Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-25T23:37:14.064Z Has data issue: false hasContentIssue false
  • English
  • Français

IDENTIFYING LATENT GROUPED PATTERNS IN COINTEGRATED PANELS

Published online by Cambridge University Press:  22 July 2019

Wenxin Huang ,
Sainan Jin  and
Liangjun Su
Wenxin Huang
Affiliation:
Shanghai Jiao Tong University
Sainan Jin
Affiliation:
Singapore Management University
Liangjun Su*
Affiliation:
Singapore Management University
*
*Address correspondence to Liangjun Su, School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903, Singapore; e-mail: ljsu@smu.edu.sg, Phone: +65 6828 0386.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a panel cointegration model with latent group structures that allows for heterogeneous long-run relationships across groups. We extend Su, Shi, and Phillips (2016, Econometrica 84(6), 2215–2264) classifier-Lasso (C-Lasso) method to the nonstationary panels and allow for the presence of endogeneity in both the stationary and nonstationary regressors in the model. In addition, we allow the dimension of the stationary regressors to diverge with the sample size. We show that we can identify the individuals’ group membership and estimate the group-specific long-run cointegrated relationships simultaneously. We demonstrate the desirable property of uniform classification consistency and the oracle properties of both the C-Lasso estimators and their post-Lasso versions. The special case of dynamic penalized least squares is also studied. Simulations show superb finite sample performance in both classification and estimation. In an empirical application, we study the potential heterogeneous behavior in testing the validity of long-run purchasing power parity (PPP) hypothesis in the post–Bretton Woods period from 1975–2014 covering 99 countries. We identify two groups in the period 1975–1998 and three groups in the period 1999–2014. The results confirm that at least some countries favor the long-run PPP hypothesis in the post–Bretton Woods period.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 3 , June 2020 , pp. 410 - 456
Copyright
Copyright © Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The authors sincerely thank the co-editor Anna Mikusheva and two anonymous referees for their many constructive comments on the early versions of the article. They also thank Peter C.B. Phillips and Qiying Wang for discussions on the subject matter and the participants in the 2017 Asian Meeting of the Econometric Society at CUHK and the 2017 Advances in Econometrics Conference at SJTU for their valuable comments. Su gratefully acknowledges the Singapore Ministry of Education for Academic Research Fund under Grant MOE2012-T2-2-021 and the funding support provided by the Lee Kong Chian Fund for Excellence. Huang gratefully acknowledges the funding support provided by the Shanghai Institute of International Finance and Economics.

References

REFERENCES

Adler, M. & Lehmann, B. (1983) Deviations from purchasing power parity in the long run. Journal of Finance 38(5), 1471–1487.CrossRefGoogle Scholar
Ando, T. & Bai, J. (2016) Panel data model with grouped factor structure under unknown group membership. Journal of Applied Econometrics 31(1), 163–191.CrossRefGoogle Scholar
Ando, T. & Bai, J. (2017) Clustering huge number of financial time series: A panel data approach with high-dimensional predictors and factor structures. Journal of the American Statistical Association 112(519), 1182–1198.CrossRefGoogle Scholar
Andrews, D.W. (1984) Non-strong mixing autoregressive processes. Journal of Applied Probability 21(4), 930–934.CrossRefGoogle Scholar
Bai, J. (2004) Estimating cross-section common stochastic trends in nonstationary panel data. Journal of Econometrics 122(1), 137–183.CrossRefGoogle Scholar
Bai, J. (2009) Panel data models with interactive fixed effects. Econometrica 77(4), 1229–1279.Google Scholar
Bai, J. & Kao, C. (2006) On the estimation and inference of a panel cointegration model with cross-sectional dependence. In Baltagi, B. (ed.), Contributions to Economic Analysis, pp. 3–30. Elsevier.Google Scholar
Bai, J., Kao, C., & Ng, S. (2009) Panel cointegration with global stochastic trends. Journal of Econometrics 149(1), 82–99.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2004) A PANIC attack on unit roots and cointegration. Econometrica 72(4), 1127–1177.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2010) Panel unit root tests with cross-section dependence: A further investigation. Econometric Theory 26(4), 1088–1114.CrossRefGoogle Scholar
Balassa, B. (1964) The purchasing-power parity doctrine: A reappraisal. Journal of Political Economy 72(6), 584–596.CrossRefGoogle Scholar
Beveridge, S. & Nelson, C.R. (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cycle’. Journal of Monetary Economics 7(2), 151–174.CrossRefGoogle Scholar
Bonhomme, S. & Manresa, E. (2015) Grouped patterns of heterogeneity in panel data. Econometrica 83, 1147–1184.CrossRefGoogle Scholar
Davidson, J. (1994) Stochastic Limit Theory. Oxford University Press.CrossRefGoogle Scholar
Donsker, M.D. & Varadhan, S.R.S. (1977) On laws of the iterated logarithm for local times. Communications on Pure and Applied Mathematics 30(6), 707–753.CrossRefGoogle Scholar
Dooley, M.P., Folkerts-Landau, D., & Garber, P. (2004) The revived Bretton woods system. International Journal of Finance & Economics 9(4), 307–313.CrossRefGoogle Scholar
Doukhan, P. (1994) Mixing. Springer.CrossRefGoogle Scholar
Fan, J. & Peng, H. (2004) Nonconcave penalized likelihood with a diverging number of parameters. Annals of Statistics 32, 928–961.CrossRefGoogle Scholar
Fan, J. & Yao, Q. (2008) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer.Google Scholar
Frenkel, J.A. (1981) The collapse of purchasing power parities during the 1970’s. European Economic Review 16(1), 145–165.CrossRefGoogle Scholar
Groen, J.J.J. & Kleibergen, F. (2003) Likelihood-based cointegration analysis in panels of vector error-correction models. Journal of Business & Economic Statistics 21(2), 295–318.CrossRefGoogle Scholar
Hamilton, J.D. (1994) Time Series Analysis. Princeton University Press.Google Scholar
Kao, C. & Chiang, M.H. (2000). On the estimation and inference of a cointegrated regression in panel data. Advances in Econometrics 20, 179–222.CrossRefGoogle Scholar
Ke, Z.T., Fan, J., & Wu, Y. (2015). Homogeneity pursuit. Journal of the American Statistical Association 110(509), 175–194.CrossRefGoogle ScholarPubMed
Lai, T.L. & Wei, C.Z. (1982a) Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Annals of Statistics 10(1), 154–166.CrossRefGoogle Scholar
Lai, T.L. & Wei, C.Z. (1982b) Asymptotic properties of projections with applications to stochastic regression problems. Journal of Multivariate Analysis 12(3), 346–370.CrossRefGoogle Scholar
Lam, C. & Fan, J. (2008) Profile-kernel likelihood inference with diverging number of parameters. Annals of Statistics 36(5), 2232–2260.CrossRefGoogle ScholarPubMed
Lin, C.-C. & Ng, S. (2012) Estimation of panel data models with parameter heterogeneity when group membership is unknown. Journal of Econometric Methods 1(1), 42–55.CrossRefGoogle Scholar
Lu, X. & Su, L. (2015) Jackknife model averaging for quantile regressions. Journal of Econometrics 188(1), 40–58.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(3), 729–760.CrossRefGoogle Scholar
Oh, K.Y. (1996) Purchasing power parity and unit root tests using panel data. Journal of International Money and Finance 15(3), 405–418.CrossRefGoogle Scholar
Mark, N.C. & Sul, D. (2003) Cointegration vector estimation by panel DOLS and long-run money demand. Oxford Bulletin of Economics and Statistics 65(5), 655–680.CrossRefGoogle Scholar
Papell, D.H. (1997) Searching for stationarity: Purchasing power parity under the current float. Journal of International Economics 43(3–4), 313–332.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1988) Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4(3), 468–497.CrossRefGoogle Scholar
Park, J.Y. & Phillips, P.C.B. (1989) Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5(1), 95–131.CrossRefGoogle Scholar
Pedroni, P. (2001) Fully modified OLS for heterogeneous cointegrated panels. Advances in Econometrics 15, 93–130.CrossRefGoogle Scholar
Pedroni, P. (2004) Panel cointegration: Asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis. Econometric Theory 20(3), 597–625.CrossRefGoogle Scholar
Pesaran, M.H. (2006) Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74(4), 967–1012.CrossRefGoogle Scholar
Pesaran, M.H., Shin, Y., & Smith, R.P. (1999) Pooled mean group estimation of dynamic heterogeneous panels. Journal of the American Statistical Association 94(446), 621–634.CrossRefGoogle Scholar
Phillips, P.C.B. (1996) Econometric model determination. Econometrica 64, 763–812.CrossRefGoogle Scholar
Phillips, P.C.B. & Moon, H.R. (1999) Linear regression limit theory for nonstationary panel data. Econometrica 67(5), 1057–1111.CrossRefGoogle Scholar
Phillips, P.C.B. & Solo, V. (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.CrossRefGoogle Scholar
Qian, J. & Su, L. (2016a) Shrinkage estimation of regression models with multiple structural changes. Econometric Theory 32(6), 1376–1433.CrossRefGoogle Scholar
Qian, J. & Su, L. (2016b) Shrinkage estimation of common breaks in panel data models via adaptive group fused lasso. Journal of Econometrics 191(1), 86–109.CrossRefGoogle Scholar
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7(1), 1–21.CrossRefGoogle Scholar
Samuelson, P.A. (1964) Theoretical notes on trade problems. Review of Economics and Statistics 46, 145–154.CrossRefGoogle Scholar
Sarafidis, V. & Weber, N. (2015) A partially heterogeneous framework for analyzing panel data. Oxford Bulletin of Economics and Statistics 77(2), 274–296.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (1993) A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61(4), 783–820CrossRefGoogle Scholar
Su, L. & Ju, G. (2018) Identifying latent grouped effects in panel data models with interactive fixed effects. Journal of Econometrics 206(2), 554–573.CrossRefGoogle Scholar
Su, L., Shi, Z., & Phillips, P.C.B. (2016) Identifying latent structures in panel data. Econometrica 84(6), 2215–2264.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(2), 334–349.CrossRefGoogle Scholar
Sun, Y. (2004) Estimation of the long-run average relationship in nonstationary panel time series. Econometric Theory 20(6), 1227–1260.CrossRefGoogle Scholar
Wang, W., Phillips, P.C.B., & Su, L. (2018) Homogeneity pursuit in panel data models: Theory and applications. Journal of Applied Econometrics 33(6), 797–815.CrossRefGoogle Scholar
Wang, W. & Su, L. (2019) Identifying latent group structures in nonlinear panels. Journal of Econometrics, forthcoming.Google Scholar
White, H. (2001) Asymptotic Theory for Econometricians. Emerald.Google Scholar
Supplementary material: File

Huang et al. supplementary material

Huang et al. supplementary material 1

Download Huang et al. supplementary material(File)
File 143.9 KB
Supplementary material: PDF

Huang et al. supplementary material

Huang et al. supplementary material 2

Download Huang et al. supplementary material(PDF)
PDF 373.7 KB