Abstract
This paper develops a model of the process of reallocation of labor from the state sector to the private sector. When growth is exogenously determined, we show that in the initial stages of transition unemployment will rise. After a critical stage in the transition process, restructuring is accompanied by a decline in unemployment. When growth is endog-enously determined, and human capital is acquired by learning-by-doing, we show that whether or not restructuring eventually occurs is determined by the level of human capital in the private sector and the rate of unemployment. The effects of various shocks and government policies on the costs, speed, and eventual outcome of restructuring are analyzed.
The process of transition following the introduction of reforms and liberalization in the previously centrally planned economies (PCPEs) of Central and Eastern Europe has proved costly in terms of unemployment and output.1 In all of these economies, open unemployment was absent prior to the reforms. Figure 1 indicates that the unemployment rate has steadily increased, and so far—except in Czechoslovakia—there are no signs of a reversal in this trend, or even of a leveling off of the unemployment rate. In most PCPEs, increases in the unemployment rate have occurred despite rapid growth of the private sector.2 Thus, increasing unemployment reflects a gap between the speed at which the state sector is shedding labor and the speed at which the private sector is absorbing it.
Unemployment Rate in the PCPEs, 1990–92
(In percent)
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
This paper develops a simple model of the process of reallocation of labor from the state sector to the private sector and examines several questions relating to the dynamics of the transition process. The model emphasizes important institutional features of economies in transition that affect incentives and behavior in both the state and the private sector. Specifically, the transition economy is characterized by the asymmetric behavior and market power of labor in the two sectors. In the state sector, labor dominates the decision process of enterprises, while in the private sector employment and wage decisions are determined by profit-maximizing firms. It is assumed that firms in the private sector are concerned with worker effort and productivity, but that these considerations play a minor role in the state sector. Worker effort in the private sector is endogenously determined by the differential of wages over the alternative income of workers. In order to boost the productivity of the work force, firms find it optimal to pay a premium over the market-clearing wage, resulting in unemployment. Unemployment acts as a disciplining device so that, at any wage rate, worker effort increases with unemployment. Unemployment thus exerts downward pressure on the equilibrium wage paid in the private sector.3
The level and behavior of the unemployment rate over time is determined by the relative speeds of growth in the private sector and of decline in the state sector. The scope for productivity growth is assumed to be greater in the private sector and two alternative processes driving growth and restructuring are considered: a neoclassical exogenous productivity growth model, where transition is inevitable; and an endogeng80 ous growth model, where the work force acquires human capital through learning-by-doing, and restructuring is endogenously determined. The exogenous growth version of the model is related to recent work by Blanchard (1991) and Atkeson and Kehoe (1992) on the costs and speed of transition following major reform in a two-sector economy.4 A key difference of our approach is that the relative speeds at which the private sector expands and the state sector contracts are determined endogenously and vary over time.
When growth and restructuring are exogenously determined, we show that the dynamic behavior of unemployment is determined by the initial distribution of the labor force. If the initial level of employment in the state sector is “high” and the level of unemployment is “low”—a stylized feature of the initial conditions in most PCPEs—then, in the early stages of the transition process, the unemployment rate will rise. Once private sector activity has expanded beyond a critical level, the private sector begins to absorb labor at a faster pace than it is shed by the state sector, and the unemployment rate falls over time. The framework presents a manifestation of popular notions about the cost of transition from an economy dominated by the state sector to one dominated by the private sector. In the initial stages of transition, as a natural consequence of the reallocation of labor accompanying the restructuring of production, the economy will not only suffer a cost in terms of unemployment but this cost will rise. Only after a critical stage in the transition process is restructuring accompanied by declining unemployment.
When growth is endogenously determined, and the work force acquires human capital through learning-by-doing, we show that there are two potential long-run equilibria. Whether or not the restructuring of production toward the private sector eventually occurs is determined by the level of human capital in the private sector and the prevailing rate of unemployment. With low levels of human capital or of skills specialized in the production of the private sector good, a relatively high rate of unemployment is necessary to place the economy on a self-sustaining path of restructuring toward the private sector. In this framework, the speed of transition, as measured by the share of the labor force employed in the private sector at any point in time, takes on a critical importance. Policies that succeed in allocating labor toward the private sector either by increasing unemployment, thus depressing private sector wages and expanding employment in the sector, or by directly subsidizing employment in that sector will result in the acquisition of comparative advantage in production of the private sector good and could place the economy on a path of restructuring toward the private sector good.
The effects of various shocks—such as changes in relative prices—and government policies on the dynamic path of unemployment are analyzed. The role of government policies differs significantly depending on whether growth is viewed as an exogenous or an endogenous process. When growth is exogenously determined, the speed of transition has no long-run impact, and restructuring is inevitable. Therefore, policies that reduce unemployment in the early stages of transition—for instance, subsidies to the state sector—may reduce short-term costs without affecting the long-run equilibrium. In this framework, the budgetary costs of policies that attempt to lower unemployment need to be compared only against the welfare and budgetary costs of unemployment. In contrast, when growth is endogenous, policies that reduce unemployment will slow down the transition process and can jeopardize the restructuring and eventual convergence to long-run specialization in the private sector good.
I. A Model of Growth and Restructuring
We consider an open economy comprising a “state” sector and a “private” sector. Each sector produces a (basket of) traded good(s), the prices of which are determined in the rest of the world. Each sector’s good is produced with labor as an input. For simplicity, and so as to focus on forces emanating directly from the employment decisions in each sector and the movement of labor across sectors, we abstract from the presence of physical capital and other factors in the production process. The population, or labor supply, is assumed to be constant and normalized to equal unity.
State Sector
The model used here to characterize the state sector closely follows the model developed in Commander, Coricelli, and Stahr (1992) and is similar in spirit to that presented by Dinopoulos and Lane (1991).5 The stylized feature of the state sector that these models emphasize is that of a labor-dominated firm: a firm controlled by a worker council, for example, whose interference in management is nontrivial. The implications of active participation of workers in management have been extensively explored in the literature (Ward (1958), Vanek (1970), and Brewer and Browning (1982)). For our purposes, worker control is treated as equivalent to a powerful trade union presence where wages and employment are subject to joint maximization.6 In contrast to the classical labor-managed firm, the union modeled here also cares about employment and accordingly maximizes the expected utility of a representative worker in the firm or union. We assume further that the selection of workers who remain employed and who are laid off from the state sector is random. A worker who is laid off either remains unemployed and receives an exogenously set level of unemployment benefits from the government or gains employment in the private sector and earns the wage prevailing in that sector. These assumptions allow us to view the labor-dominated firm as a limiting case of an efficient-bargaining model of the type commonly used to describe capitalist firms. The wage bill of the worker-controlled firm will be constrained by the level of output, which is adjusted for any subsidies to (or taxes on) the sector. Since all profits are appropriated by workers, the wage and employment combination picked by the union will not generally correspond to the point on the contract curve picked in bargaining between union and employer in a conventional capitalist firm.
The union maximizes the expected utility of a representative worker over prospects of employment at the contract wage against the expected utility of being laid off from the state sector. The expected utility of a worker who is laid off is a weighted average of unemployment benefits and the private sector wage, where the weights are defined by the probability that a laid-off worker remains unemployed and the probability that he or she obtains employment in the private sector, respectively. All current workers or members of the union (Mt) receive equal treatment. The union’s utility function is given by
where
where
where τ is a parameter determined by the subsidy (or tax) the enterprise receives (pays) from the government. P denotes the ratio of the internationally given price of the state sector good to that of the private sector good. We assume that the union does not care about its size over time per se and that membership evolves according to
so that some proportion, ψ, of union members who get laid off leave the union.
Again, to keep the analysis simple, and to highlight the effects of certain forces in the labor market on the transition process, we assume that the union is risk neutral and that
while the real wage in the sector equals the (subsidy-adjusted) average product of labor. Note that the left-hand side of equation (5), the marginal product of labor, is a decreasing function of employment in the state sector. Equation (5) therefore implies that, for any given value of δt (the probability that a worker laid off from the state sector remains unemployed), an increase in the level of unemployment benefits or an increase in the wage rate in the private sector will, by increasing the expected income of a worker laid off from the state sector, lower employment in the state sector. As employment in the state sector falls, the marginal and average product of labor will rise and the wage paid to those remaining employed will rise.9 Similarly, at a given level of unemployment benefits and private sector wages, a rise in 8, reduces the expected income of a worker laid off by the union and will tend to maintain employment in the state sector.10
Private Sector
The private sector is populated by firms whose employment and wage decisions are determined purely by profit-maximization considerations. In particular, firms in the private sector, unlike the union in the state sector, derive no returns from maintaining employment per se and are free to fire workers.11 Worker effort in the private sector is endogenously determined by an efficiency-wage mechanism, which is elaborated below.12 Output in the private sector,
where
The representative firm in the private sector maximizes profits with respect to wages and employment, given the skill level in the sector, the level of unemployment benefits, and the aggregate level of unemployment. The firm’s first-order conditions for profit maximization can be solved for wages and employment in the sector as functions of the level of unemployment in the economy and the level of human capital in the private sector.16 Wages are determined by the well-known condition in efficiency-wage models that the elasticity of effort with respect to the real wage is unity:
Equation (7) can then be used to solve for a unique real wage in the private sector as a function of the unemployment rate for any given level of unemployment benefits:
where signs underneath the arguments in the W2 function indicate signs of the partial derivatives, which can be derived by differentiating equation (7). Equation (8) implies that for any given level of unemployment benefits, an increase in the aggregate unemployment rate leads the firm to offer a lower wage to workers. This effect corresponds to standard models of the Phillips curve. In our model, however, the effect results from the assumption that an increase in the aggregate unemployment rate raises each worker’s effort at the existing wage. This allows the firm to lower the wage offered and still obtain the same level of effort from workers.
The optimal level of employment in the private sector can be expressed as a function of the wage:
It is straightforward to show that the optimal level of employment in the private sector is a decreasing function of the wage offered by the firm. Employment in the private sector can, therefore, be described by the function
where the signs underneath the last three arguments can be obtained directly by examination of equation (9). For later purposes, it is useful to distinguish two separate channels through which an increase in unemployment affects employment in the private sector: through the lowering of wages and more directly through an increase in worker effort at the existing wage, as equation (9) brings out. Equation (10) implies that employment in the private sector can be written simply as
that is, as an increasing function of the unemployment rate and the level of human capital in the private sector and as a decreasing function of the level of unemployment benefits.
Labor Market Equilibrium
Equilibrium in the economy at any point in time can be defined by the identity
In other words, the labor force is either employed in one of the two sectors or is unemployed. Further, we impose that in general equilibrium the probabilities perceived by union members of a worker laid off from the state sector becoming unemployed or gaining employment in the private sector are equal to their actual values. Assuming that the private sector randomly selects the desired number of workers from the pool of workers who are not employed in the state sector, we define this probability by17
Substituting this definition into the employment rule of the state sector union, equilibrium employment in the state sector can be expressed as a function of the unemployment rate, the level of employment in the private sector, the wage rate in the private sector, and the exogenous variables of the system:
where the signs of the partial derivatives are straightforward from equation (5). Substituting in equations (8) and (11), which define employment and the wage rate in the private sector, equilibrium employment in the state sector can be written as
that is, as a function of the unemployment rate, the level of human capital in the private sector, and the exogenous variables in the system. Substituting both this expression for
To establish the nature of the relation between unemployment and private sector human capital, it is necessary first to determine the response of state sector employment to changes in unemployment and the level of human capital in the private sector. Note from equation (15) that employment in the state sector is a decreasing function of the level of human capital in the private sector. An increase in the level of human capital in the private sector expands employment in the private sector, lowering the probability that a worker laid off from the state sector becomes unemployed. This raises the expected wage of a worker laid off from the state sector, causing the union to lay off workers.
The response of employment in the state sector to an increase in unemployment is more complicated. Three separate effects can be identified. First, an increase in unemployment raises the probability that a worker laid off from the state sector will remain unemployed, thus discouraging the union from laying off workers. Second, an increase in unemployment reduces wages in the private sector, also discouraging the union from laying off workers. Third, an increase in unemployment raises employment in the private sector, lowering the probability that a worker laid off from the state sector will become unemployed, thus encouraging the union to lay off workers. The latter effect works through two channels: through a decline in the real wage and through a direct effect on worker effort in the private sector. The Appendix establishes that, under a condition that places an upper bound on the elasticity of effort in the private sector with respect to unemployment, employment in the state sector is an increasing function of the unemployment rate. This condition is assumed to hold.
While the employment effects of changes in relative prices and in the rate of subsidy to the state sector are straightforward to establish, the effect of a change in unemployment benefits is ambiguous as suggested by equation (15). We postpone a detailed discussion of the effects of unemployment benefits on employment in the state sector to the discussion of policies below, and for now simply leave the partial derivative unsigned. To summarize, we have shown that
General equilibrium in the economy at each point in time is defined by
The Appendix establishes that the slope of this curve in the unemployment and private sector human capital plane, referred to as the UH curve, eventually becomes negative as the level of private sector human capital increases. However, at small values, the slope can be negative or positive. The latter case implies that the slope of UH switches sign at some level of human capital: unemployment will first rise, even as human capital in the private sector grows and employment opportunities in that sector expand. It is shown that whether or not this curve first slopes upward is determined by the initial distribution of the labor force between employment in the state sector and unemployment. The larger the initial size of the state sector, and hence the smaller the initial unemployment rate, the more likely it is that this curve will slope upward at small levels of H2. Since high levels of state sector employment and low unemployment are characteristic of initial conditions in most PCPEs—with, in many cases, almost the entire labor force having been employed in the state sector and unemployment nonexistent—this is the case we focus on in the remainder of the paper. Figure 2 plots such a hump-shaped UH curve with the unemployment rate rising as H2 increases and then eventually declining as H2 continues to increase.18
Dynamic Path of Economy with Exogenous Accumulation of Human Capital
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
Growth and Restructuring: Dynamic Path of the Economy
In both cases, we assume that the speed of productivity growth, and thus the potential for technological advance, is faster in the private sector. The assumption of a higher speed of productivity growth in the private sector is the driving force behind restructuring in the model. There are several reasons to expect this to be the case. First, to the extent that private sector activity represents a “new” activity while state sector activity represents an “old” activity, the scope for learning and hence productivity increases should be greater in the new activity. Second, if the private sector good is interpreted as representing goods produced in Western markets, while the state sector good is interpreted as representing goods produced in an insulated market, in the former Eastern trading bloc CMEA, for example, then the higher speed of productivity growth can be interpreted to be a result of the greater potential for productivity increases as the economy “catches up” to Western total factor productivity levels. Third, rather than as a catch-up effect owing to level differences, it could be argued that the underlying speed of innovation was greater in Western markets, so that one would expect a greater potential for technology transfer from the rest of the world to the PCPEs. Finally, it could be argued that the inherent distortions in the state sector—the low quality of inherited physical capital (plants and machinery) and the obsolete technologies embodied in them—present an environment in which productivity increases are likely to be slow.
Exogenous Growth
Skills are acquired according to
We posit further that γ2 < γ1, so that the skill level, or productivity, grows at a faster rate in the private sector than in the state sector. Equation (18) then implies that the production possibility frontier of the economy will shift out over time in favor of production of the private sector good. Comparative advantage in producing the private sector good will thus grow over time and, at unchanged relative prices, employment and production will be restructured in favor of the private sector good.
The skill accumulation equations can be combined to yield a relative skill accumulation equation:
where Ht, represents the ratio of the skill level or human capital in the private sector to that in the state sector. To keep the analysis tractable, while still allowing for a higher speed of productivity growth in the private sector, we model the limiting case where skills accumulate in the private sector but the skill level in the state sector is constant and normalized to equal unity. Ht is then used to denote the level of human capital in the private sector, and the sectoral subscript on it is dropped.
Dynamic Path of the Economy
With unchanged policies, the UH curve in Figure 2 describes the dynamic path of the economy as the (relative) level of productivity, skills, or human capital in the private sector grows over time. It is possible to show that along this path, employment in the state sector shrinks continuously, while employment in the private sector expands continuously. Eventually, the unemployment rate goes to zero,20 and subsequently the economy specializes in the production of the private sector good.21 On the left-hand side of the peak unemployment rate, as the economy traverses up the UH curve, both unemployment and the level of human capital are increasing. Since employment in the private sector is an increasing function of both, it must be expanding. Since private sector employment and unemployment are both expanding, the remainder of the labor force, which is employed in the state sector, must be shrinking. On the right-hand side of the peak unemployment rate, unemployment is falling, while the level of human capital is rising. Employment in the state sector is an increasing function of the level of unemployment and a decreasing function of the level of human capital in the private sector. It follows that employment in the state sector will continue to decline as the economy traverses down the UH curve from the peak unemployment rate. Since both state sector employment and unemployment are falling, the remainder of the labor force, which is employed in the private sector, must be rising. The entire restructuring process is characterized by a monotonic decline of employment in the state sector and a monotonic rise of employment in the private sector. However, in the early stages of the transition process, when the level of employment in the state sector is high and the level of employment in the private sector is low, the analysis shows that the speed at which the state sector sheds labor is greater than the speed at which the private sector absorbs labor, leading to a rise in unemployment. In the later stages of transition, the opposite is true. Once the private sector has expanded to a critical stage, it absorbs labor at a faster pace than the state sector sheds it, leading to a decline in unemployment.22
Consider the path of wages in each sector during the restructuring process. As employment in the state sector declines, the marginal and average products of labor in the state sector will rise and so the wage paid in that sector will rise. In the private sector, however, in the early stages of the transition process, as the unemployment rate rises, the wage rate will fall until the unemployment rate peaks. Subsequently, the wage in the private sector will begin to rise.
The analysis presents a manifestation of popular notions of the costs of transition from an economy dominated by a state sector to one largely comprising a private sector. The forces in such a system imply that in the initial stages of transition, as a natural consequence of the process of reallocation of labor accompanying the restructuring, the economy will not only suffer unemployment but it will rise over time even as the private sector expands. It is worth emphasizing that this is dictated by the intrinsic dynamics of the economy and happens in the absence of any new shocks to the system. It is only after a critical level of development has been attained by the private sector that continued restructuring will be accompanied by a decline in the unemployment rate. There are thus two distinct stages in the transition process: an early difficult stage and a relatively easier later stage. There is clearly a potential role for government policies in affecting the dynamic path of the economy during the restructuring process and thus in reducing the costs of the transition. However, policies that attempt to reduce the costs of the transition by lowering the unemployment rate are also going to affect the speed of the transition. We show in the next section that the speed of transition can play an important role in determining the outcome of the restructuring process when the accumulation of skills in the private sector is endogenously determined.
Endogenous Growth
Following Lucas (1988) and Chadha (1991), suppose now that skills or human capital specialized in the production of each sector are acquired according to
where, as before, skills are assumed to be entirely external to any single firm. The growth of the skill level should now be interpreted as occurring through the learning-by-doing of the work force. The rate of growth of the skill level in equation (20) is a positive function of both a pure speed-of-learning parameter θi and the effort or resources devoted to producing good i, which is assumed to be related to the proportion of the labor force employed in the production of good t. It is posited further that the speed of learning or potential for productivity increases is greater in the private sector, so that θ2 < θ1. In terms of the previous discussion of the role for different rates of technology transfer from the rest of the world to the two sectors, imagine that “available” technological progress globally is greater in the production of the private sector good than in the production of the state sector good. The present formulation then implies that the speed at which technologies are adopted, or the actual technology transfer, will also be a function of the resources devoted to producing the private sector good.
The skill accumulation equations can be combined to obtain a relative learning equation and, on substituting in the labor market identity,
where Ht denotes the ratio of human capital in the private sector to that in the state sector. Equation (21) brings out that there will exist distributions of the labor force between the two sectors such that the ratio of skill levels remains exactly constant over time: where, for example, the effect of a smaller share of labor in the private sector on the growth of the relative skill level is exactly offset by the higher speed of learning in that activity.
To keep the analysis tractable, we assume, as in the previous subsection, that whereas skills are accumulated in the private sector through learning-by-doing, the skill level in the state sector is constant and normalized to equal unity. Again we use Ht to denote the level of human capital in the private sector and suppress sectoral subscripts. To retain the essence of the effects of differential speeds of learning-by-doing in the two sectors on relative skill accumulation, as in equation (21) above, we assume that
where the θi now represents arbitrary constants and the term in the unemployment rate has been dropped for simplicity.23 Then, substituting in the employment rule in the private sector from equation (11) yields
The locus of points where the (relative) skill level in the private sector remains constant can then be plotted as a function of unemployment and human capital, or the downward-sloping H= 0 curve in Figure 3. The arrows indicate the direction of movement of the (relative) skill level in the private sector when the economy is off the H= 0 locus. To the right of the locus, human capital increases, while to the left it falls.
Dynamic Path of Economy with Endogenous Accumulation of Skills
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
The UH curve represents the equilibrium of the economy at each point in time. The direction of movement along the UH curve, however, will be determined by the intersection of the UH curve with the H= 0 locus. The Appendix establishes that the slope of the UH curve is always greater than the slope of the H= 0 locus so that there is a unique intersection of the two curves. The intersection can in general occur below, at, or above the peak unemployment rate on the UH curve and will be determined by all the parameters and exogenous variables of the system. Since the economy is always on the UH curve, the double arrows in Figure 3 are used to denote the actual path of the economy starting from any initial level of human capital given by history. The intersection of the H= 0 locus with the UH curve defines a critical level of human capital,
The production possibility frontier of the economy shifts out, over time, with experience gained by the labor force proportionately in favor of one of the two goods, depending on the speed of learning-by-doing in each sector and the resources devoted to learning in each activity. The implications of the analysis differ markedly from those of the exogenous growth framework in the previous subsection. There are now no forces in the system that would necessarily place the economy on a path converging to eventual specialization in the private sector good. Thus, a clear role for government intervention emerges. In particular, policies that allocate labor toward the private sector would lead to the acquisition of comparative advantage in the production of the private sector good and could place the economy on a path to self-sustained restructuring in production, leading eventually to specialization in the private sector good. Under our assumptions, specialization in the private sector good implies a higher long-run growth rate of output.
We turn now to an examination of the effects of policies and exogenous variables on the time path of unemployment during the transition process and on the speed of transition.
II. Effects of Policies and External Shocks
We examine first the effects of changes in exogenous parameters and policy variables in the exogenous growth model.
Case of Exogenous Growth
We focus first on the effects of once-and-for-all changes in these variables and then examine the effects of a policy that attempts to continuously reduce unemployment.
Changes in the Terms of Trade or a Liberalization of Prices
Consider the effect of an exogenous increase in the internationally given relative price of the private sector good. If the private sector good is interpreted as a (basket of) good(s) predominantly produced in Western markets, and the state sector good is thought of as one produced for an insulated market (for trade within the former CMEA, for example), then the process of price liberalization and the opening of markets to competition from the West, which has taken place in the PCPEs of Central and Eastern Europe, can be likened to an exogenous decline in the relative price of the state sector good. Note that P denotes the ratio of the price of the state sector good to that of the private sector good, An increase in the relative price of the private sector good thus corresponds to a decline in P. Then, differentiating equation (17) and noting the sign of the partial derivative of employment in the state sector with respect to an increase in P, we find that at each level of Ht
Since we have established that the denominator is positive, the curve UH unambiguously shifts upward in response to a decline in P as shown in Figure 2. Since the private sector good is treated as the numeraire, a change in relative prices has no direct effect on the employment decision of the private sector. For the state sector, however, an increase in the relative price of the private sector good raises the expected income of a laid-off worker, measured in units of the state sector good, leading the union to lay off workers. While there is no direct effect of a change in the relative price on the private sector’s employment decision, there is an indirect effect. Since unemployment is now higher at each level of Ht, the wage paid by the private sector will be lower, and employment in the private sector will expand. Since at each level of Ht, and therefore at each point in time during the transition process, unemployment and private sector employment are higher, employment in the state sector is lower. The speed of transition of the economy is thus higher as a result of an increase in the relative price of the private sector good.
Changes in State Sector Subsidies
The effects of once-and-for-all changes in the parameter τ. which is used to represent (one plus) the rate of subsidy (or tax) on output of the state sector in equation (3), are completely analogous to the effects of a change in relative prices. This can be seen by noting that τ and P appear jointly in equation (5), the state sector’s employment rule, and do not directly affect the private sector’s employment decision. A decline in the rate of subsidy to the state sector, which corresponds to a decline in the value of the parameter t, would therefore shift the UH curve up, exactly as in Figure 2, increasing unemployment at each point in time, reducing the share of the labor force in the state sector, and increasing the share of the labor force employed in the private sector.
At the level of aggregation employed in the mode! here, the effects of changes in the parameter τ can also be interpreted as the effects of changes in other policy variables on the state sector: a tariff on the state sector; an employment or wage tax (or subsidy) in the state sector; and the effects of wage-bill ceilings. While these interpretations are not pursued here, it is useful to bear them in mind as alternative instruments for achieving the policy objectives discussed.
Employment or Wage Subsidy in the Private Sector
Since unemployment rises in the early stages of the transition because the state sector sheds labor at a faster rate than the private sector absorbs labor, a natural question is the effect of an employment or wage subsidy in the private sector. If firms in the private sector are granted an exogenous subsidy at the rate μ. for each unit of labor they hire, the firm’s first-order conditions imply
so that the elasticity of effort with respect to the real wage, adjusted for the rate of subsidy, equals unity. The real wage can then be expressed as a function of the rate of subsidy. It is straightforward to establish that
so that the wage paid in the private sector declines with an increase in the rate of the employment subsidy. By lowering the cost of raw labor, the employment subsidy lowers the firm’s cost per unit of effective labor. The firm will therefore offer a lower wage rate to achieve the same cost per unit of effective labor and expand employment. Employment in the private sector is now given by
Therefore,
Noting that an employment subsidy to the private sector will also directly affect the state sector’s employment decision by changing the expected wage of a worker laid off by the union, the impact on unemployment at any given level of Ht, or the vertical shift of the UH curve, is given by
The denominator of equation (29) is positive. It can be shown that the sign of the numerator is determined by the sign of
Whereas the second term in the expression is negative, the sign of the first term is determined by the sign of the term in the curly brackets. This expression in the curly brackets is exactly the expression that determines the slope of the UH curve (see equation (A7) in the Appendix). It follows that when the slope of the UH curve is zero or negative, as it is for large values of Ht, expression (30) must be negative, so that the curve UH shifts down. For small values of Ht, however, when the UH curve is positively sloped, the first term in (30) is positive. Note further that, in the limiting case when Ht equals zero,
Increase in Private Sector Employment Subsidy with Exogenous Growth
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
We now establish that private sector employment is higher at each point during the transition as a result of the increase in the employment subsidy to the sector. In Figure 4, for values of Ht up to H1 an increase in the employment subsidy in the private sector creates higher private sector employment, since at each level of Ht, in addition to the effects of the subsidy, unemployment is higher. To establish that private sector employment is higher for all levels of Ht, first note that at H1, where the values of unemployment and human capital in the private sector are the same on both curves, private sector employment is higher on the shifted UH curve since the rate of subsidy to the sector is higher. Then, note that the response of private sector employment to changes in H can be written as
so that the response increases with an increase in the rate of subsidy. It follows that since the level of private sector employment at H1 is higher after the increase in subsidy and its slope with respect to Ht increases, private sector employment is higher at all subsequent levels of Ht.
Unemployment Benefits
An increase in unemployment benefits, by raising the alternative income of a worker employed in the private sector, that is, his or her reservation wage, causes firms in the private sector to raise offered wages and cut back employment. For workers in the state sector, the expected wage of a laid-off worker increases because of both the increase in unemployment benefits and the increase in private sector wages, creating an incentive for the union to lay off workers. However, the outflow of workers from each sector increases the probability that a worker leaving the state sector will remain unemployed, thus creating an incentive for the union to retain workers. The total impact on unemployment at any level of Ht is given by
where the denominator is always positive. The sign of the numerator can be shown to be determined by the sign of
It follows that when the slope of the UH curve is negative or zero (as determined by the term in curly brackets), the expression is positive so that the UH curve shifts up. For values of Ht between zero and that corresponding to the peak unemployment rate, however, the effect is ambiguous. Note that the intercept of the UH curve unambiguously shifts up (see equation (A5) in the Appendix). Figure 5 plots two possible shifts of the UH curve in response to an increase in unemployment benefits.
Alternative Effects of an Increase in Unemployment Benefits
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
Policies to Reduce the Unemployment Rate Continuously
There is, of course, no reason why policy variables should be adjusted only in a once-and-for-all manner in the present framework. Since the analysis suggests that with unchanged policies the unemployment rate will rise over time in the early stages of the transition, it is natural to consider policies that prevent the unemployment rate from rising or even, since the analysis predicts the unemployment rate will eventually fall to zero, to consider policies that attempt to reduce unemployment monotonically to such a level, and thereby reduce the costs of transition, In the absence of specifying a particular objective function for the government, there are an infinite number of paths for the unemployment rate that would satisfy this objective. To focus ideas, we examine one that seems intuitive. In Figure 6, with unchanged policies, unemployment rises from
Time-Varying Stale Sector Subsidy to Continuously Lower Unemployment with Exogenous Growth
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
Consider how policies can achieve such a path. An employment subsidy to the private sector was shown to raise unemployment for small values of H without affecting the initial unemployment rate. This suggests that a policy to reduce the unemployment rate at small levels of H would actually need to tax employment in the private sector, and would succeed in lowering unemployment by preventing an outflow of workers from the state sector. A more direct way of doing this would be to subsidize employment or output in the state sector.24 Moreover, since changes in the rate of subsidy to the private sector are powerless to affect the vertical intercept of the UH curve, and the curve is positively sloped at this point for any rate, it follows that there will exist some range of Ht over which such a policy cannot succeed in lowering the unemployment rate monotonically over time.
Consider instead an output subsidy to the state sector.25 This was shown to shift the UH curve down for all levels of H. Figure 6 plots several UH curves as the rate of subsidy to the state sector increases. Figure 6 makes clear that for the economy to traverse on a straight line from ̱U to ¯H the rate of subsidy to the state sector will have to increase over time as Ht increases to H′. That the rate of subsidy needs to increase over time is intuitive since the subsidy will be preventing potentially increasing amounts of unemployment. As H exceeds H′ in Figure 6, however, if the rate of subsidy is maintained, then the economy will simply traverse down the right-hand side of the UH curve tangent to the straight line ̱U¯H at H = H′. Therefore, amore gradual reduction in the unemployment rate, as implied by a movement along the ̱U¯H line would imply that the rate of subsidy can be relaxed or reduced over time.
Now compare the implications of a transition path along the straight line ̱U¯H to a transition path along the original UH curve on the speed of transition. Since unemployment is lower for each level of Ht and the state sector subsidy does not directly affect the private sector’s employment decision, it follows that employment in the private sector will be lower at each point in time. Since private sector employment and unemployment are both lower at each point in time, it follows that state sector employment is higher at each point in time.
By maintaining employment in the state sector at a higher level, the policy succeeds in reducing the costs of the transition but it slows the speed of the transition process. In this framework, where the transition is inevitable because of an exogenously assumed faster rate of skills accumulation in the private sector, the budgetary costs of the subsidies to the state sector need to be compared only against the budgetary and welfare costs of unemployment. The speed of transition has no long-run impact. If the process of skill accumulation driving the transition process is endogenously determined, however, as discussed in the next section, the extent of transformation at any point in time, as measured by the relative size of employment in the private sector, takes on a critical importance in whether or not restructuring actually takes place.
Case of Endogenous Restructuring
The H= 0 locus of combinations of unemployment and human capital separates initial conditions that imply eventual convergence to specialization in either the state sector or the private sector good. If the equilibrium level of unemployment for any given level of human capital is higher than that implied by the H= 0 locus, the economy will converge to specialization in the private sector good. Note that the curve is negatively sloped in the unemployment-human capital plane. This implies that at low levels of human capital a high rate of unemployment is necessary to place the economy on a path leading to specialization in the private sector good. This characteristic of the present framework creates the fundamental dilemma for policies, in that unemployment, although it represents a cost to the economy, may be necessary for creating downward pressure on wages, such that private sector employment can expand sufficiently. The negative slope also implies, on the other hand, that at high levels of human capital, a (relatively) low level of unemployment may be sufficient for eventual specialization in the private sector good.
Consider now the effects of various policies and exogenous variables on restructuring toward the private sector good. Essentially, policies that succeed in reducing the critical level of human capital necessary for attaining a self-sustained path toward restructuring will increase the set of initial conditions converging to such a path, and can thus potentially alter the long-run equilibrium of the economy. Alternative policies will, however, have alternative implications for the unemployment rate.
An increase in the relative price of the private sector good, or a reduction in the rate of subsidy to the state sector, will shift the UH curve up as in Figure 7. Skill levels between
Decrease in Stale Sector Subsidy with Endogenous Skill Accumulation
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
Increase in Employment Subsidy to Private Sector with Endogenous Skill Accumulation
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
In summary, then, policies that affect the state sector alone affect restructuring by shifting the UH curve, with an increase in unemployment increasing the set of initial conditions converging to specialization in the private sector good. Policies that affect the private sector, on the other hand, while affecting the UH curve, have the advantage that by also shifting the H= 0 locus they reduce the unemployment necessary at any level of human capital to bring about restructuring toward the private sector good.
III. Concluding Remarks
This paper has developed a simple model of the process of reallocation of labor from the state to the private sector in PCPEs. When growth and restructuring are viewed as exogenously driven, we showed that unemployment may increase in the transition because of the intrinsic dynamics of the reallocation process and in the absence of any new shocks to the economy. In explaining the actual experience of unemployment in the PCPEs, several factors are likely to have contributed to the rise in unemployment. First, the rise in unemployment can be viewed as resulting from a sequence of unanticipated exogenous shocks that generated and have sustained increases in unemployment.27 While the initial reforms probably represented the largest shock, they were followed by a series of subsequent reforms, so that there were actually several shocks. Similarly, the collapse of the CMEA, and the subsequent loss of markets, could be viewed as having generated a sequence of shocks. Second, the rise in unemployment could be interpreted as a one-time movement toward an equilibrium rate of unemployment, in an economy characterized initially by “excessive” employment. Our analysis is not intended to diminish the role of these or other such factors in explaining the rise in unemployment in the PCPEs. Rather, it complements their role by highlighting a set of intrinsic dynamics that will tend to exacerbate increases in unemployment triggered by exogenous shocks.
The effects of alternative policies in reducing the unemployment costs of the transition process, and their impact on the speed of transition, were examined when growth was viewed as exogenous and restructuring as inevitable. In that context, several policies could be adopted to reduce or prevent a rise of unemployment during the initial stages of the transition without jeopardizing the final outcome of restructuring. Nevertheless, we showed that these unemployment-reducing policies would slow down the restructuring process. In a framework where growth was endogenous and the eventual outcome of restructuring determined by initial conditions, we showed that unemployment may be necessary to ensure that restructuring occurs. Policies that reduce unemployment, thus alleviating the costs of the transition, may jeopardize the final outcome of the restructuring.
It should be noted that in order to focus on the intrinsic dynamics generated by the transition it was implicitly assumed that any budgetary balance could be financed. The fiscal implications of the transition and the effects of alternative policies on the fiscal balance were ignored. In this sense, the analysis of the paper represents the unconstrained path of the economy. The fiscal dimension of the transition process is, of course, an important one.28 The interaction of fiscal constraints with the endogenous process of restructuring and the reallocation of resources from the state to the private sector are examined in Chadha and Coricelli (1993). It is shown there that with constant tax rates on the state sector and a fixed real level of unemployment benefits per worker, the path of the budget deficit will mirror the behavior of unemployment. The budgetary balance will deteriorate continuously during the early stages of the transition, recovering only when the savings in unemployment expenditures are sufficient to compensate for the continuing decline in tax revenues from the state sector. Attempts to improve or maintain the budgetary balance during the transition are shown to create pressures to maintain the state sector, slow the transition process, and could jeopardize the eventual outcome of the process of restructuring.
APPENDIX
This Appendix establishes several propositions employed in the text.
State Sector Employment and Unemployment
Differentiating the union’s employment rule, the response of employment in the state sector to an increase in unemployment can be written as the sum of the four effects mentioned in the text, with the first two positive and the second two negative:
By combining terms,
where the first term is positive, since the direct effect of a decline in private sector wages on state sector employment dominates the indirect effect by which the decline in private sector wages raises private sector employment and thus tends to reduce state sector employment. The second two terms represent the difference between the direct effect of unemployment on state sector employment and the indirect effect of unemployment, which raises worker effort in the private sector, and the consequent expansion in private sector employment. As equation (A2) shows, as long as the elasticity of effort with respect to unemployment is less than a positive constant, this term will be positive:
We assume that this is the case. It is worth noting that this condition is not necessary for any of our results. It is, however, sufficient.29
Shape of the UH Curve
Note from equation (9) in the main text that when the level of human capital in the private sector is zero, employment in the private sector will be zero. The probability that a worker laid off from the state sector will remain unemployed is then unity. Therefore, the initial share of employment in the state sector is determined by solving
for
so that the higher are unemployment benefits, the lower is the initial level of employment in the state sector and the higher the initial unemployment rate.
For positive levels of human capital in the private sector, the evolution of the unemployment rate with the accumulation of private sector human capital is determined by differentiating equation (A5):
The denominator is always positive. In the numerator, whereas employment in the state sector is a decreasing function of the level of human capital, employment in the private sector is an increasing function of the level of human capital. Differentiating equation (5) from the main text, and combining terms, the numerator in (A6) can be expressed as
Since the terms outside the curly brackets are all positive, the sign of this expression will be determined by the sign of the expression in the curly brackets:
the difference of two positive terms.
It is useful to note several features of the expression in equation (A8), which can be rewritten as
First, note that as
This section establishes that (i) the slope of the UH curve is always greater than the slope of the H= 0 locus so that there is a unique intersection of the two curves and that (ii) in response to an increase in the private sector employment subsidy, when both the UH curve and the H= 0 locus are downward sloping, the H˙—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 H= 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
Proof by Contradiction of Unique Intersection of UH and H˙=0 Curves
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
Increase in Employment Subsidy to Private Sector
Citation: IMF Staff Papers 1993, 003; 10.5089/9781451930856.024.A002
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Mussa, Michael, “Dynamic Adjustment in the Heckscher-Ohlin-Samuelson Model,” Journal of Political Economy, Vol. 86 (1978), pp. 775–91.
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Shapiro, Carl, and Joseph E. Stiglitz, “Equilibrium Unemployment as a Worker Discipline Device,” American Economic Review, Vol. 74 (1984), pp. 433–44.
Tanzi, Vito, “Fiscal Policy and Economic Restructuring of Economies in Transition,” IMF Working Paper 93/22 (Washington: International Monetary Fund, 1993).
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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).
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.
See also Lane (1991).
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
Since
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.
Kornai (1992) and Tanzi (1993), among others, discuss the budgetary implications of restructuring in Eastern Europe.
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.
