1130 The Methods of Growth Econometrics
follows a random walk, the induced non-stationarity in many of the levels series
raises attendant unit root questions.
Beyond such issues of asymptotics, thead hocaddition of regression errors
described above leaves unanswered the question of the substantive economic
assumptions implicitly made by a researcher. Brock and Durlauf (2001a) address
this issue using the concept of “exchangeability” and many criticisms of growth
regressions can be interpreted as claims that exchangeability has been violated.
Loosely, their argument is that researchers working with regressions such as (24.11)
typically think of the errorsεias interchangeable across observations, so that dif-
ferent patterns of realized errors would be equally likely to be observed if the
realizations were permuted across countries. That is, the information available to
a researcher about the countries is not informative about the error terms.
This idea can be formalized asF-conditional exchangeability, defined as:
μ(
ε 1 =a 1 ,...,εN=aN∣
∣F 1 ...FN)=μ(
ερ( 1 )=a 1 ,...,ερ(N)=aN∣
∣F 1 ...FN)
,
(24.12)where, for each observationi,Fiis the associated information set available to the
researcher andρ()is an operator that permutes theNindices. In the growth con-
text,Fimay include knowledge of a country’s history or culture as well as any more
purely “economic” variables that are known. Omitted regressors then, for example,
induce exchangeability violations as these regressors are elements ofFi. Parameter
heterogeneity similarly leads to non-exchangeability.
Brock and Durlauf argue that exchangeability can be an organizing principle to
connect substantive social science knowledge with the error structure. This suggests
that it would be good empirical practice if researchers were to question whether
or not the errors in their model are genuinely exchangeable and, if not, to deter-
mine whether the violation invalidates the purposes for which the regression is
being used. As subject-specific knowledge is needed to evaluate the plausibility
of exchangeability: this cannot be done in an algorithmic fashion, but instead
requires judgments by the analyst.^5
24.4 Statistical models of the growth process
Although the initial focus of empirical work in this field was the convergence
hypothesis, the primary focus of more recent work has been the identification
of potential growth determinants. This work may be divided into three main cat-
egories, which we discuss in turn in the next three subsections. Section 24.4.1
discusses the analysis of whether specific determinants affect growth, focusing
on alternative ways to address the uncertainty about which explanatory vari-
ables should be included in a model. Section 24.4.2 explores methods to account
for parameter heterogeneity and summarizes some of the relevant evidence.
Section 24.4.3 focuses on the analysis of nonlinearities and multiple regimes in
the growth process. Models of poverty traps and endogenous growth are often
highly nonlinear, or associated with multiple steady-states in the growth process,