via empirical examples focused on wages and economic growth.

The second chapter focuses on the use of elastic-net regression for instrumental variable estimation. I investigate the relative performance of the lasso and elastic-net estimators for fitting the first-stage as part of IV estimation. Because elastic-net includes a ridge-type penalty in addition to a lasso-type penalty, it generally improves upon lasso in finite samples when correlations among the instrumental variables are not negligible. I show that IV estimators based on the lasso and elastic-net first-stage estimates can be asymptotically equivalent. Via a Monte Carlo study, I demonstrate the robustness of the sample-split elastic-net IV estimator to deviations from approximate sparsity, and to correlation among instruments that may be high-dimensional. Finally, I provide an empirical example that demonstrates potential improvement in estimation accuracy gained by the use of IV estimators based on elastic-net.

The third chapter, a joint work with S. Anatolyev, contributes to wider use of advanced conventional methods for dealing with instrumental variable regression with many, possibly weak, instruments in Stata. We introduce a STATA command, mivreg, that implements consistent estimation and testing in linear IV regressions with many instruments, which may be weak. The command mivreg covers both homoskedastic and heteroskedastic environments, estimators that are both non-robust and robust to error non-normality and projection matrix limit, and both parameter tests and specification tests, both with and without correction for the existence of moments. We also run a small simulation experiment using mivreg and illustrate how mivreg works with real data.

Full Text: "Essays on Model Uncertainty and Model Averaging"