1092 The Econometrics of Convergence
some have (perhaps with a degree of irony) accorded the 2% value a status akin
to that of a universal constant in physics, others have been rather more skeptical
of its generality. There is nothing in the logic of the neoclassical growth model to
suggest that this parameter should be invariant across environments, and this in
itself might lead to skepticism about the supposed universality of the 2% figure.
On the other hand, there are reasons to believe that the time series structure of
per capita output data could produce a “universal” convergence estimate because
of inadequate attention to temporal dependence in the data. Quah (1996b), for
example, suggests that the 2% finding may be a statistical artifact that arises for
reasons unrelated to convergenceper se. Specifically, he argues that, if each per
capita output series in a cross-section regression contains a unit root, this can
produce aβestimate such that a 2% convergence rate is produced, even if the series
are independent. Quah’s argument is important in motivating the importance of
time series approaches to evaluating convergence, which are discussed later.
23.2.3 Critiques
The evidence of convergence obtained from cross-country growth regressions has
been subjected to a number of criticisms. Here we focus on those that seem
most important (see Durlauf, Johnson and Temple, 2005, for a more complete
treatment).
The first criticism relates to the choice of control variables, and whether claims
about convergence are robust to alternative choices. Any claims about conditional
convergence, in particular, necessarily depend on a specific choice for the set of
control variablesZi. This is a serious concern, given the lack of consensus in growth
economics about which growth determinants are empirically important. This lack
of consensus is reflected in the “growth regression industry” that has arisen, as
researchers have added a range of controls, of varying degrees of plausibility, to
those of the basic Solow model.^12
The most conceptually satisfying response to this problem has been the use of
model averaging methods, as in Fernandez, Ley and Steel (2001) and Sala-i-Martin,
Doppelhofer and Miller (2004). The model averaging approach constructs esti-
mates (or posterior means, depending on whether one is evaluating convergence
along frequentist or Bayesian lines) based upon a model space of candidate growth
regressions. Information on convergence in each model is aggregated with weights
corresponding to posterior model probabilities. These studies show that the cross-
country finding of conditionalβ-convergence is robust to the choice of controls.
Both studies conclude that the posterior probability that initial income is part of
the linear growth model is high. The Sala-i-Martinet al.study reports a posterior
expected value for theβregression parameter of−0.0085, implying an estimated
convergence rate of 1% per year.
A second critique, which is perhaps better called a class of critiques, is that there
are many good reasons to believe that the model errors in growth regressions are
correlated with the associated regressors, leading to inconsistent estimates. One
can understand a number of developments in the econometrics ofβ-convergence
as efforts to address this problem.