1. State sector

The model used to characterize the state sector here closely follows the model developed in Commander, Coricelli, and Stahr (1992), and is similar in spirit to that presented by Dinopoulos and Lane (1991). ^1/ The presentation here is, therefore, brief. The stylized feature of the state sector 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 has been extensively explored in the literature (Ward (1958), Vanek (1970), 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. ^1/ In contrast to the classical labor-managed firm, the union modelled here also cares about employment and accordingly maximizes the expected utility of a representative worker in the firm or union. We assume further that there is a random selection of workers among those that remain employed and those that are laid off from the state sector. 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 implemented for capitalist firms. The wage bill of the worker controlled firm will be constrained by the level of output, 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 by 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 as 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 obtains employment in the private sector, respectively. All current workers or members of the union (M_t) receive equal treatment. The union’s utility function is given by

where ${\mathrm{L}}_{\mathrm{t}}^1$ denotes the (share of the) labor force employed in the state sector--sector one; ${\mathrm{W}}_{\mathrm{t}}^1$ represents the real wage in the state sector expressed in units of the private sector’s good, which is assumed to be the numeraire; δ_t represents the probability that a worker laid off from the state sector remains unemployed, and (1-δ_t) represents the probability that he obtains employment in the private sector; B denotes the exogenous level of unemployment benefits paid by the government. The production function in the state sector is assumed to be of the Cobb-Douglas type, with diminishing returns to labor, so that

where ${\mathrm{H}}_{\mathrm{t}}^1$ represents the skill level or human capital specialized in the production of the state sector’s good. The union maximizes its utility function with respect to wages and employment subject to a zero profit condition. ^1/ Expressed in units of the numeraire, the private sector’s good, this condition is

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 relative price of the state sector’s good to the private sector’s good. We assume that the union does not care about its size over time, per se, and that membership evolves according to

so that a proportion of the members of the union that 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 $\mathrm{V}\left({\mathrm{W}}_{\mathrm{t}}^1\right)$ simply equals ${\mathrm{W}}_{\mathrm{t}}^1$. ^2/ Then, maximizing the union’s expected utility subject to the zero profit constraint, first order conditions can be combined to yield the union’s employment rule as

while the real wage in the sector equals the (subsidy adjusted) average product of labor. Note that the left hand side in 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 δ_t, the probability that a worker laid off from the state sector remains unemployed, an increase in the level of unemployment benefits or the wage level 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. ^1/ Similarly, at a given level of unemployment benefits and private sector wages, a rise in δ_t reduces the expected income of a worker laid off by the union and will tend to maintain employment in the state sector. ^2/

2. Private sector

The private sector is characterized as 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. ^3/ Worker effort in the private sector is endogenously determined by an efficiency-wage mechanism that is elaborated below. ^4/ Output, ${\mathrm{Q}}_{\mathrm{t}}^2$, is produced by a technology of the Cobb-Douglas type, with diminishing returns to labor measured in efficiency units

where ${\mathrm{H}}_{\mathrm{t}}^2$ represents the skill level or human capital specialized in the production of the private sector’s good. Labor measured in efficiency units, or the effective labor input, $\left[\mathrm{E}\left({\mathrm{W}}_{\mathrm{t}}^2-\mathrm{B},{\mathrm{U}}_{\mathrm{t}}\right)\cdot {\mathrm{L}}_{\mathrm{t}}^2\right]$ is defined as the product of the effort of an individual worker, $\mathrm{E}\left({\mathrm{W}}_{\mathrm{t}}^2-\mathrm{B},{\mathrm{U}}_{\mathrm{t}}\right)$, and the number of workers employed in the private sector, ${\mathrm{L}}_{\mathrm{t}}^2$. In the spirit of standard efficiency–wage theory ^1/ we posit that an individual worker’s effort in the private sector is an (i) increasing concave function of the differential of the real wage in the sector, ${\mathrm{W}}_{\mathrm{t}}^2$, over the level of unemployment benefits, B, which the worker would earn if he were fired from the private sector; it is assumed that a worker fired from the private sector cannot be immediately hired into the state sector since he is not a member of the state sector union, and so the workers reservation wage is given by the level of unemployment benefits; ^2/ (ii) an increasing function of the aggregate level of unemployment, U_t. ^3/ As shown below, this specification implies that aggregate unemployment acts as a disciplinary device, constraining wages in the private sector. For simplicity we assume that the effort function is separable in the two arguments.

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. ^4/ 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, that is

where signs underneath the arguments in the W² function indicate signs of the partial derivatives, and can be derived by differentiating (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 workers effort at the existing wage. This allows the firm to lower the wage offered and still obtain the same effort level from workers.

The optimal level of employment in the private sector can be expressed as a function of the wage as

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 signs underneath the last three arguments can be obtained directly by examination of (9). For later purposes it is useful to distinguish two separate channels through which an increase in unemployment affects employment in the private sector: one associated with the lowering of wages; the other directly through an increase in worker effort at the existing wage, as (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 a decreasing function of the level of unemployment benefits.

3. Growth and restructuring

${\mathrm{H}}_{\mathrm{t}}^{\mathrm{i}}$ in each sector’s production function represents the skill level or human capital specialized in the production of each sector’s good, or the level of total factor productivity. The effect of the skill level or human capital is assumed to be entirely external to any single firm and it cannot be captured by it. In this section, in the spirit of neoclassical growth models we assume that the growth of this human capital or total factor productivity occurs exogenously. 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 (12) then implies that the Production Possibility Frontier of the economy will shift out over time in favor of production of the private sector’s 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’s good.

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, for an insulated market in the former CMEA, for example, then the higher speed of productivity growth can be interpreted as resulting from 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 due to level differences, it could be argued that the underlying speed of innovations was greater in Western markets, so that one would expect a greater potential for technology transfer from the rest of the world. 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 where productivity increases are likely to be slow.

The skill accumulation equations can be combined to yield a relative skill accumulation equation

where H_t represents the ratio of the skills 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. H_t is then used to denote the level of human capital in the private sector, and the sectoral subscript on it is dropped.

4. Equilibrium

Equilibrium in the economy at any point in time, that is for any level of the one state variable in the system given by history, the level of human capital in the private sector, can be defined by the identity

that is, 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 members of the union that a worker laid off from the state sector becomes unemployed or gains 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, this probability is defined by

Substituting this definition into the state sector union’s employment rule, 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 to note 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 this expression for ${\mathrm{L}}_{\mathrm{t}}^1$ and the solution for ${\mathrm{L}}_{\mathrm{t}}^2$ in equation (11), into equation (14), then yields an equation that can be solved for equilibrium unemployment as a function of the level of private sector human capital. Since H_t is, for now, posited to grow exogenously over time, this curve represents the phase diagram of the economy, that is the dynamic path of unemployment as the private sector grows.

To establish the nature of the time path of unemployment 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 (17) 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. As we have noted earlier, an increase in unemployment increases employment in the private sector through two channels: through a decline in the real wage and through a direct effect on worker effort. 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 mentioned effects with the first two positive and the second two negative

Combining terms

where the first term is positive, as the direct effect of a decline in wages in the private sector 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 through its effect on worker effort in the private sector and the consequent expansion in private sector employment. As equation (19) shows, as long as the elasticity of effort with respect to unemployment is less than a positive constant, this term will be positive, that is

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. ^1/ Under this condition, then, employment in the state sector is an increasing function of the unemployment rate.

While the effects of changes in relative prices and the rate of subsidy to the state sector on employment in the sector are straightforward to establish, the effect of a change in unemployment benefits is ambiguous as suggested by equation (17). 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 that

General equilibrium in the economy at each point in time is defined by

We now proceed to establish the shape of this curve, which we shall refer to as the UH curve in the unemployment-private sector human capital plane. Note from equation (9) 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 remain unemployed is then unity. Therefore, the initial share of employment in the state sector is determined by solving

for ${\mathrm{L}}_{\mathrm{t}}^1$. The initial unemployment rate is then

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 (22)

The denominator is always positive. In the numerator, however, 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), and combining terms, the numerator in (25) can be expressed as

Since the terms outside the square brackets are all positive, the sign of this expression will be determined by the sign of the expression in square brackets, that is

the difference of two positive terms.

We will now show that the slope of the UH curve eventually becomes negative as the level of human capital increases. However, at small values of human capital 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 the sector expand. We show 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 upwards at small levels of H.

It is useful to note several features of the expression in (27), which can be rewritten as

First, note that as ${\mathrm{L}}_{\mathrm{t}}^1$ becomes small, the absolute value of the second term increases and the expression must, at some value of ${\mathrm{L}}_{\mathrm{t}}^1$, become negative. In fact as ${\mathrm{L}}_{\mathrm{t}}^1$ approaches zero the expression will approach negative infinity. Since ${\mathrm{L}}_{\mathrm{t}}^1$ is a decreasing function of H_t, it follows that as H increases, the slope of the UH curve eventually becomes negative. Second, note that when ${\mathrm{L}}_{\mathrm{t}}^1$ is large the second term is small. In fact as ${\mathrm{L}}_{\mathrm{t}}^1$ approaches unity the second term approaches zero. The magnitude of the first term depends also on the level of unemployment. Since the wage in the private sector is a decreasing function of the level of unemployment, the first term, i.e. the term in square brackets, will be largest when employment in the state sector is high, so that the marginal product of labor in the state sector is low, and when unemployment is low, so that the level of unemployment does not exert much downward pressure on the private sector wage. In such circumstances the private sector wage will be determined predominantly by considerations of worker efficiency and hence tend to be relatively high. The expression is likely to be positive, therefore, when the initial level of employment in the state sector is high and the level of unemployment low. Since this is a feature of the initial condition of most PCPEs--with, in many cases, almost the entire labor force employed in the state sector and unemployment non existent--this is the case we focus on in the remainder of the paper. Figure 1 plots such a hump-shaped UH curve with the unemployment rate rising as H increases and then eventually declining as H continues to increase.

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Dynamic Path of Economy with Exogenous Accumulation of Human Capital.

Citation: IMF Working Papers 1993, 016; 10.5089/9781451843323.001.A001

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Whether or not the UH curve first slopes upward is determined by the initial distribution of the labor force between the state sector and unemployment. The initial distribution of the labor force is determined, as equations (23) and (24) show, by the level of unemployment benefits, the magnitude of the subsidy to the state sector, and the relative prices of the two goods. While we postpone for later a detailed discussion of the effects of policies on the path of unemployment, the above discussion implies that, for example, unemployment benefits can be increased sufficiently to ensure that the UH curve is downward sloping. Note, however, that this 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 process is simply brought forward in time.

5. Dynamic path of the economy

With unchanged policies, the UH curve in Figure 1 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 ^1/, and subsequently the economy specializes in the production of the private sector good. ^2/ 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. Now, 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. ^1/

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 the 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 comprised largely of a private sector. The forces in the system just discussed 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 that this cost 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 of the private sector will continued restructuring 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 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 impact on the speed of the transition. ^1/ 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 are endogenously determined. 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 their effect on the speed of transition. 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.

6. Changes in the terms of trade or a liberalization of prices to international levels

Consider the effect of an exogenous increase in the internationally given relative price of the private sector’s good. If the private sector’s good is interpreted as the (basket of) good(s) predominantly produced in western markets, and the state sector’s good is thought of as 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 that 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’s good. Note that P denotes the ratio of the state sector’s good to the private sector’s good. An increase in the relative price of the private sector’s good thus corresponds to a decline in P. Then, differentiating equation (22) and noting the sign of the partial derivative of employment in the state sector with respect to an increase in P, we have that, at each level of H_t

Since we have established that the denominator is positive, the curve UH unambiguously shifts up in response to a decline in P as shown in Figure 2. Since the private sector’s 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’s good raises the value of the expected income of a laid off worker, measured in units of the state sector’s 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 H_t, the wage paid by the private sector will be lower, and employment in the private sector will expand. Since at each level of H_t, and therefore 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’s good.

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Effect of an Increase in the Price of the Private Sector’s Good.

Citation: IMF Working Papers 1993, 016; 10.5089/9781451843323.001.A001

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7. Effect of 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 just discussed. 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 impact on the private sector’s employment decision. The effect of a decline in the rate of subsidy to the state sector, which corresponds to a decline in the value of the parameter τ 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.

We note that at the level of aggregation employed in the model developed here, the effects of changes in the parameter τ can also be interpreted as the effects of changes in various 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 hence 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.

8. Effect of an employment or wage subsidy in the private sector

Since unemployment rises in the early stages of the transition process 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 employment subsidy. By lowering the cost of raw labor, the employment subsidy lowers the cost to the firm 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

and therefore

Noting that an employment subsidy to the private sector will directly impact also 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 H_t, or the vertical shift of the UH curve is given by

The denominator of (34) 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 square brackets. This expression in square brackets is exactly the expression that determines the slope of the UH curve (see equation (27)). It follows that when the slope of the UH curve is zero or negative, as it is for large values of H_t, the expression in (35) must be negative, so that the curve UH shifts down. For small values of H_t, however, when the UH curve is positively sloped, the first term in (35) is positive. Note further that in the limiting case when H_t equals zero ${\mathrm{L}}_{\mathrm{t}}^2$ equals zero, so that the expression will be positive. By continuity it follows that there exists a range of values of H_t starting with zero such that the UH curve shifts up. Such a shift of the UH curve is plotted in Figure 3 where for small values of H_t the UH curve shifts up, while for larger values of H_t it shifts down. The downward shift of the UH curve or the reduction in unemployment at large values of H_t is intuitive. The reason for the upward shift at low levels of H_t should also be clear. Essentially, subsidizing employment in the private sector causes employment to expand. However, the size of the sector also affects the extent to which it will expand. At the same time, the expansion of employment opportunities in the private sector causes an outflow of workers from the state sector. What we have established is that at low levels of H_t, the outflow from the state sector will exceed the flow into the private sector.

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Effect of increase in rate of employment subsidy to private sector.

Citation: IMF Working Papers 1993, 016; 10.5089/9781451843323.001.A001

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We now establish that private sector employment is higher at each point in the transition process as a result of the increase in the employment subsidy to the sector. In Figure 3, for values of H_t up to H₁, the increase in employment subsidy in the private sector creates higher private sector employment since at each level of H_t, in addition to the effects of the subsidy, unemployment is higher. To establish that private sector employment is higher for all levels of H_t, 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 H_t increases, private sector employment is higher at all subsequent levels of H_t.

9. Unemployment benefits

An increase in unemployment benefits, by raising the alternative income of a worker employed in the private sector, that is, his 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 remain unemployed, thus creating an incentive for the union to retain workers. The total impact on unemployment at any level of H_t is given by

where the denominator is always positive, while 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 square brackets), the expression is positive so that the UH curve shifts up. For values of H_t between zero and that corresponding to the peak unemployment rate, however, the effect is ambiguous. Note from equation (24) that the intercept of the UH curve unambiguously shifts up. Figure 4 plots two alternative possible shifts of the UH curve in response to an increase in unemployment benefits.

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Alternative Effects of an Increase in Unemployment Benefits.

Citation: IMF Working Papers 1993, 016; 10.5089/9781451843323.001.A001

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10. Policies to continuously reduce the unemployment rate

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 over time or even, as 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 the transition. In the absence of specifying a particular objective function for the government there are, of course, an infinite number of paths for the unemployment rate that one could pick. To focus ideas, we examine one that seems intuitive. In Figure 5, with unchanged policies, unemployment rises from U, then subsequently falls, eventually reaching zero at H. We consider a policy that seeks to take the economy in a linear fashion from U to H, so that the dynamic path is given by the straight line joining U and H. Starting at the initial unemployment rate, therefore, such a policy would succeed not only in lowering the unemployment rate at each point in time compared to what it would be in the absence of such a policy, but also in lowering the rate of unemployment monotonically over time.

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Time Varying State Sector Subsidy to Lower Unemployment Continuously.

Citation: IMF Working Papers 1993, 016; 10.5089/9781451843323.001.A001

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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 of course be to subsidize employment or output in the state sector. ^1/ Moreover, since changes in the subsidy (or tax) 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 of tax or subsidy to the private sector, it follows that there will exist some range of H_t over which a such a policy cannot succeed in lowering the unemployment rate monotonically over time.

Consider instead an output subsidy to the state sector. ^2/ This was shown to shift the UH curve down for all levels of H, Figure 5 plots several UH curves as the rate of subsidy to the state sector increases. Figure 5 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 H_t increases up 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 5, 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 UH at H=H’. Therefore, a more gradual reduction in the unemployment rate, as implied by a movement along the UH 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 UH to a transition path along the original UH curve for the speed of transition or transformation of the economy. Since unemployment is lower for each level of H_t and the state sector subsidy does not directly impact on 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 or transformation has no long-run impact. If the process of skill accumulation driving the transition process were endogenously determined, however, as 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, as we show, a critical importance in determining whether or not restructuring actually takes place.

1. Role of policies with endogenous restructuring

The Ḣ = 0 locus of unemployment and human capital combinations 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 Ḣ = 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 while unemployment represents a cost to the economy it 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 alternative policies and exogenous variables in affecting 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 to restructuring toward the private sector good 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’s 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 ${\mathrm{H}}_{\mathrm{t}}^{\mathrm{c}}$ and ${\mathrm{H}}_{\mathrm{t}}^{\mathrm{c,}}$ which were previously levels of human capital implying convergence to the state sector good, now imply with the higher rates of unemployment on the new UH curve, UH’, convergence to production of the private sector’s good. Figure 8 shows the effects of an increase in the rate of employment subsidy to the private sector. This will shift the UH curve leftward, ^1/ implying at low levels of H higher unemployment, and at higher levels of H lower unemployment. In addition, the Ḣ = 0 locus shifts to the left, implying a lower level of unemployment necessary at any given level of human capital to place the economy on a path to self-sustained restructuring toward the private sector good. Figure 8 depicts two potential alternative situations: when the Ḣ = 0 locus intersects the UH curve on the upward sloping portion of the UH curve and when it intersects it on the downward sloping portion of the curve. In the former case the Ḣ = 0 locus is downward sloping while the UH curve is upward sloping. Since both curves shift leftward it follows that the critical level of human capital unambiguously falls. In the latter case when both curves are downward sloping it is possible to show--as is done in appendix I--that the Ḣ = 0 locus shifts down by more than the UH curve so that the critical level of human capital again falls.