1254 Spatial Analysis of Economic Convergence
They are transformed in ways implied by the model (see Durlauf and Quah, 1999,
for additional insights into this specification).X2,iis a set of additional control
variables capturing differences in aggregate production functions andεiis an error
term with the following properties:εi∼i.i.d.(0,σε^2 ).
In this specification, the average growth rate in per capita income over the period
t 0 tot 0 +Tis related to the initial level for incomeyi,t 0 and a set of steady-state
determinants (X1,iandX2,i). There is conditional convergence if the estimate ofβ
is significantly negative, with a convergence speed equal tob=−log( 1 +Tβ)/T
and a half-life equal toτ=−log( 2 )/log( 1 +β). The concept of unconditional con-
vergence is defined when all the economies are assumed to be structurally similar,
that is, that they are characterized by the same steady-state, and differ only by
their initial conditions. This assumption is tested with the cross-sectional model,
including only the initial per capita income as an explanatory variable.
As frequently pointed out in the growth econometrics literature, the tests of
conditional convergence face several problems, such as robustness with respect
to choice of control variables, multicollinearity, heterogeneity, endogeneity, and
measurement problems (Durlauf and Quah, 1999; Temple, 1999; Durlaufet al.,
2005). Durlaufet al. question the assumption usually made on the error terms.
Indeed, by assuming that they are independent and identically distributed (i.i.d.),
the researcher thinks of them as interchangeable across observations. This is the
concept of exchangeability: “different patterns of realized errors are equally likely
to occur if the realizations are permuted across countries. In other words, the
information available to a researcher about the countries is not informative about
the error terms” (2005, p. 36). They show that many econometric problems
highlighted in growth regressions can be interpreted as violations of exchange-
ability. Parameter heterogeneity (discussed below) or omitted regressors induce
non-exchangeability.
The assumption of constant returns to scale, on which neoclassical theory is
based, has been challenged by new economic growth and new economic geogra-
phy theories. Consequently, Fingleton and McCombie (1998) suggest alternative
theoretical frameworks that allow increasing returns to scale, especially when one
deals with regions. At the heart of this approach is Verdoorn’s law, based on Kaldor’s
second law, which has been traditionally estimated as a linear relationship between
the exponential growth rate of labor productivity (p) and output (q):
p=b 0 +b 1 q+ε, (27.2)whereε∼i.i.d.(0,σε^2 ). In equation (27.2), the coefficientb 0 is the autonomous
rate of productivity and the coefficientb 1 is called the Verdoorn coefficient. Its
estimated value is consistently about one-half when the model is fitted to vari-
ous data on manufacturing productivity growth and output growth. This implies
that a one-percentage-point increase in output growth induces an increase in the
growth of employment of one-half of a percentage point and an equivalent increase
in the growth of productivity. The increasing returns implied by Verdoorn’s law
have been illustrated by Fingleton (2000) using a static Cobb–Douglas production