This appendix establishes that (i) the slope of the UH curve is always greater than the slope of the Ḣ = 0 locus so that there is a unique intersection of the two curves; and (ii) in response to an increase in the private sector employment subsidy, when both the UH curve and the Ḣ = 0 locus are downward sloping, the Ḣ = 0 locus shifts down by more than the UH curve, and the critical level of human capital falls.
To establish that the two curves have a unique intersection, two observations are necessary.
First, note that the Ḣ = 0 locus can be written as
We have established that an increase in the private sector employment subsidy shifts the UH curve to the left and
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The International Monetary Fund, the World Bank, and the Massachusetts Institute of Technology, respectively. We would like to thank Peter Clark, Richard Jackman, Mohsin Khan, Paul Masson, and seminar participants at the World Bank for useful comments. Any errors and all views expressed here are our 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 in transition 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 of course, 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 process, Blanchard (1991) develops a model where an initial shock due to reform of the state sector creates a pool of unemployed workers. Unemployment then declines over time as the unemployed 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 constant 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 where 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 type technology, the average product of labor is, of course, simply a linear function of the marginal product of labor.
Assuming--as will be evident below is always the case--that wages in the private sector are 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 “nonsocialized” sector. However, our specifications differ. While they posit effort to be a function of the wage rate in the 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, for motivations of our specification see, in particular, 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 the punishment for 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.
Both of which the firm treats as exogenous to its actions at any point in time. The specific assumptions on human capital are discussed below in the subsection on growth and restructuring.
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 private sector with respect to unemployment was negative.
Or some positive number representing the natural rate of unemployment. Here the natural rate has been “normalized” to zero.
In microeconomic models of efficiency wages, as for example in 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 will cease to play any role and wages will be 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
Therefore, dδ must be negative. On the right hand side of the peak unemployment rate, Ut is falling, while
A detailed examination of budgetary pressures on the transition process are examined in Chadha and Coricelli (1993).
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.
Maintaining the vertical intercept, however.