On the potential pitfalls in estimating β-convergence by means of pooled and panel data

Abstract

We show that the use of pooled and panel data in estimating β-convergence across countries (or other territorial areas) may involve some pitfalls, since these techniques cannot properly distinguish between actual convergence and the possibility of decreasing growth rates over time within each country (or territorial unit). We also show how the possible bias in the estimates can be eliminated.

Acknowledgements

We wish to thank all friends and colleagues who read a previous version of the present article and made useful comments and suggestions. The usual disclaimers obviously apply.

Notes

¹ The empirical tests usually distinguish between absolute convergence (directly measuring the relationship between growth rates and initial incomes) and conditional convergence (including variables capable of capturing the differences in the various countries steady states).

² It is worthwhile emphasizing that this article is not concerned with the issue of the most appropriate measure of economic convergence and thus with the debate around the so-called Galton's fallacy, stimulated by Quah (1993). Indeed the aim of the work is to show that, within the traditional β-convergence approach, the use of pooling and panel techniques may produce misleading results.

³ For the interpretation of this model see Islam (1995) and Durlauf and Quah (1999).

⁴ It should be noticed that Mankiw, Romer and Weil's original estimates concerned a cross-section of countries in a single period of time and that they also considered a model including human capital. In this article we neglect human capital in order to simplify the exposition, while maintaining the validity of the conclusions we reach.

⁵ It is worth emphasizing that pooling and panel techniques are used to test the conclusions of a wide variety of models, besides the convergence issue. The possible shortcomings shown in this article only refer to the specific problem examined.

⁶ If we let Y_nt stand for the so-called natural or potential output, that is the trend level of output that would prevail in the Solow–Swan model in the absence of shocks, then the subsequent output gap between actual and potential output would be (Y_t  − Y_nt )/Y_nt , usually approximated by log (Y_t /Y_nt ) = log u_t . In line with the actual experience of developed countries we constrain the shock to produce an output gap not greater, in absolute value, than 3%. Since the shock is normally distributed, i.e. , then σ² will be such that, for instance, .

⁷ It is worthwhile noticing that the values of the output growth rates after 100 years reported in Fig. 1 are the averages of the 1000 simulations for each economy.

⁸ In our example the variables s, n, d and g are assumed to be constant. For this reason the estimates are performed using initial income as the unique regressor, since the values of s, n, d and g are captured by the constants of the regressions. For simplicity, the estimates are performed using the ordinary least square technique.

⁹ It should be added that the β-coefficients are also highly significant in every single regression run, with average t-values around −13, −18.5 and −41 respectively for Equations 1–3.

¹⁰ This conclusion is somehow related to Islam's (2003, p. 315 and p. 321) observations about the existence of a ‘within-across’ tension in the concept of convergence, due to the use of the single-economy Solow model in a cross-country framework. In this perspective, our work shows that this tension may produce misleading results when pooling and panel regressions are used and indicates how the possible bias can be removed.

¹¹ It should be noticed that Equation 5 is formally equivalent to estimating a model where time-specific, but no country-specific, fixed effects are introduced, i.e. to estimate Equation 3 with α_j  = 0 ∀j.

¹² The average t-value of the β-coefficient in the 1000 regressions run is 3.9.

¹³ Obviously, the method proposed in this article is quite general and is therefore also capable of showing the existence of convergence in the opposite, though less relevant, case where rich countries grow less than poor ones but per capita income growth rates in each economy increase over time.

¹⁴ Obviously, since there are many variables that can affect technology, this solution may suffer from the problem of the potential omission of relevant variables. This problem, however, in our opinion, is not a sufficient reason for reintroducing country-effects, given the possible bias in estimating convergence by means of panel equations shown in Section II, yielding false results.