Note on the interpretation of the convergence speed in the dynamic panel model

Abstract

Studies using dynamic panel regression approach have found a high speed of income convergence among the world and the regional economies. For example, Lee et al. (1997, 1998) report 30% per annum. This note argues that their estimates of the convergence speed can be seriously overstated. Using a factor model, we show that the coefficient of the lagged income in their specification may not be the long-run convergence speed, but the adjustment speed of the short-run deviation from the long-run equilibrium path. We give an example of an empirical analysis, where the short-run adjustment speed is about 40%.

Keywords:

• convergence speed
• real income
• dynamic panel regression
• factor model

JEL Classification:

• O40
• C23

Notes

¹ For simplicity, we exclude some exogenous variables as the determinants of economic growth such as the savings rate, measures of investment in physical and human capital and so on to focus on the interpretation of the convergence speed using the panel data approach.

² In response, Islam (1998) argues that Lee et al. (1997, 1998) are assessing an economically uninteresting form of convergence when they allow for trend differences. Durlauf et al. (2005) comment that ‘this debate is an excellent example of the issues of interpretation that are raised in moving between specific economic hypotheses and more general statistical models’.

³ We can understand that the Lee et al. (1997, 1998)’s specification is appropriate by looking at the recent literatures of the panel unit root test, e.g. Phillips and Sul (2003). They argue that, if the cross-sectional correlation for the error term is not accounted for, the estimates of the autoregressive coefficients will be biased. In order to control the cross-sectional correlation, the error term is given by a three-component model that contains a fixed effect (), a common factor (), and a purely idiosyncratic factor (). Then, it becomes the standard to use a similar specification to Equation 2 in panel unit root test.

⁴ Although we explain the case that and follow the first-order autoregressive model in Equations 4 and 5 for simplicity, the argument applies for any order of the autoregressive model.

⁵ Bernard and Durlauf (1995)’s Definition 2.2 of ‘common trends in output’ embodies this idea.

⁶ We add as explanatory variables four lags of the first difference of in Equation 4 to remove the autocorrelation of the residuals.

⁷ They admit that interpretation of this value as the -convergence speed is highly questionable.