Indebtedness and Unemployment:
A Durable Relationship
Tore Ellingsen∗
Steinar Holden∗∗
April 4, 2002
Abstract
Within a simple formal model, we show that there is a link between workers’
indebtedness and the outcome of wage bargaining. Large debts, arising from purchases of illiquid durables (houses and cars), serve to make unemployment experiences more unpleasant. Hence indebted workers are more willing to accept a low
wage in order to reduce the probability of unemployment. In line with this prediction, cross–country regressions based on data from sixteen OECD countries indicate
that high household indebtedness serves to reduce the level of unemployment for a
given set of labour market institutions.
JEL classification: E24, J51, J64.
Keywords: Wage setting, debt, unemployment.
∗
Department of Economics, Stockholm School of Economics, Box 6501, S—113 83 Stockholm, Sweden.
Phone: +46-8 736 9260. Fax: +46-8 34 78 18.
∗∗
Department of Economics, University of Oslo, Box 1095 Blindern, 0317 Oslo, Norway. Phone: +4722 85 51 56.
This paper is part of the research project “Unemployment, institutions and policy” at SNF–Oslo. Financial support from the Swedish Council for Research in the Humanities and Social Sciences is gratefully
acknowledged. We have benefitted from presenting the paper at the Industrial Institute for Economic
and Social Research, London School of Economics, Stockholm School of Economics, the Trade Union Institute for Economic Research and Uppsala University. Helge Holden and Arne Strøm generously helped
us proving Proposition 1. We thank Douglas Hibbs, Richard Jackman, Per Lundborg, Henry Ohlsson,
John Sutton, Anders Vredin, and in particular Charlie Bean, for helpful comments and discussion.
1
1
Introduction
Unemployment differs across countries. To some extent this can be explained by the fact
that countries have different endowments and hence do not face exactly the same shocks.
However, there is now a solid body of empirical research which suggests that countries
have different long–run rates of unemployment.
What causes this variation? The usual answers (e.g., Layard et al., 1991) point to the
differences in labour market institutions. Some countries support their unemployed for an
extended period of time, and hence have more persistent unemployment; some countries
give more power to trade unions, and hence have a higher wages and more unemployment;
in some countries employers coordinate their wage bargaining, thus lowering wages and
unemployment.
Here we shall argue that, while labour market institutions are important, factors outside the labour market matter as well. More precisely we shall claim that the composition
of workers’ consumption, in particular the degree to which expenditures are fixed by prior
commitments, has an impact on wages. The reason is that the greater the share of expenditures that is fixed, the narrower are the margins for adjustment, and the more painful
is a loss of income; a big house is a small comfort for someone who cannot afford to eat.1
In other words, workers who are heavily indebted and/or spend much of their income
on illiquid durable goods such as housing are hit harder by a reduction in income, and
hence resent unemployment more. In consequence, indebted workers exert less pressure
on wages, and unemployment goes down.
Our story begs the question why indebtedness varies across workers in the first place.
One possible answer is that access to household credit has historically varied greatly
across countries. As documented by Jappelli and Pagano (1994), differences in liquidity
constraints have been due to differences in regulation, enforcement costs and information
availability. Actually, the variation in capital market imperfections explains much of the
historical variation in savings rates across OECD countries. Thus, the paper suggests that
1
While adjustment of durable goods consumption is rarely impossible, it is frequently prohibitively
costly. In the housing market, transaction costs are considerable. Sales taxes and brokerage fees frequently
constitute between five and ten per cent of the house price (see OECD (1994, p. 67)). Markets for other
durables, such as used cars and stereos, also work poorly.
2
workers who live in countries with well developed financial markets (or heavily subsidized
housing finance for otherwise credit constrained households) will take on more debt, and
as a consequence will accept lower pay in order to avoid the risk of becoming unemployed.2
The theoretical prediction that indebtedness affects unemployment is tested using data
from sixteen OECD countries. These are the only countries for which the relevant data is
available. The regressions include standard variables capturing labour market institutions,
but add a measure of household indebtedness. This measure captures housing loans, which
constitute the major part, as well as loans for personal consumption. To control for any
impact of unemployment on indebtedness, we also run two–stage least squares regressions,
using measures of capital market imperfection as instruments for household indebtedness.
Indebtedness has the expected sign in all our regressions, and is both economically and
statistically significant in accounting for differences in unemployment rates.
We are not aware of any previous work which studies the effect of consumption patterns on wage levels. Perhaps the most closely related literature is that which links
unemployment to the structure of the housing market. Hughes and McCormick, in a
series of papers on labour mobility in Britain, have found that home ownership and subsidized rental housing constitute barriers to regional migration and may therefore raise
unemployment (see Hughes and McCormick (1987) and the references therein). Oswald
(1996) tests this theory using cross–section data. Note however that our theory concerns
a different relationship; how illiquid durable consumption affect the wage and unemployment levels within a region for a given level of migration. Since the two effects go in
opposite directions, it is an empirical matter to decide which one dominates.3 Another
important difference between our work and that of Hughes, McCormick and Oswald is
that they mainly emphasize the magnitude of transaction costs, whereas we are primarily
concerned with the budget share of housing and other illiquid durables.
While our theory identifies a new connection between workers’ consumption patterns
and their labour market behaviour, the two key steps of our argument have both been
2
An earlier version of this paper also considered additional predictions regarding real and nominal
wage rigidity. We neglect these issues here.
3
While we did not set out to test the home ownership hypothesis in any detail, we report one empirical
finding in the final section.
3
noted before. The first mechanism, the impact of illiquid assets on risk–taking, has been
explored by Flemming (1969), Dickinson and de Meza (1984) and Grossman and Laroque
(1990). It is also well understood in the literature on consumption that realistic levels
of transaction costs leads to non–adjustment of durables for large variations in income.4
The second mechanism, the impact of risk aversion on unemployment, has appeared in
different guises. In models of one–sided search, risk aversion has been thought to reduce
wages because workers’ reservation wages go down, cf. Nachman (1975) and Hall et al.
(1979). In the bargaining literature, it is well known that risk aversion is a disadvantage
in negotations; see Osborne and Rubinstein (1990, Chapter 2) for a recent textbook
exposition and Rubinstein, Zafra and Thomson (1992) for a deeper analysis.5 A closely
related paper to ours in this respect is McDonald (1991), who has showed that in trade
union models the bargained wage is negatively related to workers’ risk aversion under
quite general assumptions. However, it is worth noting that neither search nor bargaining
is necessary for the negative relationship between risk aversion and unemployment to
prevail; as shown in a previous version of our paper the result holds even if the wage is
set unilaterally by the union (the monopoly union model). Of course, the fact that there
are other channels from risk aversion to wage moderation than the one we identify in our
model indicates that our key empirical prediction is robust; it does not hinge critically on
the particulars of our labor market model.
The rest of the paper is organized as follows. In Section 2, we set up and analyse the
full model. Section 3 confronts the model with data, and Section 4 concludes.
4
The role of fixed adjustment costs in understanding aggregate consumption dynamics was first studied
by Mishkin (1976), and is convincingly documented by Bertola and Caballero (1990), Bar–Ilan and
Blinder (1992), Caballero (1993) and Eberly (1994). For empirical evidence on the relationship between
non–traded assets and financial portfolios, see e.g. Giraldi, Hamaui and Rossi (1993) and the references
therein.
5
Recently, Vesterlund (1998) has shown, in an equilibrium search–matching model with heterogeneous
workers, how more risk averse workers get lower average wages and have lower average unemployment
duration. Her result appears to be driven by a mixture of the reservation wage effect and the bargaining
weakness effect.
4
2
Model
Before setting up the complete model, it is useful to point out very briefly the first of
its key relationships, namely that indebtedness related to durable consumption may lead
to risk aversion. Consider for simplicity the situation of a person that from the outset
is risk neutral. Specifically, let utility be u = C 1−δ Dδ , where C denotes non–durable
consumption and D denotes durable consumption. Let y be the person’s income, and
assume that prices of consumption goods are exogenously given. If C and D are both
freely variable, it is a simple exercise to show that the person’s indirect utility is linearly
increasing in y. In this case, the person is risk neutral. However, if durables expenditures
are fixed at some level D̄ which cannot be varied with income, e.g. because the mortgage
payments are fixed and transaction costs are high, then the indirect utility function is
strictly concave in y, and the person is risk averse. Moreover, the coefficient of absolute
risk aversion is an increasing function of D̄; in other words, a person with fewer margins for
adjustment becomes more risk averse. (The explicit expressions can be derived in textbook
fashion. Normalize the price of non–durables to 1 and let q denote the price of durables.
When both are varied freely, maximize u with respect to C and D subject to the budget
constraint C + qD ≤ y. Maximum utility is then v(y) = (1 − δ)1−δ δ δ y/q δ . If, on the other
hand, durables are fixed at D̄, indirect utility is ν(y, D̄) = (y − q D̄)1−δ D̄δ . In the latter
case, the Arrow–Pratt measure of absolute risk aversion is −νyy /νy = 1/(δ(y − q D̄).) This
insight, that indebtedness related to durable consumption implies increased risk aversion,
is at the heart of our argument.
Now to the full model. The economy we consider consists of many identical firms and
a large number of identical workers. All workers are organized in firm-specific unions;
in a number L in each union. The firms produce a non-durable consumption good with
labour as the only input. The production function of a firm is
Yt =
1
ηt Ntβ ,
β
(1)
where β is a parameter between 0 and 1, ηt is a positive, stochastic, aggregate productivity
parameter and t indicates time period. Firms are price takers, and set employment so as
5
to maximize profits. Thus, the labour demand of a representative firm is
Nt = N (Wt /ηt ) = (Wt /ηt )−1/(1−β) ,
(2)
where Wt is the real wage in period t (the price of non-durable goods is normalized to
unity). The profit of the firm, πt = Yt − Wt Nt , is then
πt = π(ηt , Wt ) = (1 − β)β −1 ηt
1/(1−β)
−β/(1−β)
Wt
.
(3)
Workers consume non–negative quantities of two kinds of goods; durables and non–
durables. As durables, we consider goods which are consumed over a long period of
time and are costly to adjust.
The analysis covers two periods, and to sharpen the focus, we impose the restriction
that workers may only buy durable goods in period 1, so that consumption of durable
goods cannot be adjusted between the two periods. Assuming Cobb-Douglas preferences,
the workers’ utility of consumption is
v = C11−δ Dδ + θC21−δ Dδ ,
(4)
where Ct is the quantity of non-durables in period t, D is the quantity of durables, δ and
θ are parameters between 0 and 1 (θ is the discount factor). The budget condition is
Y1 +
1
1
Y2 = C1 + qD +
C2 ,
1+i
1+i
(5)
where i is the nominal interest rate, the price on non-durables is unity in both periods
(for simplicity, inflation is set to zero), q is the price of durables and Yt = {Wt , B} is the
income in period t, depending on whether or not the worker is employed; if unemployed,
the worker receives the unemployment benefit B (alternatively, B can be interpreted as
the non-market income of unemployed workers).
The sequence of moves is as follows. At the beginning of period 1, the productivity
parameter, η1 is realized, and W1 and N1 are set, the former in a bargain at firm level
between workers and the firm, the latter according to the labour demand function (2),
6
given the outcome of the wage bargain. Then the individual workers know whether they
have a job, and the income they receive, W1 or B; they know the price of durables, q; they
know the nominal interest rate, i, at which they can borrow or lend as well as any quantity
restrictions on borrowing. Workers purchase the durable good and period 1 non-durables,
so as to maximize expected utility (the expectation of (4). However, at this stage η2 is
unknown (but with a known probability distribution), thus workers do not know whether
they will have a job in period 2, nor do they know the realization of W2 . The workers do
know the probability distribution of the income in period 2.
Between the two consumption periods, the productivity parameter, η2 is realized.
Then the real wage in period 2, W2 is set separately at each firm, in a bargain between
workers and the firm.
In period 2, firms set employment according to the labour demand function (2). Workers spend their available income, that is, Y2 less any debt (or wealth) from the previous
periods, on non-durable consumption C2 . At the bargaining over W2 , workers and firms
are able to perfectly predict the subsequent employment decision of the firm, and the resulting aggregate unemployment rate u ≡ (L − N2 )/L (as all firms are identical, it is not
necessary to distinguish between firm level and aggregate variables). Thus, the outcome
of the wage bargain depends on the realization of the productivity parameter, η2 , via the
effect on the rate of unemployment.
The focus of the paper is how debt affects the wage setting. Thus, we do not solve
for period 1 of the model; we do not analyze the wage and employment setting in period
1, we do not derive the purchase of durables and non-durables at this stage6 , nor do we
derive the market clearing price of durables. We simply denote the optimal quantities of
durable goods DY , (where the subscript Y = W indicates employed workers, while Y = B
indicates unemployed workers), and then proceed to the analysis of the bargaining over
the wage in period 2.
From the budget condition, we derive period 2 consumption of non-durables as
C2 = Y2 − ZY ,
6
Such an analysis is given in a similar model in Ellingsen and Holden (1998).
7
(6)
where
ZY = (1 + i)(C1 + qDY − Y1 ),
Y1 = {W1 , B},
(7)
is the debt incurred in period 1, including interests. Workers’ utility in period 2 is thus
v2 (Y2 ; DY ) = (Y2 − ZY )1−δ DYδ .
(8)
The outcome of the wage negotiation is assumed to be given by the Nash bargaining
solution, that is, W2 is set so as to maximize
Ω = (V − V0 )(π − π0 ),
(9)
subject to (2), V ≥ V0 and π ≥ π0 . Equation (9) can be motivated as follows. In case of
a dispute, workers go on strike, so that no production takes place and the firm receives
no profits, thus π0 = 0. Regarding the workers’ part of the Nash maximand, we assume
that7
δ
V − V0 = [(W2 − ZW )1−δ DW
− v]N2γ .
(10)
δ
is the period 2 payoff of workers employed in both periods, and
where (W2 − ZW )1−δ DW
v is the alternative utility that is available to workers who were employed in period 1,
but become unemployed in period 1. This specification is based on the presumption that
union preferences reflect the members who were employed in period 1, as they are in
majority. Workers on strike have zero payoff; one interpretation being that they have no
strike pay and thus zero consumption of non-durables. Workers who do not get a job in
the firm in period 2 do not participate in a possible strike, and are thus not affected.
The parameter γ determines the weight the union puts on employment. Consider
the two extreme cases: γ = 1 corresponds to the case where period 2 employment is
determined randomly among all members, where the job probability of an individual
worker does not depend on whether he was employed in period 1. (Strictly speaking, (10)
should then be multiplied by the constant, L, so that the term N2 /L is the probability
7
As shown by Manning (1991), the above formulation can be derived from a more explicit dynamic
model; in the present model that would require that period 2 was of infinite length, divided into shorter
subperiods, and that there was exogenous job turnover between subperiods.
8
of having a job.) The case γ = 0 corresponds to a seniority system among the employed
workers, so that the median voter is entirely sheltered from the risk of redundancy, and
thus neglects employment all together. Equation (10) has the virtue that it encompasses
alternative specifications concerning the decision of who will be employed; our main results
do not depend on which specification is preferred (obviously the optimal consumption
behaviour in period 1 depends on the value of γ, but this does not affect our qualitative
results).
The alternative utility available to workers who lose their job, v, is given by
δ
δ
v = (W2A − ZW )1−δ DW
(1 − φu) + (B − ZW )1−δ DW
φu.
(11)
where W2A is the average wage elsewhere in the economy; thus v is a weighted average
of the payoff of obtaining a new job and the payoff of remaining unemployed. In an
extended dynamic model, a possible interpretation of (11) is that unemployed workers
have a possibility of obtaining a new job, at wage W2A , sooner or later, and 1 − φu
is the weight attached to this possibility, while φu is the weight attached to remaining
unemployed. The variable φ lies between 0 and 1 and reflects the likelihood of remaining
unemployed, appropriately discounted. While φ is an increasing function of the aggregate
wage level, there is a sufficiently large number of firms, so each union will take φ as given.8
Substituting out for (11) in (10) gives us
δ
δ
− (W2A − ZW )1−δ DW
(1 − φu)
V − V0 = [(W2 − ZW )1−δ DW
δ
− (B − ZW )1−δ DW
φu]N2γ .
(12)
The specification of V presumes that the productivity parameter η2 takes a value so that
the outcome of the wage setting entails positive unemployment, N (W2 /η2 ) < L. Finally,
to guarantee a that the equilibrium wage is finite, we put the following mild restriction
on the parameters.
8
Thus φu should be interpreted as a linear approximation to the true relationship between the probability of remaining unemployed and the aggregate rate of unemployment. Clearly, the approximation is
only valid locally (cf, Layard, Nickell and Jackman, 1991, page 145, or Manning, 1991).
9
Assumption 1 The parameters of the model satisfy the inequality
β>
1−δ−γ
.
2−δ
Two different conditions, each sufficient for Assumption 1 to hold, are: (i) the insider–
outsider problem is small (γ ≥ 1 − δ); (ii) the returns to scale are not decreasing too fast
(β ≥ 1/2).
We focus on a symmetric equilibrium of the model, where the same wage is set is all
firms, that is, W2 = W2A . Our first result establishes the existence and uniqueness of a
symmetric equilibrium.
Proposition 1 There exists a unique symmetric equilibrium outcome, where wages in all
firms are the same. The equilibrium wage W2∗ is strictly increasing in productivity, η2 .
The resulting rate of unemployment u∗ is decreasing in productivity.
The latter part of Proposition 1 implies that variation in the productivity parameter, η2 ,
maps out a downward sloping wage curve in the unemployment - real wage - space. The
focus of the paper is, however, on the the relationship between the debt and the outcome
of the wage setting.
Proposition 2 Both the wage W2∗ and unemployment u∗ are decreasing in indebtedness,
ZW .
The main intuition is, as indicated in the introduction, that indebtedness makes workers
risk–averse. Highly indebted workers face a larger loss if they lose their job, because they
have a sub–optimal consumption profile with too much consumption of durables and too
little consumption of non–durables. The larger loss from unemployment make workers
push less hard for high wages. This effect would be present even in a model where the
union sets the wage unilaterally (a case which was explored in an earlier version of this
paper). The dampening effect of debt on unemployment is just a consequence of the
negative impact on wages, reflecting that lower wages lead to lower unemployment.
10
3
Empirical Analysis
In this section we study the effect of intertemporal consumption on the natural rate
unemployment. The key explanatory variable is household indebtedness, i.e. household
debt as a fraction of disposable income.9
Our cross–section analysis is based on data for 16 OECD countries, indebtedness
being measured in or around 1983. The indebtedness data are mainly taken from a
survey conducted by the Bank for International Settlements (BIS), reported in Kneeshaw
(1995), relying on information from the central banks of thirteen countries.10 Data for
an additional three countries (Denmark, Finland, and Norway) are from Berg (1994).
For a few of the countries, there are substantial discrepancies between the BIS numbers
and those of other sources. For example, Jappelli and Pagano (1989) who use official
statistics to compute the sum of personal consumer loans and home mortgage loans for
seven countries in the same period, report much lower figures for Italy and Spain than
BIS does.11 Nevertheless, we have here chosen not to tinker with the BIS numbers. The
only adjustment we have made is an upward revision for Denmark, because the 1983
figure is extremely low compared to the surrounding years. (The revision turns out to be
inconsequential for our results.) As shown in Table A2, there is considerable variation in
indebtedness across countries. Three countries, Norway, Sweden, and Switzerland, play
in a league of their own. The average household debt in these countries exceeds one year’s
disposable income, whereas in Italy and Belgium, the indebtedness is less than a quarter
of this level.
Given that one of our independent variables have been computed from time series of
more than thirty years, one might worry that a single observation of the key explanatory
9
We do not investigate the role of durables directly. The measures of durables consumption in the
national accounts does not allow separation of liquid durables consumtion (renting a house or living with
parents) from consumption of illiquid durables. Relative to durables consumption, indebtedness also has
the advantage of being concentrated on households which are (relatively early) in their working careers,
and hence are more likely to experience unemployment and affect wage determination.
10
See Kneeshaw’s Table 3. For most countries, total financial liabilities equal debt claims. Otherwise,
we have used the former figure.
11
Japelli and Pagano also report a lower figure for Japan, but acknowledge that this number may
be downward biased. Indeed, the OECD figure for household liabilities in Japan is even higher than
Kneeshaw’s number.
11
variable is not a fair representation of its historical value. However, Kneeshaw (1995)
reports the variable for both 1983 and 1993 for the thirteen countries, and Berg reports a
longer yearly time series for the remaining three. Regressing the 1993 value on the 1983
value gives an R̄2 = 0.85. This tells us that even after a decade of large changes in the
operations of financial markets across the world, and huge swings in economic activity,
the household indebtedness of each country in 1993 can be predicted extremely well by
the indebtedness in 1983.12 We would expect that the relationship is even more stable
before 1983.
Clearly, reverse causality poses a potential problem. Household indebtedness could be
affected by labour market conditions, as people are more willing to borrow (and banks
more willing to lend) if the unemployment risk is small. In order to tackle this problem,
we need to find variables which correlate with indebtedness but not (directly) with unemployment. In our view, there are two kinds of variables which may have this property.
First, there are measures of credit market imperfections, which affect the private supply
of credit. For the household sector, Jappelli and Pagano (1994) have proposed to use
the maximum loan–to–value (LTV) ratio, and we will do so as well. If households are
able to borrow a large fraction of the durable’s value, they will be less credit constrained.
Second, there is the issue of publicly provided and/or subsidized credit. Boleat’s (1985)
comparative study of housing finance systems reveals that Sweden, Norway and Finland
stand out in this respect, with exceptional support for housing in general and (in the period in question) for new, debt financed private housing in particular. In these countries,
subsidies were to a considerable extent targeted towards the lower end of the market, so
that it was indeed workers’ borrowing which was affected. Hence, we construct a subsidy
dummy, which is equal to one for the three mentioned countries and zero for all others.
This dummy and the LTV ratio are used in the first stage of our 2SLS regressions below,
and both of them are significantly related to indebtedness.
Apart from the indebtedness variable and its associated instruments, information on
all explanatory variables are taken from Layard, Nickell and Jackman (1991), and we
12
In fact, if we were to exclude Sweden, where a near collapse of property markets (and consequently
credit markets) lead to an unprecedented 30% decrease in household indebtedness between 1988 and
1993, R2 goes up to 0.90.
12
refer to their book for detailed sources and definitions. (See the Appendix for exact
references to their data tables.) These variables capture the key features of unemployment
insurance, such as the duration of benefits and the ratio of benefits to past wages (the
replacement ratio); the organization of the labour market, in particular the degree of
organized coordination at each side of the market; as well as the duration and indexation
of contracts. We report the values of the explanatory variables in Table A2 and of the
dependent variables in Table A3.
3.1
Results
We want to explain cross–country differences in unemployment rates. Throughout, we will
look at simple linear econometric models. Our theoretical model does not admit an explicit
solution, so we are not sure what would be the theoretically correct specification of the
functional form. Moreover, the existing cross–country studies consider linear relationships
between labour market institutions and unemployment, so this specification facilitates
comparison with earlier work.
Table 1 reports the results. We consider three measures of unemployment. First we
attempt to explain the actual unemployment in the period 1974-1979, a period during
which there were no great aggregate shocks. In regressions (1) and (2), the dependent
variable is the average of the actual rate of unemployment in this period. Secondly, since
we have indebtedness data for 1983, we also try to explain average unemployment in the
rather more turbulent period 1980-85.13 Indebtedness is statistically significant at the
5% level in all these regressions, even when the two–stage procedure is used, and the size
of the coefficient is also about the same in the 2SLS as in the OLS regressions. For the
period 1980-85, the 2SLS procedure even yields a larger and statistically more significant coefficient than OLS does. The other variables also enter with their conventional
signs, except contract flexibility, which appears to raise unemployment, but is statistically
insignificant.14
13
We have not investigated the post-1990 experience. The reason is that while we know indebtedness
for 1993, the values of several of the other explanatory variables have changed considerably since the
late seventies and early eighties for which we have data. And since some of these variables have been
constructed in quite elaborate ways, we are unable to make a credible update ourselves.
14
The coefficient on contract flexibility is not sensitive to the inclusion of indebtedness. A possible
13
Table 1: Unemployment
Independent variables
Dependent variable: Unemployment Rates
Actual 74–79 Actual 80–85
“Natural”
(1)
(2)
(3)
(4)
(5)
(6)
OLS
2SLS
OLS
2SLS
OLS
2SLS
Benefit duration
0.056
(3.60)
0.057
(2.62)
0.088
(2.18)
0.085
(2.16)
0.0001
(0.02)
0.0004
(0.08)
Replacement ratio
0.015
(1.23)
0.015
(0.88)
0.094
(2.92)
0.095
(3.04)
0.0016
(0.44)
0.0016
(0.34)
Union coordination
-0.700
(1.20)
-0.663
(0.81)
-1.430
(0.94)
-1.560
(1.06)
0.478
(2.75)
0.490
(2.24)
Employer coordination
-1.682
(3.85)
-1.737
(2.80)
-3.395
(3.00)
-3.21
(2.88)
-0.714
(5.53)
-0.735
(4.43)
Contract flexibility
0.100
(0.47)
0.102
(0.34)
0.468
(0.85)
0.459
(0.86)
-0.088
(1.40)
-0.087
(1.10)
C–D corporatism
-0.301
(4.39)
-0.303
(3.11)
-0.210
(1.16)
-0.223
(1.27)
-0.051
(2.48)
-0.050
(1.91)
Indebtedness
-0.044 -0.041 -0.059 -0.071 -0.0094 -0.0080
(4.39) (2.62) (2.31) (2.51)
(3.23)
(1.90)
R̄2
0.85
0.70
0.77
0.78
0.83
0.74
“Natural” is Bean’s empirical estimate of κi . Constants are not reported. Number of observations: 16.
t-values in parentheses.
Actual unemployment figures are of course contaminated by the fact that countries do
not face identical shocks. To evade this problem, one might try to construct a measure
of “natural” unemployment for time series data. For the OECD countries, such measures
have been provided by Bean (1994b), who studied a generalized fixed effects model of the
kind
∆f (uit ) = µi [κi + βi γt − f (uit−1 )] + it ,
explanation of its sign could be that contract flexibility is itself endogenous.
14
(13)
where κi is the country–specific fixed effect, γt is a time–specific fixed effect whose impact
differs across countries through βi , µi is a parameter which allows the speed of adjustment
to differ across countries, and it is an idiosynchratic error. Notice that if µi = 1, then
κi + βi γt would be an estimate of f (uit ). Bean uses the functional form f (u) = 2(u0.5 − 1),
as this form appears to fit the data for the sample period 1956–92 quite well. Regressions
(5) and (6) explain Bean’s empirical estimate of κ̂i (which in Bean is referred to as α̂).15
Indebtedness has the expected sign; it is significant at the 1% level in (5), but only at
the 10% level in (6). However, as was the case in Bean (1994b, p552), union coordination
enters with the “wrong” sign. Of course, an objection to regressions (5) and (6) is that the
explanatory variables have hardly been constant for the 35 years over which the natural
rate of unemployment has been estimated.
Let us also add that simple univariate regressions give roughly similar estimates for
the effect of indebtedness on unemployment. (The OLS estimates for the three different
specifications of unemployment are -0.051 (-3.68), -0.101 (-3.25), and -0.01 (-2.79).) Thus,
the relationship between indebtedness and unemployment is not due to correlation with
some of the other explanatory variables.
Indebtedness also appears economically significant in our regressions. As a measure
of economic significance we use the change of the dependent variable (evaluated at its
mean) from a one standard deviation change in the independent variable. Table 2 shows
the number of percentage points change in the unemployment implied by the parameter
estimates in column (1), (3), and (5) of Table 1. Given the uncertainty of some of the
parameter estimates, these numbers should of course be taken with a pinch of salt.
In interpreting the numbers, one should also keep in mind that the actual unemployment 1974–79 was in the 5-7.5 per cent range for several countries and had risen much
further in the next five years, whereas the long–run unemployment figures computed by
Bean tend to range from one to four per cent (essentially representing the pre–1973 experience). The table shows that, regardless of how we define it, unemployment is quite
a bit lower in countries with high household indebtedness. Only employer coordination
appears consistently to matter more to the unemployment figures.
15
We are grateful to Charlie Bean for sharing his numbers with us.
15
Table 2: Change in Unemployment
From a one std.dev. change in
Change, percentage points
Act. 74-79 Act. 80-85 “Natural”
Benefit duration
1.1
1.73
0.0
Replacement ratio
0.3
2.0
0.0
Union coordination
-0.5
-1.0
0.6
Employer coordination
-1.5
-3.0
-1.2
0.2
0.8
0.3
C–D corporatism
-1.6
-1.1
-0.4
Indebtedness
-1.1
-1.5
-0.4
Contract flexibility
4
Final remarks
At a general level, our results indicate that the causes of unemployment are not all to
be found within the labour market itself. Factors outside the labour market affect the
workers’ behaviour and hence unemployment outcomes. For example, we have shown that
better access to household credit might lead to lower wages and unemployment, through
a consumption channel. As far as we know, this is the first study to find a reasonably
robust cross–country relationship between unemployment and a variable outside the labor
market after controlling for a comprehensive set of labor market institutions.16
Two caveats are in order. First, our theory is highly stylized, with labour market
institutions taken as given. An interesting avenue for further research is to investigate
whether consumption patterns, apart from its direct effect on unemployment, might also
influence labor market institutions, and if so how. For example, how does worker in16
Oswald (1996) argues that cross–country differences in home ownership correlate with differences in
unemployment, with higher home ownership ratios being associated with higher unemployment. However, when we introduce home ownership ratios into our regressions, the coefficients are negative and
insignificant regardless of whether we control for indebtedness (which, incidentally, is unrelated to home
ownership).
16
debtedness affect trade unions’ ability to coordinate wage negotiations17 or their desired
benefit duration and replacement ratios? A brief look at a correlation table is mildly
encouraging; indebtedness is positively correlated with the replacement ratio, negatively
correlated with benefit duration, but uncorrelated with union coordination.
Secondly, cross–country regressions have severe limitations, not least due to the low
number of observations. This implies that our results can only be taken as suggestive.
An alternative approach would be to use microempirical data on the (un)employment
experiences of individual workers. Such work could clearly provide a further valuable test
of the theory. However, an obstacle to using data from a single country would be to find
exogenous sources of variations in indebtedness. Thus, we view the two approaches as
complementary.
5
Appendix
Below are the proofs of our main propositions as well as two data tables.
5.1
Proof of Proposition 1
Substituting out for (3), (12) and (2), and letting lower case letters denote natural logarithm, the Nash product reads (omitting subscript W )
ln(Ω) = ln((W2 − Z)1−δ Dδ − (W2A − Z)1−δ Dδ (1 − φu) − (B − Z)1−δ Dδ φu)
γ
1
β
1−β
γ
ln η2 −
w2 + ln
ln η2 −
w2 .
+
(14)
+
1−β
1−β
β
1−β
1−β
The first order condition for a solution W2∗ is
W2∗ (1 − δ)(W2∗ − Z)−δ Dδ
d ln(Ω)
=
d ln W2∗
(W2∗ − Z)1−δ Dδ − (W2A − Z)1−δ Dδ (1 − φu) − (B − Z)1−δ Dδ φu
β
γ
−
= 0.
(15)
−
1−β 1−β
We first show that this equation has a unique solution.
17
For a non–cooperative analysis of union coordination, see Holden and Raaum (1991).
17
Manipulate the above expression to get
W2∗ (1 − δ)(W2∗ − Z)−δ
d ln(Ω)
=
− K1 ,
d ln W2∗
(W2∗ − Z)1−δ − K0
(16)
where
K0 = (1 − φu)(W2A − Z)1−δ + φu(B − Z)1−δ ,
and
K1 =
β+γ
.
1−β
As a preliminary step, observe that we can rule out wages below a critical value, denoted
W0 . To see this, note that
(B − Z)1−δ < K0 < (W A − Z)1−δ .
Thus, there exists some wage W0 in the interval (B, W A ) such that K0 = (W0 − Z)1−δ .
From (12), we must have W > W0 in order for V − V0 > 0.
Define the function
F (W ) = (1 − δ)W − K1 (W − Z) + K0 K1 (W − Z)δ .
Then rewrite (16) as
(17)
F (W2∗ )
d ln(Ω)
=
.
d ln W2∗
(W2∗ − Z)1−δ − K0
Using the definition of W0 , we see that the denominator is positive for W2∗ > W0 . Hence,
sign
d ln(Ω)
= signF (W2∗ ).
d ln W2∗
Observe that, by the definition of W0 , F (W0 ) = (1−δ)W0 > 0, and that F (Z) = (1−δ)Z >
0. Observe that F (W ) is strictly concave, and that limW →∞ F (W ) = W (1 − δ − K1 ).
The latter expression is negative by Assumption 1. Hence, given W A , there is a unique
W2∗ > Z such that F (W2∗ ) = 0, i. e., we have identified the solution to the individual
firm–union problem.
Having solved the problem for each firm, it remains to characterize the equilibrium
18
wage level in the economy, where W2∗ = W A = W ∗ . The equilibrium condition is that
F (W ∗ ) = 0, which can be written
(1 − δ)W ∗ − K1 (W ∗ − Z) + K0 K1 (W ∗ − Z)δ = 0.
(18)
Substituting for K0 , we get
(1 − δ)W ∗ − φuK1 (W ∗ − Z)δ [(W ∗ − Z)1−δ − (B − Z)1−δ ] = 0
To show that this expression defines a unique value for W ∗ , define the function
G(W ∗ ) = (1 − δ)W ∗ − φu K1 (W ∗ − Z)δ [(W ∗ − Z)1−δ − (B − Z)1−δ ].
Observe that G(Z) > 0 and that G is strictly concave. Furthermore, limW ∗ →∞ G(W ∗ ) =
1 − δ − φuK1 . Now, observe that limW ∗ →∞ φu = 1 (the employment in each firm goes to
zero as the wage goes to infinity, hence both the unemployment rate and the probability
of remaining unemployed go to 1). Thus, limW ∗ →∞ G(W ∗ ) = 1 − δ − K1 , which is negative
by Assumption 1. This completes the proof that there is a unique symmetric equilibrium
wage level.
To show that W2∗ is strictly increasing in η2 , while u is strictly decreasing in η2 , observe
that W2∗ and u are simultaneously determined by the two equations (18) and
u = 1 − N(
W2∗
)/L.
η2
(19)
We first prove that (18) viewed in isolation gives W ∗ as a strictly decreasing function of
u. To do this, we differentiate the condition G(W ∗ , u) = 0 to get
dW ∗
G
= − u .
du
GW ∗
(20)
We have already established that GW ∗ < 0, and it is readily checked that G u < 0. Note
also that η2 does not enter (18), so it has no direct impact on this equation.
The next step is the immediate observation that (19) viewed in isolation gives us u as
a strictly decreasing function of W2∗ and a strictly increasing function of η2 .
19
Finally, assume that the statement in the Proposition is false, that a increase in η2
leads to an increase in u. From (19), this would require that W2∗ increased. However, from
(18), W ∗ can only increase if u decreases. Thus, we have a contradiction. It follows that
a increase in η2 leads to an increase in u. It is then clear from (20) that an increase in η2
leads to an increase in W2∗ , which completes the proof.
5.2
Proof of Proposition 2
Observe that W ∗ and u are simultaneously determined by the two equations (18) and
(19). The first step is to establish that (18) viewed in isolation yields W ∗ as strictly
decreasing in Z.
The effect of Z on the equilibrium wage level W ∗ can be derived by exploiting that G is
also a function of Z, so that W ∗ is implicitly defined as a function of Z by G(W ∗ , Z) = 0.
Implicit differentiation yields
dW a
G
= − Z .
dZ
GW ∗
As GW ∗ < 0, it follows that sign(dW ∗ /dZ) = sign(GZ ). We want to show that GZ < 0.
We get
GZ = φu K1 [1 − δ(W ∗ − Z)δ−1 (B − Z)1−δ − (1 − δ)(W ∗ − Z)δ (B − Z)−δ ].
Thus, GZ < 0 if and only if 1 − δxδ−1 − (1 − δ)xδ < 0, where
x=
W∗ − Z
> 1.
B−Z
Define
H(δ) = 1 − δxδ−1 − (1 − δ)xδ .
Observe that H(0) = 0 and H (δ) = δ(1 − δ)(xδ−2 − xδ−1 ) < 0 for all δ ∈ (0, 1). By
implication, H < 0 for all δ in this interval. Thus, W ∗ is decreasing in Z.
The second step is based on a contradiction. Assume that the statement in Proposition
2 is false, that a increase in Z leads to an increase in W ∗ . From (18), this would require
that u decreased. However, from (19), u can only decrease if W ∗ decreases. Thus, we
20
have a contradiction. It follows that a increase in Z leads to an increase in W ∗ . It is then
clear from (18) that an increase in Z leads to an decrease in u, which completes the proof.
21
5.3
Data tables
Table A2: Explanatory Variables
Countries
Belgium
Denmark
France
Germany
Italy
Netherlands
Spain
UK
Australia
Canada
USA
Japan
Finland
Norway
Sweden
Switzerland
Mean
Std. dev.
Ben.
dur.
Rep.
ratio
Union
coord.
Empl. Cont.
coord. flex.
C–D Indebt.
corp.
LTV
48
30
45
48
6
48
42
48
48
6
6
6
58
18
14
12
60
90
57
63
2
70
80
36
39
60
50
60
75
65
80
70
2
3
2
2
2
2
2
1
2
1
1
2
3
3
3
1
2
3
2
3
1
2
1
1
1
1
1
2
3
3
3
3
4
6
3
4
4
5
5
2
6
2
1
4
3
4
4
0
14
2
16
9
11
13
16
12
17
4
5
10
8
2
3
6
25.2
49.0
41.2
71.9
27.7
51.7
44.3
67.1
70.2
56.6
71.0
63.8
50.0
108.0
102.4
111.8
70
90
80
72.5
53
75
70
84
77.5
77.5
84.5
60
82.5
77.5
92.5
75
30.2
19.7
59.8
21.1
2.0
0.73
2.0
0.89
3.56
1.67
9.3
5.2
63.2
26.1
76.3
10.1
The following independent variables are taken from Layard, Nickell and Jackman (1991, ch 9 Table 7):
Benefit duration, Replacement ratio, Employer coordination, Union coordination, and the Calmfors–
Driffill corporatism index C–D corp (= CORP in LNJ). The variable referred to here as Contract
flexibility is defined by LNJ as the sum of their indices of synchronization of wage contracts (SW C;
higher the more synchronization), wage indexation (IW ; higher with more indexation) and contract
renewal (LW C; higher for shorter contract duration) and can be computed from LNJ ch.9 Table 11. LNJ
does not report the value for Spain. Like Bean (1994b) we have set it equal to 5. Data on indebtedness
is collected by the Bank of International Settlements for 13 countries, see Kneeshaw (1995), and by Berg
(1994) for the three Scandianvian countries. The maximum loan–to–value ratio (LTV) is reported for 15
of our countries by Jappelli and Pagano (1994). Here we use the average for the period 1971–1987. For
the remaining country, Switzerland, we use a conservative estimate. (Higher numbers improve the fit of
our 2SLS regressions.)
22
Table A3: Dependent Variables
κ
Countries
Belgium
Denmark
France
Germany
Italy
Netherlands
Spain
UK
Australia
Canada
USA
Japan
Finland
Norway
Sweden
Switzerland
1.37
1.40
1.61
0.79
2.20
1.32
1.76
1.31
1.43
2.20
2.18
1.09
1.31
1.06
1.23
0.10
Actual
unemp.
74-79
Actual
unemp.
80-85
6.3
5.5
4.5
3.2
4.6
5.1
5.3
5.1
5.0
7.2
6.7
1.9
4.4
1.8
1.5
1.0
11.3
9.3
8.3
6.0
6.4
10.1
16.6
10.5
7.6
9.9
8.0
2.4
5.1
2.6
2.4
1.7
The variable definitions and sources are:
• κ is a transformation of the long run rate of unemployment as estimated by Bean (1994b). This is
the ”natural” rate we explain in Table 1. To compute the implied long run rate of unemployment,
apply the formula u = (κ/2 + 1)2 .
• Actual unemployment 74-79 and 80-85 are the average unemployment rates in the years 1974-1979
and 1980-1985 respectively, as reported in Layard, Nickell and Jackman (1991, ch 9 Table 1).
23
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