and 0 otherwise. The default is thus the group of proportional countries. Mixed-
proportional systems such as Germany, for which the electoral formula is strictly
proportional at the level of the whole nation, are coded as proportional.20 The
model also assumes that proportional elections are performed in a nation-wide
district and majoritarian elections in single-member districts. In the empirical
work, we include the variable district to allow for the positive association ex-
pected (from earlier work) between large districts and party proliferation. This
variable codes district magnitude in the conventional way, namely as the number
of seats awarded in the average electoral district, re-scaled to vary between 0 and
1. These three variables vary both across countries and over time, and they are
not very highly correlated with each other (their simple correlation coefficients
are always below 0.34 both in the cross sections and in the panel on legislatures).
But the time variation is small: there are only seven electoral reforms relevant
enough to change our classification of maj or semi, including two reforms in
France (that switched from majoritarian and then back to proportional in the
mid 1980s) District magnitude varies more frequently over time, although the
size of these changes is often small.
Party structure When it comes to the party structure in the legislature,
our simplified model has only three possible outcomes: two, three or four par-
ties. To normalize real-world party structures into a comparable measure, we use
a Herfindahl-like index of party fragmentation, which is commonly used in the
political science literature. It is labeled party_frag and defined as 1 - ΣP (sP)2,
where — as in the model — sP is the seat share of party P and the summation runs
over all parties in the legislature (lower house). As an alternative measure, we
also use the number of parties in the lower house, nparties.
Types of government Our simple model only allows for two types of gov-
ernment: single-party majority and coalition governments; minority governments
are not observed. We follow the model, and we classify these types of govern-
ment through simple indicator variables, called single and coalition, respectively,
omitting minority government. Thus, for instance, single takes a value of 1 if
the government consists of single-party majority in that year and country, and 0
otherwise. Of course, these two variables do not always sum to 1 for any given
country and year, since we sometimes observe minority governments. We never
20In this respect, our definition of semi differs slightly from the variable mixed in Persson
and Tabellini (2003), that instead classified mixed-proportional systems as mixed.
34