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POST-SELECTION INFERENCE IN THREE-DIMENSIONAL PANEL DATA

Published online by Cambridge University Press:  15 March 2022

Harold D. Chiang
Affiliation:
University of Wisconsin-Madison
Joel Rodrigue
Affiliation:
Vanderbilt University
Yuya Sasaki*
Affiliation:
Vanderbilt University
*
Address correspondence to Yuya Sasaki, Department of Economics, Vanderbilt University, VU Station B #351819, 2301 Vanderbilt Place, Nashville, TN 37235-1819, USA; e-mail: yuya.sasaki@vanderbilt.edu.
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Abstract

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Three-dimensional panel models are widely used in empirical analysis. Researchers use various combinations of fixed effects for three-dimensional panels while the correct specification is unknown. When one imposes a parsimonious model and the true model is rich in complexity, the fitted model inevitably incurs the consequences of misspecification including potential bias. When a richly specified model is employed and the true model is parsimonious, then the consequences typically include a poor fit with larger standard errors than necessary. It is therefore useful for researchers to have good model selection techniques that assist in determining the “true” model or a satisfactory approximation. In this light, Lu, Miao, and Su (2021, Econometric Reviews 40, 867–898) propose methods of model selection. We advance this literature by proposing a method of post-selection inference for regression parameters. Despite our use of the lasso technique as the means of model selection, our assumptions allow for many and even all fixed effects to be nonzero. This property is important to avoid a degenerate distribution of fixed effects which often reflect economic sizes of countries in gravity analyses of trade. Using an international trade database, we document evidence that our key assumption of approximately sparse fixed effects is plausibly satisfied for gravity analyses of trade. We also establish the uniform size control over alternative data generating processes of fixed effects. Simulation studies demonstrate that the proposed method is less biased than under-fitting fixed effect estimators, is more efficient than over-fitting fixed effect estimators, and robustly allows for inference that is as accurate as the oracle estimator.

Type
ARTICLES
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

First arXiv version: March 30, 2019. We benefited from very useful comments by Peter C.B. Phillips (editor), Liangjun Su (co-editor), three anonymous referees, Antonio Galvao, Hiro Kasahara, Kengo Kato, Carlos Lamarche, Whitney Newey, participants in 2019 Cemmap/WISE Workshop on Advances in Econometrics and 2019 University of Tokyo Workshop on Advances in Econometrics. All remaining errors are ours. Code files are available upon request from the authors. Chiang is supported by the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin–Madison with funding from the Wisconsin Alumni Research Foundation.

References

REFERENCES

Balazsi, L., Matyas, L., & Wansbeek, T. (2017) Fixed effects models. In Matyas, L. (ed.), The Econometrics of Multi-Dimensional Panels , chapter 1, pp. 134. Springer.Google Scholar
Baltagi, B.H., & Bresson, G. (2017) Modelling housing using multi-dimensional panel data. In Matyas, L. (ed.), The Econometrics of Multi-Dimensional Panels , chapter 12, pp. 349376. Springer.CrossRefGoogle Scholar
Baltagi, B.H., Egger, P.H., & Erhardt, K. (2017) The estimation of gravity models in international trade. In Matyas, L. (ed.), The Econometrics of Multi-Dimensional Panels , chapter 11, pp. 323348. Springer.CrossRefGoogle Scholar
Belloni, A., Chen, D., Chernozhukov, V., & Hansen, C. (2012) Sparse models and methods for optimal instruments with an application to eminent domain. Econometrica 80, 23692429.Google Scholar
Belloni, A., Chernozhukov, V., Chetverikov, D., Hansen, C., & Kato, K. (2018) High-dimensional econometrics and regularized GMM, preprint, arXiv:1806.01888.Google Scholar
Belloni, A., Chernozhukov, V., Chetverikov, D., & Wei, Y. (2018) Uniformly valid post-regularization confidence regions for many functional parameters in z-estimation framework. Annals of Statistics 46, 36433675.CrossRefGoogle ScholarPubMed
Belloni, A., Chernozhukov, V., & Hansen, C. (2014) Inference on treatment effects after selection among high-dimensional controls. The Review of Economic Studies 81, 608650.CrossRefGoogle Scholar
Belloni, A., Chernozhukov, V., Hansen, C., & Kozbur, D. (2016) Inference in high-dimensional panel models with an application to gun control. Journal of Business & Economic Statistics 34, 590605.CrossRefGoogle Scholar
Box, G.E.P. (1976) Science and statistics. Journal of the American Statistical Association 71, 791799.CrossRefGoogle Scholar
Caner, M., & Han, X. (2014) Selecting the correct number of factors in approximate factor models: The large panel case with group bridge estimators. Journal of Business & Economic Statistics 32, 359374.CrossRefGoogle Scholar
Caner, M., Han, X., & Lee, Y. (2018) Adaptive elastic net GMM estimation with many invalid moment conditions: simultaneous model and moment selection. Journal of Business & Economic Statistics 36, 2446.CrossRefGoogle Scholar
Caner, M., & Kock, A.B. (2018a) Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso. Journal of Econometrics 203, 143168.CrossRefGoogle Scholar
Caner, M., & Kock, A.B. (2018b) High dimensional linear GMM, preprint, arXiv:1811.08779.Google Scholar
Galvao, A.F., & Montes-Rojas, G.V. (2010) Penalized quantile regression for dynamic panel data. Journal of Statistical Planning and Inference 140, 34763497.CrossRefGoogle Scholar
Head, K., & Mayer, T. (2014) Gravity equations: Workhorse, toolkit, and cookbook. In Handbook of International Economics , vol. 4, pp. 131195. Elsevier.Google Scholar
Javanmard, A., & Montanari, A. (2014) Confidence intervals and hypothesis testing for high-dimensional regression. The Journal of Machine Learning Research 15, 28692909.Google Scholar
Kock, A.B. (2013) Oracle efficient variable selection in random and fixed effects panel data models. Econometric Theory 29, 115152.CrossRefGoogle Scholar
Kock, A.B. (2016) Oracle inequalities, variable selection and uniform inference in high-dimensional correlated random effects panel data models. Journal of Econometrics 195, 7185.CrossRefGoogle Scholar
Kock, A.B., & Tang, H. (2019) Uniform inference in high-dimensional dynamic panel data models with approximately sparse fixed effects. Econometric Theory 35, 295359.CrossRefGoogle Scholar
Koenker, R. (2004) Quantile regression for longitudinal data. Journal of Multivariate Analysis 91, 7489.CrossRefGoogle Scholar
Lamarche, C. (2010) Robust penalized quantile regression estimation for panel data. Journal of Econometrics 157, 396408.CrossRefGoogle Scholar
Leeb, H., & Pötscher, B.M. (2005) Model selection and inference: Facts and fiction. Econometric Theory 21, 2159.CrossRefGoogle Scholar
Li, D., Qian, J., & Su, L. (2016) Panel data models with interactive fixed effects and multiple structural breaks. Journal of the American Statistical Association 111, 18041819.CrossRefGoogle Scholar
Lu, X., Miao, K., & Su, L. (2021) Determination of different types of fixed effects in three-dimensional panels. Econometric Reviews 40, 867898.CrossRefGoogle Scholar
Lu, X., & Su, L. (2016) Shrinkage estimation of dynamic panel data models with interactive fixed effects. Journal of Econometrics 190, 148175.CrossRefGoogle Scholar
Lu, X., & Su, L. (2017) Determining the number of groups in latent panel structures with an application to income and democracy. Quantitative Economics 8, 729760.CrossRefGoogle Scholar
Lu, X., & Su, L. (2020) Determining individual or time effects in panel data models. Journal of Econometrics 215, 6083.CrossRefGoogle Scholar
Mátyás, L. (1997) Proper econometric specification of the gravity model. The World Economy 20, 363368.CrossRefGoogle Scholar
Mátyás, L. (2017) The Econometrics of Multi-Dimensional Panels . Springer.CrossRefGoogle Scholar
Phillips, P.C.B. (2005) Automated discovery in econometrics. Econometric Theory 21, 320.CrossRefGoogle Scholar
Qian, J., & Su, L. (2016) Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso. Journal of Econometrics 191, 86109.CrossRefGoogle Scholar
Ramos, R. (2017) Modelling migration. In Matyas, L. (ed.), The Econometrics of Multi-Dimensional Panels , chapter 13, pp. 377395. Springer.CrossRefGoogle Scholar
Rudelson, M., & Vershynin, R. (2008) On sparse reconstruction from Fourier and Gaussian measurements. Communications on Pure and Applied Mathematics: A Journal Issued by the Courant Institute of Mathematical Sciences 61, 10251045.CrossRefGoogle Scholar
Su, L., & Ju, G. (2018) Identifying latent grouped patterns in panel data models with interactive fixed effects. Journal of Econometrics 206, 554573.CrossRefGoogle Scholar
Su, L., Shi, Z., & Phillips, P.C.B. (2016) Identifying latent structures in panel data. Econometrica 84, 22152264.CrossRefGoogle Scholar
Su, L., Wang, X., & Jin, S. (2019) Sieve estimation of time-varying panel data models with latent structures. Journal of Business & Economic Statistics 37, 334349.CrossRefGoogle Scholar
Tinbergen, J.J. (1962) Shaping the World Economy: Suggestions for an International Economic Policy . Twth Century Fund.Google Scholar
van de Geer, S., Bühlmann, P., Ritov, Y., & Dezeure, R. (2014) On asymptotically optimal confidence regions and tests for high-dimensional models. Annals of Statistics 42, 11661202.CrossRefGoogle Scholar
Zhang, C.-H., & Zhang, S.S. (2014) Confidence intervals for low dimensional parameters in high dimensional linear models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 76, 217242.CrossRefGoogle Scholar
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