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Risk-Aversion and Trade Union Membership
Laszlo Goerke and Markus Pannenberg
CESifo GmbH
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Risk-Aversion and Trade Union Membership*
Laszlo Goerke
Eberhard Karls Universität Tübingen
Department of Economics
Melanchthonstraße 30
D – 72074 Tübingen, Germany
E-Mail: Laszlo.Goerke(at)uni-tuebingen.de
IZA, Bonn and CESifo, Munich
Markus Pannenberg
DIW Berlin
SOEP
Königin-Luise-Straße 5
D – 14195 Berlin, Germany
E-Mail: mpannenberg(at)diw.de
University of Applied Sciences Bielefeld and IZA, Bonn
preliminary version: 04.5.2007
Abstract
In an open-shop model of trade union membership with heterogeneity with respect to risk
attitudes, a worker's relative risk-aversion can affect the decision to join a trade union and the
collective bargaining outcome. Using German panel data (GSOEP) and three novel direct
measures of individual risk-aversion, we find evidence for a significantly positive relationship
between individual risk-aversion and the likelihood of being a union member. Moreover, our
findings suggest that risk-aversion is correlated negatively with wages and, thereby, positively
with employment.
JEL Classification: J 51
Keywords: employment, membership, risk-aversion, trade union
* We are grateful to Carsten Hefeker for helpful comments.
1. Introduction
The changes in wellbeing owing to a variation in consumption possibilities are determined by the
slope and curvature of an individual's utility function. Accordingly, an assessment of the gains and
costs of trade union membership is likely to vary with risk attitudes. However, the nature of such a
linkage is largely unexplored. Understanding the impact of risk aversion on the net gain from
being a trade union member can consequently contribute to a more profound appreciation of the
determinants of trade union density. In addition, the number of members can affect a trade union's
bargaining power. Accordingly, being aware of the exact relationship between risk attitudes and
union membership can also help to predict how bargaining power and collective negotiations are
influenced by changes in the distribution of individual risk-preferences.
Risk attitudes and collective bargaining can be related if trade unions attempt to insure their
members against income variations by reducing wage and employment uncertainty (e.g. Agell and
Lommerud 1992, Burda 1995). The strength of this desire will depend on the risk preferences of
union members. However, this literature assumes a given union membership. This is the case
because a reduction in income variability represents a public good and, thus, provides no
incentives for an individual to join a trade union, unless there are closed-shops. To establish a
relation between risk attitudes and an individual's net gain from trade union membership, a union
must supply an excludable good. Therefore, in this paper we initially investigate an open-shop
union model in the tradition of Booth (1985) and Booth and Chatterji (1995).
We assume that workers differ in their aversion to risk and, hence, evaluate the income loss
resulting from the union membership fee differently. This establishes an – ambiguous –
relationship between the Arrow-Pratt measure of relative risk-aversion and the net gains from
union membership. The relation allows us to analyse the effects of risk-aversion on wages and
employment which are, again, theoretically indeterminate. The linkage between an individual's
extent of risk-aversion and union membership status and the implications for collective bargaining
outcomes are, therefore, largely empirical issues. In the respective part of the paper, we use data
from the German Socio-Economic Panel (GSOEP), a nationally representative longitudinal survey,
and, in particular, exploit a novel set of direct measures of individual risk attitudes. We find that a
worker is more inclined to be a trade union member, the more risk-averse he is. An increase in
risk-aversion of the decisive union member, ceteris paribus, reduces the preferred wage. However,
the rise in membership increases the union's bargaining power and, thereby, contributes to higher
wages. Our empirical findings suggest that the first effect may dominate, so that more risk-averse
workers obtain lower wages, although their unionisation rate is higher. Accordingly, risk-aversion
may contribute to wage moderation and have positive employment consequences.
1
In the literature on open-shop models of collective bargaining - surveyed, for example, by
Schnabel (2003) - only few papers have explicitly incorporated notions of risk-aversion and
predict either no or a negative impact on union membership. In contrast, we find that a positive
relationship can exist. In addition, none of the empirical contributions estimating the determinants
of trade union membership known to us has explicitly evaluated the effects of an individual's risk
attitude. Finally, open-shop models of union membership have assumed workers to be
heterogeneous with respect to the valuation of a union-provided good or a social norm. Variations
in individual risk attitudes have not been allowed for. Our contribution is, therefore, twofold: First,
it generates predictions on the impact of a worker's risk attitude on the propensity to unionise and
the ensuing consequences for collective bargaining outcomes. Second, our paper contains an
explicit test of the membership predictions.
The paper unfolds as follows. Section 2 sets out the model of endogenous union membership and
collective wage bargaining, and relates the findings to the literature. Section 3 contains the
description of the data and our empirical specification. In Section 4 we present the empirical
results, while Section 5 concludes.
2. Risk-aversion in a Model of Wage Bargaining with Endogenous Union Membership
The theoretical model presented below allows determining union membership and wages. The
analysis focuses on one open-shop trade union and one firm (or employer association). Wages are
not differentiated according to a worker's union status. This assumption is in line with the legal
situation in Germany, not allowing for closed shops. Additionally, it is consistent with empirical
evidence – elaborated upon in Section 4. To provide an incentive for joining a trade union, despite
the existence of a membership fee and the absence of a wage premium, the union supplies a
private good solely to its members.1 The incentives to join a union vary across workers, although
all of them appraise the private union good identically. This is because the utility loss due to the
membership fee varies owing to distinct risk preferences.
Membership Decision
Let total utility be additively separable in the utility from income and the utility C from consuming
the private good.2 Additionally, the utility of worker i from a wage w is assumed to be given by
w(1 – σi)/(1 – σi), 0 < σi ≠ 1, implying a constant individual Arrow-Pratt measure σi of relative
1
See Olson (1965) for the notion of selective incentives. A private good may consist of legal advice, the provision of
insurances or pensions at lower prices than available elsewhere, or the supply of job-related information.
2
This simplifying hypothesis suffices to illustrate the main features of the linkage between risk-aversion and trade
union membership.
2
risk-aversion. The measure of relative risk-aversion is distributed on the interval [σmin + ε;
σmax + ε], ε ≥ 0. Increasing ε from ε = 0 mimics a general rise in risk aversion. The effects of such
a rise will be looked at later on.
The membership fee is an increasing and weakly convex function G of the wage w, 0 < G(w) < w,
~ := w –
1 > G' > 0, G'' ≥ 0. Accordingly, the income of an employed union member equals w
G(w). An unemployed worker receives unemployment benefits which are normalised to zero
without loss of generality, derives no benefits from membership, and does not pay a membership
fee. Alternatively, it can be assumed that unemployed workers lose their union status. An
employed non-member also receives the wage w. The probability that a worker is employed equals
N(w), assuming a random draw from the population of all workers, the size of which is normalized
to unity. Hence, 0 < N(w) ≤ 1 also describes the employment level.
Worker i decides about union membership, anticipating the (equilibrium) levels of union density
and wages. The worker will join the union if the gain Z(σi) from doing so is positive. Since the
evaluation of incomes differs across workers, there is a wage w making a particular worker just
indifferent between leaving the trade union and remaining in it. This worker represents the
marginal member. The marginal member's measure of relative risk-aversion is denoted by σ. The
gain from membership for this member is zero and then defined by:
Z(σ,...) :=
~ 1− σ
w
w1− σ
=0
+C−
1− σ
1− σ
(1)
The derivatives of Z(σ,…) are given by:
∂Z(σ,...)
~ − σ (1 − G ' ) − w − σ
:= Z w = w
∂w
(2)
~ 1− σ ln w
~ − w1− σ ln w
∂Z(σ,...)
w
:= Z σ = −
∂σ
1− σ
(3)
If the marginal union member is characterized by a measure of relative risk-aversion less than
unity (σ < 1) the gain from membership will rise with risk-aversion, implying Zσ > 0.
Accordingly, all workers characterised by σi > σ derive a positive gain from membership so that
the gains rise with the measure of risk-aversion. Therefore, workers characterized by the highest
measure of relative risk-aversion are the first to join the union. However, for a measure of relative
risk-aversion greater than unity (σ > 1) the sign of Zσ is theoretically indeterminate. The sign of
Zw is also a priori uncertain. Empirically, a worker's wage has not been found to alter the
probability of union membership (see the estimates presented below and also Wagner 1990, 1991,
3
Fitzenberger et al. 1999, and Goerke and Pannenberg 2004). In addition, in our empirical analysis
we obtain evidence that the marginal trade union member's measure of relative risk-aversion is less
than unity. This implies Zw = 0 and Zσ > 0.3 The further theoretical analysis will make use of
these findings to simplify the exposition.
The impact of risk-aversion on the incentive to become a union member has previously been
investigated in a number of theoretical contributions. In Booth's (1984) seminal paper the
membership decision is independent of the measure of risk-aversion, for a given wage. This is
because the marginal trade union member is defined in such a manner that the utility resulting
from the wage less membership fee equals the utility from unemployment. This situation will be
attained if the arguments of the utility function coincide. Hence, changes in the slope or curvature
of the utility function do not alter the identity of the marginal member (Booth 1984, eq. (13)). In
Moreton's (1998, 1999) set-up, a variation in risk-aversion is modelled as a change in the second
derivative of the utility function, holding constant the first derivative. Since the membership curve
only depends on utility levels, it is unaffected by a change in risk-aversion. Finally, Oswald (1982)
~ >w
presumes that the income of a union member is higher than that of a non-member, i.e. that w
holds. In this case, the benefits from union membership decline with the measure of relative riskaversion. According to our knowledge the present contribution is, therefore, the first allowing for a
positive impact of individual risk-aversion on the incentives to join a trade union.
Wage Bargaining
The outcome of the wage bargain between the firm and the union is determined by the (symmetric)
Nash-solution. The union's preferences are given by those of the median member, whose ArrowPratt measure of relative risk-aversion is denoted by µ. The firm uses labour as only input, while
the output price is normalized to unity. The firm's payoff is given by its profits Π. Profit
maximization leads to ∂Π/∂N = 0, ∂Π/∂w = -N(w) by the envelope theorem, and ∂N/∂w := N'(w) <
0. The fallback payoff of the firm is normalised to unity, while the median member's utility in the
case of no agreement is determined by unemployment benefits, set equal to zero. The wage,
~ 1− µ /(1 − µ) + C > 0 , is consequently determined by:
making use of Ω := w
V :=
~ − µ (1 − G ' )
N( w ) w
− K(w ) = 0 ,
Ω
where K ( w ) :=
( N( w )) 2
− N' ( w ) > 0
Π
Moreover, we have:
3
Using Zw = 0 in equation (3) does not allow to derive further restrictions for the sign of Zσ.
4
(4)
Vw =
2 ~ − µ ~ −1
~ −µ
~ −µ
w
(N' (w )(1 − G ' ) − N(w )G ' ') − N(w ) (1 − G ' ) w (µw Ω + w ) − K w
Ω
Ω2
(5)
Subsequently, an interior solution to the wage bargaining problem is assumed (Vw < 0), which
yields a wage above the full employment level, implying N(w) < 1. For Vw < 0, the wage effect of
an increase in the measure of relative risk-aversion µ of the median member is determined by:
Vµ = −
~ −µ ⎡
~ 1− µ ⎤
N( w )(1 − G ' ) w
~− w
⎥
⎢C ln w
⎢⎣
(1 − µ) 2 ⎥⎦
Ω2
(6)
The sign of Vµ is determined by two effects: A larger measure of relative risk-aversion lowers the
gain from a higher wage, while its costs in terms of the fall in employment remain unaffected.
Moreover, a rise in µ generally alters the gain from bargaining for the median member and will
unambiguously raise the incentives to increase wages for σ < 1. The overall impact is, thus,
uncertain. A negative wage and positive employment impact of higher risk-aversion in (closedshop) collective bargaining models have been derived, for example, by Sampson (1983),
McDonald (1991), Oswald (1982), and Blair and Crawford (1984). The employment result extends
to a setting in which the alternative income is endogenised (see Nickell 1990). The findings for the
open-shop model suggest that these predictions are strongly influenced by the assumption of a
given number of union members.
Comparative Statics
The present analysis aims at determining the membership and the ensuing wage effects of a change
in risk-aversion in an open-shop setting. To do so, first, the impact of a rise in the measure of
relative risk-aversion of all workers on the incentives to join a trade union is looked at.
Subsequently, the consequences for wages are investigated.
Since a change in the wage does not alter the probability of membership (that is, since Zw = 0), the
membership curve is vertical in the wage - risk-aversion space. This implies that the marginal
trade union member - and, hence, union density - is uniquely defined by Z(σ,…) = 0. In particular,
if the interval [σmin + ε; σmax + ε], ε ≥ 0, from which the measure of risk-aversion can stem,
shifts to the right because ε rises from zero to ε > 0, as depicted in Figure 1, the new marginal
member will be characterised by the same value of relative risk-aversion than the original one
(∂σ/∂ε = 0). However, the level of risk-aversion of the marginal member will be closer to the lower
bound of the interval. For Zσ > 0, this effect is equivalent to an increase in the number of union
members. If everyone becomes more risk-averse, the worker who just refrained from being a union
5
member, prior to the general rise in risk-aversion, will experience a rise in utility from joining (for
Zσ > 0) and become a unionist. The result is independent of the wage and can be summarised in:
Proposition 1:
For Zw = 0, a general rise in the Arrow-Pratt measure of relative risk-aversion raises trade union
density for Zσ > 0.
Figure 1: Equilibrium Wage and Marginal Member in Wage - Risk-aversion Space
w
Z
V0
V1
σ min σ min + ε
σ
σ max σ max + ε
σi
Given Vw < 0 and an indeterminate sign of Vµ, that is the risk preferences of the median member
have an ambiguous wage effect, the slope of the wage-bargaining curve in the wage – riskaversion space cannot be ascertained. For Zw = 0 and ∂σ/∂ε = 0, the wage effect of a shift in the
distribution of the measure of risk-aversion is determined by:
dw
=−
dε
Vµ
∂µ
∂σ
+ Vσ
∂ε = − Vµ ∂µ
∂ε
Vw
Vw ∂ε
(7)
The measure µ of risk-aversion of the median member is likely to increase with a general shift of
the distribution to the right (implying ∂µ/∂ε > 0). However, theoretically a fall of µ cannot be ruled
6
out either (that is, ∂µ/∂ε < 0). The intuition for the ambiguity is the following: The original median
member, prior to the general increase in risk-aversion, will obviously be characterised by a greater
level of risk-aversion subsequent to the shift of the distribution. Since more workers become union
members, the identity of the median will change. If a relatively large mass of the distribution lay to
the left of the original marginal member, but were to the right of σ subsequent to the shift of the
distribution, the median member's measure of risk-aversion may decline. This possibility can be
ruled out if the distribution of the measure of risk-aversion is fairly symmetric around the positions
of the original and new marginal member. Assuming, therefore, a uniform distribution the measure
of relative risk-aversion of the median member is given by µ = [σ + (σmax + ε)]/2. Accordingly, a
general increase in risk-aversion also raises the median member's risk-aversion µ (∂µ/∂ε = 0.5). In
addition, Vµ = 2Vσ = 2Vε holds. From equation (7) the wage effect is then given by dw/dε = Vµ/(2Vw) and can be summarised in:
Proposition 2:
Assume Vµ < 0, that is, a negative relationship between the measure of risk-aversion of the
median member and the bargained wage. If, in addition, Zw = 0 holds and the Arrow-Pratt
measure of relative risk-aversion is distributed uniformly, a general rise in the measure of relative
risk-aversion will lower the bargained wage.
To illustrate Proposition 2, suppose that the bargained wage falls with the measure of risk-aversion
of the median member (implying Vµ, Vε < 0). A general rise of risk-aversion has two effects: For
a given density level, the higher measure of risk-aversion induces the median member to accept a
lower wage in the bargaining process. However, a higher union density will result in workers
joining the trade union which are characterised by a lower measure of risk-aversion, relative to the
maximum. This effect, ceteris paribus, lowers the median member's relative risk-aversion. Given a
uniform distribution of risk-aversion, the general rise in risk-aversion dominates the impact of a
rise in union density. In this case, the wage-bargaining curve is downward-sloping in the wage risk-aversion space, as depicted in Figure 1. Moreover, a general rise in risk-aversion shifts the
wage-bargaining curve downward from V0 to V1.
The employment consequences of an increase in risk-aversion are directly determined by the wage
effects and summarised in:
Corollary 3:
For Zw = 0, Vµ < 0, and a uniformly distributed Arrow-Pratt measure of relative risk-aversion, a
general rise in the measure of relative risk-aversion raises employment.
7
The net consequences of a change in risk-aversion of all workers on the bargained wage and
employment are, therefore, determined by the impact on the median worker's preferred wage, i.e.
the sign of Vµ, and the effect of a change in the marginal member on the median's preferences.
Since the first effect is theoretically indeterminate and because the second hinges on the
distribution of the measure of risk-aversion, the relation between an encompassing rise in riskaversion and the bargained wage is ultimately an empirical issue.
3. Data and Empirical Specifications
Data
In our theoretical model wages result from negotiations between a trade union and employer. To
capture this setting, data on firm characteristics and the bargaining relationship would be desirable.
Moreover, information on individual risk preferences of workers is required. Ideally, we would,
hence, use matched employer-employee data with detailed information on firms and workers.
However, the available linked employer-employee data sets for Germany provide no information
on individual risk attitudes, pivotal for putting our theoretical model to an empirical test.
Therefore, we utilise data from the German Socio-Economic Panel (GSOEP), a nationally
representative longitudinal survey of the resident German population (Wagner et al. 1993, SOEP
Group 2001) which provides three novel direct measures of individual risk attitudes. We use data
for the years 2003 and 2004, because the 2003 survey includes information on union membership,
while the survey in 2004 contains the risk indicators. Our sample consists of full-time workers
with valid information on the relevant measures of risk attitudes and union membership from West
and East Germany.4 Observations from self-employed persons, apprentices and civil servants
('Beamte') are excluded. Moreover, in the regression analyses all respondents with missing
information on relevant variables are dropped.
In our theoretical framework the individual decision to join the union depends on wages, the utility
of the private good provided by the trade union and the membership fee. Hence, information on
how individual risk attitudes affect the evaluation of monetary payments is required. To meet this
requirement we, first, utilize a survey question requiring respondents to indicate their willingness
to take risks in financial matters. This willingness is recorded on an eleven-point scale. A value of
zero (ten) indicates a total unwillingness (readiness) to take risks. We, second, employ a survey
question corresponding more closely to a standard lottery measure in experiments. In particular,
information is collected on the individual's investment choices, based on a hypothetical lottery
4
Schnabel and Wagner (2003) conclude that the same set of variables can be used to analyse the determinants of
union membership in West and East Germany. To control for regional differences in the level of union density we
include a full set of state dummies in our regression analysis.
8
prize of 100.000 €. The questionnaire allows for 6 opportunities to invest this prize. More
precisely, the household can purchase a risky asset for 100.000 €, 80.000 €, 60.000 €, 40.000 €, or
20.000 € or can, finally, refrain from such an acquisition, with equal chances of doubling the
amount invested or losing half of it. Since the second measure is based on explicit stakes and
probabilities, it holds risk perceptions constant across individuals. Moreover, within the expected
utility framework, the hypothetical lottery allows us to calculate the Arrow-Pratt measure of
relative risk-aversion for each respondent (see for example Caliendo et al. 2006 or Guiso and
Paiella 2005).5 As a check of robustness, we additionally employ a survey question on the
willingness to take risks in general.
The GSOEP risk measures have been validated in a field experiment with representative subject
pools. Dohmen et al. (2005) find that questionnaire responses to the general risk question are
reliable predictors of actual risk-taking behaviour in the field experiment. Moreover, answers to
the general risk question are strongly correlated with those to the other two questions. Finally,
Dohmen et al. (2005) demonstrate that the best predictor of a specific outcome is the risk measure
most closely related to the relevant context. Therefore, we are confident that the GSOEP risk
measures we use are high-quality proxies for actual risk preferences in our specific context.
Due to data availability we link the information on individual risk attitudes collected in 2004 with
data on union membership and its determinants measured in 2003. Hence, the crucial assumption
of our empirical work is that individual union membership in 2003 does not alter peoples' risk
attitudes until they are collected in 2004. This requirement is consistent with evidence provided by
Andersen et al. (2005) and Barsky et al. (1997) that risk preferences elicited from hypothetical
lotteries in surveys are stable over time.
Empirical Specifications
Since we are interested in assessing the effect of individual risk attitudes on trade union
membership we start with the following specification of a standard probit model:
P (U i ,03 = 1| Ri ,04 , X i ,03 ) = Φ (α Ri ,04 + β ' X i ,03 ) ,
(8)
where U i ,03 =1 if the individual is a union member (in 2003), Ri ,04 is the relevant measure of
individual risk attitudes (in 2004), X i ,03 is a vector of control variables (also measured in 2003),
α , β ' are (vectors) of unknown parameters and Φ () is the cdf of the standard normal distribution.
Estimated marginal effects and standard errors robust with respect to clustering at the household
level are documented.
5
Given the construction of the lottery, the Arrow-Pratt measure of relative risk-aversion is bounded by 0.4 (4) from
below (above). See also Table A1 in the Appendix.
9
To address the potential endogeneity of our plain risk measures, we also use an instrumental
variable probit estimator (Wooldridge 2002, 472-477). Our according specification builds on a
structural form latent variable specification of latent union membership ( U i*,03 ), where U i ,03 = 1
[ U i*,03 > 0 ] and on a reduced-form specification of the particular risk measure Ri ,04 :
U i*,03 = α Ri ,04 + β ' X i ,03 + ε1,i
Ri ,04 = ∂Heighti ,04 + ∂ ' X i ,03 + ε 2,i
(9)
(10)
We assume that the errors ( ε1,i , ε 2,i ) follow a zero mean, bivariate normal distribution and are
independent of the instrument Heighti ,04 . Individual height is used as an instrument, since height
(i) is plausibly exogenous to the indicators of individual risk attitudes and has a significant impact
on individual risk preferences, (ii) is not correlated with the error term in the union membership
equation and (iii) has no direct impact on the likelihood of being a union member. The parameters
are estimated using maximum likelihood as the estimation criterion. Standard errors are robust
with respect to clustering at the household level. Standard tests for the validity of the instruments
and for endogeneity of our risk measures as well as marginal effects of the estimated parameters
and their standard errors are documented.
Both probit estimators require a distributional assumption to be made, i.e. a particular normality
assumption. However, there is no prior knowledge on the validity of this assumption. As a check
of robustness, we therefore employ a semi-nonparametric estimator originally suggested by
Gallant and Nychka (1987) and used in applied work, for example, by Gabler et al. (1993), Gerfin
(1996) and Stewart (2005). Essentially, this estimator approximates the true distribution of the
error terms by a Hermite series. The approximation can be expressed as the product of the normal
density and a squared polynomial and thus nests the standard probit model of equation (8). It can
be estimated by maximizing a pseudo-likelihood function and usual test procedures can be applied.
We adopt the framework proposed by Stewart (2004) to test the validity of the distributional
assumption of the probit model in our application and to estimate the parameters of interest.6
The vector of control variables consists of the usual covariates which have been found to affect the
probability of union membership in Germany in previous studies: Age, age squared, tenure, tenure
squared and dummy variables for being a foreigner, being male, different firm size categories,
having completed an apprenticeship, having a university degree, being member of a works council,
having preferences for the social democratic party (SPD) or the Christian-democratic parties
(CDU/CSU), the father being self-employed when the respondent was 15 years old, being a blue
6
See Stewart (2004) for a detailed description of the econometric specification and his corresponding stata-tool.
10
collar worker, the industry (NACE 1-digit) in which the respondent works and the state of
residence ('Bundesland').7 Since we link data from the years 2003 and 2004 in our sample,
longitudinal sample weights are calculated and used to take into account the sampling design of
the different subsamples of the GSOEP as well as panel attrition (cf. Pannenberg et al. 2004).
4. Results
Descriptive Evidence
Figure 2 shows the distribution of individual risk attitudes in financial matters by union
membership status. Each bar in the histograms indicates the percentage of respondents choosing a
number on the eleven-point scale, indicating their willingness to take risks in financial matters.
The degree of reluctance to take risks in financial matters is striking: 86% of all non-members and
91% of all union members choose a value of 5 or less on the eleven-point scale. Moreover, Figure
2 reveals that union members are more risk-averse than non-unionists. This is confirmed by means
of a Kolmogoroff/Smirnov test, which rejects the null hypothesis of equality of the distributions of
risk attitudes for union members and non-members at the α = 0.002 level. Figure 3 corroborates
this impression with respect to the lottery measure of individual risk attitudes: 64% of all union
members and 54% of all non-members in Germany do not invest a positive amount of the
hypothetical lottery prize in the risky asset. In this case a Kolmogoroff/Smirnov test rejects the
null hypothesis of equality of the distributions of the lottery measure for union members and nonmembers at the α = 0.061 level. With respect to general risk attitudes, Figure A1 (in the Appendix)
documents that roughly 63% of all workers choose a value of 5 or less on the eleven-point scale.
However, for this measure we do not observe significant differences in the distributions of risk
attitudes for members and non-unionists.
Considering the Arrow-Pratt measure of relative risk-aversion the findings confirm our previous
results that non-members are less risk-averse than union members, given that the mean of the
Arrow-Pratt measure is higher for union members (see Table A1 in the Appendix). The
Kolmogoroff/Smirnov test again rejects the equality of the distributions (α = 0.061). This is
consistent with the assumption in the theoretical section of the paper that those workers
characterized by the highest measure of relative risk-aversion are the first to join the union.
Moreover, the figures indicate that the minimum of the coefficient of relative risk-aversion is less
than unity, as it has been assumed in Section 2.
7
Descriptive statistics for all control variables are presented in Table A3 in the Appendix.
11
Regression Results
The descriptive evidence points to remarkable degrees of risk-aversion in our sample of full-time
workers. Furthermore, risk-aversion seems more prevalent among union members. In a first step,
we therefore use the standard weighted probit specification to assess whether individual risk
attitudes have an impact on union membership, conditional on a set of control variables. For the
sake of a more intuitive interpretation we recoded the eleven-point scale of the two GSOEP
measures of risk attitudes for our regression analysis in reverse order, i.e. '0' indicating strong risklove and '10' total reluctance to take risks. Consequently, for all measures of risk a higher value
indicates greater risk-aversion.8
As a preliminary exercise, we estimated regressions also including the log of the monthly gross
wage as covariate. Irrespective of the measure of individual risk-aversion employed, we could
replicate previous findings by Wagner (1990, 1991), Fitzenberger et al. (1999), and Goerke and
Pannenberg (2004) that the individual gross wage does not influence the probability of
membership.9 Accordingly, the wage is not included into our main specifications. In terms of our
theoretical model, the assumption Zw = 0 captures the insignificant wage effect.
Table 1 presents the estimated marginal effects and their standard errors for the four measures of
individual risk attitudes using the probit specification. Since our focus is on the relationship
between risk-aversion and union membership we do not discuss the parameter estimates for the set
of control variables which are in line with results from other studies.10 Column 1 reveals that fulltime workers who are more risk-avers in financial affairs exhibit a significantly higher probability
of being a union member than their less risk-averse colleagues. The marginal effects imply that
someone who switches from extremely risk-loving ('0') to extremely risk-averse ('10') in financial
matters exhibits a roughly 7 percentage points higher likelihood of being a union member than
before. Given that the unconditional mean of being a union member is around 20 % in our sample,
the size of the estimated marginal effect is remarkable. Column 2 presents the estimates for the
lottery measure of individual risk-aversion. Again, we observe a similar significant increase in the
probability of being a union member if someone decides not to invest a positive fraction of the
hypothetical prize in the risky asset. Column 3 contains the findings when using the Arrow-Pratt
measure of relative risk aversion. These estimates are in line with the ones for the lottery measure
8
With respect to the lottery measure, we do not have to recode our variable, since “1” indicates an investment of
100.000 € and “6” indicates an investment of 0 €.
9
Table A2 in the Appendix documents the parameter estimates for a specification with the measure of individual risk
attitudes in financial matters.
10
See, for example, Fitzenberger et al. (1999), Fitzenberger et al. (2006), Goerke and Pannenberg (2004), and
Schnabel and Wagner (2003). Only the significantly positive effect of acting as a works councillor represents a new
result. See Goerke and Pannenberg (2007) for evidence on the relationship between union membership and works
councillorship.
12
itself. If we use the encompassing measure of individual risk attitudes - instead of the two
measures related to financial affairs - we do not find a significant effect (column 4). This is in line
with evidence presented by Dohmen et al. (2005) that a context specific measure of individual risk
attitudes is the best predictor of actual individual behaviour in that context.
Summing up, we observe a significantly positive association between individual risk-aversion in
financial affairs and the likelihood of being a union member. Hence, in terms of the theoretical
discussion of Section 2 an overall increase in risk-aversion leads to an increase in union density, a
finding which is consistent with Proposition 1.
The previous empirical specifications have assumed that the measures of individual risk attitudes
are not correlated with the errors in the union membership equation. However, one might argue
that union membership is endogenous with respect to risk attitudes. We assess the potential
endogeneity of individual risk attitudes in the membership equation by means of the IV-probitestimator, using the instrument “individual height” as described above.
To test the validity of the instrument “height”, we start with a simple Wald-test of the estimated
parameter of height in a reduced-form equation in which the individual risk measures are regressed
on height and the set of control variables of the union membership equation. It turns out that height
is a valid instrument in terms of significant parameter estimates for the two risk measures based on
the willingness to take risks in financial matters and in general, but not for the two measures of
individual risk preferences based on the hypothetical lottery (see Table 2, Wald_IV). Moreover,
the Wald-tests of exogeneity indicate that we cannot reject the hypothesis that the relevant
measures of risk-aversion are exogenous (see Wald_Ex).11 Hence, taking these test statistics at
face value, there is no need for the IV-specification. However, the estimated parameter of
individual risk-aversion in financial matters on the probability of being a union member is
significantly positive and, once again, points to a positive association of risk-aversion and trade
union membership. Moreover, the estimated parameter of the overall risk-aversion measure is
significantly positive and the marginal effect indicates that a worker revealing the average degree
of risk-aversion of 5.2 in the sample ceteris paribus has a roughly 50 percentage points higher
probability of being a union member than an extremely risk-loving worker. This again suggests a
positive relationship between individual risk-aversion and trade union membership and puts into
perspective the insignificant effect for the encompassing measure of risk attitudes in our base
regression (cf. Table 1, column 4).
11
This result is confirmed by the test-statistic of the Rivers/Vuong test of exogeneity. See Wooldridge (2002, pp. 472)
for a description of both tests.
13
As pointed out above, a priori there is no evidence that the normality assumption underlying the
probit models is appropriate. Performing likelihood-ratio tests comparing the log-likelihoods of the
probit and the semi-nonparametric specification of the union membership equation described
above indeed indicate that the normality assumption of the probit model might not be upheld.
Therefore, in Table 3 we additionally present the estimated parameters for the different measures
of individual risk attitudes based on the semi-nonparametric specification. The estimated
parameters of the two direct measures of individual risk preferences as well the one of the
individual measure of relative risk aversion are significantly positive. Moreover, they are similar in
size to the estimated parameters of the standard probit specification (not documented). Hence,
relaxing the distribution assumptions of our econometric specifications again leads to parameter
estimates which confirm the finding of a positive relationship between individual risk-aversion and
trade union membership.
Summing up, there is substantial evidence that the probability of trade union membership of
German full-time workers rises with their aversion to risk.
Further Correlation Analysis
The theoretical model shows that the degree of risk-aversion of the median trade union member
has an impact on the bargained wage and therefore on the level of employment. Our estimates
indicate that an overall increase in the degree of risk-aversion raises the individual probability of
union membership and, ceteris paribus, leads to a rise in union density. Our preliminary
estimations also suggest that Zw = 0 applies (see Table A2 in the Appendix). As a consequence,
the bargained wage will decrease and the employment level increase if Vε, Vµ < 0 hold, i.e. if
there is a negative relationship between the bargained wage and the measure of risk-aversion of the
median member (see Proposition 2 and Corollary 3).
To get a crude grasp of the sign of Vµ, we specify standard Mincer-earnings regressions including
our measures of individual risk attitudes, an estimate of the industry-specific union density based
on the GSOEP data, individual union membership as well as the set of covariates used in the
regression analysis described above. Table 4 documents the parameter estimates for the measures
of individual risk attitudes, union density and individual union status.
We observe significantly negative correlations between (log) gross monthly wages and both
measures of the individual willingness to take risks, while the parameter estimates of the two risk
measures based on the hypothetical lottery are not significantly different from zero. Our finding of
a negative correlation between the individual willingness to take risks and individual wages (see
Bonin et al. 2006 for a similar result) is consistent with the assumption of Vε, Vµ < 0. Moreover,
14
the parameter estimates reveal a significantly positive correlation between industry-specific union
densities and wages, while the individual union membership status has no impact on wages.
Our simple correlation exercise provides supportive evidence for the two opposite effects of an
increase in individual risk-aversion in the theoretical model: On the one hand, greater risk-aversion
leads to a rise in union density, which tends to increase bargained wages. On the other hand,
higher risk-aversion goes along with lower wages. This finding is consistent with the interpretation
that an increase in individual risk-aversion leads to a change in the preferences of the median
member, which unions take into account when bargaining over wages and which ceteris paribus
has a negative impact on wages.
5. Conclusions
Why do workers belong to a trade union? Our theoretical analysis is based on the assumption that
a union provides its members with an excludable good. This constitutes the gain from union
membership. We, furthermore, assume that the costs of membership, namely the utility losses
resulting from the membership fee, vary with the extent of risk-aversion. Our empirical findings
are consistent with these presumptions. Using the German Socio-Economic Panel (GSOEP), a
nationally representative survey, we find that the probability of union membership increases
significantly and by a sizeable amount with indicators of individual aversion to risk. In a collective
bargaining set-up, a change in risk-aversion will then have two effects. First, the preferred wage
(and employment) outcome of the median member will change with his risk attitude. In addition,
the change in the level of union membership will alter the identity of the median member.
Accordingly, variations in risk-aversion have wage and employment effects. Our findings suggest
that wages may fall and employment may rise with an increase in risk-aversion of the labour force.
The impact of individual, direct measures of risk-aversion on the individual decision to become a
member of a trade union has not been analysed before. Since our information relates to Germany,
it will be interesting to see whether this positive correlation between risk-aversion and
unionisation is a robust one also existing in other industrial relations systems. The wider
implications of a positive relationship, for example, with respect to the effectiveness of union
organising campaigns, the preferred degree of centralisation in bargaining, the interaction of
product and labour market imperfections, or the role of trade unions as insurance devices in openshop settings also represent topics for future investigations.
15
Figure 2:
0: non-member;
1: member of a trade union
Figure 3:
0: non-member;
1: member of a trade union
16
Table 1: Union Membership and Individual Risk Attitudes in Germany
- Probit Estimates Risk_finance
Risk_lottery
Arrow-Pratt – RRA
Risk_general
Blue_collar
Father_self-employed
Prefers SPD
Prefers CDU/CSU
Member of works
council
Tenure
Tenure (sqrd)
Apprenticeship
University degree
Firm size:
20 ≤ X < 200 workers
Firm size:
200 ≤ X < 2000 workers
Firm size:
X > 2000 workers
Male
Foreigner
Age
Age (sqrd)
ME / s.e.
ME / s.e.
ME / s.e.
ME / s.e.
0.007*
---(0.003)
----0.013*
---(0.006)
----0.013**
---(0.005)
-----0.003
---(0.003)
0.124**
0.125**
0.124**
0.129**
(0.020)
(0.019)
(0.019)
(0.020)
-0.051*
-0.057*
-0.057*
-0.054*
(0.021)
(0.020)
(0.020)
(0.020)
0.105**
0.103**
0.103**
0.101**
(0.022)
(0.021)
(0.021)
(0.021)
-0.046**
-0.047**
-0.046**
-0.050**
(0.016)
(0.016)
(0.016)
(0.016)
0.364**
0.360**
0.361**
0.359**
(0.044)
(0.043)
(0.043)
(0.043)
0.010**
0.010**
0.010**
0.010**
(0.002)
(0.002)
(0.002)
(0.002)
-0.000*
-0.000*
-0.000*
-0.000*
(0.000)
(0.000)
(0.000)
(0.000)
0.017
0.017
0.018
0.016
(0.026)
(0.025)
(0.025)
(0.025)
-0.042
-0.041
-0.039
-0.044
(0.027)
(0.027)
(0.027)
(0.027)
0.095**
0.094**
0.094**
0.094**
(0.027)
(0.027)
(0.027)
(0.026)
0.189**
0.185**
0.185**
0.186**
(0.033)
(0.033)
(0.033)
(0.033)
0.256**
0.253**
0.252**
0.251**
(0.035)
(0.035)
(0.035)
(0.035)
+
0.029
0.027
0.020
0.028
(0.016)
(0.015)
(0.015)
(0.016)
0.016
0.016
0.016
0.020
(0.028)
(0.028)
(0.028)
(0.028)
+
+
+
+
0.011
0.011
0.010
0.011
(0.006)
(0.006)
(0.006)
(0.006)
+
+
+
-0.000
-0.000
-0.000
-0.000
(0.000)
(0.000)
(0.000)
(0.000)
Industry dummies &
yes
yes
yes
yes
state dummies
Wald_X
547.2**
547.0**
547.3**
551.5**
N
5369
5370
5370
5372
Source: SOEP 2003-2004. Longitudinal weights are used.
ME/s.e.: marginal effect/standard error. Robust standard errors also allow for
clustering at the household level.
Wald_X: Wald-Test with H0: no joint significance of all regressors. (df=45)
Significance levels: ** (0.01), * (0.05), + (0.10).
17
Table 2: Union Membership and Individual Risk Attitudes in Germany
- IV-Probit-Estimates Risk_finance
α̂
(s.e.)
ME(αˆ )
Wald_Ex
Wald_IV
Wald_X
N
0.336*
(0.151)
0.099
1.76
5.47*
1083.5**
5350
Risk_general
0 .328*
(0 .148)
0 .101
2.06
3.95*
1229.3**
5353
Source: SOEP 2003-2004. Longitudinal weights are used.
α̂ : Parameter estimate of particular risk measure.
s.e.: standard error. ME( αˆ ) : marginal effect α̂ .
Robust standard errors also allow for clustering at the household level.
Significance levels: ** (0.01), * (0.05), + (0.10).
Set of covariates is identical to specifications in Table 1.
Wald_Ex: Wald-Test with H0: no significant correlation between the error terms in
the structural and the reduced-form equation of the endogenous variable “riskaversion”. (df=1)
Wald_IV: Wald-Test with H0: no significant effect of the instrumental variable
“height” in a regression of the reduced-form equation for the endogenous variable
“risk- aversion“. (df=1)
Wald_X: Wald-Test with H0: no joint significance of all regressors. (df=45)
Table 3: Union Membership and Individual Risk Attitudes in Germany
- Semi-Nonparametric Estimates (SNP) Risk_finance
α̂
(s.e.)
LR_D
Wald_X
N
0.035*
0.017
17.1**
877.4**
5369
Risk_lottery
0.067*
0.033
15.5**
953.0**
5370
Arrow-Pratt –RRA
0.066*
0.028
16.2**
877.1**
5370
Risk_general
-0.008
0.015
14.4**
900.6**
5372
Source: SOEP 2003-2004. Longitudinal weights are used.
α̂ : Parameter estimate of particular risk measure.
s.e.: standard error.
Robust standard errors.
Significance levels: ** (0.01), * (0.05), + (0.10).
Hermite polynomial is of order 3, i.e. three additional parameters are estimated.
Set of covariates is identical to specifications in Table 1.
LR_D: Likelihood-Ratio test of Probit-Model against SNP extended model. (df=1)
Wald_X: Wald-Test with H0: no joint significance of all regressors. (df=45)
18
Table 4: Gross Wages and Individual Risk Attitudes in Germany
Risk_finance
Risk_lottery
Arrow-Pratt-RRA
Risk_general
Union density
Union membership
N
R2
ME / s.e.
ME / s.e.
ME / s.e.
ME / s.e.
-0.014**
---(0.004)
----0.001
---(0.007)
----0.002
---(0.005)
-----0.015**
---(0.004)
0.010**
0.010**
0.010**
0.010**
(0.003)
(0.003)
(0.003)
(0.003)
-0.015
-0.018
-0.018
-0.020
(0.018)
(0.018)
(0.018)
(0.018)
4881
4881
4881
4883
0.51
0.51
0.51
0.51
Source: SOEP 2003-2004. Longitudinal weights are used.
OLS-Regression of log gross monthly wages on a measure of individual risk
aversion, union density, individual union membership and the set of covariates
used in the specifications in Table 1.
Robust standard errors allow for clustering at the household level.
Significance levels: ** (0.01), * (0.05), + (0.10).
19
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21
Appendix
Figure A1:
0: non-member;
1: member of a trade union
22
Table A1: Arrow-Pratt Measure of Relative Risk-Aversion for Hypothetical Lottery
Union Member Non-Member
Minimum
0.40
0.40
Mean
3.04
2.81
Maximum
4
4
Source: SOEP 2003-2004. Longitudinal weights are used.
Table A2: Union Membership and Individual Risk Attitudes in Germany
- Probit Estimates ME / s.e.
0.007*
(0.003)
Log(gross wage)
-0.028
(0.025)
Male
0.043*
(0.017)
Foreigner
0.002
(0.028)
Age
0.011
(0.006)
Age (sqrd)
-0.000
(0.000)
Tenure
0.012**
(0.003)
Tenure (sqrd)
-0.000*
(0.000)
Apprenticeship
-0.008
(0.027)
University degree
-0.050
(0.028)
Prefers SPD
0.106**
(0.022)
Prefers CDU/CSU
-0.048**
(0.017)
Blue_collar
0.110**
(0.022)
Father_self-employed
-0.030
(0.022)
Firm size:
0.099**
(0.028)
20 ≤ X < 200 workers
Firm size:
0.198**
(0.035)
200 ≤ X < 2000 workers
Firm size:
0.255**
X > 2000 workers
(0.038)
Member of works council
0.355**
(0.047)
Industry dummies & state dummies
yes
N
4881
Wald_X
500.2**
Source: SOEP 2003-2004. Longitudinal weights are used.
ME/s.e.: marginal effect/standard error.
Robust standard errors also allow for clustering
at the household level.
Wald_X: Wald-Test with H0: no joint significance
of all regressors. (df=45)
Significance levels: ** (0.01), * (0.05), + (0.1)
Risk_finance
23
Tab A3: Descriptive Statistics of Covariates
Variable
Mean
Std. Dev.
Male
0.631
Foreigner
0.078
Age (in years)
41.089
Tenure (in years)
10.512
Apprenticeship
0.658
University degree
0.212
Prefers Social Democrats (SPD)
0.191
Prefers Christian Parties (CDU/CSU)
0.185
Blue collar worker
0.367
Father was self-employed
0.101
0.305
Firm size: 20 ≤ X < 200 workers
0.247
Firm size: 200 ≤ X < 2000 workers
Firm size: X ≥ 2000 workers
0.235
Member of works council
0.040
Schleswig-Holstein
0.033
Hamburg
0.025
Lower Saxony
0.085
Bremen
0.007
North Rhine-Westphalia
0.219
Hessen
0.065
Rhineland-Palatinate, Saarland
0.054
Baden-Wuerttemberg
0.134
Bavaria
0.160
Berlin (East)
0.015
Mecklenburg/West-Pomerania
0.019
Brandenburg
0.030
Saxony-Anhalt
0.029
Thuringia
0.034
Saxony
0.055
Mining/ quarrying
0.011
Manufacturing
0.004
Electricity/ gas/ water supply
0.320
Construction
0.014
Wholesale and retail trade/ repair
0.067
Hotels/ restaurants
0.120
Transport, storage/ communication
0.022
Financial intermediation
0.059
Real estate/ renting/ business
0.054
Public administration/ defence
0.082
Education
0.056
Health/ social work
0.038
Other services/ Private households
0.106
Individual height (cm)
174.297
Source: SOEP 2003-2004. Longitudinal weights are used. N=5908.
24
0.482
0.267
10.75
9.666
0.474
0.409
0.393
0.388
0.482
0.302
0.460
0.431
0.424
0.197
0.181
0.156
0.279
0.087
0.414
0.247
0.226
0.341
0.366
0.122
0.139
0.173
0.169
0.182
0.229
0.108
0.067
0.466
0.119
0.250
0.325
0.146
0.236
0.227
0.275
0.231
0.193
0.308
9.116