Paul Johnson, Steven Durlauf and Jonathan Temple 1143conditions. If there are two (stochastic) steady-states, and large shocks are suffi-
ciently infrequent,^16 the system will, under suitable regularity conditions, exhibit
an invariant probability measure that can be described by a “reduced form” model
in which the long-run behavior of logyi,tdepends only on the exogenous variables,
mi, such as:
logyi,t=logy 1 ∗(
mi)
+u1,i,twith probabilityp(
mi)
, (24.28)and:
logyi,t=logy 2 ∗(
mi)
+u2,i,twith probability 1−p(
mi)
, (24.29)whereu1,i,tandu2,i,tare independent, zero mean deviations from the steady-state
log means logy 1 ∗(mi)and logy 2 ∗(mi)respectively, andp(mi)is the probability that
countryiis in the basin of attraction of the first of the two steady-states. From
the perspective of the econometrician, logyi,tthus obeys a mixture process. The
two steady-states associated with (24.28) and (24.29) might be interpreted as a low-
income regime or poverty trap, and a high-income or growth regime, respectively.
Bloomet al.(2003) estimate a linear version of this model using 1985 income data
from 152 countries, with the absolute latitude of the country as the fundamental
exogenous variable. They are able to reject the null hypothesis of a single regime
model in favor of the alternative of a model with two regimes: a high-income
steady-state in which income is independent of absolute latitude, and a low-income
(“agricultural”) steady-state in which income is increasing in absolute latitude. In
addition, the probability of being in the high-income steady-state is found to be
increasing in absolute latitude.
Adding extra complexity to this model could well be constrained by the small
number of countries available. More generally, the empirical investigation of
multiple steady-states raises some complex problems for standard methods. One
response is to draw more heavily on structural theoretical models as a framework
for understanding the data, as in Graham and Temple (2006). Another possibility
would be to exploit time series variation in a single country, in order to identify
jumps from one equilibrium or steady state to another. But in either case, it is clear
that these forms of analysis would have to proceed under strong assumptions, some
of which will be difficult to test.
24.5 Time series methods, panel data and event studies
Our discussion now explores alternative ways of modeling growth: time series mod-
els, the use of panel data, and studies based on discrete “events” which draw on
panel data methods. At the risk of stating the obvious, choices on research design
involve significant trade-offs, which depend partly on statistical considerations
and partly on the economic context. This means that attempts at universal pre-
scriptions are misguided, and we will try to show the desirability of matching
techniques to the economic question at hand. One example, to be discussed below,
would be the choice between panel data methods and the estimation of separate