Geoscience Reference
In-Depth Information
∧
ineq
ir
it
is instrumented by the variables determining the territorial
structure of inequality (8.1) in an effort to ensure that its impact on
IPR
is
exogenous (independent of) the effect of
IPR
on the geography of inequality
itself. To the extent that the independent variables included in (8.1) do not
have a direct effect on
IPR
other than the one they have through their impact
on
Note that
∧
ineq
ir
it
, the results will not be affected by an endogeneity problem.
3
Because
the restriction assumptions are highly contestable, and because the use of a
weak instrument might artificially create relationships that are not very robust
otherwise, for both equations I report several specifications with different sets
of instruments. In addition, these specifications also vary in their approach to
two issues that could potentially bias the results, namely the potential impact
of serial correlation and the potentially confounding effect of unobserved unit-
specific effects. In an effort to deal with these multiple sources of concern, I
estimate each of the two specifications of the conditional relationship between
the geography of income inequality and the balance of power between the
center and the regions in three different ways. A brief description follows.
First, I report an OLS estimation with panel corrected standard errors with
a common (ar1) serial correlation correction (a version that applies the Prais-
Winsten first differences correction to panel data. In
Table 8.3
I label this
model as PCSE, AR1. Second, I report an application of the standard two-
stage instrumental variable approach for panel data created by Baltagi (Baltagi
2008
). I refer to the Baltagi estimation as TSIV in
Table 8.2
. Finally, I report
estimates from a panel regression with vector decomposition following the
procedure developed by Pl umper and Troeger (
2007
). This model is referred to
in
Table 8.2
as FEVD. This procedure is particularly helpful to control for the
presence of unobserved unit effects when, as is the case in these models, some
of the control variables are time invariant. I should note that all three sets of
results are instrumental variables approaches, that is to say, they try to contain
the effects of endogeneity by using the values of
∧
ineq
ir
it
, as predicted by (8.1).
The difference between them lies in the set of instruments being included. While
the OLS with panel corrected standard errors and the vector decomposition
approaches restrict the list of instruments to those included in the opening
section, the Baltagi approach takes as instruments all the exogenous variables
in the system.
4
3
There is a problem of endogeneity when “the values of our explanatory variable are sometimes
the consequence, rather than the cause, of our dependent variable” (King, Keohane, and Verba
1994
: 185;Manski
1995
). More technically, endogeneity refers to the fact that an independent
variable is potentially a choice variable, correlated with unobservables in the error term. In
the real world this distinction is often subtle and complicated. Indeed, the specialized literature
seems to have taken a different path by establishing the conditions under which an independent
variable x can be considered strictly exogenous in relation to y. These are mainly two: weak
exogeneity and absence of Granger causality. For a discussion on these issues see Greene (
2000
).
Additional statistical tests indicate that, whereas trade openness is a “good” instrument (that is,
strong effect on
∧
ineq
ir
it
yet unrelated to the error term of (6.2)), mobility qualifies only as a weak
instrument.
4
Note that the estimation of (8.2) using a standard one-way OLS approach supports the argu-
ment's predictions strongly. These results are available upon request.
