6.3. Panel estimates
In this subsection we turn to the time variation in the data. On the one hand,
this exercise is more demanding, as electoral rules only exhibit limited variation
over time. There have been a few reforms of electoral formulas, generally towards
a mixed system from both extremes (plurality and strict proportionality), mainly
but not exclusively in the 1990s. Variations in the magnitude of electoral districts
have been somewhat more common. But variations in the type of government
occur more frequently.
On the other hand, using the time variation in the data is also more rewarding.
Inference about true causality drawn from time-series variation may be more re-
liable than inference from cross-country variation, because simultaneity bias due
to omitted (time-invariant) confounding variables is less likely.
We confine the analysis to the 1960-98 data set. As discussed above, we define
a time period as either a whole legislature, or a calendar year. Defining time
periods to conform with legislatures allows us to remain more faithful to the the-
oretical model. This is the unit of time over which our political and institutional
variables remain constant (in practice, for party structure or type of government,
or by definition, for the electoral rules variables). Time measured in legislatures
seems particularly appropriate when studying the political effects of electoral rules.
Because almost all the reforms are clustered in the two most recent decades, we
include at most six legislatures in each country in the legislatures panel. When
it comes to government spending, however, it may also be relevant to consider
calendar time, because different countries may be affected by worldwide events in
similar ways, and because the duration of legislatures varies across countries. For
government spending we thus show results also for a yearly panel.
Our empirical strategy is similar to the one in the previous section. We start
by the political effects of electoral rules, then go on to study their effects on gov-
ernment spending. In both cases, we estimate reduced forms, as well as structural
forms. Panel data analysis raises a few new estimation issues. All our endoge-
nous variables (party structure, type of government, spending) move slowly over
time. The endogenous variables are also likely to reflect the effect of unobserved,
country-specific determinants. To cope with these features of the data, we report
on estimates obtained by two alternative methods.
One method is to estimate in levels, including country fixed effects and lagged
dependent variables (but no correction for serial correlation). This is equivalent
to estimating the parameters of interest from variables measured as deviations
from country means. It is well known that fixed-effects estimates are biased in
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