the presence of lagged dependent variables. But the bias becomes negligible if the
panel is sufficiently long. In our yearly panel, we have on average 25 years per
country so the problem is likely to be negligible.
With only six observations per country in the legislature panel, however, the
bias can be more serious. In these cases, we instead estimate in first differences
by GMM, with the procedure pioneered by Arellano and Bond (1991). Here, we
use lags of dependent and endogenous variables, and exogenous variables as in-
struments. This method produces consistent estimates even if the error term has
first-order serial correlation, and makes efficient use of the instruments. But it
makes some demanding assumptions on the validity of the instruments. Because
of the uncertain finite-sample properties of GMM estimators with many overiden-
tifying restrictions, we choose a parsimonious set of instruments, exploiting only
one extra lag of dependent or endogenous variables (rather than the full set of
lags to the beginning of the sample).
We comment more extensively on these methods in context. Generally, and
luckily, they produce similar estimates.
Political effects of electoral rules Table 4 displays the political effects of
alternative electoral rules as estimated from the legislatures panel. The structure
of the table is similar to that of Table 2. Thus, we first ask how electoral rules in-
fluence party fragmentation (here we omit the number of parties); then, how they
(and other electoral /constitutional variables) influence the type of government on
reduced form; finally, how party structure influences the type of government, in-
cluding the test of whether electoral rules affect the type of government exclusively
through party structure.
Columns 1 shows GMM estimates (for first differences) of the effect of electoral
rules on party fragmentation. We include lagged party fragmentation, and control
for country size (measured by population) and quality of democracy (measured
by polity_gt), as many countries in the sample have become better democracies in
more recent periods. As expected, district magnitude raises party fragmentation,
confirming the cross sectional results in Table 2. Plurality rule (measured by maj)
has the expected negative sign, but is at best borderline significant (p-value of
0.11). We cannot reject the assumptions of no second-order serial correlation or
validity of the lagged values used as instruments.
The reduced form results for coalition and single-party governments are dis-
played in columns 2-3. We now include two lags of the dependent variable in the
specification, plus the quality of democracy and population size. The constitu-
42