Does Female Suffrage Increase Public Support for Government Spending?
Evidence from Swiss Ballots
Katharina E. Hofer ∗
University of St.Gallen
November 30, 2016
Abstract
Do men and women have distinct preferences over the size of governments, as previous literature
seems to suggest? To answer this question, I exploit Swiss referendums concerning the federal
government’s authorization to levy taxes. A comparison of two similar referendums before and
after the female suffrage extension in 1971 reveals that women did not vote more liberally on
fiscal issues than men.
A mediation analysis allows to evaluate the influence of economic mediators with large
gender gaps like employment and income on gender preferences, using post-ballot surveys after
comparable votes taken between 1981 and 2004. Women vote more conservatively than men, and
mediators have little explanatory power for the gender preference gap. Intrinsic or unobserved
gender differences prove to be the driving force for preferences. The results help explain why
female suffrage has led to lower government spending in many countries, despite a poorer median
voter who could have been expected to prefer more redistribution and more public spending.
Keywords: Female suffrage; Gender preference gaps; Government spending; Direct democracy; Mediation
JEL Classification Numbers: J16, H10, D72
∗
Katharina E. Hofer, SEW-HSG University of St.Gallen, Switzerland, [email protected]. For valuable
comments, I thank Monika Bütler, Patricia Funk, Martin Huber, and Alois Stutzer, as well as participants at the
Meeting of the European Public Choice Society (2013, Zurich, Switzerland), Spring Meeting of Young Economists
(2013, Aarhus, Denmark), European Political Science Association Annual Meeting (2013, Barcelona, Spain), CESifo
Venice Summer Institute (2013, Venice, Italy), European Economic Association Congress (2013, Gothenburg, Sweden), Jahrestagung Verein für Socialpolitik (2013, Düsseldorf, Germany), Swiss Society for Economics and Statistics
(2015, Basel, Switzerland), Workshop on Direct Democracy (2016, Berlin, Germany), Workshop on Uncovering Causal
Mechanisms (2016, Munich, Germany) and seminar participants at the University of St.Gallen (2016). I appreciate
helpful input by the following discussants at conferences and workshops: Luna Bellani, Andreas Bernecker, Krisztina
Kis-Katos, and Silke Übelmesser.
1
Introduction
The relation between female suffrage and fiscal outcomes has been investigated extensively. Several
studies document an expansion of government activities once women were given the right to vote.
Analyzing historical data from the U.S., Lott and Kenny (1999) find that the introduction of female
suffrage increased government spending and revenues as gradually more women made use of their
voting rights. Similarly, Abrams and Settle (1999) find that Swiss federal government spending grew
by about 12% after the introduction of female suffrage in 1971. Bertocchi (2011) provides empirical
support that allowing women to vote increases government spending, however, only in non-Catholic
countries in which the cost of disenfranchisement is relatively high. While this research supports
the view of larger governments following the extension of suffrage to women, the general account
in the literature is mixed at best.
A negative connection between female voting and fiscal outcomes has been shown by a stream
of the literature. Stutzer and Kienast (2005) who use the variation in the timing of female suffrage
in Swiss cantons find that government expenditures at cantonal level decreased after enfranchising
women. In a similar vein, Krogstrup and Wälti (2011) observe reduced cantonal budget deficits
after female suffrage. Aidt and Jensen (2009) find lower government spending and tax revenues as
shares of GDP for western European countries after women got voting rights. Aidt, Dutta, and
Loukoianova (2006) provide only weak evidence for any impact of female suffrage on government
spending.
A common explanation for the expansion of governments following female franchise comes from
Meltzer and Richard (1981). They famously hypothesized that enfranchising constituents such
that the new decisive voter is poorer than before, increases the demand for redistribution and thus
the size of government. Since women have on average lower wages than men, this theory predicts
stronger female than male preferences for government spending.1 An alternative explanation for a
positive effect concentrates on women’s role as mothers. In marriage, husbands tend to earn more
and transfer income to their wives who specialize in household production and child care (Becker
1974). While income differences and specialization are internalized in marriage, the possibility of
divorce, however, makes women economically vulnerable if rendered to solely care for the children.
Historically increasing divorce rates then lead to higher demand for insurance from the state in
form of government spending (Edlund and Pande 2002).
Explaining the result of decreasing government spending turns out to be more challenging.
Potentially, women have stronger preferences for only some of the budgetary items but feel less
strongly about other government spending categories. For example, Aidt, Dutta, and Loukoianova
(2006) find that female voting increased spending on health, welfare and education. Aidt and
Dallal (2008) report rising social spending out of GDP for six western European countries. Miller
(2008) documents rising levels of public health expenditure to enhance child welfare that can be
1
E.g., in Switzerland women earned 51% of the male hourly wage in 1930, 66% in 1971 and 67% in 1995, which is
a seizable gender wage gap despite its tendency to decrease over time (Swiss Economic and Social History Online
Database).
1
attributed to the enfranchisement of women. When women started to vote, many government
budgets were still dominated by military or infrastructure expenditure, while items women care
for were still underrepresented. Aidt and Jensen (2009) argue that the immediate effect of female
franchise might differ from the long-run effect if it took time for women to exercise their franchise.2
Or women take fiscally more conservative decisions due to their preferences which might differ
from what men want.3 The wealth of alternative – and sometimes opposing – interpretations
demonstrates the need for a more in-depth analysis of the causal relation between female suffrage
and government size.
The goal of this paper is to determine whether differences in gender preferences for government
spending exist and what their determinants are. This could help explain why fiscal variables
changed when women received voting rights. In particular, it is interesting to investigate whether
such a gender preference gap is due to “being female” or can be explained by observable economic
differences between men and women. For example, Husted and Kenny (1997) find that enfranchising
poorer men by the repeal of literacy tests and poll taxes in the U.S. has led to higher welfare
spending, indicating that potentially not only the gender of the new franchise matters.
I exploit the voting outcomes of referendums laying down the constitutional basis for the Swiss
government to levy income, capital and goods turnover taxes. They are a measure of preferences
for the federal government’s spending: without popular approval at the ballot, the Swiss government would be deprived of its authorization to levy federal taxes which are crucial for financing
government expenditures. While taxation of income and consumption is commonly found all over
the world, it is a Swiss particularity that voters even nowadays need to accept it’s legislative basis
in a referendum every few years. Therefore, over time a large number of comparable votes on the
federal financial system exists.
Economic gender gaps were pronounced in terms of employment and income at the time women
received voting rights. If they were a driving force behind the gender preference gap, this gap should
be expected to decrease over time simultaneously with closing socioeconomic gender gaps. If in
contrast time-invariant differences between men and women are relevant for spending preferences,
the preference gap should more likely persist over time.
Surveys did not exist when women received voting rights, calling for a different approach. The
average gender preference gap at the time of female suffrage extension is estimated by using the
voting outcomes of two such very similar referendums. The first one took place in November 1970
shortly before the extension of suffrage to women in 1971, and the other one directly thereafter.
Since the two ballots took place under two distinct suffrage regimes, changes in voting outcomes
can be attributed to changes in the electorate. Using voting data at municipal level, I estimate
female support by relating changes in the number of voters to changes in the number of yes votes.
I refine the estimation by taking into account the share of women in municipal populations.
2
3
Aidt and Dallal (2008) and Lott and Kenny (1999) provide some support for this argument.
Stutzer and Kienast (2005) provide an institutional interpretation for lower spending growth in Swiss cantons: the
effect might stem from the existence of direct democracy instruments in Swiss cantons for which research shows that
they are likely to lead to smaller government size (e.g., Feld and Matsusaka (2003) provide some evidence).
2
Though very similar, the two ballot propositions are not identical but differ in so far that
the second proposition included a time limit. Even in case of acceptance the second proposition
would have required a new referendum after 10 years whereas the first one did not. Traditionally,
permanent federal financial orders have been rejected in Switzerland, suggesting that the inclusion
of a time limit is an important factor influencing voter decisions. I use voting results from a similar
ballot in 1963 under the men-only suffrage to proxy for the difference in the content of the two
ballots which might have induced some men to change their vote choice between the two ballots. I
provide extensive evidence for the validation of this approximation.
Results show that women were not more likely to support the referendums measure than men.
In some specifications women even vote fiscally more conservatively. Notwithstanding seizable
economic gender gaps which would have predicted a positive gender preference gap, women were
as (or even less) supportive of the fiscal referendum than men. Potentially, individual economic
factors are less important determinants for fiscal preferences. In theory, it is also possible that
economic and intrinsic gender gaps offset each other, leading to a zero or insignificant gender gap.
A mediation analysis allows to disentangle the total gender gap into its mediated and residual
components using individual-level data from randomized post-ballot surveys after four comparable
referendums about the federal fiscal order in 1981, 1991, 1993 and 2004. As argued above, being
female is generally related to lower employment and income, which in turn affects preferences for
government spending. These variables are called mediators. At the same time, other potentially
intrinsically female factors might influence gender support. To decompose both potential channels, I semi-parametrically estimate the direct and indirect effects of being female in a mediation
framework. Estimates are based on inverse propensity score weighting, which allows to control for
potentially confounding factors affecting both mediators and the outcome variable (Huber 2014,
2015; Imai, Keele, and Yamamoto 2010).
The mediation results substantiate that women are on average less likely to support the taxation
propositions even well after the original extension of voting rights to women. Surprisingly, there is
no evidence for a mediated effect through employment or income at any point in time. Economic
gender gaps cannot explain different gender preference neither at times when these gaps were still
considerable nor later on. The direct or residual effect (i.e., unexplained by the mediator) in contrast
is important for explaining the gender preference gap. This result fits the persistently non-positive
difference in gender support for the referendums. Candidate direct effects are gender differences
in time preferences or altruism. An extensive sensitivity analysis validates that relatively large
departures from the identifying assumptions could be accepted without changing the conclusions.
This paper adds to the literature on the effects of franchise extension on government spending.
The main contribution is to provide a direct way of eliciting the gender preference gap for government spending from results of referendum votes instead of relating suffrage to government spending.
Direct democratic votes are better suited to make statements about preferences than macroeconomic outcomes since they involve decision-making by the franchise. Moreover, preferences can be
measured at the time of a vote, whereas it takes time until female preferences start materializing
and lead to changes in spending. My approach is related to Funk and Gathmann (2015) who
3
utilize post-ballot polls in Switzerland for the analysis of gender preference gaps regarding specific
spending items.
This paper extends research on consequences of female representation for policy making (e.g.,
Chattopadhyay and Duflo 2004). The mechanism behind the relation between female voting and
aggregate fiscal outcomes potentially runs through changed politicians’ behavior. They either adjust
their policies, or women elect new politicians (possibly female ones).4 E.g., Svaleryd (2009) finds
that higher shares of women in Swedish local councils lead to more expenditures on child-related
items compared to spending for the old. The advantage of using referendum outcomes is that
voters are the ultimate decision-makers in the direct democratic process. Their preferences lead
to immediate policy consequences. It allows me to go a step further and investigate the causal
mechanism behind gender preferences, in particular, the role of economic discrepancies for fiscal
preferences which was traditionally expected in the literature.
The remainder of the paper is organized as follows. Section 2 provides information on the
institutional setting. Section 3 contains the empirical framework, data and results for the estimation
of the average gender effect around the enfranchisement of women in Switzerland. In a similar
manner, Section 4 deals with estimating the direct and indirect gender effect. The concluding
remarks are in Section 5.
2
Institutional Setup
Beginning with the foundation of the Swiss state in 1848, duties were the main revenue source at
federal level.5 It took until the First World War, collapsing international trade and growing state
expenditure before an income tax was introduced. But income was only taxed in times of need such
as during the war, or when budgetary problems got out of hand in the 1930ies. In 1941 a defense
tax, the Wehrsteuer (an income and capital tax; referred to as direct federal tax in what follows),
was introduced to finance growing military expenditure. In the same year, a goods turnover tax
(Warenumsatzsteuer) was introduced on goods but not on services, resembling a value-added tax
(Stockar 2007). Both taxes were a product of an increased need of state revenue during war and
emergency times.
After the Second World War both taxes remained in place. Besides revenues from duties, the
goods turnover tax and the direct federal tax were the most important revenue sources for the
Swiss government. In the 1960ies, roughly 10 to 15% of revenues came from the direct federal
tax, and around 25% from the goods turnover tax. Revenues from duties then dropped by 10
percentage points (Swiss Statistical Office 1973). The main reason for the decline was the increasing
international integration and the general trend to reducing duties in connection with the World
4
Lott and Kenny (1999) also look at the politicians’ voting behavior in the U.S. senate and find that after the
introduction of female suffrage politicians voted more liberally. However, they do not show that women were more
likely to vote for liberal politicians and did so because they desired higher government spending.
5
Information about the history of the Swiss Federal Tax are from Grütter (1968). Oechslin (1967) gives an overview
of the overall development of the Swiss tax system.
4
Trade Organization’s rounds (Federal Announcement 1969 II, 754).6
The main items of expenditure at federal level were defense and the social security system which
together accounted for nearly 50% of total expenses. Other growing and new expenditure categories
were infrastructure and energy, as well as culture and sports. Agricultural expenditure remained
relatively stable at around 10% of total expenditure (Swiss Statistical Office 1974).
Due to the initially provisional and time-restricted character of taxation it lacked a permanent
constitutional basis, without which the federal government would not have had the right to continue
levying federal taxes. In Switzerland, all changes to the constitution are subject to a mandatory
referendum (Linder 2007). For a referendum to be successful, the majority of voters and a majority
of cantons is required. Table 1 provides an overview of the wealth of ballots concerning the federal
government’s admission to file taxes. Next to the date and outcome of the vote, it reports the
time frame of the ballot proposition. Either the constitutional article was time limited, triggering
the next referendum within several years. Alternatively the proposition was for a permanent
constitutional article. All time-limited propositions were accepted by voters, whereas the permanent
orders always failed at ballot. Even nowadays, it thus remains a Swiss particularity that citizens
Table 1
Chronology of Swiss Federal Financial Order Referendums
Ballot date
Time limit
Decision
% yes votes
Accepting cantons
06.12.1953
24.10.1954
11.05.1958
08.12.1963
15.11.1970
06.06.1971
12.06.1977
20.05.1979
29.11.1981
02.06.1991
28.11.1993
28.11.2004
permanent
1955 - 1958
1959 - 1964
1964 - 1974
permanent
1972-1982
permanent
permanent
1982-1994
permanent
1994-2006
2006-2020
rejected
approved
approved
approved
rejected
approved
rejected
rejected
approved
rejected
approved
approved
42.0
70.0
54.6
77.6
55.4
72.7
40.5
34.6
69.0
45.6
66.7
73.8
3
21
17 1/2
22
10
22
1
0
23
2 1/2
22
22
Data about acceptance are available on the homepage of the Swiss Federal Chancellery, http://www.bk.admin.ch. The time limits are from Federal Announcements published by the Swiss Federal Archive (cf. Appendix A).
For approval, the referendum needs more than half of total votes and at least
13 accepting cantons. In 1971, 19 cantons are “full” cantons while six cantons
count only as “half” cantons. Since 1978, there are 20 “full” cantons, and still
six “half” cantons. Votes from 1970, 1971, 1981, 1991, 1993, and 2004 are used
in the empirical part.
6
All Federal Announcements (Bundesblatt) are collected by the Swiss Federal Archive (Schweizerisches Bundesarchiv)
and published by the Federal Chancellery (Bundeskanzlei). A detailed list and possibility of online access is described
in the Appendix A.
5
have to approve the federal financial order.
In 1953 the parliament issued the very first proposition for permanently including the direct
federal tax and the goods turnover tax in a constitutional article. It was rejected. Only one
year later, a similar proposition but this time with a limit of four years was put to the vote, and
eventually approved by a majority of voters. It was followed by another temporary financial order
from 1959 to 1964,7 and extended by further ten years with some minor changes in 1963 (Federal
Announcement 1962 I, 997).
The first of the two ballots at the core of this paper’s analysis took place on 15 November,
1970, and the second referendum with a new franchise on 6 June, 1971: Switzerland was the last
European country to grant women voting rights at federal level on 7 February, 1971. It came into
force on 16 March, 1971 as a result of a century-long fight for women’s rights. Particularly in
the aftermath of both world wars when democratization was spreading all across Europe, Swiss
women were demanding suffrage more intensively. They received support from male politicians
who recognized that the women’s position in society had changed to a more active role in public
live and private employment (Ruckstuhl 1986). However, in Switzerland female suffrage could only
be brought about by a constitutional amendment, which required the male population to hold a
vote on extending the franchise. While at a first ballot in 1959 female suffrage was rejected with
66.9% of the male votes,8 a second run in 1971 saw the majority of voters and majority of cantons
accepting the constitutional amendment.
The next paragraphs describe the propositions on government spending from 1970 / 1971 and
1981-2004 in more detail.
Ballot proposition 1: 15 November 1970
The government and parliament proposed to discard the time limit from the constitution in the
“Federal Enactment about the Amendment of the Federation’s Financial Order”9 (Federal Announcement 1969 II, 749). Facing a big budget deficit, income, capital and goods turnover taxes
would be increased and old rebates reduced in the 1970 proposition. In more detail, the tax burden
would be shifted from the direct income tax to the indirect goods turnover tax such that revenue
from the goods turnover tax would increase considerably and revenue from income taxes would
stay roughly constant. The enactment encompassed higher goods turnover taxes for retailers (from
3.6 to 4 percent), and for wholesalers (from 5.4 to 6 percent). The income tax set in progressively
at an annual income of 8,500 Swiss Francs after deductions (7,700 Swiss Francs before). It allowed
for deductions for married couples (2,500 Swiss Francs), children under 18 years and dependents
(1,200 Swiss Francs) (Federal Announcement 1970 II, 3). Regarding the income tax, high income
households would be worse off with the new regulation than low income households because of
7
The comparably low acceptance rate of this financial order with time limit compared to other time-limited proposition
is most likely due to a heated debate of the large interest groups (Bolliger 2010).
8
Only three francophone cantons, Geneva (60.0%), Neuenburg (52.2%), and Waadt (51.3%) had a majority favoring universal suffrage. They were also the first three cantons to introduce universal cantonal suffrage which is
independent of federal voting rights in Switzerland.
9
The original German title is “Bundesbeschluss über die Änderung der Finanzordnung des Bundes”.
6
a more progressive system. Married couples or families with many children would be better off
compared with the old regulation.
The government argued that an increase in goods turnover taxes to generate state revenue was
the preferable revenue source: it was not a typical consumption tax because of various exemptions
for goods of daily use like food. It mainly taxed investment goods purchased by firms and the
government, in addition to goods like alcohol, tobacco, and clothing purchased by households
(Federal Announcement 1969 II, 778). Though presumably the biggest load would be paid by
enterprises, there seemed to be a general uncertainty about who would carry the burden of the
higher goods turnover tax.
Critics of the proposition mostly pointed to an unsatisfactory regulation concerning the Swiss
cantons (Année Politique Suisse 2012). In particular it lacked a clear division of revenue and
expenditures between the federal government and the cantons because direct income taxes were an
important revenue source for cantons and municipalities (Federal Announcement 1969 II, 773).
All major parties, associations and unions recommended their voters to accept the proposition.
Exceptions were the small Liberal Party of Switzerland (LPS), and the Labor Party (PdA) who
opposed the proposition for not being progressive enough (Année Politique Suisse 2012). These
almost unanimously positive voting recommendations indicate the importance of the issue at stake.
On 15 November 1970 the Swiss voters – which was the male eligible population at that point
– rejected the proposition in a mandatory referendum. Though 55.4% of the voters were in favor
the proposition, it failed to accomplish a majority of cantons: in 13 of 22 cantons the approval rate
was below 50 percent. Figure 1 shows the approving (white) and rejecting (grey) cantons. The
rejecting cantons were mainly concentrated in rural, German-speaking areas.
Figure 1: Cantonal Approval for Ballot 1 (15 November, 1970)
Note: Cantonal Approval Rates for Fiscal Financial Referendum for Ballot 1 (15 November 1970).
Accepting (white) and rejecting (grey) cantons. Based on swissvotes.ch, a project of the Institute
of Political Science at the University of Bern, Switzerland, and the Année Politique Suisse.
7
Ballot proposition 2: 6 June, 1971
The Swiss government immediately prepared a new proposition10 to secure the flow of government
revenues (Federal Announcement 1970 II, 1581). In the major parts, the new proposition was
identical to the one from 1970.11 The most significant change was the inclusion of a time limit of
10 years (Federal Announcement 1971 I, 487). Even in case of approval at the polls, the federal
financial order had to be voted upon again in 1980 at the latest. As a further change, income
tax ceilings of 9.5 percent for natural persons and 8 percent for legal persons were included. The
income tax schedule became slightly more progressive and started to tax individuals at incomes
after deductions of 9,000 Swiss Francs. These measures were taken to account for price inflation.
As in the first proposition, the parties and associations almost unanimously asked the voters to
accept the proposition in their voting recommendations. Only the Labor Party (PdA), the Swiss
Evangelic Party (EVP), and the Alliance of Independents (LdU) were opposed to the proposition because it disregarded deductions for working wives and was not progressive enough (Année
Politique Suisse 2012).
The ballot proposition was accepted by a majority of voters (72.7%) and all cantons – with
universal suffrage.
Ballot propositions in 1981, 1991, 1993, and 2004
The votes in 1981, 1991, 1993, and 2004 are used to decompose the total gender preference gap into
its mediated and residual components. The fiscal order approved by voters in 1971 was about to
phase out in 1982. Both referendums in 1977 and 1979 which tried to change the tax system from
the goods turnover tax as explained above to a permanent fiscal order with value added tax (VAT)
similar to other European countries were rejected at ballot. The financial order voted in 1981 and
limited to the years 1982 to 1994 was therefore essentially a continuation of the old financial order
from 1971. Minor changes included reliefs in the direct income tax which had to be compensated
by increases in the goods turnover tax (Federal Announcement 1981 I, 20). In 1991 government
and parliament tried again to switch from goods turnover taxes to the VAT. Again, the proposition
was rejected at ballot. It was argued that the proposition might have been a too complex package,
which led to the rejection. Two years later a new financial order in a less complex proposition
finally brought about the change to the VAT system, and secured the fiscal fundament for the
federal state until 2006 (Année Politique Suisse 2012). The 2004 vote secured the government’s tax
power until 2020.
10
“Federal Enactment about the Continuation of the Federation’s Financial Order”. Original title in German is
“Bundesbeschluss über die Weiterführung der Finanzordnung des Bundes”
11
Comparing the precise wording of both original legislative texts shows that they are almost identical in all paragraphs.
8
3
Average Gender Preference Gap for Government Spending
3.1
Baseline Empirical Framework
The aim is to estimate approval for government spending by gender at the time of franchise extension. I first introduce the notation. A finite population is divided into two groups G, with the
realizations g = 1 (female) and g = 0 (male). For each individual, outcome Y (g) is observed and
takes on value 1 for supporters of government spending, and 0 else. It is a function of gender.
Relating the outcomes to referendum votes, supporters vote “yes” whereas opponents vote “no”.
The total effect τ of being female on the probability of supporting government spending is the
average treatment effect (ATE). It is the difference in expected support for government spending
between women and men. When averaging over the entire population, it can be written in the
following way using expected values:
τ = E[Y (1)] − E[Y (0)]
(1)
Positive values of (1) point to stronger female than male preferences for government spending, and
the opposite for negative values. If the effect were zero, no gender preference gap existed. The
empirical counterpart of E[Y (1)] is the female acceptance rate and E[Y (0)] the male acceptance
rate. Since the observed total acceptance rate can be written as the gender turnout-weighted sum
of female and male acceptance rates, it is enough to estimate the acceptance rate of women from
which the ATE follows immediately.
3.2
Estimation Strategy: Identifying the Total Gender Effect
To estimate the female acceptance rate, I follow the idea of Lott and Kenny (1999) who recognize
that the effect of female suffrage on voting outcomes depends on how intensely women make use of
their voting rights. The intuition is that changes in voting outcomes can be explained by changes
in the electorate’s composition. I use the voting results of the two Swiss referendum ballots in 1970
and 1971. As explained above they are very similar content-wise, but women were only allowed to
vote on the second date.
What makes the analysis more complicated is the fact that the ballots are not entirely identical.
They mainly differ with regard to a time limit of ten years in the second proposition. As explained
above, propositions regarding the federal financial order including time limits have also been approved by the male voting population, like in 1954, 1958, and 1963. Some men can consequently
be expected to change from voting no to yes instead. To account for the change in content, I use
voting results of the related vote in 1963 which also included a time limit and was accepted by a
large margin (cf. Table 1). Denote the true number of men who have switched from voting no to
voting yes in municipality m by ∆menm . It is approximated by a variable ∆men
d m and the error
term m . ∆menm is the difference between the number of yes votes in the years 1963 and 1970
normalized by the growth rate of the number of voters during the seven year difference. Then the
9
true number of men changing their voting behavior can be written in the following way.
∆menm = ∆men
d m + m
votersm1970
− yesm1970 + m
= yesm1963 ∗
votersm1963
(2)
(3)
Let acceptancef be the female acceptance rate for the second ballot proposition. For notational
ease, denote the year 1970 by t = 1, and 1971 by t = 2. Define the change in the number of yes
votes between the ballots in municipality m as ∆yesm ≡ yesm2 − yesm1 , and the change in the
number of valid votes as ∆votersm ≡ votersm2 − votersm1 . The female acceptance rate can be
written in the following form:
acceptancef =
∆yesm − ∆menm
∆votersm
(4)
Female acceptance is the change in the number of yes votes relative to the change in the electorate,
net of the change in male voting behavior where ∆menm is defined in (3). Equation (4) can be
easily transformed to
∆yesm − ∆menm = acceptancef ∗ ∆votersm
(5)
In the last step, I use Equation (3) to account for the approximation of men changing their voting
behavior. This leads directly to the baseline estimation equation.
∆yesm − ∆men
d m = β1 ∆votersm + m
(6)
Equation (6) is a first difference equation at municipal level. The dependent variable is the change
in the number of yes votes net of the number of men switching from voting no to yes. The
independent variable is the change in the number of voters. It measures the number of women
voting as I will argue below. β1 then identifies the female acceptance rate acceptancef under
the exogeneity assumption E(∆voters0m m ) = 0. I will discuss the identifying assumptions and
potential bias in the next section.
3.3
Identifying Assumptions
The validity of the above estimation equation is based on two identifying assumptions. The first
one concerns the independent variable ∆votersm measuring the change in the number of voters
between the ballots in 1970 and 1971. The main above argument was that the change in the number
of voters is connected to the female franchise and thus reflects the number of female voters. I will
now discuss the direction of bias if men changed their participation rate between the ballots and
potential sources of bias.
The direction of the bias depends on whether men decrease or increase participation. If men
decreased their participation, the observed ∆votersm would be smaller than the true number of
women voting. Estimating (4) would consequently yield an upward-biased coefficient and suggest
10
a too high female acceptance rate. The gender gap defined as the difference between female and
male preferences would also be upward-biased. The opposite would be true, if men increased
their participation: fewer women than suggested by the measure ∆votersm would vote leading
to downward-biased estimates of the average female acceptance rate and the gender gap. With
constant male participation no bias would occur, since ∆votersm would precisely measure the
number of women voting.
Anticipating the main result of a non-negative gender preference gap, the relevant case to be
ruled out is a positive turnout response of the male population (because more male turnout leads
to a downward-biased gender gap). The first assumption is thus:
Assumption 1 Men are not more likely to participate in ballot 2 than in ballot 1.
Changes of the male participation rate could be expected for two reasons: first, the inclusion of a
time limit, and second, as a reaction to female voting.
To get evidence for the male turnout reaction due to the time limit, I compare turnout for the
two ballots in 1953 and 1954. Both were held under male suffrage. The 1953 vote without time
limit was highly contested. 60.27% of the male eligible population turned out. In contrast, the less
disputed proposition including a time limit in 1954, drew only 46.77% of eligible men to the polls.12
Hence, the time limit itself is unlikely to induce higher male participation but could potentially
even decrease it.
There is no unambiguous expectation regarding the participation reaction of men to female
voting. On the one hand, male participation might decrease since the marginal benefit to vote is
reduced when the electorate roughly doubles. On the other hand, if men expect female preferences
to differ from their preferred outcome, they might increase turnout as a strategic response.
To explain away a negative gender gap by a male participation response, in addition, a low female
participation would be required. Ballot 2 is the first federal voting date after the introduction of
female suffrage on which voters decided on two bills.13 Women may not have made use of their
new rights immediately but have gradually grown accustomed to exercising the franchise.
Figure 2 provides evidence on the female usage of voting rights in Swiss parliamentary elections.
The x-axis shows the election year t before and after the introduction of female suffrage in 1971.
The number of voters as share of the Swiss adult population participationt = 100 × voterst /adultst
is depicted on the y-axis.14 The fraction of voters as compared to the total adult population was
steadily decreasing before the introduction of female suffrage. The participation rate almost doubles
in the 1971 election with universal suffrage. Afterwards the participation rate has a decreasing trend
12
Turnout on a particular day is influenced by all votes on the ballot list. On the ballot day in 1954 there were no
other federal votes, so turnout was truly for the vote under investigation. On the ballot day in 1953 there was one
additional federal vote about the protection of waters. It received a smaller turnout than the other vote and was
thus unlikely the main reason to turn out on that day.
13
The other proposition was about the protection of humans and their environment.
14
It is preferable to depict participation in election than in referendums since the latter varies a lot which might be
due to the importance of an issue or campaigning effects. I take the total number of Swiss people above 20 years
old from Swiss censuses in 1950, 1960, and 1970, and interpolate the numbers for the inter-census years. The data
are from the Swiss Statistical Office. Since 1971 eligiblet can be directly used from official election data.
11
50
40
30
Participation in %
60
Figure 2: Participation Rate in %
1955
1963
1971
1979
1987
Election
Note: Participation rate in % (100 × voterst / Swiss adult populationt ) for Swiss federal parliamentary elections over time. Without female suffrage (1951-1967) and with female suffrage (since
1971). Data are from the Swiss Statistical Office.
again. This contrasts with the observation of Lott and Kenny (1999) who show that the turnout
rate in the U.S. continued increasing many years after the introduction of female suffrage. Thus
on average women in Switzerland made use of their voting rights relatively quickly. This is not
surprising since female suffrage was introduced relatively late in history. The timing coincides with
higher education levels among women than in countries that enfranchised women around the first
world war. Also, in some cantons women have received female voting rights for cantonal votes
independently of federal voting rights such that they have gathered some voting experience even
before 1971.
The institutional setup allows for a robustness check regarding the number of women voting
for a subset of observations. On the day of the second vote, June 6, 1971, 11 cantons had no
female suffrage for cantonal votes. Women in these cantons were thus allowed to vote on federal
measures but not on cantonal ones. Of these eleven cantons, five held concurrent cantonal votes
on 6 June, 1971, and for three of them data from 269 municipalities are available.15 The voters for
the cantonal referendums correspond to the number of men voting, whereas federal voters are the
sum of men and women voting. Assuming no male roll-off between cantonal and federal votes, the
number of women voting follows from the difference between voters on the federal and the cantonal
vote. I call this the true number of women. Figure 3 plots the true number of women on the x-axis
and the estimated one (∆votersm ≡ voters2m − voters1m ) on the y-axis. Most of the observations
are close to the 45-degree line, indicating that both numbers are similar. On average, the true
number of women voting exceeds the estimated one by -2.5 voters. This check thus suggests that
the independent variable is a good measure of female voting. If there was a bias, then female voting
15
These were the cantons Graubünden, Schwyz, and Uri (data available) and Bern and Thurgau (no municipal data).
Data were collected from the Swiss National Library in Bern.
12
0
1000
Delta voters
2000
3000
4000
Figure 3: Female Voters
0
1000
2000
3000
Federal-cantonal voters
4000
Note: Robustness check for independent variable. Subsample of 269 municipalities from cantons
without cantonal female suffrage and cantonal referendums taking place on 6 June, 1971. The yaxis shows the independent variable. The x-axis shows the difference in voters between the federal
(women voting) and cantonal (women not voting) ballot.
would be underestimated and male voting consequently overestimated, which is no threat to the
identification strategy. In sum, the above evidence supports Assumption 1.
The second identifying assumption relates to the change in content regarding the time limit
restriction. The number of men voting yes instead of no because of the time limit, ∆menm , is
proxied with voting results from 1963 as stated in equation (3). The validity of the proxy requires
relatively time-constant fiscal preferences between 1963 and 1970. Results could be biased if more
or less men changed their voting behavior than captured by the proxy. If more men switched to
voting yes, my dependent variable ∆yesm − ∆men
d m would be larger than it should. An upwardbiased female acceptance rate and gender gap would be the consequence. The reverse holds in the
eventuality of smaller male support. Again, in light of a estimated non-negative gender preferences
gap the case to be argued against is fewer switchers from voting no to voting yes than captured by
the proxy.
Assumption 2 Men who have approved of the first proposition should also be in favor of the second
one which includes a time limit and is thus less radical. The inclusion of the time limit in the second
ballot proposition makes some men switch from rejecting to approving.
One argument presumably speaking against constant male preferences between 1963 and 1971 is
the rejection of female suffrage in a 1959 referendum followed by its acceptance in 1971. The (male)
public opinion regarding female voting turned from decided rejection (33.1% yes share) to decided
acceptance (65.7% yes share) suggesting a liberalization of preferences. However, this seems to go
against evidence regarding the federal financial order. Even after female suffrage, all three votes
trying to implement a permanent constitutional article (1977, 1979, 1991) were rejected. The Swiss
13
seem to have a – virtually time-invariant – preference for not granting the government permanent
tax powers.
To substantiate this claim, I again provide evidence from the two comparable ballots on the
federal financial order in 1953 and 1954. Recall, the first one had no time limit and was rejected,
while the second one had a time limit and was approved. The population-weighted average difference
in approval rates for the two propositions was 27.7 percentage points, which is substantial, and
similar to the difference between 1963 and 1970 amounting to 29.8 percentage points. A t-test of
both differences is highly significant. Because preferences between 1953 and 1954 can be assumed
time constant, the comparison shows that the inclusion of a time limit is indeed responsible for
higher acceptance rates among the male population. Theoretically, some men might have radical
preferences and vote against the second proposition even though they supported the first one to
protest and signal dissatisfaction. However, based on the supporting evidence from past ballots
that including a time limit on average increases voter support, this should rarely be the case.
3.4
Data
I collected a dataset of 2,109 Swiss municipalities with voting information for the relevant ballots
on November 15, 1970, June 6, 1971, and December 8, 1963. Voting results include the number
of yes and no votes, valid votes and eligible citizens. Data from the cantons of Aargau, Freiburg,
and Ticino are not available at municipal level. Instead I include the data from voting districts
which comprise several municipalities each for these three cantons adding 26 voting districts to the
dataset.16 For the canton Geneva, data are missing for the vote in 1963. Therefore, it is excluded
from the analysis. All voting data come from the Political Atlas of Switzerland provided by the
Swiss Statistical Office.
Since voting data come from ballots taken at different points in time, municipal mutations
need to be taken into account, because several municipalities merged during this time. Therefore,
Table 2: Descriptives of Voting Results from 1970 and 1971
Variable
Obs
Mean
Std. Dev.
Min
Max
% yes1970
% yes1971
∆yesm − ∆men
dm
∆votersm
2135
2135
2135
2135
46.95
73.15
188
277
17.43
10.67
862
1251
0
2.74
-115
-87
100
100
23678
33728
NOTE: Based on voting data from referendums on 28 November,
1970 and 6 June, 1971. Municipal data, district data in cantons of
Aargau, Freiburg and Ticino from the Political Atlas of Switzerland provided by the Swiss Statistical Office.
16
I have contacted the cantonal archives of the three cantons in question. For only 20 municipalities in the canton of
Freiburg complete voting data required for the estimation exist. Using district data is thus the only way to include
data from these cantons in the regressions.
14
I adjust the voting data such that all municipalities are comparable. Information on municipal
mergers comes from the online register of municipal mutations provided by the Swiss Statistical
Office.
Table 2 summarizes descriptive statistics of the main voting variables. It shows the increase
in acceptance rates from 46.95% in 1970 to 73.15% in 1971. The dependent variable indicates an
increase in yes votes by 188 after proxying for changed male preferences, and the change in voters
was 277 on average. I drop all observations for which the dependent and independent variable take
on negative values since they go against the intuition that suffrage extension led to more voters.17
3.5
Results: Average Treatment Effect
The female acceptance is estimated with a linear estimator and standard errors are clustered at
cantonal level to account for potential serial correlation of the error terms among municipalities.18
Table 3 shows the regression results based on the votes in 1970 and 1971. The first row reports the
gender preference gap, while the second one refers to the estimate of the female acceptance rate.
For the gender gap, I first calculate the male acceptance rate from the official voting result
which has to be the gender turnout-weighted sum of the male and female acceptance rates. The
gender gap is the difference of the gender acceptance rates. Standard errors are bootstrapped with
1,999 repetitions. Significance is evaluated with a one-sided test, which tests against a positive
gender preference gap that might have been expected from literature. I run different specifications
excluding municipalities with many inhabitants to account for potential outliers. On average, 1,630
Swiss adults lived in a municipality, and 75 percent of observations have less than 1,200 eligible
citizens. In specifications (2)-(5) municipalities with more than 50,000, 10,000, 2,000 and 1,000
inhabitants are dropped respectively. Excluding large municipalities technically means that data
from three cantons with district data are excluded, as well as cities.
Estimates of the female acceptance rate are highly significant. In the baseline specification (1)
with full sample the female acceptance rate amounts to 68.2%. It varies between 64.4% and 69.8%
in columns (1)-(5). Compared with the sample average acceptance rate of 73.2%, female support
is below the average. Estimates of the gender preference gap confirm negative values throughout
all specifications. In columns (2), (4) and (5) a positive gender gap can be rejected: women
are not more likely than men to support the federal fiscal order. In economic terms, the gender
gap is significant as well. It varies between -14.2 and -18.7 percentage points in the significant
specifications, which constitutes a seizable difference.
I refine the independent variable ∆votersm by multiplying it with the share of women in a
municipality. Intuitively, if there were no women in a municipality, female suffrage should not
have any effect on the change in voting. Conversely, if a municipality was populated by women
17
18
I run the regressions with all observations and the results are robust to the inclusion of all municipalities.
25 cantons is a relatively small number of clusters. However, Cameron, Gelbach, and Miller (2008) show that after
correcting for few clusters, hypotheses are accepted even more often. In their empirical analysis, Hodler, Lüchinger,
and Stutzer (2015) find the same for clustering with Swiss cantons.
15
exclusively, the change in voters would reflect the change in acceptance with certainty. I get
the share of Swiss adult women from the change in the number of eligible voters, %womenm =
(eligiblem2 − eligiblem1 )/eligiblem2 .19 The population-weighted average share of women in the
Swiss adult population amounts to 53.8%, but it varies between 0 and 72.2%. In total, 22 (11)
municipalities have shares below (above) the band of 40 to 60%. Municipalities with low shares
of Swiss adult women are located in 4 cantons Bern, Graubünden, Waadt, and Wallis, and have
only 89 inhabitants on average.20 Municipalities with high shares of Swiss women are located in
six cantons and have 812 Swiss adults on average. Most of the shares are, however, close to 60%
and thus not such big outliers. The regression equation is stated below. The female acceptance
b
c
rate can then be recovered by calculating acceptance
f = β3 ∗ %womenm .
∆yesm − ∆men
d m = β3 %womenm ∆votersm + m
(7)
Columns (6)-(10) show the results. In comparison to results in (1)-(5) the female acceptance rate
drops in all specifications (e.g., from 68.2% to 62.0% in column (1)). Consequently, the estimated
gender gap widens and a positive value is rejected in specifications (6), (7) and (9). In column (7)
the gender gap takes on the largest value of -28 percentage points which is significantly different
from zero.
Overall, the results provide evidence for a non-positive gender preference gap, and some weak
support for even a negative gender difference.21 The results show that the considerable economic
gender gaps in terms of labor force participation or income at the time when women started voting
cannot be the (only) driving forces behind differences in preferences. Otherwise, a positive value
would have been expected. At the same time, this evidence conforms with some of the findings in
the literature suggesting a drop in aggregate public spending with female voting. The non-positive
gender gap could result from counter-veiling factors offsetting each other, e.g., economic variables
and fiscal conservatism. It is thus interesting to study how the gender preference gap evolves over
time when economic gender gaps close to find out whether work-related outcomes can explain
differences in preferences.
19
The variable %womenm is calculated assuming away population growth between November 1970 and June 1971.
Bern, Graubünden, Vaud, and Vallais are the four largest cantons in terms of area, and encompass some of the
least densely inhabited regions in Switzerland.
21
Switzerland has a strong federal structure, so a substitution effect from federal to cantonal spending due to female
suffrage is of concern. Also, some “female” spending items like education mainly fall under the cantons’ responsibility. However, the results of Stutzer and Kienast (2005) suggest decreasing cantonal spending with female suffrage,
which speaks against a substitution effect.
20
16
Table 3: Results: Average Gender Preference Gap
17
Sample
(1)
All
(2)
<50,000
Average
(3)
<10,000
(4)
<2,000
(5)
<1,000
(6)
All
Gender
gap
-0.109
(0.113)
-0.187*
(0.128)
-0.077
(0.106)
-0.142*
(0.105)
-0.159*
(0.102)
0.682***
(0.026)
0.644***
(0.045)
0.698***
(0.023)
0.664***
(0.021)
0.983
1,926
0.968
1,920
0.973
1,878
0.961
1,651
Female
acceptance
Adj. R2
Obs.
Interacted with %womenm
(7)
(8)
(9)
<50,000 <10,000
<2,000
(10)
<1,000
-0.237*
(0.149)
-0.280**
(0.158)
-0.149
(0.134)
-0.176*
(0.134)
-0.176
(0.151)
0.658***
(0.020)
0.620***
(0.039)
0.598***
(0.075)
0.663***
(0.036)
0.648***
(0.033)
0.650***
(0.036)
0.950
1,369
0.985
1,926
0.970
1,920
0.977
1,878
0.960
1,651
0.941
1,369
One-sided test: * p<0.1, ** p<0.05, *** p<0.01. Based on voting data from referendums on 28 November, 1970 and 6 June, 1971.
First difference (FD) estimation for Female acceptance. The dependent variable is change in the number of yes votes net of men
changing from voting no to yes. The independent variable is the change in the number of voters. Canton-clustered standard errors
at cantonal level in brackets. Gender preference gap is calculated from the estimated female acceptance and the official voting result.
Standard errors for the gender preference gap are bootstrapped with 1,999 repetitions. Specifications vary by municipality size. In
(6)-(10) change in voters is multiplied with the municipal share of Swiss women.
4
Direct and Indirect Gender Effect on Government Spending
4.1
Mediation Framework
For the subsequent analysis, I sketch the framework that allows to identify the causes of gender
preference gaps for government spending. My focus is on evaluating whether (part of) the differences
in gender preferences can be explained by labor-related outcomes that are typically argued to affect
fiscal preferences and tend to vary by gender.
Gender affects the outcome support of spending Y via two different channels. First, the gender
effect on preferences is mediated through an economic variable (mediator) which is commonly
termed the indirect effect. In my study, employed individuals potentially prefer lower taxation and
less government spending than individuals not holding a paid occupation. However, employment
itself is a function of gender since women are on average less likely to work and more likely to
stay at home to care for children than men. Part of the gender effect on support for government
spending is thus mediated by employment status. The mediator is an observable M (g) and depends
on gender g. In the jargon of the mediation literature M (g) “lies on the causal path” from gender
to preferences, where gender marks the start of the causal chain (Baron and Kenny 1986; Imai
and Yamamoto 2013). The second channel is henceforth referred to as the direct effect which
encompasses all residual effects of gender on preferences with the exception of channels controlled
for by the mediator. It reflects intrinsic gender differences or unobserved mediators.
The outcome variable is a function of both gender and the mediating variable, Y (g, M (g)) such
that the total effect τ is:
τ = E[Y (1)] − E[Y (0)] = E[Y (1, M (1))] − E[Y (0, M (0))]
(8)
E [Y (1 , M (1 ))] and E [Y (0 , M (0 ))] are observable outcomes for women and men depending on
female and male employment respectively. Decomposition of the total effect is based on the potential
outcome framework (e.g., Rubin 2004). Note that potential outcome Y (g, M (1 − g)) is never
observed because for a particular individual gender is fixed at g and cannot be varied to 1 − g.
The indirect η(g) and direct δ(g) effects are defined as:
η(g) = E[Y (g, M (1))] − E[Y (g, M (0))]
(9)
δ(g) = E[Y (1, M (g))] − E[Y (0, M (g))]
(10)
The indirect effect in (9) captures the difference in expected outcomes when evaluating mediators
for both groups while keeping gender constant at g. More specifically, the indirect effect for women
η(1 ) = E [Y (1 , M (1 ))] − E [Y (1 , M (0 ))] compares preferences of women with expected female employment M (1 ) to potential female preferences under counterfactual male employment M (0 ). The
direct effect in (10) shows how expected outcomes change when comparing a woman to a man,
keeping the mediator constant at its value for g.
In this study, being female is the treatment. I discuss potential downsides of using an unchangeable characteristic as treatment variable later on. For identification, it is required that assignment
18
into treatment G is random, and mediator M is exogenous when conditioning on G (Huber 2015).
While it can be argued that assignment into gender is random or non-manipulable by other factors (at least in the context of this paper), independence of the mediator is a strong assumption.
Conditional on G, the error term is not allowed to impact mediators M and the outcome Y at the
same time. This assumption is easily violated: for example, conservative attitudes might influence
government spending preferences but at the same time also life choices like employment which is a
mediator as argued above.
The solution is to replace the traditional independence assumption by a set of conditional independence assumptions. Let C be a vector of observables. It confounds G, M , and Y which means
that it influences some or all of the three variables. Conservatism would be such a confounding
factor by the above argumentation. η(g) and δ(g) are then correctly identified under a Sequential
Ignorability Assumption (e.g., Huber 2014; Imai, Keele, and Yamamoto 2010).
Assumption 3 (Sequential Ignorability)
3.1 {Y (g 0 , m), M (g)} ⊥ G|C ∀ g 0 , g ∈ {0, 1}
3.2 {Y (g 0 , m)} ⊥ M |G = g, C = c ∀ g 0 , g ∈ {0, 1}
3.3 P (G = g|M = m, C = c) > 0 ∀ g ∈ {0, 1}
Assumption 3.1 implies that assignment into treatment (gender) conditional on confounders C
is independent of outcome and mediator. Ignorability thus means that besides confounders C
all other variables can be ignored, or that all confounders must be observed. Assumption 3.2
goes a step further: assignment into the binary mediator is independent of the outcome after
conditioning on gender G and confounders C . For a given set of observed confounders and the same
gender, employment can be treated as a random variable. Assumption 3.3 is a common support
assumption requiring enough comparable observations for both groups g = 1 and g = 0 in order
to have comparable units across both groups. There should be enough individuals in the sample
that are similar regarding the mediator and confounders but differ by gender. If employment status
and conservatism were the only mediators and confounders, all feasible combinations of the two
variables should be observed in the data for men as well as women (e.g., employed and conservative,
unemployed and conservative, etc.). None of the variables can be a perfect predictor of gender for
mediation analysis to work.
A graphical representation of the mediation framework is depicted in Figure 4 and summarizes
the causal chains. The solid lines represent direct effects while the dashed lines visualize the indirect
gender effect. It makes clear that confounders are pre-treatment variables, whereas the mediator
is determined after the treatment.
4.2
Estimation Strategy: Identifying the Direct and Indirect Gender Effect
The standard way of estimating η(g) and δ(g) is through a set of linear equations (e.g., Baron and
Kenny 1986; Judd and Kenny 1981, or Blinder (1973) or Oaxaca (1973) for linear wage decompositions, but without confounding factors). However, linearity imposes a strong functional form
19
Figure 4: Mediaton Framework
G
Y
M
C
Note: G are groups, M are mediators, C are confounders, and Y the outcome. Solid lines represent
direct effects, and dashed ones indirect or mediated effects. Direction of arrows indicates the causal
chain.
assumption which might be overly restrictive for a bivariate outcome variable (Hicks and Tingley
2011). Huber (2014, 2015) proposes to use a semi-parametric model instead that can accommodate
a binary outcome and mediator. The mediator is a function of treatment and confounders due to
the order of the causal chain. The outcome is also a function of group and confounders as well as
the mediator:
M
= χ(G, C, υ)
(11)
Y
= φ(G, M, C, )
(12)
This approach is more flexible and appropriate for my analysis since χ and φ are functions that
do not need to be specified more precisely. Denote the correlation of error terms υ and by ρ.
Under the Sequential Ignorability Assumptions 3.1 to 3.3 errors are shown to be uncorrelated such
that ρ = 0 (Imai, Keele, and Yamamoto 2010). If this holds, Huber (2014) shows that the direct
and indirect effects are non-parametrically identified. But Sequential Ignorability poses a strong
assumption which cannot be tested for. I will conduct a sensitivity analysis showing how large
departures from the perfect world characterized by ρ = 0 can be such that results do not change
qualitatively.
Identification relies on a reweighing mechanism according to propensity scores P (G = 1 |M , C )
and P (G = 1 |C ) which are the conditional probabilities of assignment into treatment. From this
the direct and indirect effects for women can be calculated by inserting g = 1 , replacing propensity
scores with its estimates (e.g., from a probit regression), and using sample moments. The effects
for men are derived analogously by substituting g = 0 .
P (G = 1|M, C) 1 − P (G = 1|M, C)
Y · 1{G = g}
−
(13)
η(g) = E
P (G = g|M, C)
P (G = 1|C)
1 − P (G = 1|C)
Y ·G
Y · (1 − G)
P (G = g|M, C)
δ(g) = E
−
·
(14)
P (G = 1|M, C) 1 − P (G = 1|M, C)
P (G = g|C)
For estimation, I use the normalized variants of (13) and (14) as in Huber (2014) and suggested by
20
Imbens (2004). Their exact forms can be found in Appendix B. The connection between the total
effect and the indirect and direct effects is that they can we written as a sum evaluated under the
opposite gender respectively:
τ
= E[Y (1, M (1))] − E[Y (0, M (0))]
= E[Y (1, M (1))] − E[Y (1, M (0))] + E[Y (1, M (0))] − E[Y (0, M (0))]
= η(1) + δ(0)
(15)
= E[Y (1, M (1))] − E[Y (0, M (1))] + E[Y (0, M (1))] − E[Y (0, M (0))]
= η(0) + δ(1)
(16)
b ) = ηb(0 ) + δ(1
b ).
For the estimated counterparts, it is straightforward that τb = ηb(1 ) + δ(0
4.3
Data
Post-ballot surveys are conducted shortly after all referendum and initiative ballots at national level
in Switzerland since 1981. The project is called VOXit, and the data are published by the Swiss
foundation for research in social sciences.22 Randomly chosen respondents answer a questionnaire
by telephone. Among the information included are the voting behavior and various socioeconomic
controls as well as contextual information. Voters as well as eligible citizens who did not go to the
polls answer the questions. Until the end of 1999 they also include the hypothetical answer of the
nonparticipating respondents to the question of how they would have decided if they had voted.
This allows me to distinguish between preferences of voters and nonvoters.
The mediation analysis is based on the four votes regarding the federal financial order held
between 1981 and 2004. These are the ballots voted on 29 November, 1981, 2 June, 1991, 28
November, 1993 and 28 November, 2004. Though the details of the constitutional article have
changed since the ballot propositions in 1971, the topic is the same as in the propositions analyzed
above. The propositions from 1981, 1993 and 2004 include time limits until 1994, 2006, and 2020
respectively. The 1991 proposition does not have a time limit. While it might be of concern that
women have not yet grown accustomed to their voting rights in 1971 and potentially hesitated to
participate, at the time of the surveys female voting rights were already well established. Moreover,
any potentially strategic male voting behavior stemming from the introduction of female suffrage
should have ceased to exist by then.
I use observations for which the participation and voting decisions as well as the mediator and
confounders (which I detail below) are available. Observations from respondent submitting an
empty vote are dropped in order to follow the official rule of calculating voting results. I drop
observations when the respondent claims to have turned out for the vote but there is an answer for
the voting behavior of non-participants in the data set (and vice versa for non-participants with
information on voting for that individual). These are only 11 and 17 cases respectively and most
22
Data are available online on the following homepage: http://nesstar.sidos.ch/webview/index.jsp
21
likely the result of data mistakes. In the pooled sample of all ballots, there are 2,375 respondents
of which 46% are women. 1,634 respondents voted on the measures.
A typical concern about using surveys to elicit voter preferences is survey bias: either respondents misrepresent their voting behavior, or they choose not to participate in the survey conditional
on their characteristics. To evaluate potential survey bias, Funk (2016) proposes to compare the
official voting results with the share of survey respondents claiming they have voted “yes”. Subtracting the official results from the survey results based on the voting population only, yields a
difference of 10.37 (1981), -1.84 (1991), 1.64 (1993) and 4.1 (2004) percentage points between the
two. The last three values confirm Funk’s (2016) result that on average no significant survey bias
occurs in votes concerning federal finances. However, the first value points to a seizable survey bias
and problems with the accuracy of the survey results from 1981.
4.4
Empirical Specification
The outcome Y takes on value 1 if a respondent voted yes or would have voted yes, and 0 else. The
main variable of interest is the gender indicator G which becomes 1 for women, and 0 for men. I use
employment and income as mediators since factors relating to the labor market are traditionally
thought to influence preferences for government spending (Meltzer & Richard 1981), and gender
gaps are traditionally large with regard to these variables. It is interesting to consider both variables
since they might capture alternative channels. Especially, married female respondents might not
be employed but live in a high-income household. Work is 1 if the respondent indicated to be
employed, and 0 for individuals who do not work, i.e., the non-employed, the unemployed, students,
and retirees. Income was only asked for in the 1993 and 2004 surveys. It is measured as household
income with a five-step categorical variable.23 I define Income as 1 if a respondent reports income
above the second level which corresponds to above-average household income. Household income
reflects the sum of incomes earned in a household, which may be larger for married couples than
singles. I will therefore use civil status as a confounder.
Table 4 provides a comparison of both mediator means in the subgroups of men and women for
all respondents and voters, in the pooled sample and separately for each ballot. There is a negative
and persistent gender gap in employment. Women are on average 19.4 percentage points less likely
to hold a job than men. The value is similar (18.2) in the subsample of voters. While there is
variation in the size of the gender gap across the four ballots, it tends to get smaller over time. As
expected, there exists a negative income gender gap. Among all 1993 respondents, women are 9.9
percentage points less likely to have above-average income than men. This gap varies little over
time in the subsamples of voters by ballot.
The choice of confounders is restricted by survey design. Conceptually, confounders are thought
of as pre-treatment variables. The following variables come close to this requirement. To account
for cultural differences between the geographical and linguistic areas in Switzerland, I control for
23
The five categories of monthly household income in Swiss Francs are:
(1) Income ≤ 3 , 000 ; (2)
3 , 000 < Income ≤ 5 , 000 ; (3) 5 , 000 < Income ≤ 7 , 000 ; (4) 7 , 000 < Income ≤ 9 , 000 ; (5) Income > 9 , 000 .
22
Table 4: T-test of mediators Work and Income by Gender
Sample
Women
Men
Difference
t-statistic
p-value
All
1981
1991
1993
0.532
0.452
0.598
0.545
0.726
0.763
0.753
0.712
-0.194***
-0.311***
-0.155***
-0.167***
-10.003
-7.656
-4.330
-4.874
0
0
0
0
All
1981
1991
1993
2004
0.523
0.447
0.602
0.517
0.510
0.705
0.762
0.690
0.720
0.653
-0.182***
-0.315***
-0.088*
-0.203***
-0.144***
-7.697
-5.750
-1.825
-4.977
-2.967
0
0
0.069
0
0.003
1993
0.421
0.521
-0.099***
-2.628
0.009
All
1993
2004
0.493
0.438
0.561
0.610
0.553
0.695
-0.117***
-0.116**
-0.134***
-3.432
2.555
-2.630
0.001
0.011
0.009
Work
All
Voters
Income
All
Voters
Based on data from VOX-surveys no. 161, 421, 511, and 862. Data are available online on http://nesstar.sidos.ch/webview/index.jsp. T-test of mediators Work and Income by gender. Evaluated among all survey respondents,
voters, in pooled samples of all ballots and separately for all ballots.
* p<0.1, ** p<0.05, *** p<0.01.
region dummies West, Center, Center-West, and Center-East. The Southern region is left out as
reference group.24 Age denotes the respondent’s age, and may influence employment status as well
as preferences in general. If the respondent is Catholic this variable takes on value 1.25 The variable
is typically related to work-ethic or conservatism.
Other variables decided at the time of birth are not available. However, further socioeconomic
factors may play a role for explaining gender preferences. I use several post-treatment outcomes
as confounders and subsequently conduct robustness tests showing that results are insensitive to
the inclusion of these variables. As explained above, civil status is an important control. Partner
24
The region of residence might already constitute a choice if an individual moved away from his home region.
Alternatively, I specify German (as opposed to French or Italian) as a language indicator which should mainly be
determined by the language spoken in the parental home. It is closely correlated with the regions and results are
not sensitive to this specification.
25
The majority of the Swiss population is either Roman Catholic (46.2% in 1980), or Protestant (45.3% in 1980)
(data are from the website of the Swiss Statistical Office www.bfs.admin.ch).
23
Table 5: T-Tests of Confounders by Gender
Confounders
West
Center
Center-West
Center-East
Age
Catholic
Partner
Education
Urban
Homeowner
House
Mean
(women)
Mean
(men)
Difference
t-statistic
p-value
0.212
0.246
0.260
0.262
46.6
0.417
0.633
0.268
0.636
0.418
0.378
0.216
0.246
0.252
0.249
48.0
0.436
0.650
0.355
0.588
0.450
0.389
-0.004
0.000
0.008
0.013
-1.360
-0.019
-0.017
-0.087
0.049
-0.032
-0.010
-0.218
0.002
0.461
0.738
-1.941
-0.956
-0.864
-4.592
2.420
-1.558
-0.522
0.827
0.998
0.645
0.461
0.052
0.339
0.388
0
0.016
0.119
0.602
Data from VOX-surveys no.
161, 421, 511, and 862.
Pooled
sample with 2,375 respondents.
Data are available online on
http://nesstar.sidos.ch/webview/index.jsp.
indicates whether the respondent is either married or has a partner, in contrast to being single,
divorced or widowed. Education is a well-known driver of income and affects the way individuals
make decisions. Education takes on value 1 for individuals with high-school or university degrees.
Urban is one if the respondent lives in a city in contrast to a rural area. Urbanity relates to labor
market characteristics and exposure to public goods, thus potentially confounding employment and
preferences. Homeowner indicates that the respondent lives in his owned property. If the respondent lives in a detached house in contrast to an apartment, House takes on value 1. Both variables
relate to the standard of living but potentially also to circumstances an individual originates from.
To summarize, the vector of confounders is C = {West, Center, Center-West, Center-East, Age,
Catholic, Partner, Education, Urban, Homeowner, House}. Summary statistics of the variables by
gender, the mean difference, t-statistics and p-values are reported in Table 5. Though there is little
selection into treatment, age, urbanity and most importantly education display significant gender
gaps.
Propensity scores P (G = 1|M, C) and P (G = 1|C) required for identification are estimated with
probit regressions and reported in Appendix D (Tables 12 – 14). For validation of the common
support assumption 3.3, histograms of propensity scores are provided. Figure 5 shows exemplary
histograms for the mediator Work in the pooled sample of all four ballots. They visualize a sufficient
overlap of propensity scores for men and women. There is moreover no mass concentrated at the
values zero and one such that the mediator and confounders do not perfectly predict gender and
propensity score trimming is unnecessary (Huber, Lechner, and Wunsch 2013). Propensity score
histograms by gender for all ballot subsamples are attached in Appendix E.
24
Figure 5: Common Support Histograms
(a) P (G = 1|C) for Women
10
6
Density
4
6
0
0
2
2
4
Density
8
8
10
12
(b) P (G = 1|C) for Men
.2
.4
.6
.8
.2
.4
P(C)
.8
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
(d) P (G = 1|M, C) for Men
6
(c) P (G = 1|M, C) for Women
Density
.6
P(C)
.2
.4
.6
.8
.2
P(M,C)
.4
.6
.8
P(M,C)
Note: Histograms of propensity scores from probit estimates for full sample with mediator Work.
P (G = 1|M, C) propensity scores control for the mediator and confounders, P (G = 1|C) only
for the latter. Corresponds to column (1) in Table 6. a: Propensity scores P (G = 1|C) based
on confounders for women; b: propensity scores P (G = 1|C) based on confounders for men; c:
propensity scores P (G = 1|M, C) based on mediator and confounders for women; d: propensity
scores P (G = 1|M, C) based on mediator and confounders for men. Based on data from VOXsurveys no. 161, 421, 511, and 862. Pooled sample with 2,375 respondents. Data are available
online on http://nesstar.sidos.ch/webview/index.jsp.
25
4.5
Results: Direct and Indirect Effects
Results from the mediation analysis based on the mediator Work are reported in Table 6. Column
(1) shows the results for the pooled sample, while in specifications (2)-(4) the results are reported
separately for the individual ballots. In columns (5)-(9) the sample is reduced to respondents who
reported to have voted.
The total gender effect τ in the first row is the marginal effect from a probit regression of acceptance on gender while controlling for all confounders. Significance is determined with a two-sided
test. While coefficients are negative throughout almost all specifications, they only turn significant
in the total sample (column (1)), in the 1993 ballot (column (4)), and voters in 1991 (column (7)).
On average, being female decreases the probability of voting yes by 4.4 percentage points in the
total sample. Moreover, a positive gender gap can be rejected at conventional significance levels in
six out of nine specifications (columns (1), (3)-(5),(7) and (9)).
The direct and indirect effects evaluated for women, δ(1) and η(1), are in the second and third
row of the results table. The respective values for men are reported in the lower part of the table
for completeness. Standard errors are bootstrapped with 1,999 iterations. The direct effect for
women is negative in all specifications. Among all respondents and in the pooled sample of voters
the difference is significant. Conditional on work outcomes for women, being female reduces the
probability of accepting the proposals by 7.5 percentage points on average (column (1)). The effect
is slightly smaller in the sample of voters (6.8 percentage points in column (5)). The mediated
effect through employment for women has small economic significance since most coefficients are
close to zero. Moreover, it is never significant. Neither a negative nor a positive gender gap caused
by gender differences in employment can be rejected. This means than comparing women with
average female employment and counterfactual employment of men cannot explain differences in
gender preferences.
Results for the mediation through income are reported in Table 7. The findings are similar to
the ones using employment as a mediator. The total gender gap is always significantly negative
and varies between 7.5 and 9.9 percentage points. The direct effect, though always negative, is
only significant in the pooled sample of voters from 1993 and 2004. The mediated effect for women
always takes on insignificant values.
The direct and indirect effects were obtained using a semi-parametric approach. While such
estimations generally have the advantage of good robustness since they rely on few functional
form assumptions, they produce larger standard errors than parametric estimations. I rerun the
mediation analysis using a parametric approach and specify the mediation and outcome regressions
(11) and (12) as probit models since both mediator and outcome are binary. But also specifying the
mediator equation as a linear function yields very similar results. The derivation of the direct and
indirect effects follows Imai, Keele, and Yamamoto (2010). Results are in Appendix C in Tables 8
and 9. Conclusions regarding the total and direct effects are virtually the same and effect size is very
similar as in the semi-parametric specification. As expected, standard errors are smaller such that
the total and direct effects are negative and significant in almost all specifications. Interestingly,
26
the mediated effect through employment becomes significant in several specifications. Women with
average female employment are between 1.2 to 2.1 percentage points more likely to vote yes than
women with counterfactual average (and thus higher) male employment. The effect goes into the
expected direction that employed individuals should prefer lower public spending levels than not
working ones. Quite surprisingly, the indirect effect becomes negative for the mediator income:
women with female average income were 1.3 to 1.6 percentage points less likely to vote yes than
women with counterfactual male income. This means that women with lower household incomes
supported the ballot measures more than women in relatively richer households, though by a pure
redistributive motive the opposite would have been expected.
This robustness check shows that functional form assumptions play a role for the estimation
of mediated effects. In the parametric approach, mediated effects become significant. However,
if the model was misspecified, parametric estimation is more prone to error, and semi-parametric
estimation should be preferred. The direct effect, in contrast, is robust to different specifications.
I will use this parametric specification to check for sensitivity of the results to model misspecification in the next section.
27
Table 6: Results: Direct and Indirect Effects - Mediator Work
(1)
All
(2)
All
(3)
All
(4)
All
(5)
Voters
(6)
Voters
(7)
Voters
(8)
Voters
(9)
Voters
τ
-0.044**
(0.020)
-0.027
(0.038)
-0.095***
(0.037)
-0.053
(0.033)
-0.035
(0.023)
0.024
(0.048)
-0.073*
(0.049)
-0.049
(0.039)
-0.055
(0.041)
Women
Direct effect
δ(1)
Indirect effect
η(1)
-0.075***
(0.024)
0.004
(0.019)
-0.057
(0.053)
-0.018
(0.042)
-0.123**
(0.058)
0.000
(0.044)
-0.082***
(0.025)
-0.005
(0.019)
-0.068**
(0.029)
0.004
(0.026)
-0.038
(0.086)
-0.035
(0.066)
-0.111
(0.125)
0.005
(0.064)
-0.090
(0.086)
-0.008
(0.058)
-0.062
(0.079)
0.008
(0.169)
Men
Direct effect
δ(0)
Indirect effect
η(0)
-0.048*
(0.027)
0.031**
(0.016)
-0.009
(0.055)
0.030
(0.040)
-0.095
(0.058)
0.028
(0.047)
-0.049*
(0.027)
0.029*
(0.016)
-0.039
(0.035)
0.033*
(0.019)
0.059
(0.079)
0.062
(0.077)
-0.078
(0.082)
0.038
(0.119)
-0.041
(0.066)
0.041
(0.078)
-0.063
(0.171)
0.008
(0.073)
all
2,375
1981
525
1991
671
1993
771
all
1,634
1981
287
1991
397
1993
542
2004
408
Sample
Total
28
Ballots
Observations
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. The binary dependent variable is 1 if the respondent voted yes, 0
if no. Standard errors of total effect τ are from marginal effects after probit estimates. Inverse propensity score weighted results
for direct (δ) and indirect (η) effects. Standard errors for direct and indirect effects are based on 1,999 bootstrap iterations.
The mediator Work takes on value 1 if the respondent was employed. The confounding variables are West, Center, CenterWest, Center-East, Age, Catholic, Partner, Education, Urban, Homeowner, and House. Based on data from VOX-surveys no.
161, 421, 511, and 862. Data are available online on http://nesstar.sidos.ch/webview/index.jsp.
Table 7: Results: Direct and Indirect Effects - Mediator Income
Sample
Total
τ
Women
Direct effect
δ(1)
Indirect effect
η(1)
Men
Direct effect
δ(0)
Indirect effect
η(0)
Ballots
Observations
(1)
Voters
-0.081***
(0.030)
(2)
Voters
-0.075*
(0.041)
(3)
Voters
-0.099**
(0.043)
(4)
All
-0.076**
(0.034)
-0.073*
(0.040)
-0.010
(0.057)
-0.069
(0.105)
-0.009
(0.082)
-0.097
(0.059)
0.001
(0.165)
-0.073
(0.064)
-0.011
(0.051)
-0.072
(0.062)
-0.009
(0.032)
-0.065
(0.091)
-0.006
(0.099)
-0.101
(0.167)
-0.002
(0.056)
-0.065
(0.062)
-0.003
(0.055)
1993, 2004
842
1993
488
2004
354
1993
695
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. The binary dependent variable is 1 if the respondent voted yes, 0 if no. Standard errors of total effect τ are from marginal effects after probit estimates. Inverse propensity score weighted results for direct (δ) and indirect (η) effects. Standard errors for direct and indirect effects are based
on 1,999 bootstrap iterations. The mediator Income takes on value
1 if the respondent has above average income. The confounding variables are West, Center, Center-West, Center-East, Age, Catholic, Partner, Education, Urban, Homeowner, and House. Based on data from
VOX-surveys no. 161, 421, 511, and 862. Data are available online on
http://nesstar.sidos.ch/webview/index.jsp.
4.6
Sensitivity
Validity of the Sequential Ignorability Assumptions is crucial for the identification of causal effects.
There are two potential sources for violation of these assumptions in my study. First, the treatment
in my case is “being female”. Gender, however, is not a typical treatment as e.g. in a medical trial.
It is a personal attribute comparable to ethnicity or nationality and thus precedes confounders
which are not determined at birth (Greiner and Rubin 2011). In the empirical application above,
variables like education are used as confounders. However, they are determined after treatment
and thus likely affected by the treatment. This is certainly true for education since men and women
make different educational choices. I encounter this problem by checking how sensitive the results
are to control for post-treatment variables. Second, a general threat to identification in mediation
studies relates to the issue that not all relevant confounders may be observed and controlled for. I
29
conduct a sensitivity analysis which determines how badly the Sequential Ignorability Assumptions
need to be violated in order to arrive at different conclusions than in the above analysis.
Regarding post-treatment confounders, I rerun the mediation analysis discarding all confounders
that are determined after treatment and only keep the regional indicators, catholic faith and age
as confounders. The idea is to check whether results are sensitive to controlling for post-treatment
confounders. Result Tables 10 and 11 are in the Appendix. Leaving out post-treatment variables
leads to more negative total gender gaps and direct effects for women. The effects become significantly different from zero in even more specifications. The mediated effects remain small and
insignificant. Controlling for post-treatment variables produces the more conservative results in
terms of absolute value and significance. Consequently, conclusions regarding the sign of all effects
are robust to this manipulation, and it is uncritical to have post-treatment mediators in the model.
A sensitivity analysis as described by Imai, Keele, and Yamamoto (2010) is a way of testing the
result’s susceptibility to violation of the Sequential Ignorability Assumptions. In an ideal world,
mediated and direct effects are identified under the assumption than no unobserved pre-treatment
variables jointly affect the mediator and the outcome. It can be expressed as a zero correlation
of the error terms from equations determining the mediator and outcome which is denoted by
ρ ≡ corr (υ, ) = 0 .26 The sensitivity analysis allows to determine the direct and indirect effects as
functions of the sensitivity parameter ρ. Departures from ρ = 0 point to violation of Sequential
Ignorability. ρ > 0 (ρ < 0 ) refers to the case when unobserved confounders affect the mediator and
outcome in the same (opposite) direction(s).
I conduct the sensitivity analysis for female direct and indirect effects. For the mediator Work
the pooled sample of all ballots is used, and for Income the sample of voters from the 1993 and
2004 surveys. The point of departure are the parametrically estimated effects. The reason is that
the indirect effect was significantly negative such that a sensitivity analysis is meaningful in this
case.
The four panels in Figure 6 show plots of ρ against the average (in)direct effect. The gray area
refers to the 95% confidence interval of the effects. For the direct effects (panels 6.a and 6.c) the
relation between ρ and δ(1 ) is negative. The critical sensitivity parameter equals ρ = −0 .4 (panel
6.a, mediator Work ) and ρ = −0 .65 (panel 6.c, mediator Income) respectively. The conclusion
regarding a negative direct effect is robust to the omission of all (unobserved) pre-treatment confounders that affect the mediator and outcome in the same direction because δ(1 ) < 0 whenever
ρ > 0 . The direct effect would turn zero or positive only if the correlation of error terms gets
smaller (i.e., more negative) than −0.4 or −0.65 respectively. The numbers indicate that relatively
large departures from Sequential Ignorability are permissible without drawing the conclusion that
the direct effect is positive.
For the indirect effect, panels 6.b and 6.d indicate that the finding is extremely sensitive to
violations of the Sequential Ignorability Assumptions. Recall that the mediated effect through
employment was positive. A correlation of error terms as small as ρ = −0 .1 , would result in a
zero effect. The negative mediated effect through income would turn zero for ρ = 0 .15 , and even
26
Recall from Section 4.2 that these function are M = χ(G, C , υ) and Y = φ(G, M , C , ).
30
Figure 6: Sensitivity Analysis
(a) Mediator Work : Direct Effect
(b) Mediator Work : Indirect Effect
0.1
0.0
Average Mediation Effect1
−0.2
−0.1
0.0
−0.2
−0.1
Average Direct Effect0
0.1
0.2
Employed
0.2
Employed
−0.5
0.0
0.5
−1.0
−0.5
Sensitivity Parameter: ρ
(c) Mediator Income: Direct Effect
0.5
1.0
(d) Mediator Income: Indirect Effect
0.1
0.0
Average Mediation Effect1
0.0
−0.2
−0.1
−0.2
−0.1
0.1
0.2
Income
0.2
Income
Average Direct Effect1
0.0
Sensitivity Parameter: ρ
−1.0
−0.5
0.0
0.5
1.0
Sensitivity Parameter: ρ
−1.0
−0.5
0.0
0.5
1.0
Sensitivity Parameter: ρ
Note: Sensitivity analysis for direct and indirect effects for women (g = 1 ). Sensitivity parameter
ρ = 0 if Sequential Ignorability holds. Based on data from VOX-surveys no. 161, 421, 511, and 862.
Pooled sample of all votes in a and b. Voters from surveys 511 and 862 in c and d. a: Mediator
Work : δ(1 ) = 0 if ρ = −0 .4 . b: Mediator Work : η(1 ) = 0 if ρ = −0 .1 . c: Mediator Income:
δ(1 ) = 0 if ρ = −0 .65 . d: Mediator Income: η(1 ) = 0 if ρ = 0 .15 .
positive for sensitivity parameters above this critical value.
A complementary way to make statements about sensitivity is through the product of R 2 from
the mediator and outcome equation (Imai, Keele, and Yamamoto 2010). This measure can express
31
how much of the residual variance an unobserved confounder would have to explain such that the
(in)direct effects would turn zero. For the direct effects the respective values are 0.16 (mediator
Work ) and 0.43 (mediator Income). The high values again underline the robustness of the direct
effects to omitted pre-treatment confounders. In contrast, the values for the indirect effects are
0.01 (mediator Work ) and 0.02 (mediator Income) respectively, suggesting extreme sensitivity of
the model specification.
The sensitivity analysis demonstrates that relatively large departures from the ideals of Sequential Ignorability can be accepted without triggering different results regarding the direct effect of
being female on government preferences. In contrast, it shows that the indirect effect, which was
only significant once making parametric form assumptions, can easily be violated if pre-treatment
confounders were not controlled for.
4.7
Discussion
Comparing the total effect to the results from the 1970/1971 referendums in the previous section,
suggests qualitatively similar results. Throughout the history of referendums on the federal fiscal
order, women are not more inclined to support the ballot measures. However, the size of the gender
preference gap is considerably smaller in the post-ballot surveys. There are several explanations.
First, though similar, the ballot propositions are not identical, which also might explain part of
the variation over time. Further, there is a survey bias in the 1981 survey suggesting problems
with the representativeness of the data from that year. It might explain why most of the results
for this subsample yield insignificant results. Second, the post-ballot surveys are based on data
from votes that took place at later points in time. Time effects not captured by the mediator and
confounders – the political context and unobserved factors like ideology – might have changed over
time, causing different results. Last, the results from 1970/1971 rely on aggregate voting data and
approximations which are sources of measurement error. In contrast, individual-level data allow for
precise control over treatment, mediators and outcome which might be an alternative explanation
for the different results. The size and significance of the direct effect are considerable and robust,
whereas there is little evidence for mediated effects through employment or education.
In sum, evidence points to the importance of direct gender effects when explaining the gender
gap in support for the fiscal order. It is particularly pronounced in the total population, but less
prominent among voters. On the one hand, this may be a relict of the fact that voters constitute
a selective subsample of the total population. Though descriptives showed significantly different
mediators by gender both among all respondents and voters, voting is a non-random decision and
typically depends on observables. This might explain why the results based on voters only tend
to be less significant. In general, sample size in the subsamples of individual ballots are relatively
small, working against precise estimates.
The direct effect may capture several diverse aspects regarding the gender preference gap. Most
broadly, the direct effect for women subsumes all differences between men and women that are unconfounded and not captured by the mediator. I.e., it is a residual effect. Therefore, it may
32
not only refer to observable gender differences. Potential alternative explanations are unobserved
mediators. Research based on experimental techniques examines gender gaps other than socioeconomic differences which might explain why women could have different preferences for government
spending than men (cf. Croson and Gneezy (2009) as well as Shapiro and Mahajan (1986) for
literature reviews). Literature documents that women are more risk averse (e.g., Holt and Laury
2002, 2005; Schubert et al. 1999) and dislike competition (Gneezy, Niederle, and Rustichini 2003;
Niederle and Vesterlund 2007). Experimental evidence suggests that women are more altruistic,
and display less variance in altruism (Andreoni and Vesterlund 2001; Goree, Holt, and Laury 2002,
Selten and Ockenfels 1998). Women are found to be more patient than men, suggesting that they
care more strongly about the future (Krogstrup and Wälti 2011). These variables are unobserved
in the survey data and thus candidate explanations for a direct gender effect. While for part of
them it is unclear in which direction they should affect preferences for government spending, care
for the future or patience would be compatible with preferring smaller governments and reducing
the fiscal burden for the next generations.
5
Concluding Remarks
The aim of this paper is to provide evidence for gender preferences for government expenditure
from ballot analysis. This method is preferable to analyzing indirect links between the electorate,
politicians, and their subsequent choice of budgets or policies since the relation between preferences
and subsequent voting behavior is much clearer. The analysis of the gender preference gap around
the introduction of female voting rights is based on aggregate voting data such that individual
voting behavior remains unobserved. However, I argue extensively that my preference measures
are likely to identify gender preference gaps.
I find that approval for government spending is not higher among women than men, but potentially the reverse. This is true at the point in time when women got the right to vote, and
the finding persists over time. The results are compatible with the literature identifying smaller
governments after the franchise was extended to women. Though employment and wage gender
gaps were large in the past, time-invariant preferences like fiscal conservatism are more suitable
candidate explanations for the observed changes in public spending.
Interestingly, around 1971 government budgets were still made of items like military spending
which women tend to dislike. More “female” budgetary items like social security or education
have become more important government responsibilities over time. If these factors were the sole
determinants of the negative gender preference gap, a diminishing gap should have been observed
over time. The findings of this paper suggest that part of the fiscal gender preference gap cannot
be explained away by employment status or education. Intrinsic or unobserved gender differences
play a role in explaining diverse gender preferences. Therefore, it is unlikely that these gender gaps
will disappear in future even when socioeconomic gender differences continue changing. This has
implications for policy-making and political representation depending on the gender of legislators.
33
Appendix
A
Date Sources and Federal Announcements
• Information about mutations of the municipalities are taken from the historical municipality
register of the Swiss Statistical Office available online
http : //www.bf s.admin.ch/bf s/portal/de/index/inf othek/nomenklaturen/blank/blank/
gem liste/02.html
• The Année Politique Suisse (2012) is accessible online and provides additional background
information on ballots.
http : //www.anneepolitique.ch/de/aps − online.php
• Number of voters for cantonal votes is available online from the Centre for research on direct
democracy.
www.c2d.ch.
• Information about municipalities counting votes together in the canton Bern, and political
municipalities in the canton Thurgau were received by email from the Swiss Statistical Office.
• Data used from Swiss census (1970): total population
• Voting data are from the Political Atlas of Switzerland of the Swiss Statistical Office. They
were retrieved for the following ballots:
– Bundesbeschluss vom 27.09.1963 über die Weiterführung der Finanzordnung des Bundes
(Verlängerung der Geltungsdauer von Art.41ter BV und Ermässigung der Wehrsteuer).
Ballot on 8 December 1963.
– Bundesbeschluss vom 24.06.1970 über die Änderung der Finanzordnung des Bundes.
Ballot on 15 November 1970.
– Bundesbeschluss vom 09.10.1970 über die Einführung des Frauen- stimm- und
Wahlrechts in eidgenössischen Angelegenheiten. Ballot on 7 February 1971.
– Bundesbeschluss vom 11.03.1971 über die Weiterführung der Finanzordnung des Bundes.
Ballot on 6 June 1971.
• VOX-survey no.
161, 421, 511, and 862 are accessible online.
The source is:
Longchamp, Claude, Ulrich Klöti, Sibylle Hardmeier, Wolf Linder, Hanspeter Kriesi, Dominique Wisler, Hans Hirter, Lukas Golder, Marina Delgrande, Lionel Marquis, and
Urs Bieri. VOX 105-109 [Datasets]. gfs.bern, Markt- und Sozialforschung; Universität Zürich; Universität Bern; Universit¨ de Gen¨‘ve. Distributed by FORS, Lausanne.
http://nesstar.sidos.ch/webview/index.jsp
34
Federal Announcements are accessible online http : //www.amtsdruckschrif ten.bar.admin.ch.
• Federal Announcement 1962 I, 997-1014. Botschaft des Bundesrates an die Bundesversammlung über die Weiterführung der Finanzordnung des Bundes.
• Federal Announcement 1969 II, 749-807. Botschaft des Bundesrates and die Bundesversammlung über die Änderung der Finanzordnung des Bundes.
• Federal Announcement 1970 II, 1-5. Bundesbeschluss über die Änderung der Finanzordnung
des Bundes.
• Federal Announcement 1970 II, 1581-1608. Botschaft des Bundesrates an die Bundesversammlung über die Weiterführung der Finanzordnung des Bundes.
• Federal Announcement 1971 I, 486-491. Bundesbeschluss über die Weiterführung der Finanzordnung des Bundes.
• Federal Announcement 2003 I, 1531-1565. Botschaft über die neue Finanzordnung.
35
B
Estimators of Direct and Indirect Effects
To estimate the direct and indirect effects, I estimate normalized versions of (13) and (14) (Huber,
2014). For the normalization weights are adjusted such that they add up to one for both men
and women. For simplification, write p(M, C) ≡ P (G = 1|M, C) and p(C) ≡ P (G = 1|C), with
their their estimated counterparts pb(M, C) and pb(C). Let i denote the index for each of the N
observations. Then the direct effect evaluated at g = 1 and g = 0 respectively is identified by the
following equations:
"
b
δ(1)
=
"
b
δ(0)
=
N
X
Yi Wi1
#" N
X
i=1
i=1
N
X
#" N
X
Yi Wi3
i=1
#−1
Yi Wi1
"
−
#−1
Yi Wi3
i=1
"
−
N
X
Yi Wi2
#" N
X
i=1
i=1
N
X
#" N
X
Yi Wi4
i=1
#−1
Yi Wi2
(17)
#−1
Yi Wi4
(18)
i=1
The four weights are defined as:
Wi1 ≡
Gi
b
P (Ci )
Wi2 ≡
(1 − Gi )Pb(Mi , Ci )
(1 − Pb(Mi , Ci ))Pb(Ci )
Wi3 ≡
Gi (1 − Pb(Mi , Ci ))
Pb(Mi , Ci )(1 − Pb(Ci ))
Wi4 ≡
1 − Gi
1 − Pb(Ci )
Pb(Mi , Ci ) and Pb(Ci ) are estimated with probit regressions, and the rest of the estimator is based
b
b
on sample moments from which it is straightforward to calculate both δ(1)
and δ(0).
36
37
η(1)
δ(0)
η(0)
Indirect effect
Men
Direct effect
Indirect effect
all
2,375
-0.075***
(0.00)
0.016***
(0.00)
-0.074***
(0.00)
0.017***
(0.00)
-0.058***
(0.00)
(1)
All
1991
671
-0.130***
(0.00)
0.017**
(0.02)
-0.131***
(0.00)
0.016**
(0.02)
-0.114***
(0.00)
(2)
All
1993
771
-0.077**
(0.02)
0.012*
(0.09)
-0.075**
(0.02)
0.014*
(0.09)
-0.063*
(0.05)
(3)
All
all
1,634
-0.063**
(0.01)
0.015**
(0.01)
-0.061**
(0.01)
0.017**
(0.01)
-0.046*
(0.06)
(4)
Voters
1991
397
0.108**
(0.03)
0.013**
(0.01)
-0.109**
(0.03)
0.012**
(0.01)
-0.096**
(0.04)
(5)
Voters
1993
542
-0.076*
(0.06)
0.019*
(0.05)
-0.073*
(0.06)
0.021*
(0.05)
-0.055
(0.15)
(6)
Voters
2004
408
-0.073*
(0.06)
0.007
(0.17)
0.071*
(0.06)
0.008
(0.17)
-0.064*
(0.09)
(7)
Voters
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. The binary dependent variable is 1 if the
respondent voted yes, 0 if no. Standard errors of total effect τ are from marginal effects after probit estimates. Parametric estimation with probit models for direct (δ) and indirect (η) effects. Standard errors
for direct and indirect effects are based on 1,999 bootstrap iterations. The mediator Work takes on value 1
if the respondent was employed. The confounding variables are West, Center, Center-West, Center-East,
Age, Catholic, Partner, Education, Urban, Homeowner, and House. Based on data from VOX-surveys no.
161, 421, 511, and 862. Data are available online on http://nesstar.sidos.ch/webview/index.jsp.
Ballots
Observations
δ(1)
τ
Women
Direct effect
Total
Sample
Table 8: Parametric Estimation: Direct and Indirect Effects - Mediator Work
C
Tables Robustness Checks
Table 9: Parametric Estimation: Direct and Indirect Effects - Mediator Income
Sample
Total
τ
Women
Direct effect
δ(1)
Indirect effect
η(1)
Men
Men
Direct effect
δ(0)
Indirect effect
η(0)
Ballots
Observations
(1)
Voters
-0.092**
(0.01)
(2)
Voters
-0.083**
(0.03)
(3)
Voters
-0.108**
(0.01)
(4)
All
-0.080**
(0.02)
-0.078**
(0.02)
-0.016***
(0.00)
-0.069*
(0.07)
-0.016**
(0.01)
-0.100**
(0.01)
-0.010
(0.12)
-0.069*
(0.05)
-0.013**
(0.01)
0.076**
(0.02)
-0.014***
(0.00)
-0.068*
(0.07)
-0.014**
(0.01)
-0.098**
(0.01)
-0.008
(0.12)
-0.068*
(0.05)
-0.011**
(0.01)
1993, 2004
842
1993
488
2004
354
1993
695
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. The binary dependent variable is 1 if the respondent voted yes, 0 if no. Standard errors of total effect τ are from marginal effects after probit estimates. Parametric estimation with probit models for direct (δ) and
indirect (η) effects. Standard errors for direct and indirect effects are
based on 1,999 bootstrap iterations. The mediator Income takes on value
1 if the respondent has above average income. The confounding variables are West, Center, Center-West, Center-East, Age, Catholic, Partner, Education, Urban, Homeowner, and House. Based on data from
VOX-surveys no. 161, 421, 511, and 862. Data are available online on
http://nesstar.sidos.ch/webview/index.jsp.
38
Table 10: Sensitivity Analysis: Direct and Indirect Effects - Mediator Work
(1)
All
(2)
All
(3)
All
(4)
All
(5)
Voters
(6)
Voters
(7)
Voters
(8)
Voters
(9)
Voters
τ
-0.057***
(0.020)
-0.031
(0.038)
-0.116***
(0.037)
-0.061*
(0.033)
-0.045*
(0.023)
0.028
(0.047)
-0.098**
(0.049)
-0.053
(0.039)
-0.065
(0.041)
Women
Direct effect
δ(1)
Indirect effect
η(1)
-0.090***
(0.024)
0.008
(0.016)
-0.061
(0.045)
-0.013
(0.038)
-0.151***
(0.048)
0.005
(0.034)
-0.089***
(0.024)
0.000
(0.016)
-0.079***
(0.028)
0.007
(0.018)
-0.031
(0.060)
-0.019
(0.050)
-0.131
(0.107)
-0.001
(0.046)
-0.100
(0.060)
-0.003
(0.031)
-0.071
(0.107)
0.007
(0.107)
Men
Direct effect
δ(0)
Indirect effect
η(0)
-0.066***
(0.025)
0.033**
(0.014)
-0.018
(0.053)
0.030
(0.029)
-0.120**
(0.052)
0.036
(0.034)
-0.061
(0.025)
0.029
(0.014)
-0.052*
(0.029)
0.034**
(0.017)
0.047
(0.068)
0.059
(0.044)
-0.097
(0.067)
0.033
(0.102)
-0.050
(0.049)
0.047
(0.045)
-0.073
(0.099)
0.006
(0.099)
all
2,375
1981
525
1991
671
1993
771
all
1,634
1981
287
1991
397
1993
542
2004
408
Sample
Total
39
Ballots
Observations
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. The binary dependent variable is 1 if the respondent voted yes, 0
if no. Standard errors of total effect τ are from marginal effects after probit estimates. Inverse propensity score weighted results
for direct (δ) and indirect (η) effects. Standard errors for direct and indirect effects are based on 1,999 bootstrap iterations. The
mediator Work takes on value 1 if the respondent was employed. Only with pre-treatment confounding variables West, Center,
Center-West, Center-East, Age, Catholic. Based on data from VOX-surveys no. 161, 421, 511, and 862. Data are available online
on http://nesstar.sidos.ch/webview/index.jsp.
Table 11: Sensitivity Analysis: Direct and Indirect Effects - Mediator
Income
Sample
Total
τ
Women
Direct effect
δ(1)
Indirect effect
η(1)
Men
Direct effect
δ(0)
Indirect effect
η(0)
Ballots
Observations
(1)
Voters
-0.092***
(0.030)
(2)
Voters
-0.083**
(0.041)
(3)
Voters
-0.109**
(0.043)
(4)
All
-0.084**
(0.034)
-0.080**
(0.033)
-0.015
(0.016)
-0.075
(0.048)
-0.013
(0.029)
-0.102**
(0.051)
-0.010
(0.044)
-0.078**
(0.038)
-0.018
(0.021)
-0.077**
(0.035)
-0.012
(0.013)
-0.070
(0.050)
-0.008
(0.028)
-0.099
(0.061)
-0.007
(0.037)
-0.067
(0.041)
-0.007
(0.018)
1993, 2004
842
1993
488
2004
354
1993
695
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. The binary dependent variable is 1 if the respondent voted yes, 0 if no. Standard
errors of total effect τ are from marginal effects after probit estimates. Inverse propensity score weighted results for direct (δ) and indirect (η) effects. Standard errors for direct and indirect effects are based on 1,999
bootstrap iterations. The mediator Income takes on value 1 if the respondent has above average income. Only with pre-treatment confounding
variables West, Center, Center-West, Center-East, Age, Catholic. Based
on data from VOX-surveys no. 161, 421, 511, and 862. Data are available
online on http://nesstar.sidos.ch/webview/index.jsp.
40
D
Tables Propensity Scores
Table 12: Propensity Score Estimates with Mediator Work : Sample of all Respondents
Sample
Work
West
Center
Center-West
Center-East
Age
Catholic
Partner
Education
Urban
Houseowner
House
Constant
Ballots
Observations
(1)
All
-0.729***
(0.062)
0.395**
(0.173)
0.418**
(0.173)
0.423**
(0.173)
0.407**
(0.172)
-0.013***
(0.002)
-0.022
(0.057)
0.020
(0.057)
-0.314***
(0.059)
0.170***
(0.059)
-0.048
(0.073)
0.069
(0.073)
0.563***
(0.211)
All
2,375
(2)
All
(3)
All
(4)
All
(5)
All
0.439**
(0.172)
0.468***
(0.172)
0.457***
(0.172)
0.447***
(0.171)
-0.003**
(0.002)
-0.024
(0.056)
-0.032
(0.056)
-0.291***
(0.057)
0.177***
(0.058)
-0.041
(0.071)
0.066
(0.072)
-0.361*
(0.194)
-1.292***
(0.148)
0.063
(0.171)
0.109
(0.176)
0.038
(0.163)
0.092
(0.161)
0.119
(0.167)
-0.093
(0.155)
-0.026***
(0.004)
-0.049
(0.127)
-0.122
(0.125)
-0.267*
(0.160)
0.227*
(0.126)
0.427**
(0.173)
-0.192
(0.172)
1.877***
(0.322)
-0.007**
(0.003)
-0.066
(0.120)
-0.076
(0.121)
-0.239
(0.151)
0.263**
(0.120)
0.404**
(0.162)
-0.184
(0.161)
0.151
(0.235)
-0.707***
(0.123)
0.397
(0.300)
0.434
(0.297)
0.366
(0.296)
0.320
(0.295)
-0.014***
(0.003)
-0.109
(0.107)
0.100
(0.108)
-0.434***
(0.123)
0.018
(0.115)
-0.212
(0.142)
0.161
(0.147)
0.708*
(0.388)
All
2,375
1981
525
1981
525
1991
671
(6)
All
(7)
All
(8)
All
0.370
(0.294)
0.425
(0.291)
0.376
(0.290)
0.327
(0.289)
-0.005
(0.003)
-0.091
(0.105)
0.065
(0.106)
-0.340***
(0.119)
0.004
(0.113)
-0.205
(0.140)
0.158
(0.144)
-0.204
(0.347)
-0.628***
(0.106)
0.357
(0.267)
0.235
(0.266)
0.429
(0.266)
0.369
(0.263)
-0.013***
(0.003)
0.006
(0.100)
0.154
(0.102)
-0.380***
(0.101)
0.167
(0.107)
-0.302**
(0.131)
0.151
(0.133)
0.576*
(0.334)
0.432
(0.267)
0.316
(0.265)
0.526**
(0.267)
0.467*
(0.263)
-0.007**
(0.003)
-0.002
(0.099)
0.076
(0.100)
-0.393***
(0.099)
0.167
(0.106)
-0.272**
(0.129)
0.122
(0.131)
-0.150
(0.310)
1991
671
1993
771
1993
771
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. Propensity score estimates (probit
model) with mediator Work. Dependent variable is dummy being 1 for female, 0 for men. Odd columns
are P (G = 1|M, C). Even columns are P (G = 1|C). Based on data from VOX-surveys no. 161, 421,
511, and 862.
41
Table 13: Propensity Score Estimates with Mediator Work : Sample of Voters
VARIABLES
Work
West
Center
Center-West
Center-East
Age
Catholic
Partner
42
Education
Urban
Houseowner
House
Constant
Ballots
Observations
(1)
Voters
(2)
Voters
-0.687***
(0.075)
0.517**
(0.221)
0.497**
(0.220)
0.427*
(0.221)
0.448**
(0.219)
-0.014***
(0.002)
0.036
(0.069)
-0.040
(0.070)
-0.276***
(0.068)
0.245***
(0.071)
-0.032
(0.085)
0.124
(0.085)
0.455*
(0.264)
0.573***
(0.220)
0.538**
(0.219)
0.472**
(0.219)
0.489**
(0.218)
-0.005**
(0.002)
0.037
(0.068)
-0.120*
(0.069)
-0.273***
(0.067)
0.240***
(0.070)
-0.018
(0.084)
0.118
(0.084)
-0.409*
(0.245)
All
1,634
All
1,634
(3)
Voters
(4)
Voters
(5)
Voters
-1.401***
(0.212)
0.545**
(0.241)
0.559**
(0.247)
0.219
(0.219)
0.546**
(0.224)
0.518**
(0.233)
0.033
(0.205)
-0.031***
(0.006)
-0.167
(0.180)
-0.109
(0.183)
-0.109
(0.208)
0.471***
(0.179)
0.470**
(0.228)
-0.007
(0.222)
1.737***
(0.466)
-0.009*
(0.005)
-0.229
(0.171)
-0.055
(0.176)
-0.158
(0.197)
0.438***
(0.168)
0.356*
(0.210)
-0.033
(0.204)
-0.131
(0.343)
-0.526***
(0.153)
0.784
(0.480)
0.582
(0.470)
0.300
(0.472)
0.426
(0.473)
-0.018***
(0.005)
0.138
(0.141)
0.106
(0.146)
-0.351**
(0.153)
0.193
(0.156)
-0.321*
(0.192)
0.456**
(0.196)
0.331
(0.559)
1981
287
1981
287
1991
397
(6)
Voters
(7)
Voters
(8)
Voters
(9)
Voters
(10)
Voters
0.769
(0.468)
0.536
(0.457)
0.288
(0.460)
0.418
(0.461)
-0.012***
(0.004)
0.157
(0.139)
0.063
(0.145)
-0.294*
(0.150)
0.146
(0.153)
-0.259
(0.188)
0.414**
(0.193)
-0.270
(0.518)
-0.751***
(0.130)
0.382
(0.341)
0.250
(0.339)
0.535
(0.342)
0.506
(0.334)
-0.015***
(0.004)
0.046
(0.122)
0.093
(0.128)
-0.355***
(0.120)
0.173
(0.129)
-0.218
(0.154)
0.070
(0.156)
0.665
(0.426)
0.502
(0.337)
0.360
(0.336)
0.726**
(0.338)
0.650**
(0.331)
-0.006*
(0.003)
0.068
(0.119)
-0.045
(0.124)
-0.388***
(0.117)
0.165
(0.127)
-0.186
(0.150)
0.047
(0.152)
-0.271
(0.389)
-0.353**
(0.154)
0.361
(0.407)
0.661
(0.409)
0.556
(0.408)
0.604
(0.408)
-0.000
(0.005)
0.123
(0.142)
-0.163
(0.141)
-0.325**
(0.130)
0.240*
(0.142)
0.001
(0.164)
0.002
(0.157)
-0.218
(0.517)
0.380
(0.410)
0.699*
(0.412)
0.556
(0.412)
0.588
(0.411)
0.005
(0.004)
0.112
(0.141)
-0.202
(0.139)
-0.323**
(0.130)
0.251*
(0.141)
-0.001
(0.163)
0.008
(0.156)
-0.718
(0.474)
1991
397
1993
542
1993
542
2004
408
2004
408
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. Propensity score estimates (probit model) with mediator
Work. Dependent variable is dummy being 1 for female, 0 for men. Odd columns are P (G = 1|M, C). Even columns are
P (G = 1|C). Based on data from VOX-surveys no. 161, 421, 511, and 862.
Table 14: Propensity Score Estimates with Mediator Income
VARIABLES
Income
West
Center
Center-West
Center-East
Age
Catholic
Partner
Education
Urban
Houseowner
House
Constant
Ballots
Observations
(1)
Voters
(2)
Voters
(3)
Voters
(4)
Voters
(5)
Voters
-0.255**
(0.101)
0.480*
(0.270)
0.521*
(0.269)
0.725***
(0.272)
0.697***
(0.270)
-0.003
(0.003)
0.181*
(0.097)
-0.140
(0.102)
-0.321***
(0.094)
0.265***
(0.100)
-0.039
(0.118)
0.047
(0.115)
-0.345
(0.312)
1993, 2004
842
(6)
Voters
(7)
All
(8)
All
0.483*
(0.269)
0.504*
(0.268)
0.697***
(0.270)
0.660**
(0.268)
-0.002
(0.003)
0.169*
(0.097)
-0.218**
(0.097)
-0.384***
(0.091)
0.226**
(0.099)
-0.070
(0.117)
0.048
(0.115)
-0.407
(0.310)
-0.290**
(0.133)
0.458
(0.355)
0.368
(0.352)
0.763**
(0.356)
0.690**
(0.350)
-0.009**
(0.004)
0.183
(0.127)
-0.027
(0.135)
-0.360***
(0.130)
0.188
(0.136)
-0.192
(0.163)
0.090
(0.164)
-0.076
(0.407)
0.471
(0.351)
0.344
(0.348)
0.708**
(0.352)
0.656*
(0.346)
-0.008**
(0.004)
0.165
(0.127)
-0.096
(0.130)
-0.436***
(0.125)
0.127
(0.133)
-0.238
(0.162)
0.098
(0.164)
-0.106
(0.404)
-0.209
(0.167)
0.384
(0.430)
0.734*
(0.429)
0.575
(0.431)
0.665
(0.432)
0.004
(0.005)
0.222
(0.156)
-0.239
(0.165)
-0.326**
(0.142)
0.302**
(0.153)
0.157
(0.179)
-0.068
(0.169)
-0.643
(0.514)
0.359
(0.430)
0.715*
(0.429)
0.561
(0.430)
0.620
(0.431)
0.006
(0.005)
0.215
(0.155)
-0.320**
(0.151)
-0.360***
(0.139)
0.292*
(0.153)
0.143
(0.178)
-0.066
(0.169)
-0.749
(0.507)
-0.218**
(0.108)
0.264
(0.286)
0.206
(0.284)
0.418
(0.285)
0.352
(0.282)
-0.009***
(0.003)
0.059
(0.104)
0.062
(0.108)
-0.373***
(0.109)
0.145
(0.113)
-0.228
(0.141)
0.125
(0.141)
0.162
(0.332)
0.287
(0.285)
0.202
(0.283)
0.400
(0.283)
0.334
(0.281)
-0.008***
(0.003)
0.051
(0.104)
0.012
(0.105)
-0.426***
(0.105)
0.116
(0.112)
-0.270*
(0.139)
0.134
(0.141)
0.108
(0.329)
1993, 2004
842
1993
488
1993
488
2004
354
2004
354
1993
695
1993
695
* p<0.1, ** p<0.05, *** p<0.01. Standard errors in brackets. Propensity score estimates (probit model)
with mediator Income. Dependent variable is dummy being 1 for female, 0 for men. Odd columns are
P (G = 1|M, C). Even columns are P (G = 1|C). Based on data from VOX-surveys no. 511, and 862.
43
Propensity Score Histograms
5
4
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
6
a P (G = 1|C) for Women
3
E
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
P(M,C)
.2
.4
.6
P(M,C)
Figure 7: Histograms of propensity scores from probit estimates for the 1981 survey (all respondents) with mediator Work. P (M, C) propensity scores control for the mediator and confounders,
P (C) only for the latter. Corresponds to column (2) in Table 6. a: Propensity scores P (C) based
on confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 161.
44
b P (G = 1|C) for Men
3
Density
0
0
1
2
2
4
Density
4
6
5
8
6
a P (G = 1|C) for Women
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
.2
.4
P(M,C)
.6
P(M,C)
Figure 8: Histograms of propensity scores from probit estimates for the 1991 survey (all respondents) with mediator Work. P (M, C) propensity scores control for the mediator and confounders,
P (C) only for the latter. Corresponds to column (3) in Table 6. a: Propensity scores P (C) based
on confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 421.
a P (G = 1|C) for Women
6
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
P(M,C)
.2
.4
.6
P(M,C)
Figure 9: Histograms of propensity scores from probit estimates for the 1993 survey (all respondents) with mediator Work. P (M, C) propensity scores control for the mediator and confounders,
P (C) only for the latter. Corresponds to column (4) in Table 6. a: Propensity scores P (C) based
on confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 511.
45
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
6
a P (G = 1|C) for Women
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
.2
.4
P(M,C)
.6
P(M,C)
Figure 10: Histograms of propensity scores from probit estimates for full sample (only voters) with
mediator Work. P (M, C) propensity scores control for the mediator and confounders, P (C) only for
the latter. Corresponds to column (5) in Table 6. a: Propensity scores P (C) based on confounders
for women; b: propensity scores P (C) based on confounders for men; c: propensity scores P (M, C)
based on mediator and confounders for women; d: propensity scores P (M, C) based on mediator
and confounders for men. Based on data from VOX-surveys no. 161, 421, 511, and 862.
a P (G = 1|C) for Women
6
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
P(M,C)
.2
.4
.6
P(M,C)
Figure 11: Histograms of propensity scores from probit estimates for the 1981 survey (only voters)
with mediator Work. P (M, C) propensity scores control for the mediator and confounders, P (C)
only for the latter. Corresponds to column (6) in Table 6. a: Propensity scores P (C) based on
confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 161.
46
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
6
a P (G = 1|C) for Women
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
.2
.4
P(M,C)
.6
P(M,C)
Figure 12: Histograms of propensity scores from probit estimates for the 1991 survey (only voters)
with mediator Work. P (M, C) propensity scores control for the mediator and confounders, P (C)
only for the latter. Corresponds to column (7) in Table 6. a: Propensity scores P (C) based on
confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 421.
a P (G = 1|C) for Women
6
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
P(M,C)
.2
.4
.6
P(M,C)
Figure 13: Histograms of propensity scores from probit estimates for the 1993 survey (only voters)
with mediator Work. P (M, C) propensity scores control for the mediator and confounders, P (C)
only for the latter. Corresponds to column (8) in Table 6. a: Propensity scores P (C) based on
confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 511.
47
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
6
a P (G = 1|C) for Women
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
.2
.4
P(M,C)
.6
P(M,C)
Figure 14: Histograms of propensity scores from probit estimates for the 2004 survey (only voters)
with mediator Work. P (M, C) propensity scores control for the mediator and confounders, P (C)
only for the latter. Corresponds to column (9) in Table 6. a: Propensity scores P (C) based on
confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 862.
a P (G = 1|C) for Women
6
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
P(M,C)
.2
.4
.6
P(M,C)
Figure 15: Histograms of propensity scores from probit estimates for the surveys from 1993 and
2004 with mediator Income. P (M, C) propensity scores control for the mediator and confounders,
P (C) only for the latter. Corresponds to column (1) in Table 7. a: Propensity scores P (C) based
on confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 511, and 862.
48
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
6
a P (G = 1|C) for Women
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
.2
.4
P(M,C)
.6
P(M,C)
Figure 16: Histograms of propensity scores from probit estimates for the 1993 survey (only voters)
with mediator Income. P (M, C) propensity scores control for the mediator and confounders, P (C)
only for the latter. Corresponds to column (2) in Table 7. a: Propensity scores P (C) based on
confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 511.
a P (G = 1|C) for Women
6
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
P(M,C)
.2
.4
.6
P(M,C)
Figure 17: Histograms of propensity scores from probit estimates for the 2004 survey (only voters)
with mediator Income. P (M, C) propensity scores control for the mediator and confounders, P (C)
only for the latter. Corresponds to column (3) in Table 7. a: Propensity scores P (C) based on
confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 862.
49
5
4
3
Density
0
1
2
3
0
1
2
Density
4
5
6
b P (G = 1|C) for Men
6
a P (G = 1|C) for Women
0
.2
.4
.6
.8
1
0
.2
.4
P(C)
.8
1
.8
1
5
4
3
2
1
0
0
1
2
3
Density
4
5
6
d P (G = 1|M, C) for Men
6
c P (G = 1|M, C) for Women
Density
.6
P(C)
0
.2
.4
.6
.8
1
0
P(M,C)
.2
.4
.6
P(M,C)
Figure 18: Histograms of propensity scores from probit estimates for the 1993 survey (all respondents) with mediator Income. P (M, C) propensity scores control for the mediator and confounders,
P (C) only for the latter. Corresponds to column (4) in Table 7. a: Propensity scores P (C) based
on confounders for women; b: propensity scores P (C) based on confounders for men; c: propensity
scores P (M, C) based on mediator and confounders for women; d: propensity scores P (M, C) based
on mediator and confounders for men. Based on data from VOX-surveys no. 511.
50
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