1142 The Methods of Growth Econometrics
Solow model that is based on a constant elasticity of substitution (CES) production
function, building on Duffy and Papageorgiou (2000). By using the Hansen (2000)
approach to sample splitting and threshold estimation, they find statistically sig-
nificant evidence of thresholds in the data. The estimated thresholds divide the
sample into four distinct growth regimes that are broadly consistent with those
found by Durlauf and Johnson.^14 Relative to the regression tree approach, the
Hansen methods have the significant advantage of allowing inference on the level
of the estimated threshold.
Another closely related analysis is that of Tan (2004). He employs a procedure
known as GUIDE (generalized, unbiased interaction detection and estimation),
due to Loh (2002), to identify sub-groups of countries which obey a common
growth model. Relative to CART, the GUIDE algorithm has two advantages. First,
the algorithm explicitly looks for interactions between explanatory variables when
identifying splits. Second, the penalties for model complexity are supplemented
with some within-model testing, which reduces the tendency for CART proce-
dures to produce an excessive number of splits in finite samples. Tan (2004) finds
strong evidence that measures of institutional quality and ethnic fractionaliza-
tion define convergence clubs across a wide range of countries. He also finds
some evidence that geographic characteristics distinguish the growth process for
sub-Saharan Africa from the rest of the world.
Further research has corroborated the evidence of multiple regimes using alter-
native statistical methods, including projection pursuit.^15 Desdoigts (1999) uses
these methods to identify groups of countries with relatively homogeneous growth
experiences based on the characteristics and initial conditions of each country. The
idea is to find the orthogonal projections of the data into low dimensional spaces
that best display some interesting feature of the data; this can be seen as a gen-
eralization of principal components analysis. When using principal components
analysis, a researcher will typically retain only the components needed to account
for “most” of the variation in the data. Similarly, in projection pursuit methods,
a researcher will consider as many dimensions as needed to account for “most” of
the clustering in the data. Some evidence of their utility can be found in Kourtellos
(2003b). Unlike Desdoigts, Kourtellos uses projection pursuit to construct models
of the growth process. Formally, he estimates models of the form:
γi=∑Ll= 1fl(
yi,0βl+Xiψl+Ziπl)
+εi. (24.27)Each element in the summation represents a distinct projection. Kourtellos uncov-
ers evidence of two steady-states, including one that corresponds to countries with
low initial income and low initial human capital.
Another approach to multiple regimes is employed by Bloom, Canning and
Sevilla (2003). This is based on the observation that if long-run outcomes are deter-
mined by fundamental forces alone, the relationship between exogenous variables
and income levels ought to be unique. If initial conditions play a role there will
be multiple relationships, one for each basin of attraction defined by the initial