1140 The Methods of Growth Econometrics
comparison purposes, we restate:
γi=k+βlogyi,0+πnlog(
ni+g+δ)
+πKlogsK,i+πHlogsH,i+εi. (24.23)For example, Liu and Stengos (1999) estimate a semiparametric partially linear
version of this model, namely:
γi=k+fβ(
logyi,0)
+πnlog(
ni+g+δ)
+πKlogsK,i+fπH(
logsH,i)
+εi, (24.24)wherefβ(·)andfπH(·)are arbitrary functions except for variance smoothness
requirements. They find that the value offβ(logyi,0)is only negative when ini-
tial per capita income exceeds about $1,800; below that level, there is less evidence
for the conditional convergence effect predicted by the Solow model. Banerjee
and Duflo (2003) use a similar approach to study nonlinearity in the relationship
between changes in inequality and growth, estimating a version of (24.24) where
Solow-type variables and some additional variables enter in a linear way, supple-
mented by a nonlinear functionfG(Gi,t−Gi,t− 5 ), whereGi,tis the Gini coefficient.
Using an alternative method, Durlauf, Kourtellos and Minkin (2001) estimate a
version of the augmented Solow model that allows the parameters to vary across
countries as functions of initial income:
γi=k(
yi,0)
+β(
yi,0)
logyi,0+πn(
yi,0)
log(
ni+δ+g)+πK(
yi,0)
logsK,i+πH(
yi,0)
logsH,i+εi. (24.25)Hence each initial income level defines a distinct Solow regression, and thereby
shifts the emphasis away from nonlinearity and towards parameter heterogeneity.
This study indicates considerable parameter heterogeneity, especially among the
poorer countries, and confirms the Liu and Stengos (1999) finding thatβ(yi,0)is
positive for lowyi,0values and negative for higher ones. Durlaufet al.(2001) also
find thatπK(yi,0)fluctuates greatly over the range ofyi,0values in their sample. The
extension by Kourtellos (2003a) uncovers systematic heterogeneity in the parame-
ters on initial literacy and initial life expectancy. A varying coefficient approach is
also employed in Mamuneas, Savvides and Stengos (2006), who consider a model
in which the coefficient on human capital is allowed to vary with the level of
human capital and a measure of trade openness. Constancy of the human capital
coefficient is rejected across a range of specifications.
At a minimum, it makes sense for empirical researchers to test for neglected
parameter heterogeneity, either using interaction terms or by carrying out diagnos-
tic tests. As an alternative, some authors have used panel data to identify parameter
heterogeneity without the imposition of a functional relationship between parame-
ters and various observable variables. An important early contribution along these
lines is Canova and Marcet (1995). Definingsi,tas the logarithm of the ratio of
a country’s per capita income to the timetinternational aggregate value, and
using data either on the regions of Europe or 17 western European countries, they