Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-14T05:18:22.819Z Has data issue: false hasContentIssue false
  • English
  • Français

MULTIPLE TESTING FOR OUTPUT CONVERGENCE

Published online by Cambridge University Press:  25 May 2012

Thomas Deckers  and
Christoph Hanck
Thomas Deckers*
Affiliation:
Bonn Graduate School of Economics
Christoph Hanck
Affiliation:
Rijksuniversiteit Groningen
*
Address correspondence to: Thomas Deckers, Bonn Graduate School of Economics (BGSE). Department of Economics, Kaiserstrasse 1, 53113 Bonn, Germany; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper tests for output convergence across n = 51 economies, employing the definition of Pesaran [Journal of Econometrics 138, 312–355 (2007)]. The definition requires output gaps to be stationary around a constant mean. But when all n(n − 1)/2 pairs of log per capita output gaps are considered, this results in more than 1,000 unit root tests to be conducted. Hence, because of the ensuing multiplicity of the testing problem, a nontrivial number of output gaps will be falsely declared to be stationary when each of the n(n − 1)/2 hypotheses is tested at some conventional level like 5%. To solve the problem, we employ recent multiple testing techniques that allow us to bound the expected fraction of false rejections at a desired level. Monte Carlo results illustrate the usefulness of the techniques. The empirical results show that the data do not support the notion of output convergence after controlling for multiplicity.

Keywords

Growth EmpiricsMultiple TestingConvergenceBootstrap
Type
Articles
Information
Macroeconomic Dynamics , Volume 18 , Issue 1 , January 2014 , pp. 199 - 214
Copyright
Copyright © Cambridge University Press 2012 

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.)

References

REFERENCES

Benjamini, Yoav and Hochberg, Yosef (1995) Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society. Series B 57, 289–300.Google Scholar
Benjamini, Yoav, Krieger, Abba M., and Yekutieli, Daniel (2006) Adaptive linear step-up procedure that control the false discovery rate. Biometrika 93, 491–507.CrossRefGoogle Scholar
Benjamini, Yoav and Yekutieli, Daniel (2001) The control of the false discovery rate in multiple testing under dependency. Annals of Statistics 29, 1165–1188.CrossRefGoogle Scholar
Bernard, Andrew B. and Durlauf, Steven N. (1995) Convergence in international output. Journal of Applied Econometrics 10, 97–108.CrossRefGoogle Scholar
Burridge, Peter and Taylor, A.M. Robert (2004) Bootstrapping the HEGY seasonal unit root tests. Journal of Econometrics 123, 67–87.CrossRefGoogle Scholar
Campbell, Y.J. and Mankiw, N.G. (1989) International evidence on the persistence of economic fluctuations. Journal of Monetary Economics 23, 319–333.CrossRefGoogle Scholar
Chang, Yoosoon (2004) Bootstrap unit root tests in panels with cross-sectional dependency. Journal of Econometrics 120, 263–293.CrossRefGoogle Scholar
Chong, Terence Tai-Leung, Hinich, Melvin J., Liew, Venus Khim-Sen, and Lim, Kian-Ping (2008) Time series test of nonlinear convergence and transitional dynamics. Economics Letters 100, 337–339.CrossRefGoogle Scholar
Deckers, Thomas and Hanck, Christoph (2011) Variable Selection via Multiple Testing with an Application to Growth Econometrics. Technical report, University of Groningen.Google Scholar
Demetrescu, Matei, Hassler, Uwe, and Kuzin, Vladimir (2011) Pitfalls of post-model-selection testing: Experimental quantification. Empirical Economics 40, 359–372.CrossRefGoogle Scholar
Dudoit, Sandrine and van der Laan, Mark J. (2007) Multiple Testing Procedures and Applications to Genomics, Springer Series in Statistics, Berlin: Springer.Google Scholar
Elliott, Graham, Rothenberg, Thomas J., and Stock, James H. (1996) Efficient tests for an autoregressive unit root. Econometrica 64, 813–836.CrossRefGoogle Scholar
Finner, Helmut, Dickhaus, Thorsten, and Roters, Markus (2009) On the false discovery rate and an asymptotically optimal rejection curve. Annals of Statistics 37, 596–618.CrossRefGoogle Scholar
Granger, Clive W. J and Morris, Matthew J. (1976) Time series modelling and interpretation. Journal of the Royal Statistical Society. Series A (General) 139, 246–257.CrossRefGoogle Scholar
Hanck, Christoph (2009) For which countries did PPP hold? A multiple testing approach. Empirical Economics 37, 93–103.CrossRefGoogle Scholar
Heston, Alan, Summers, Robert, and Aten, Bettina (2006) Penn World Table, Version 6.2. Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, September.Google Scholar
Holm, Sture (1979) A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65–70.Google Scholar
Inklaar, Robert and Timmer, Marcel P. (2009) Productivity convergence across industries and countries: The importance of theory-based measurement. Macroeconomic Dynamics 13 (S1), 218–240.CrossRefGoogle Scholar
Islam, Nazrul (2003) What have we learnt from the convergence debate? Journal of Economic Surveys 17, 312–355.CrossRefGoogle Scholar
Kapetanios, George, Shin, Yongcheol, and Snell, Andy (2003) Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics 112, 359–379.CrossRefGoogle Scholar
Kim, Hyeongwoo and Moh, Young-Kyu (2010) A century of purchasing power parity confirmed: The role of nonlinearity. Journal of International Money and Finance 29, 1398–1405.CrossRefGoogle Scholar
Leeb, Hannes and Pötscher, Benedikt M. (2008) Can one estimate the unconditional distribution of post-model-selection estimators? Econometric Theory 24, 338–367.CrossRefGoogle Scholar
Lim, Kian-Ping and Brooks, Robert D. (2010) Why do emerging stock markets experience more persistent price deviations from a random walk over time? A country-level analysis. Macroeconomic Dynamics 14 (S1), 3–41.CrossRefGoogle Scholar
Mello, Marcelo (2011) Stochastic convergence across U.S. states. Macroeconomic Dynamics 15, 160–183.CrossRefGoogle Scholar
Moon, Hyungsik R. and Perron, Benoit (2009) Beyond Panel Unit Root Tests: Using Multiple Testing to Determine the Non Stationarity Properties of Individual Series in a Panel. Technical report, Université de Montréal.Google Scholar
Müller, Ulrich K. and Elliott, Graham (2003) Tests for unit roots and the initial condition. Econometrica 71, 1269–1286.CrossRefGoogle Scholar
Ng, Serena and Perron, Pierre (2001) Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554.CrossRefGoogle Scholar
Norman, Stephen (2010) How well does nonlinear mean reversion solve the PPP puzzle? Journal of International Money and Finance 29, 919–937.CrossRefGoogle Scholar
Palm, Franz C., Smeekes, Stephan, and Urbain, Jean-Pierre (2011) Cross-sectional dependence robust block bootstrap panel unit root tests. Journal of Econometrics 163, 85–104.CrossRefGoogle Scholar
Papageorgiou, Chris and Perez-Sebastian, Fidel (2004) Can transition dynamics explain the international output data? Macroeconomic Dynamics 8, 466–492.CrossRefGoogle Scholar
Paparoditis, Efstathios and Politis, Dimitris N. (2003) Residual-based block bootstrap for unit root testing. Econometrica 71, 813–855.CrossRefGoogle Scholar
Pesaran, M. Hashem (2007a) A pair-wise approach to testing for output and growth convergence. Journal of Econometrics 138, 312–355.CrossRefGoogle Scholar
Pesaran, M. Hashem (2007b) A simple panel unit root test in the presence of cross section dependence. Journal of Applied Econometrics 22, 265–312.CrossRefGoogle Scholar
Phillips, Peter Charles Bonest (1987) Towards a unified asymptotic theory for autoregression. Biometrika 74, 535–547.CrossRefGoogle Scholar
Quah, Danny (1990) International Patterns of Growth: I. Persistence in Cross-Country Disparities. Working paper, MIT.Google Scholar
Romano, Joseph P., Shaikh, Azeem M., and Wolf, Michael (2008a) Control of the false discovery rate under dependence using the bootstrap and subsampling. Test 17, 417–442.CrossRefGoogle Scholar
Romano, Joseph P., Shaikh, Azeem M., and Wolf, Michael (2008b) Formalized data snooping based on generalized error rates. Econometric Theory 24, 404–447.CrossRefGoogle Scholar
Sarkar, Sanat K. (2006) False discovery and false nondiscovery rates in single-step multiple testing procedures. Annals of Statistics 34, 394–415.CrossRefGoogle Scholar
Schwert, G. William (1989) Tests for unit roots: A Monte Carlo investigation. Journal of Businnes and Economic Statistics 7, 5–17.Google Scholar
Shaffer, Juliet Popper (1986) Modified sequentially rejective multiple test procedures. Journal of the American Statistical Association 81, 826–831.CrossRefGoogle Scholar
Smeekes, Stephan (in press) Detrending bootstrap unit root tests. Econometric Reviews.Google Scholar
Storey, John D. (2002) A direct approach to false discovery rates. Journal of the Royal Statistical Society, Series B 64, 479–498.CrossRefGoogle Scholar
Storey, John D., Taylor, Jonathan E., and Siegmund, David (2004) Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: A unified approach. Journal of the Royal Statistical Society. Series B 66, 187–205.CrossRefGoogle Scholar
Ucar, Nuri and Omay, Tolga (2009) Testing for unit root in nonlinear heterogeneous panels. Economics Letters 104, 5–8.CrossRefGoogle Scholar