Transition Modeling and Econometric Convergence Tests

A new panel data model is proposed to represent the behavior of economies in transition allowing for a wide range of possible time paths and individual heterogeneity. The model has both common and individual specific components and is formulated as a nonlinear time varying factor model. When applied to a micro panel, the decomposition provides flexibility in idiosyncratic behavior over time and across section, while retaining some commonality across the panel by means of an unknown common growth component. This commonality means that when the heterogeneous time varying idiosyncratic components converge over time to a constant, a form of panel convergence holds, analogous to the concept of conditional sigma convergence. The paper provides a framework of asymptotic representations for the factor components which enables the development of econometric procedures of estimation and testing. In particular, a simple regression based convergence test is developed, whose asymptotic properties are analyzed under both null and local alternatives, and a new method of clustering panels into club convergence groups is constructed. These econometric methods are applied to analyze convergence in cost of living indices among 19 US. metropolitan cities.

[1]  David C. Ribar,et al.  Analysis of panel data, 2nd edition , 2004 .

[2]  P. Phillips.  REGRESSION WITH SLOWLY VARYING REGRESSORS AND NONLINEAR TRENDS , 2007, Econometric Theory.

[3]  P. Phillips,et al.  Linear Regression Limit Theory for Nonstationary Panel Data , 1999 .

[4]  John H. Cochrane,et al.  A Simple Test of Consumption Insurance , 1991, Journal of Political Economy.

[5]  Nancy L. Stokey,et al.  Optimal growth with many consumers , 1984 .

[6]  Jushan Bai,et al.  Estimating cross-section common stochastic trends in nonstationary panel data , 2004 .

[7]  Steven N. Durlauf,et al.  Convergence in International Output , 1995 .

[8]  Christian Zimmermann,et al.  HP-Filter (web interface) , 2005 .

[9]  J. Stock,et al.  Diffusion Indexes , 1998 .

[10]  M. Obstfeld.  Intertemporal Dependence, Impatience, and Dynamics , 1989 .

[11]  Danny Quah,et al.  The New Empirics of Economic Growth , 1998 .

[12]  Danny Quah,et al.  Empirics for Growth and Distribution: Stratification, Polarization, and Convergence Clubs , 1997 .

[13]  Cheng Hsiao,et al.  Analysis of Panel Data , 1987 .

[14]  Gregory Connor,et al.  Performance Measurement with the Arbitrage Pricing Theory: A New Framework for Analysis , 1985 .

[15]  D. Rose,et al.  Researching social and economic change : the uses of household panel studies , 2002 .

[16]  Kurt Annen,et al.  Matlab functions for HP-filter , 2004 .

[17]  E. Prescott,et al.  Postwar U.S. Business Cycles: An Empirical Investigation , 1997 .

[18]  J. Bai,et al.  Inferential Theory for Factor Models of Large Dimensions , 2003 .

[19]  David C. Ribar,et al.  Analysis of panel data: Second Edition, Cheng Hsiao, Cambridge University Press, Cambridge, United Kingdom, 2003, ISBN 0-521-81855-9, 382 pages, [UK pound]21.95 , 2004 .

[20]  Robert A. Moffitt,et al.  Trends in the Transitory Variance of Earnings in the United States , 2002 .

[21]  Stephanie Schmitt-Grohé,et al.  Closing Small Open Economy Models , 2003 .

[22]  Soyoung Kim,et al.  Dynamic risksharing in the United States and Europe , 2004 .

[23]  Bent E. Sørensen,et al.  Channels of Interstate Risk Sharing: United States 1963–1990 , 1996 .

[24]  Thomas Mikosch,et al.  Regularly varying functions , 2006 .

[25]  H. Uzawa,et al.  Time Preference and the Penrose Effect in a Two-Class Model of Economic Growth , 1969, Journal of Political Economy.

[26]  P. Howitt,et al.  R/D, Implementation, and Stagnation: A Schumpeterian Theory of Convergence Clubs , 2002 .

[27]  M. Obstfeld.  Intertemporal dependence, impatience, and dynamics☆ , 1990 .

[28]  Victor Solo,et al.  Asymptotics for Linear Processes , 1992 .

[29]  Bent E. Sørensen,et al.  Risk Sharing and Industrial Specialization: Regional and International Evidence , 2000 .

[30]  Hyungsik Roger Moon,et al.  Testing For A Unit Root In Panels With Dynamic Factors , 2002 .

[31]  Fatih Guvenen,et al.  An Empirical Investigation of Labor Income Processes , 2007 .

[32]  Gregory Connor,et al.  Risk and Return in an Equilibrium Apt: Application of a New Test Methodology , 1988 .

[33]  Stephen L. Parente,et al.  Barriers to Technology Adoption and Development , 1994, Journal of Political Economy.

[34]  M. Rothschild,et al.  Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets , 1982 .

[35]  Edward C. Prescott,et al.  FORTRAN code for the Hodrick-Prescott filter , 1982 .

[36]  David H. Autor,et al.  Changes in the Wage Structure and Earnings Inequality , 1999 .

[37]  Emmanuel Guerre,et al.  Design-Adaptive Pointwise Non-Parametric Regression Estimation for Recurrent Markov Time Series , 2004 .

[38]  Qiying Wang,et al.  ASYMPTOTIC THEORY FOR LOCAL TIME DENSITY ESTIMATION AND NONPARAMETRIC COINTEGRATING REGRESSION , 2006, Econometric Theory.

[39]  Kurt Annen,et al.  HP-Filter Excel Add-In , 2006 .

[40]  J. Temple.  Growth Econometrics , 2001, Oxford Research Encyclopedia of Economics and Finance.

[41]  Donggyu Sul,et al.  Economic Transition and Growth , 2005 .

[42]  Christian Zimmermann,et al.  HP-Filter code (Perl) , 2005 .

[43]  P. Phillips,et al.  The Elusive Empirical Shadow of Growth Convergence , 2003 .

[44]  E. Fama,et al.  Multifactor Explanations of Asset Pricing Anomalies , 1996 .

[45]  Martin Browning,et al.  Heterogeneity and Microeconometrics Modelling , 2006 .

[46]  J. Bai,et al.  Determining the Number of Factors in Approximate Factor Models , 2000 .

[47]  Thomas J. Sargent,et al.  Business cycle modeling without pretending to have too much a priori economic theory , 1976 .

[48]  Barbara J Mace.  Full Insurance in the Presence of Aggregate Uncertainty , 1991, Journal of Political Economy.

[49]  Danny Quah,et al.  Empirics for economic growth and convergence , 1996 .

[50]  Peter C. B. Phillips,et al.  Challenges of Trending Time Series Econometrics , 2004, Math. Comput. Simul..

[51]  T. Adrian,et al.  Learning About Beta: Time-Varying Factor Loadings, Expected Returns, and the Conditional CAPM , 2008 .

[52]  Per Krusell,et al.  Income and Wealth Heterogeneity in the Macroeconomy , 1998, Journal of Political Economy.

[53]  Dag Tjøstheim,et al.  Nonparametric estimation in null recurrent time series , 2001 .

[54]  Serena Ng,et al.  Evaluating latent and observed factors in macroeconomics and finance , 2006 .

[55]  Kurt Annen,et al.  HP-Filter DLL executable , 2006 .

[56]  Sydney C. Ludvigson,et al.  The Empirical Risk-Return Relation: A Factor Analysis Approach , 2005 .

[57]  Soyoung Kim,et al.  Dynamic Risk Sharing in the United States and Europe , 2000 .

[58]  Fabio Canova,et al.  Testing for Convergence Clubs in Income Per Capita: A Predictive Density Approach , 2004 .

[59]  E. Fama,et al.  Common risk factors in the returns on stocks and bonds , 1993 .

[60]  Simon van Norden,et al.  GAUSS code for the Hodrick-Prescott filter , 1995 .

[61]  Steven N. Durlauf,et al.  Multiple regimes and cross‐country growth behaviour , 1995 .

[62]  Edmund Taylor Whittaker.  On a New Method of Graduation , 1922, Proceedings of the Edinburgh Mathematical Society.

[63]  P. Phillips,et al.  Nonstationary Density Estimation and Kernel Autoregression , 1998 .

[64]  James J. Heckman,et al.  Micro data and general equilibrium models , 1999 .

[65]  A. Marcet,et al.  The Poor Stay Poor: Non-Convergence Across Countries and Regions , 1995 .

[66]  Gary Chamberlain,et al.  FUNDS, FACTORS, AND DIVERSIFICATION IN ARBITRAGE PRICING MODELS , 1983 .

[67]  Kurt Annen,et al.  HP-filter for Java , 2004 .