1112 The Econometrics of Convergence
specification. Using Hansen’s (2000) approach to sample splitting and threshold estima-
tion, they find statistically significant evidence of four distinct growth regimes, broadly
consistent with those found by Durlauf and Johnson (1995). Johnson and Takeyama
(2001) also use the regression tree approach and find evidence of thresholds in US state
economic growth behavior defined by variables likely to be proxies for the capital/labor
ratio, agglomeration effects and communication effects.- For more on GUIDE methods, see Loh (2002).
- Appendix A of Desdoigts (1999) provides a useful primer on projection pursuit which is
developed in Friedman and Tukey (1974) and Friedman (1987). - Kernel density estimation is a nonparametric method of estimating density functions
that has the attraction of flexibility as it does not imposea prioria functional form for
the density. See Silverman (1986). - The finite mixture model is a semi-parametric alternative to the nonparametric kernel
approach to density estimation. See McLachlan and Peel (2000). - Tsionas (2000) applies mixture models to US state data while Pittau (2005) and Pittau
and Zelli (2006) apply them to EU regional data. - This requirement is consistent with the documented lack of mobility within the cross-
country distribution of per capita income. - Again, multimodality in the ergodic distribution is neither necessary nor sufficient to
imply the existence of convergence clubs – not sufficient because it reveals nothing about
mobility and not necessary because the existence of multiple stochastic steady-states does
not imply multiple modes in the long-run distribution. - Applications of Markov chain methods to the study of mobility issues in the social sci-
ences predate the modern empirical growth literature. See, for example, Prais (1955).
The time-invariance and first-order Markovian assumptions are testable, with Quah
(1993b) presenting an informal test of the latter, while Fingleton (1997) and Bicken-
bach and Bode (2003) present more formal tests in the cases of EU regions and US states
respectively. - Johnson (2005) re-examines Feyrer’s (2003) results using the continuous state space
methods discussed below and finds that, rather than TFP playing an exclusive role in
the apparent bimodality in the long-run distribution of GDP per capita, the ergodic
distribution of the capital-output ratio is also bimodal. - Quah’s methods have been widely applied. For example, Andres and Lamo (1995) apply
these methods to the OECD; Lamo (2000) to the regions of Spain; Johnson (2000) to
US states; Bandyopadhyay (2004) to the Indian states; Andradeet al.(2004) to Brazilian
municipalities; Ezcurraet al.(2005) to EU regions; Fotopoulos (2006) to Greek regions,
and Pittau and Zelli (2006) to EU regions. In some cases, the small cross-section dimen-
sion of the samples must limit the reliability of the findings. These methods have also
been extended to broader notions of distributional dynamics. Fiaschi and Lavezzi (2004)
develop an analysis of the joint distribution of income levels and growth rates; their find-
ings are compatible with the existence of multiple equilibria in the sense that countries
may become trapped in the lower part of the income distribution. - Other efforts to find determinants of intertemporal mobility have produced mixed
results. For the OECD countries, Andres and Lamo (1995) condition on the steady-
state implied by the Solow model and find little change in the tendency to polarization
unless country specific effects are permitted. Lamo (2000) finds only a small increase in
mobility for Spanish regions after conditioning on interregional migration flows, while
Bandyopadhyay (2004) shows that differences in infrastructure spending and education
contribute to polarization between the rich and poor states of India. - These findings are echoed in Pesaran (2007), who uses both the Maddison and Penn
World Table datasets and employs a convergence definition that explicitly focuses on
the probability of large deviations between logyi,tand logyj,t.