This Appendix establishes several propositions employed in the text.
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Bankim Chadha is an Economist in the IMF’s Research Department. He holds a doctorate from Columbia University. Fabrizio Coricelli was an Economist at the World Bank when this paper was written. He is currently a professor of economics at the University of Siena in Italy. He received his doctorate from the University of Pennsylvania. Kornelia Krajnyak is a graduate student in the economics department at the Massachusetts Institute of Technology. This paper was written while she was visiting the World Bank in the summer of 1992. The authors would like to thank Olivier Blanchard, Eduardo Borensztein, Peter Clark, Mohsin Khan, Paul Masson, and seminar participants at the World Bank for useful comments. Any errors and all views expressed here are their own.
We follow Calvo and Frenkel (1991) in referring to these economies as PCPEs. They discuss how a centrally planned economy is likely to spend a significant period of time as a PCPE before becoming a full-fledged market economy. For a review of the experience with reform and stabilization during 1990–91 in Eastern Europe, see Bruno (1992).
This is exactly as posited by aggregative rules of disequilibrium price or wage adjustment, such as the well-known Phillips curve relation.
Atkeson and Kehoe (1992) examine the effects of social insurance for risk in search on the speed of the transition process. They show that the presence of social insurance can slow the transition. Blanchard (1991) develops a model in which an initial shock owing to a reform of the state sector creates a pool of unemployed workers. Unemployment then declines over time as the unemptoyed are absorbed into an expanding private sector, while state sector employment is constant. Once unemployment declines sufficiently, it becomes constant with the private sector expanding and the state sector shrinking at the same rate.
This contrasts with monopoly union models where the wage is either bargained or picked by the union and employment is subsequently set unilaterally by the employer; the outcome will therefore lie on the labor demand curve. See Oswald (1985) for a summary of this literature.
In other words, the hard budget constraint is assumed to be binding. While subsidies to the state sector are allowed for, they are assumed to be prespecified and set exogenously by the government.
The objective function we posit is analogous to that employed by Calvo (1978). He develops a two-sector model in which a trade union in the urban sector maximizes the difference between its members’ income and their alternative income in the rural sector. Note that when V() in equation (1) is linear, it can be rewritten as an increasing function of the differential of state sector wages over the expected alternative income of a worker laid off from the state sector.
Under the assumption of a Cobb-Douglas technology, the average product of labor is simply a linear function of the marginal product of labor.
It is shown below that wages in the private sector are always higher than the level of unemployment benefits.
There are no incentives to “hoard” labor.
Dinopoulos and Lane (1991) also employ an efficiency-wage mechanism in the private, or what they term the “non socialized,” sector. Our specifications differ. While they posit effort to be a function of the wage rate in the private sector, we posit effort to be a function of both the wage rate and the aggregate unemployment rate. The implications differ considerably.
For a recent survey and overview of efficiency-wage models, see Weiss (1990). Among the references cited there and for the motivations of our specification, see Shapiro and Stiglitz (1984) and Calvo (1979).
Since effort is an increasing function of the differential of the wage paid over unemployment benefits, it follows that the wage offered will always be greater than the level of unemployment benefits.
This specification is intended to capture the mechanism put forward, for instance, by Shapiro and Stiglitz (1984), who show that unemployment induces effort because the higher is unemployment, the greater is the punishment to a worker who is fired for shirking. The specification we adopt is chosen for analytical tractability. The main results on the dynamic path of unemployment are not affected by the presence of unemployment in the effort function.
Thefirm treats both of these as exogenous to its actions at any point in time. The specific assumptions on the form andevolution of human capital are discussed below.
An alternative approach is to allow for job tenure and define the probability of an unemployed worker obtaining a job in the private sector using the “flows” approach to labor markets as, for example, presented in Blanchard and Diamond (1992). The flows approach defines the probability of an unemployed worker obtaining employment as the ratio of job creation to the pool of unemployed—that is, in our notation as L˙2/U. The key difference is the flow change in employment in the numerator rather than the level of employment. Private sector employment and job creation are
The initial distribution of the labor force is determined, as the Appendix shows, by the level of unemployment benefits, the magnitude of the subsidy to the state sector, and the relative prices of the two goods. While a detailed discussion of the effects of policies on the path of unemployment is postponed for later, note that this implies, for example, that unemployment benefits can be increased sufficiently to ensure that the UH curve is downward sloping. This, however, would be accomplished only by increasing the initial level of unemployment so that the potential increase in unemployment that occurs at a later stage in the transition is simply brought forward in time.
See Lucas (1988) for a discussion of the ability of alternative models to explain the growth experience of various countries.
Alternatively, the rate could converge to some positive number representing the natural rate of unemployment. Here, the natural rate has been “normalized” to zero.
In microeconomic models of efficiency wages, for example, Shapiro and Stiglitz (1984), the unemployment rate can never fall to the natural rate in that there is always involuntary unemployment. With our specification of a continuous effort function, however, as Ht continues to rise, unemployment will tend toward the natural rate. Once unemployment declines to the natural rate (zero), strictly speaking there is a discontinuity in behavior in our model, as efficiency considerations cease to play any role and wages arrive at their competitive level.
It is possible to show that δt declines monotonically from unity when Ht equals zero, as the economy moves rightward along the UH curve. On the left-hand side of the peak unemployment rate, note that
There is no reason to use the same policy instrument for the entire transition process.
Recall the earlier discussion that the use of several alternative policy instruments in the state sector would be equivalent in this model to the use of an output subsidy.
The vertical intercept would be maintained, however.
If there are adjustment costs, each shock changing relative prices would generate transitory unemployment. See Mussa (1978) and Neary (1982) for two-sector models in the trade context that incorporate costs of adjustment.
The necessary condition for the analysis to be entirely unchanged is that the sum of the (i) partial derivative of employment in the state sector with respect to unemployment, (ii) the partial derivative of employment in the private sector with respect to unemployment—which is unambiguously positive, and (iii) unity be positive. Alternatively stated, the partial derivative of aggregate employment in the economy with respect to unemployment must be greater than negative unity. From a stability point of view, one would expect the partial derivative of aggregate employment with respect to unemployment to be positive. While we could assume a much weaker condition, our assumption has the advantage of keeping the presentation of the analysis transparent. We note also that in simulations of the model we were unable to find a case where the partial derivative of employment in the state sector with respect to unemployment was negative.