1096 The Econometrics of Convergence
Specifically, the Kocherlakota–Yi analysis provides conditions under which:E(logyt−logyt− 1∣∣
logA 1 , logk 1 )is decreasing in logA 1 , (23.11)even ifα ≥1. This means that a finding ofβ-convergence may occur when
endogenous growth is the relevant case. The key assumption for this case is that
logAt=g+ρlogAt− 1 +εtwith 0<ρ< 1 −δ, whereδis the discount rate. In
this case, the presence of an endogenous growth component is swamped by transi-
tional dynamics, as the effects of shocks die out. These findings parallel the result
in Bernard and Durlauf (1996) but using a different mechanism.
Kocherlakota and Yi (1995) also give conditions under which:
E(logyt−logyt− 1∣∣
logA 1 , logk 1 )is increasing in logA 1 , (23.12)even ifα<1. This means that a positiveβcan occur in a cross-country growth
regression, even when returns to capital are diminishing. The key to the result is a
unit root in the level of technology; formally, they assume logAt=g+logAt− 1 +εt.
Intuitively, intertemporal optimization, at least for their choice of utility function,
means that higher initial income leads to higher investment, and this can yield a
positive correlation between growth and initial income.
These findings show the difficulties that can arise when convergence findings are
used to discriminate between growth models. The above analyses may be under-
stood as arguing that tests forβ-convergence fail to distinguish between behavior
along a transition path to a steady-state and behavior in the steady-state, in the
way needed to allow reliable discrimination between neoclassical growth models
and newer alternatives.
23.3 Nonlinearities and multiple growth regimes
Clearly, tests forβ-convergence may have low power against the alternative
hypothesis of multiple steady-states. With this in mind, some studies have
explicitly searched for statistical evidence of multiple steady-states. Durlauf and
Johnson (1995) use classification and regression tree (CART) methods to search
for nonlinearities in the growth process implied by the existence of multiple steady-
states.^15 This procedure identifies sub-groups of countries that obey a common
linear growth model based on the Solow variables, and enables a test of the null
hypothesis of a common growth regime against the alternative hypothesis of mul-
tiple regimes. In their study, allowing for multiple regimes means that economies
with similar initial conditions (such as literacy rates) are allowed to converge or
behave in similar ways, without imposing any requirement that steady-states are
unique. Using the Mankiwet al.(1992) data, Durlauf and Johnson (1995) reject the
single regime model required for global convergence. Instead, they conclude that
there is a role for initial conditions in explaining variation in cross-country growth
behavior, even after controlling for the structural heterogeneity implied by the