(Page 9 of 22) - Ideological Space Dimensionality and the Number of Competitors authored by Stoll, Heather.

legislative and presidential elections takes on a value of zero either if there is not a presidential
executive (i.e., if the country’s political regime is parliamentary) or if the legislative election falls
in the middle of the president’s term; a value of one if the elections are concurrent; and a value
between zero and one reﬂecting the proximity otherwise. Third, the presidential candidate system
is operationalized as the index of electoral fractionalization (i.e., the transformation of the eﬀective
number of presidential candidates mentioned above). Countries without a president receive a value
of zero for this variable.

Original measures of all of these variables are constructed by Stoll (2004) from a variety of

secondary and primary sources. As part of a later sensitivity analysis, we also employ measures of
the political institutional control variables and the dependent variable from Golder (2005). Note
that Stoll’s measure of raw dimensionality is the only existing quantitative measure of this abstract
concept, as discussed in an earlier section.

Our cases consist of all minimally democratic, national

legislative elections as coded by Przeworski, Alvarez, Cheibub, and Limongi (2000) and updated by
Golder (2005) that are included in the CMP.

The resulting data set spans twenty-four advanced

industrial democracies and the time period from 1945 to 1998. Between seven and twenty-two (on
average, fourteen) elections are observed per country for a total of three hundred and forty-six
legislative elections, all of which are fully observed. The structure of the data set is accordingly
extremely non-rectangular and somewhere between time series cross-sectional and panel.

Alter-

natively, it can be viewed as multi-level (see, for example, Franzese 2005) with elections nested
within countries. Descriptive statistics for the variables are shown below in Table 1.

Table 1 about here.

Empirical Analysis

We initially present some suggestive cross-national evidence in Table 2. Averages are taken over
the entire post-war period. Note that we employ the eﬀective number of electoral parties instead
of electoral fractionalization in this table due to the former’s greater interpretability.

Table 2 about here.

The eﬀective number of electoral parties increases as one moves down the rows, supporting the
hypothesis that restrictive electoral systems encourage coordination. Further, the relationship be-
tween the raw dimensionality and the eﬀective number of electoral parties seems to depend upon

Note also that the only other time series cross-sectional measure of dimensionality, regardless of type, is Nyblade’s

(2004). Lijphart’s measures are solely cross-sectional.

A list of these countries and time periods can be found in the Appendix. Exceptions include Italy 1946; Luxem-

bourg 1945–51; and Portugal 1975, which are included in the CMP but excluded by Golder (2005). The exclusion of
the Portuguese and Italian elections are likely on democratic grounds and the Luxembourgian because the ﬁrst three
post-war elections were not national. Note that we include four minimally democratic elections from the CMP that
do not appear in Golder’s data set for the simple reason that his data begins in 1946: Denmark 1945; Finland 1945;
Norway 1945; and the United Kingdom 1945.

Time series cross-sectional data has T >> N and the asymptotics in T while panel data conversely has N >> T

and the asymptotics in N (Beck and Katz 1995). Our data set has max T = 22 and N = 24. The asymptotics are
arguably in T , which suggests viewing it as time series cross-sectional in structure; however, the fact that we have
T < N suggests viewing it as panel in structure. We lean towards the former, which eﬀectively rules out the use
of a random eﬀects model: in this case, inferences are best viewed as conditional on the set of cross-sectional units
studied, here the observed advanced industrial democracies. See Beck and Katz (1996).