Abstract
We provide an up-to-date analytical survey of methods which have been developed to deal with estimation and inference in non-stationary panels. The chapter provides information not only on the tools but also interprets the literature and highlights the important challenges that remain. We discuss the difficulties involved in formulating hypotheses within a panel framework with unit roots and cointegration. These issues include incorporating cross-sectional dependence and structural breaks in the data. Both these features are widely prevalent in the panels and lead to complications in estimation and inference. For example, factor models are a widely used class of methods used to deal with dependence but constitute only one of several ways of formulating the problems involved. We argue that the links between cointegration and factor models in panels need to be considered adequately and the asymptotic theory put on a firmer footing in many respects. The study of cross-sectional dependence, breaks, and multiple cointegrating vectors, all of which are in their relative infancy, mark the way for productive research in the years ahead.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ahn, S.K. and G.C. Reinsel (1990) Estimation for partially nonstationary multivariate autoregressive models. Journal of the American Statistical Association 85, 813–23.
Andreoni, J. and A. Levinson (2001) The simple analytics of the environmental Kuznets curve. Journal of Public Economics 80, 269–86.
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–58.
Bai, J. and J.L. Carrion-i-Silvestre (2007) Structural changes, common stochastic trends, and unit roots in panel data. Mimeo.
Bai, J. and S. Ng (2002) Determining the number of factors in approximate factor models. Econometrica 70, 191–221.
Bai, J. and S. Ng (2004) A PANIC attack on unit roots and cointegration. Econometrica 72, 1127–77.
Bai, J. and P. Perron (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66, 47–78.
Baltagi, B.H., G. Bresson and A. Pirotte (2007) Panel unit root tests and spatial dependence. Journal of Applied Econometrics 22, 339–60.
Banerjee, A. and J.L. Carrion-i-Silvestre (2007) Cointegration in panel data with breaks and cross-section dependence. Mimeo.
Banerjee, A., M. Marcellino and C. Osbat (2004) Some cautions on the use of panel methods for integrated series of macroeconomic data. Econometrics Journal 7, 322–40.
Banerjee, A., M. Marcellino and C. Osbat (2005) Testing for PPP: should we use panel methods? Empirical Economics 30, 77–91.
Bernard, A.B. and S.N. Durlauf (1995) Convergence in international output. Journal of Applied Econometrics 10, 97–108.
Bernard, A.B. and S.N. Durlauf (1996) Interpreting tests of the convergence hypothesis. Journal of Econometrics 71, 161–73.
Breitung, J. (2000) The local power of some unit root tests in panel data. In B.H. Baltagi (ed.), Nonstationary Panels, Panel-Cointegration, and Dynamic Panels, pp. 161–77. Amsterdam: Elsevier.
Breitung, J. (2005) A parametric approach to the estimation of cointegration vectors in panel data. Econometric Reviews 24, 151–73.
Breitung, J. and S. Das (2008) Testing for unit roots in panels with a factor structure. Econometric Theory 24, 88–108.
Breitung, J. and M.H. Pesaran (2008) Unit roots and cointegration in panels. In L. Matyas and P. Sevestre (eds.), The Econometrics of Panel Data: Fundamentals and Recent Developments in Theory and Practice, pp. 279–322. Boston: Kluwer Academic Publishers.
Brock, W.A. and M.S. Taylor (2004) The green Solow model. NBER Working Paper No. 10557.
Brock, W.A. and M.S. Taylor (2005) Economic growth and the environment: a review of theory and empirics. In P. Aghion and S. Durlauf (eds.), Handbook of Economic Growth, Vol. 1B, pp. 1749–821. Amsterdam: North-Holland.
Campa, J.M., L. Goldberg and J. González-Minguez (2005) Exchange-rate pass-through to import prices in the euro-area. NBER Working Paper No. 11632.
Campa, J.M. and J. González-Minguez (2006) Differences in exchange rate pass-through in the euro-area. European Economic Review 50, 121–45.
Chang, Y. (2002) Nonlinear IV unit root tests in panels with cross-sectional dependency. Journal of Econometrics 110, 261–92.
Choi, I. (2001) Unit root tests for panel data. Journal of International Money and Finance 20, 249–72.
Choi, I. (2006a) Combination unit root tests for cross-sectionally correlated panels. In D. Corbae, S. Durlauf and B. Hansen (eds.), Econometric Theory and Practice: Frontiers of Analysis and Applied Research. Essays in Honor of Peter C.B. Phillips, pp. 311–33. New York: Cambridge University Press.
Choi, I. (2006b) Nonstationary panels. In T.C. Mills and K. Patterson (eds.), Palgrave Handbook of Econometrics, Vol. 1: Econometric Theory, pp. 511–39. New York: Palgrave Macmillan.
Coakley, J. and A.M. Fuertes (1997) New panel unit root tests of PPP. Economics Letters 57, 17–22.
de Bandt, O., A. Banerjee and T. Kozluk (2008) Measuring long-run exchange rate pass-through. Economics E-Journal 2, 2008–6.
Dickey, D.A. and W.A. Fuller (1979) Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–31.
Engel, C. (2000) Long-run PPP may not hold after all. Journal of International Economics 51, 243–73.
Engle, R.F. and C.W.J Granger (1987) Co-integration and error correction: representation, estimation and testing. Econometrica 55, 251–76.
Engle, R.F. and B.S. Yoo (1991) Cointegrated economic time series: an overview with new results. In R.F. Engle and C.W.J. Granger (eds.), Long Run Economic Relationships: Readings in Cointegration, pp. 237–66. Oxford: Oxford University Press.
Evans, G.B.A. and N.E. Savin (1981) Testing for unit roots: 1. Econometrica 49, 753–97.
Evans, P. and G. Karras (1996) Convergence revisited. Journal of Monetary Economics 37, 249–65.
Fisher, R.A. (1932) Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd.
Frankel, J.A., D. Parsley and S. Wei (2005) Slow passthrough around the world: a new import for developing countries? NBER Working Paper No. 11199.
Frankel, J.A. and A.K. Rose (1996) A panel project on purchasing power parity: mean reversion within and between countries. Journal of International Economics 40, 209–24.
Garratt, A., K. Lee, M.H. Pesaran and Y. Shin (2006) Global and National Macroeconometric Modelling: A Long-run Structural Approach. Oxford: Oxford University Press.
Gengenbach, C., F.C. Palm and J.-P. Urbain (2006) Panel unit root tests in the presence of cross-sectional dependencies: comparison and implications for modelling. Oxford Bulletin of Economics and Statistics 68, 683–719.
Groen, J.J.J. and F. Kleibergen (2003) Likelihood-based cointegration analysis in panels of vector error correction models. Journal of Business and Economic Statistics 21, 295–318.
Gregory, A.W. and B.E. Hansen (1996) Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99–126.
Grossman, G.M. and A.B. Krueger (1995) Economic growth and the environment. Quarterly Journal of Economics 110, 353–77.
Hadri, K. (2000) Testing for stationarity in heterogeneous panel data. Econometrics Journal 3, 148–61.
Hadri, K. and R. Larsson (2005) Testing for stationarity in heterogeneous panel data where the time dimension is fixed. Econometrics Journal 8, 55–69.
Harris, R.D.F. and E. Tzavalis (1999) Inference for unit roots in dynamic panels where the time dimension is fixed. Journal of Econometrics 90, 1–44.
Hlouskova, J. and M. Wagner (2006) The performance of panel unit root and stationarity tests: results from a large scale simulation study. Econometric Reviews 25, 85–116.
Hlouskova, J. and M. Wagner (2008) Finite sample correction factors for panel cointegration tests. Forthcoming in Oxford Bulletin of Economics and Statistics.
Hong, S.H. and M. Wagner (2008a) Nonlinear cointegration analysis and the environmental Kuznets curve. Mimeo.
Hong, S.H. and M. Wagner (2008b) Seemingly unrelated nonlinear cointegrating regressions with an application to the environmental Kuznets curve. Mimeo.
Im, K.S. and M.H. Pesaran (2003) On the panel unit root test using nonlinear instrumental variables. Mimeo.
Im, K.S., M.H. Pesaran and Y. Shin (2003) Testing for unit roots in heterogeneous panels. Journal of Econometrics 115, 53–74.
Johansen, S. (1995) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press.
Jones, L.E. and R.E. Manuelli (2001) Endogenous policy choice: the case of pollution and growth. Review of Economics Dynamics 4, 369–405.
Kao, C. (1999) Spurious regression and residual-based tests for cointegration in panel data. Journal of Econometrics 90, 1–44.
Kao, C. and M.-H. Chiang (2000) On the estimation and inference of a cointegrated regession in panel data. In B.H. Baltagi (ed.), Nonstationary Panels, Panel Cointegration, and Dynamic Panels, pp. 179–222. Amsterdam: Elsevier.
Kuznets, S. (1955) Economic growth and income inequality. American Economic Review 45, 1–28.
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt and Y. Shin (1992) Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? Journal of Econometrics 54, 159–78.
Larsson, R. (1997) On the asymptotic expectations of some unit root tests in a first order autoregressive process in the presence of trend. Annals of the Institute of Statistical Mathematics 49, 585–99.
Larsson, R. and J. Lyhagen (1999) Likelihood-based inference in multivariate panel cointegration models. Working Paper Series in Economics and Finance 331, Stockholm School of Economics.
Larsson, R., J. Lyhagen and M. Löthgren (2001) Likelihood-based cointegration tests in heterogeneous panels. Econometrics Journal 4, 109–42.
Levin, A., C.F. Lin and C-S. J. Chu (2002) Unit roots in panel data: asymptotic and finite sample properties. Journal of Econometrics 108, 1–22.
Lothian, J.R. (1997) Multi-country evidence on the behavior of purchasing power parity under the current float. Journal of International Money and Finance 16, 19–35.
Lyhagen, J. (2000) Why not use standard panel unit root tests for testing PPP. Stockholm School of Economics, mimeo.
MacKinnon, J.G. (1994) Approximate asymptotic distribution functions for unit root and cointegration tests. Journal of Applied Econometrics 11, 609–18.
MacKinnon, J.G., A. Haug and L. Michelis (1999) Numerical distribution functions of likelihood ratio tests for cointegration. Journal of Applied Econometrics 14, 563–77.
Maddala, G.S. and S. Wu (1999) A comparative study of unit root tests with panel data and a new simple test. Oxford Bulletin of Economics and Statistics 61, 631–52.
Maddison, A. (2007) Contours of the World Economy: The Pace and Pattern of Change 1–2030 A.D. Cambridge: Cambridge University Press.
Mark, N.C. and D. Sul (2003) Cointegration vector estimation by panel dynamic OLS and long-run money demand. Oxford Bulletin of Economics and Statistics 65, 655–80.
Molinas, C. (1986) A note on spurious regressions with integrated moving average errors. Oxford Bulletin of Economics and Statistics 48, 279–82.
Moon, H.R. and B. Perron (2004) Testing for a unit root in panels with dynamic factors. Journal of Econometrics 122, 81–126.
Moon, H.R. and P.C.B. Phillips (2000) Estimation of autoregressive roots near unity using panel data. Econometric Theory 16, 927–97.
Nabeya, S. (1999) Asymptotic moments of some unit root test statistics in the null case. Econometric Theory 15, 139–49.
Newey, W.K. and K.D. West (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–8.
Newey, W.K. and K.D. West (1994) Automatic lag selection in covariance matrix estimation. Review of Economic Studies 61, 631–53.
Nickell, S.J. (1978) Biases in dynamic models with fixed effects. Econometrica 49, 1417–26.
O’Connell, P.J. (1998) The overvaluation of purchasing power parity. Journal of International Economics 44, 1–19.
Onatski, A. (2006) Determining the number of factors from empirical distributions of eigenvalues. Mimeo.
Park, J.Y. and P.C.B. Phillips (1999) Asymptotics for nonlinear transformations of integrated time series. Econometric Theory 15, 269–98.
Park, J.Y. and P.C.B. Phillips (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117–61.
Pedroni, P. (1999) Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bulletin of Economics and Statistics 61, 653–70.
Pedroni, P. (2000) Fully modified OLS for heterogeneous cointegrated panels. In B.H. Baltagi (ed.), Nonstationary Panels, Panel Cointegration, and Dynamic Panels, pp. 93–130. Amsterdam: Elsevier.
Pedroni, P. (2001) Purchasing power parity tests in cointegrated panels. Review of Economics and Statistics 83, 1371–5.
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, 597–625.
Pedroni, P.L., T.J. Vogelsang, M. Wagner and J. Westerlund (2008) Nonparametric unit root and cointegration rank tests for time series panels. Mimeo.
Perron, P. (1989) The great crash, the oil price shock, and the unit root hypothesis. Econometrica 57, 1361–401.
Pesaran, M.H. (2006) Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74, 967–1012.
Pesaran, M.H. (2007) A simple panel unit root test in the presence of cross-section dependence. Journal of Applied Econometrics 22, 265–312.
Pesaran, M.H., T. Schuerman and S. Weiner (2004) Modelling regional interdependencies using a global error-correcting macroeconometric model. Journal of Business and Economics Statistics 22, 129–62.
Phillips, P.C.B. (1986) Understanding spurious regressions in econometrics. Journal of Econometrics 33, 311–40.
Phillips, P.C.B. and B. Hansen (1990) Statistical inference in instrumental variables regressions with I(1) processes. Review of Economic Studies 57, 99–125.
Phillips, P.C.B. and H.R. Moon (1999) Linear regression limit theory for nonstationary panel data. Econometrica 67, 1057–111.
Said, S.E. and D.A. Dickey (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71, 599–607.
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegrating regressions. Econometric Theory 8, 1–27.
Saikkonen, P. (1999) Testing the normalization and overidentification of cointegrating vectors in vector autoregressive processes. Econometric Reviews 18, 235–57.
Sargan, D. and A. Bhargava (1983) Maximum likelihood estimation of regression models with first order moving average errors when the root lies on the unit circle. Econometrica 51, 799–820.
Schwert, G.W. (1989) Tests for unit roots: a Monte Carlo investigation. Journal of Business and Economic Statistics 7, 147–59.
Stern, D.I. (2006) Reversal of the trend in global anthropogenic sulfur emissions. Global Environmental Change 16, 207–20.
Stock, J.H. (1999) A class of tests for integration and cointegration. In R.F. Engle and H. White (eds.), Cointegration, Causality and Forecasting: A Festschrift in Honour of Clive W.F. Granger, pp. 135–67. Oxford: Oxford University Press.
Stock, J.H. and M.W. Watson (1988) Testing for common trends. Journal of the American Statistical Association 83, 1097–107.
Stokey, N. (1998) Are there limits to growth? International Economic Review 39, 1–31.
Wagner, M. (2008a) On PPP, unit roots and panels. Empirical Economics 35, 229–49.
Wagner, M. (2008b) The carbon Kuznets curve: a cloudy picture emitted by bad econometrics? Resource and Energy Economics 30, 388–408.
Wagner, M. (2008c) On definitions of economic convergence. Mimeo.
Wagner, M. and J. Hlouskova (2007) The performance of panel cointegration methods: results from a large scale simulation study. Forthcoming in Econometric Reviews.
Westerlund, J. (2005) New simple tests for panel cointegration. Econometric Reviews 24, 297–316.
Wu, X. (1996) Are real exchange rates nonstationary? Evidence from a panel-data test. Journal of Money, Credit and Banking 28, 54–63.
Editor information
Editors and Affiliations
Copyright information
© 2009 Anindya Banerjee and Martin Wagner
About this chapter
Cite this chapter
Banerjee, A., Wagner, M. (2009). Panel Methods to Test for Unit Roots and Cointegration. In: Mills, T.C., Patterson, K. (eds) Palgrave Handbook of Econometrics. Palgrave Macmillan, London. https://doi.org/10.1057/9780230244405_13
Download citation
DOI: https://doi.org/10.1057/9780230244405_13
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-4039-1800-0
Online ISBN: 978-0-230-24440-5
eBook Packages: Palgrave Economics & Finance CollectionEconomics and Finance (R0)