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Shrinkage estimation of dynamic panel data models with interactive fixed effects

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  • Lu, Xun
  • Su, Liangjun

Abstract

We consider the problem of determining the number of factors and selecting the proper regressors in linear dynamic panel data models with interactive fixed effects. Based on the preliminary estimates of the slope parameters and factors a la Bai (2009) and Moon and Weidner (2015), we propose a method for simultaneous selection of regressors and factors and estimation through the method of adaptive group Lasso (least absolute shrinkage and selection operator). We show that with probability approaching one, our method can correctly select all relevant regressors and factors and shrink the coefficients of irrelevant regressors and redundant factors to zero. Further, we demonstrate that our shrinkage estimators of the nonzero slope parameters exhibit some oracle property. We conduct Monte Carlo simulations to demonstrate the superb finite-sample performance of the proposed method. We apply our method to study the determinants of economic growth and find that in addition to three common unobserved factors selected by our method, government consumption share has negative effects, whereas investment share and lagged economic growth have positive effects on economic growth.

Suggested Citation

  • Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
  • Handle: RePEc:eee:econom:v:190:y:2016:i:1:p:148-175
    DOI: 10.1016/j.jeconom.2015.09.005
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    1. Liao, Zhipeng & Phillips, Peter C. B., 2015. "Automated Estimation Of Vector Error Correction Models," Econometric Theory, Cambridge University Press, vol. 31(3), pages 581-646, June.
    2. Su, Liangjun & Jin, Sainan & Zhang, Yonghui, 2015. "Specification test for panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 186(1), pages 222-244.
    3. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    4. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    5. Durlauf, Steven N. & Johnson, Paul A. & Temple, Jonathan R.W., 2005. "Growth Econometrics," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 8, pages 555-677, Elsevier.
    6. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    7. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    8. Robert J. Barro, 1991. "Economic Growth in a Cross Section of Countries," The Quarterly Journal of Economics, Oxford University Press, vol. 106(2), pages 407-443.
    9. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    10. Greenaway-McGrevy, Ryan & Han, Chirok & Sul, Donggyu, 2012. "Asymptotic distribution of factor augmented estimators for panel regression," Journal of Econometrics, Elsevier, vol. 169(1), pages 48-53.
    11. Su, Liangjun & Chen, Qihui, 2013. "Testing Homogeneity In Panel Data Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1079-1135, December.
    12. Kapetanios, George, 2010. "A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 397-409.
    13. Bai, Jushan & Ng, Serena, 2007. "Determining the Number of Primitive Shocks in Factor Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 52-60, January.
    14. Lee, Nayoung & Moon, Hyungsik Roger & Weidner, Martin, 2012. "Analysis of interactive fixed effects dynamic linear panel regression with measurement error," Economics Letters, Elsevier, vol. 117(1), pages 239-242.
    15. repec:eee:econom:v:206:y:2018:i:2:p:613-644 is not listed on IDEAS
    16. Lam, Clifford & Fan, Jianqing, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics 31548, London School of Economics and Political Science, LSE Library.
    17. Enrique Moral-Benito, 2012. "Determinants of Economic Growth: A Bayesian Panel Data Approach," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 566-579, May.
    18. Jonathan Temple, 2005. "Dual Economy Models: A Primer For Growth Economists," Manchester School, University of Manchester, vol. 73(4), pages 435-478, July.
    19. Donald W. K. Andrews, 2005. "Cross-Section Regression with Common Shocks," Econometrica, Econometric Society, vol. 73(5), pages 1551-1585, September.
    20. Leeb, Hannes & Potscher, Benedikt M., 2008. "Sparse estimators and the oracle property, or the return of Hodges' estimator," Journal of Econometrics, Elsevier, vol. 142(1), pages 201-211, January.
    21. Bai, Jushan & Ng, Serena, 2006. "Evaluating latent and observed factors in macroeconomics and finance," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 507-537.
    22. Su, Liangjun & Jin, Sainan, 2012. "Sieve estimation of panel data models with cross section dependence," Journal of Econometrics, Elsevier, vol. 169(1), pages 34-47.
    23. Pötscher, Benedikt M. & Leeb, Hannes, 2009. "On the distribution of penalized maximum likelihood estimators: The LASSO, SCAD, and thresholding," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2065-2082, October.
    24. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(01), pages 158-195, February.
    25. Pesaran, M. Hashem & Tosetti, Elisa, 2011. "Large panels with common factors and spatial correlation," Journal of Econometrics, Elsevier, vol. 161(2), pages 182-202, April.
    26. Moon, Hyungsik Roger & Shum, Matthew & Weidner, Martin, 2018. "Estimation of random coefficients logit demand models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 613-644.
    27. Sainan Jin & Liangjun Su, 2013. "A Nonparametric Poolability Test for Panel Data Models with Cross Section Dependence," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 469-512, December.
    28. Kock, Anders Bredahl, 2013. "Oracle Efficient Variable Selection In Random And Fixed Effects Panel Data Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 115-152, February.
    29. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
    30. Leeb, Hannes & Pötscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 21-59, February.
    31. Alexei Onatski, 2010. "Determining the Number of Factors from Empirical Distribution of Eigenvalues," The Review of Economics and Statistics, MIT Press, vol. 92(4), pages 1004-1016, November.
    32. Caner, Mehmet, 2009. "Lasso-Type Gmm Estimator," Econometric Theory, Cambridge University Press, vol. 25(1), pages 270-290, February.
    33. Cheng, Xu & Liao, Zhipeng, 2015. "Select the valid and relevant moments: An information-based LASSO for GMM with many moments," Journal of Econometrics, Elsevier, vol. 186(2), pages 443-464.
    34. Mehmet Caner & Xu Han, 2014. "Selecting the Correct Number of Factors in Approximate Factor Models: The Large Panel Case With Group Bridge Estimators," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 359-374, July.
    35. Seung C. Ahn & Alex R. Horenstein, 2013. "Eigenvalue Ratio Test for the Number of Factors," Econometrica, Econometric Society, vol. 81(3), pages 1203-1227, May.
    36. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, vol. 77(5), pages 1447-1479, September.
    37. A. Belloni & D. Chen & V. Chernozhukov & C. Hansen, 2012. "Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain," Econometrica, Econometric Society, vol. 80(6), pages 2369-2429, November.
    38. Liao, Zhipeng, 2013. "Adaptive Gmm Shrinkage Estimation With Consistent Moment Selection," Econometric Theory, Cambridge University Press, vol. 29(5), pages 857-904, October.
    39. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    40. Onatski, Alexei, 2012. "Asymptotics of the principal components estimator of large factor models with weakly influential factors," Journal of Econometrics, Elsevier, vol. 168(2), pages 244-258.
    41. Jonathan R. W. Temple, 2005. "Growth and Wage Inequality in a Dual Economy," Bulletin of Economic Research, Wiley Blackwell, vol. 57(2), pages 145-169, April.
    42. Hahn, Jinyong & Kuersteiner, Guido, 2011. "Bias Reduction For Dynamic Nonlinear Panel Models With Fixed Effects," Econometric Theory, Cambridge University Press, vol. 27(6), pages 1152-1191, December.
    43. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    44. repec:hal:journl:peer-00796743 is not listed on IDEAS
    45. Hallin, Marc & Liska, Roman, 2007. "Determining the Number of Factors in the General Dynamic Factor Model," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 603-617, June.
    46. B. Prakasa Rao, 2009. "Conditional independence, conditional mixing and conditional association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 441-460, June.
    47. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    48. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    49. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    50. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    51. Nazrul Islam, 1995. "Growth Empirics: A Panel Data Approach," The Quarterly Journal of Economics, Oxford University Press, vol. 110(4), pages 1127-1170.
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    More about this item

    Keywords

    Adaptive Lasso; Dynamic panel; Factor selection; Group Lasso; Interactive fixed effects; Oracle property; Selection consistency;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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