Steven Durlauf, Paul Johnson and Jonathan Temple 1095population growth, that each country has a common set of control variablesZi,
and that convergence does not occur because of the presence of a threshold exter-
nality, as in Azariadis and Drazen (1990). In the Azariadis–Drazen model, such an
externality can produce multiple steady-states, with the long-run outcome for an
economy depending on whether its initial capital stock is above or below a thresh-
old. Those starting below the threshold will converge to one steady-state, while
those starting above will converge to another.
Relative to the economic idea of convergence as manifested in the neoclassical
model, the Azariadis–Drazen model does not exhibit convergence, and different
initial conditions lead to different steady-states. Yet the data generated by the
Azariadis–Drazen model will not necessarily lead to the finding thatβ≥0, as
shown in Bernard and Durlauf (1996). To see why, consider the growth process:
γi=k+β(logyi,0−logy∗l(i))+εi, (23.9)where countryihas steady-statel
(
i)
with associated output per capitayl∗(i), a value
common across all countries with that steady-state. Suppose that the (now misspec-
ified) cross-country growth regression (23.6) is employed to test for convergence.
The regression coefficient will, in the probability limit, equal:
βm=β(
1 −cov(logy∗l(i), logyi,0)
var(logyi,0)). (23.10)
The sign ofβmcannot be determineda priori, as it depends on cov(logy∗l(i), logyi,0),
which is determined by the relationship between initial incomes and steady-states.
It is clearly possible forβmto be negative, implying statistical convergence, defined
asβ<0, despite the absence of economic convergence.
This problem is more than a theoretical possibility, as shown in Durlauf and
Johnson (1995). They estimate a model with multiple growth regimes motivated
by the Azariadis and Drazen (1990) framework and find that it fits cross-country
data better than does the linear Solow model. The issue is also highlighted in work
by Liu and Stengos (1999) and Durlauf, Kourtellos and Minkin (2001), who find
thatβappears to depend nonlinearly on initial conditions and may be equal to
zero for some countries. These and related findings will be discussed in the next
section on nonlinearities and multiple regimes.
Similar results may be derived in linear environments in which the distinc-
tion between neoclassical and endogenous growth theories depends on returns to
scale in the aggregate production function as embodied in a particular parameter
value. Kocherlakota and Yi (1995) analyze a representative agent model in which
yt=Atkαt− 1 , so that logyt=logAt+αlogkt− 1. For this production function,
the difference between the neoclassical and endogenous growth models concerns
the value of the parameterα. The case ofα≥1 represents a version of endoge-
nous growth: the model yields perpetual growth regardless of whether there is a
deterministic drift in technology.