1128 The Methods of Growth Econometrics
where the vectorXicontains a constant, log
(
ni+g+δ)
, logsK,iand logsH,i. The
variables spanned by logyi,0andXithus represent the growth determinants sug-
gested by the Solow model, whereas the vectorZirepresents growth determinants
that lie outside that model.^3 The distinction between the Solow variables andZi
is important in understanding the empirical literature. The Solow variables appear
in many of the specifications estimated in the literature, reflecting the use of the
Solow model as an organizing framework for growth analysis, but choices con-
cerning whichZivariables to include often vary greatly across studies. This clearly
introduces a degree of arbitrariness which will be discussed later in this chapter.
Equation (24.11) represents the baseline for much of growth econometrics and
these regressions are sometimes known as “Barro regressions,” following the influ-
ential early contribution of Barro (1991).^4 This workhorse of empirical growth
research has been generalized in a number of dimensions. Some of these exten-
sions reflect the application of (24.11) to time series and panel data settings. Others
reflect the use of more general production functions, or allow for nonlinearities and
parameter heterogeneity, and we will discuss all these variants below.
24.3.3 Levels regressions
An alternative approach became especially popular after the work of Hall and Jones
(1997, 1999). Their work sought to model the cross-section variation in the level
of development, rather than the growth rate over a specific time interval. In other
words, the dependent variable is the level of gross domestic product (GDP) per
capita or GDP per worker, and there is no role for initial GDP on the right-hand side
of the regression. In principle, this “levels regression” approach could be attractive
for a number of reasons. It seems better suited to theories which emphasize long-
run, fundamental sources of differences in development levels, such as geographic
characteristics or the historical path taken by institutions. It may also give a direct
answer to a key question of interest: “What is the long-run effect of a particular
variable on the level of GDP per capita or GDP per worker?”
There are two important limitations of this approach. The first can be seen by
contrasting it with the framework for modeling economic growth described above.
In that framework, modeling the level of GDP per capita, without allowing for a
conditional convergence effect, is akin to assuming that we observe the country in
its long-run steady-state. Mankiwet al.(1992) initially adopted this approach: hav-
ing derived the implications of the Solow model for the steady-state level of income,
they estimated models with the level of income as the dependent variable. But they
also noted that this approach is only valid if countries are distributed randomly
around their steady-state positions, and so they moved on to estimate conditional
convergence regressions, which did not require that strong assumption. Put differ-
ently, the levels regression approach risks omitting a relevant variable, a point that
Bhattacharyya (2007) has recently emphasized.
The second limitation is that many candidate explanatory variables are likely to
be endogenous to the level of income. A researcher could readily run a regression
which “explains” income levels in terms of luxury car ownership, or the number
of televisions, but it would be hard to interpret this as a meaningful explanation