Abstract
Given the empirical fact that workers of different ages are not perfect substitutes in production, this paper explores how change in the age pattern affects wages and (un)employment. We develop a general equilibrium model where wages for young and old workers are set by monopoly unions. Contrary to the common wisdom on this topic, we show that an increase in the relative number of older workers has no effect on young and old unemployment. If, however, unions attach a higher weight to the wishes of the old, the unemployment rate of the old (young) will increase (decrease). In this case, we observe a redistribution of wage income from the young to the old.
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Notes
In the USA, the median age of the workforce is projected to rise from 35.4 years in 1986 to 42.1 years in 2016 (see Toossi 2007). In some countries, the ageing will be even stronger. According to the World Population Prospects of the United Nations (2007), western Europe will face an increase in the median age of the population from 34.5 in 1980 to 44.7 in 2020. In Germany, the modal age of the labour force is projected to rise from 36 years in 2000 to 54 years in 2020 (Börsch-Supan 2003).
Concerning the transition from junior to senior jobs, there seems to be a flaw in the Pissarides (1989) model. He assumes that, in each period, a fraction of old workers is separated from their senior job for exogenous reasons. Some of them, or even all, will get a junior job. In subsequent periods, they stay with the junior job, and they do not have a chance to switch back to a senior job. As a consequence, the number of old workers with a senior job constantly declines and goes to zero, which cannot be an equilibrium.
A simple alternative to our specification would be to assume that young and old workers are perfect substitutes in junior jobs. The modelling of such a scenario calls for some adjustments. First, the wages are identical, \(w_{1}^{y}=w_{1}^{0}\). Second, the labour demand functions 3 and 4 collapse to a single labour demand schedule for junior jobs. Third, there is a flow equilibrium for junior jobs which turns out to be \(z(N_{1}^{y}+N_{1}^{o})=h(L_{1}-N_{1}^{y}+(1-a)(L_{2}-N_{2}-N_{1}^{o}))\). And fourth, the optimal choice between young and old workers with junior jobs is now given by the requirement that, in a steady state, the ratio between separated jobs and job-seekers has to be the same for young and old workers: \(\frac{zN_{1}^{y}}{L_{1}-N_{1}^{y}}=\frac{zN_{1}^{o}}{ (1-a)(L_{2}-N_{2}-N_{1}^{o})}\). With these modifications at hand, we can solve the model. The derivation is somewhat cumbersome, and the results do not change very much compared to the results presented below. However, in order to sign the effects, it is sometimes necessary to put some restrictions on the initial steady state around which we log-linearize. Since these restrictions are not very intuitive, we drop the presentation of the solution of this scenario.
We impose the condition of ex ante neutrality where the policy is budget neutral at the initial steady state. The concept of ex post neutrality, where the budget is assumed to be neutral after all adjustments in the economy have taken place, is explored in Michaelis and Pflüger (2000) and Lingens (2004).
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Acknowledgements
We are grateful for comments on earlier drafts of this paper to participants of research seminars at the universities of Gießen, Hamburg, Kassel, Marburg and Würzburg. Particular thanks go to Max Albert, Michael Bräuninger, Oliver Lorz, Michael Pflüger, Marco de Pinto and a referee of this journal.
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Michaelis, J., Debus, M. Wage and (un-)employment effects of an ageing workforce. J Popul Econ 24, 1493–1511 (2011). https://doi.org/10.1007/s00148-010-0325-9
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DOI: https://doi.org/10.1007/s00148-010-0325-9