Paul Johnson, Steven Durlauf and Jonathan Temple 1139different countries are realizations of a common DGP, and many of the modeling
assumptions and procedures of the empirical growth literature can appear arbitrary.
In the well-known question posed by Harberger (1987): “What do Thailand, the
Dominican Republic, Zimbabwe, Greece and Bolivia have in common that merits
their being put in the same regression analysis?”
The extent to which this objection is fundamental remains an open question,
but there seems to be agreement that, when studying growth, it will be difficult
to recover a DGP even if one exists, and the prospects for recovering causal effects
are clearly weak. The shortcomings of the relevant economic theory, as well as
those of the data and econometric analysis, are considerable. Those who will be
satisfied only with the specification and estimation of a structural model, in which
parameters are either “deep” and invariant to policy, or correspond to precisely
defined causal effects within a coherent theoretical framework, are bound to be
disappointed. The more appropriate goal for the growth literature is less ambi-
tious: investigating whether or not particular hypotheses have any support in the
data and whether it is possible to rule out some possible claims about the world, or
at least shift the burden of proof from one side of a debate to another. In practice,
growth researchers are looking for patterns and systematic tendencies that, in com-
bination with historical analysis, case studies, and relevant theoretical models, can
increase our understanding of the growth process. A related goal, more difficult
than it may appear at first sight, is to communicate the degree of support for any
patterns identified by the researcher.
The issue raised by Harberger is essentially that of parameter heterogeneity. Why
should we expect disparate countries to lie on a common regression surface? Of
course, this criticism could be made of most empirical work in social science:
whether the data points reflect the actions and characteristics of individuals and
firms, or the aggregations of their choices that are used in macroeconometrics. It
is the small sample sizes available to growth researchers that limit the scope for
addressing this problem, and mean that Harberger’s remark retains some force. In
other contexts, an appropriate response would be to use a model that has sufficient
flexibility to be a good approximation. But this approach will often be fragile when
the sample is rarely greater than 100 observations, as is the case when studying
economic growth using cross-country data.
If parameter heterogeneity is present, the consequences are potentially serious,
except in the special case where the slope parameters vary randomly across units,
and are distributed independently of the variables in the regression and the dis-
turbances. In this case, the coefficient estimate should be an unbiased estimate of
the mean of the parameter distribution. However, the assumption of independence
will often be unwarranted. For example, when estimating the relationship between
growth and investment, the marginal effect of investment will almost certainly be
correlated with aspects of the economic environment that should also be included
in the regression, such as political stability or the protection of property rights.
Some researchers have allowed greater flexibility in the functional form of
their models, often beginning with the canonical Solow regression which, for