Abstract
In the preceding chapter, a model of a two-sector economy was presented in which the search for a new job and worker caused nonnegligible costs. It was presumed that individuals behave risk-neutral. Normally, the assumption of risk neutrality is employed for simplicity, as in the preceding chapter. To posit a certain degree of risk aversion seems to be more appropriate. More important however, it can be expected that the individuals’ attitude towards risk differs across countries. Differences across countries in the private households’ saving rates or in the share of highly risky assets on total private asset holdings may indicate crosscountry disparities in the individuals’ risk behaviour.1 The OECD (1999) e. g. records a households’ saving rate of 0.5 percent of the disposable income for the United States, 13.6 percent for Japan and 11.0 percent for Germany in 1998. The saving rates suggest that the Japanese are more risk-averse than the U.S. Americans and the Germans.1 Since future employment positions are unknown, it can be expected that the individual’s risk behaviour influences the wage setting rule. As it was shown in the previous chapter, the properties of the wage agreement are important for the economy’s response to changes in the environment, as e.g. the appreciation of the domestic currency or the decline in a world market price.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
The private household’s saving rate can be used as an indicator for differences in the individual risk behaviour if a precautionary motive is responsible for the asset accumulation. Precautionary saving can occur if e.g. the future personal income is uncertain (see e.g. Abel, 1985). In this situation, individuals may accumulate assets to insure themselves against possible low income in future times.
Clearly, the accumulation of savings may stem from other reasons than insuring oneself against the unemployment risk. In this situation, the saving rates are not an appropriate indicator for differences in the individual risk behaviour. Since this example serves as a pure illustrative propose, the households’ saving rates may be exchanged by other measures of risk aversion.
As the firms are managed by individuals, it seems natural to assume that firms are risk-averse too. See e. g. Greenwald and Stiglitz (1995) for a model presuming risk-averse firms. The firms act on a conventional labour market where efficiency wages are paid. In contrast, Blanchard and Fischer (1989, p. 429) mention two reasons for firms to behave risk-neutral: either their owners or managers are risk—neutral or they have access to the perfect capital market. The latter gives a manager the possibility to insure the firm against the risk. In the present context, the firm principally has the opportunity of buying an insurance against the risk of not finding a worker during a certain period. It would pay a premium and the insurance pays the not realised profits if the firm does not find a worker within e. g. a year. The managers then act as though they are risk-neutral. Clearly, in the presence of information asymmetries such insurances will not emerge.
Shi and Wen (1997) consider an economy with risk-averse individuals. However, employed and unemployed persons form a household thereby pooling their income. Consequently, the household’s income is not stochastic so that the household does not face uncertainty. In addition, the model presents a closed economy.
The individual’s decision problem being static implies in particular that an individual’s consumption jumps each time when he or she becomes unemployed or reenters employment.
The function B(px,py) used in equation (4.1) is usually not identical to the equally labelled function used in subsection 3.1.1. This function however does not emerge in the wage equation of the preceding chapter and consequently has no influence on the properties of the reference model. Therefore, no confusion should arise from using the same label.
With σ=1, the function B(.) in equation (4.1) becomes identical to the one used in subsection 3.1.1.
Given that the firms have chosen the number of vacancies optimally, the value of an additional vacancy has to be zero. If the value were negative, firms would have offered too many unfilled jobs. Firms will respond by closing some job opportunities. In contrast, if the value of an additional vacancy were positive, it would still be profitable to open additional jobs offers.
Coles and Wright (1998) points out that the Nash bargaining and sequential bargaining approach will be not equivalent during adjustment processes if the individuals are not risk-neutral. However, in an equilibrium both methods will yield identical results as shown by Binmore et al. (1986). As the analytical analysis mainly focuses on the examination of an equilibrium, the Nash bargaining procedure is used.
Appendix 4.4.1 describes the derivation of the wage equation in detail.
See Silberberg (1990, p. 314) for the interpretation of this derivative and the relation to the shadow price.
As the Arrow-Pratt measure of relative risk aversion is higher than or equal to zero, but strictly lower than one, it is sufficient that wages are greater than one for the inequality to be satisfied.
It is sufficient that the unemployment benefits exceed one for the inequality (1–η)b-η < 1 to be satisfied. This restriction does not seem to be a particular problem.
For the derivation of the wage equation cf. Appendix 4.4.1. Since this section is mainly concerned with the properties of a medium-run equilibrium it is not necessary to deal with wage equations for adjustment processes.
Roth (1979, p. 50) also shows, that in a static symmetric Nash bargaining the agreement of the negotiation can be derived alternatively by setting the inverse of the fear of ruin of one player equal to that of the other player.
This result follows immediately from (4.6) if this equation is multiplied by α and α is subsequently set equal to zero. Using the definition of the fear of ruin Wi = b is readily obtained. Clearly, if the wage is equivalent to the unemployment benefits the employees are indifferent between working and joining the unemployment pool. Similar to the preceding chapter, it is assumed that individuals decide to work. Individuals may indeed prefer to work if employment is connected to some nonmonetary returns, as e. g. a higher social status.
He derived this result for a symmetric Nash bargaining problem where only instantaneous payoffs are considered. One would expect that this result carries over to an asymmetric Nash bargaining problem, where the Nash product consists of streams of payoffs.
A similar economic situation is understood as a situation in which in addition to the parameters of a economy sectoral employment Li as well as the value of a marginal worker λi is identical under risk aversion and risk neutrality.
η is the constant measure of relative risk aversion so that η = 0 for the economy with risk-neutral individuals and 0 < η < 1 for the other.
The result of the previous section that risk-averse individuals consent to lower wages than risk-neutral individuals, does not refer to an equilibrium but only to similar economic conditions. A similar economic condition is defined as a situation in which sectoral employment and λi are identical in both economies in addition to the parameters. However, wages interact with other endogenous variables and it cannot be concluded from the result obtained in the preceding section that equilibrium wages are lower under risk aversion compared to the one under risk neutrality.
The wage negotiation between firms and potential employees takes place after the matching process, i. e. after the firm has chosen the number of vacancies. However, the firms anticipate the wages correctly as individuals are alike. Consequently, a firm in the economy with risk-averse individuals will anticipate a different wage rate than the firms facing risk-neutral individuals. Therefore, the firm’s decision problem is independent of individual risk behaviour although the attitude towards risk will influence the wages.
As it was shown in chapter 3 this condition is not only valid for the steady state but also for a second transition period which may possibly be a part of the adjustment process.
The interpretation of this equilibrium condition is identical to the appropriate equation (3.15) of subsection 3.2.1. This subsection also describes the different forces inducing (4.12) or (3.15) and identical conditions of models with perfect labour markets.
According to equation (4.8) the value of a marginal worker is identical in both sectors. Consequently, the labour market equilibrium condition can be expressed in terms of λY or λx.
The system of equations for the generalised model includes the one of the reference model as a limiting case. If η= 0 individuals are risk-neutral and (4.9), (4.11)-(4.13) become equivalent to (3.17).
As offering a vacancy is costly for firms, an observed high evaluation of an additional worker λ shows that firms are prepared to bear high expected costs of an additional vacancy. Accordingly, there have to be some scarcities, i. e. the total unemployment level must be low. Otherwise, the firms would easily find workers
The convenient form of the indirect utility function formalised in equation (4.1) enables this approach. As risk neutrality is a limiting case of risk aversion, a change in wages due to the change in px can directly be compared for economies with risk-neutral or with risk-averse individuals.
The number of vacancies offered in each sector was used to characterise each transition period. In 3, TP 0 was defined as the situation when both sectors offer no vacancy. Accordingly, in TP I only one sector offers unfilled jobs whereas in TP II both sectors open job opportunities. However, in the generalised model, the transition periods may be distinguished according to the different criteria.
If both sectors choose the number of vacancies equal to zero they will shrink at the maximum rate s. Even if the value marginal product were equalised initially after an infinitely small period of time they would differ as long as the technologies diverge. During the first transition period only one sector chooses Vi = 0 so that the sector shrinks at the maximum rate whereas the sectoral employment of the other evolves according to (3.26). Hence, the value marginal products of labour necessarily vary.
The following approach is indeed possible as this equation only depends on wages and the value of a marginal worker λ(t), which has to be positive and is identical for both sectors.
There are three cases in which ŵy — ŵx is positive: (a) both growth rates are positive, but the absolute value of ŵy is greater than the one of ŵx, (b) ŵY is positive and ŵx is negative, and (c) both growth rates are negative but the absolute value of ŵx is greater than the one of ŵY. At the same time, ŵY —ŵx> 0 implies that the wage in sector Y is higher than in sector X, wy >wx. Situation (a) shows that wy grows faster than wx so that both wage rates diverge. In (b), the wage in sector Y grows whereas the wage in sector X declines. Consequently, the difference between the wages increases. Alternative (c) shows that the wages in both sectors decrease, but the one in sector X declines faster than the one in sector Y. Therefore, the wages diverge.
The argumentation is formally the same as in the case of ŵY —ŵx > 0.
As in the reference model, the only jump variable is the number of vacancies to be offered in each sector. Accordingly, neither the value of a marginal worker nor wages can jump in the steady state, a fact which justifies this line of argumentation.
As mentioned in subsection 3.3.3 the economy cannot choose between the different adjustment paths. The latter may be caused by different sets of parameters characterising the initial conditions of the economies.
See section 3.3 for an overview on possible adjustment paths caused by other shocks.
Clearly, a decrease in the world market price for one good can have different reasons. One is that import tariffs are reduced or effectively circumvented. On the other hand, traditional trade theory sees the comparative advantage of developing countries in the high stock of unskilled labour relative to physical or human capital so that wages are relatively low in a state of autarky. For this reason, developing countries may be able to produce certain manufacturing goods at lower costs and therefore offer these at lower prices. In this situation, the decision of developing countries to participate in international trade would tend to reduce the world market prices for these goods.
Data source: Organization for Economic Co-Operation and Development: Main Economic Indicators, new standardised unemployment rate.
See e. g. Carroll (1992) or Beaton (1992) for this argument.
See e.g. Layard, Nickell, and Jackman (1992).
This can indeed be done, since wages have to be higher than the unemployment benefits b.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Weiß, P. (2001). The Generalised Model: An Open Economy with Risk-Averse Individuals. In: Unemployment in Open Economies. Lecture Notes in Economics and Mathematical Systems, vol 496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56569-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-56569-4_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41161-1
Online ISBN: 978-3-642-56569-4
eBook Packages: Springer Book Archive