Understanding Involuntary Unemployment & Wage Inflexibility: Contracts & Minimum Wages, Study notes of Introduction to Macroeconomics

Download Understanding Involuntary Unemployment & Wage Inflexibility: Contracts & Minimum Wages and more Study notes Introduction to Macroeconomics in PDF only on Docsity! 134 U NEMPLOYMENT AND OTHER FEATURES OF L ABOR M ARKETS 1. Unemployment • Thus far we have focused on explaining fluctuations in employment. In the post-Keynesian era, economists have focused more attention on unemployment . An individual is recorded as unem- ployed if they do not have a job and are currently looking for work. These terms have a specific definition that varies from country to country. Thus, the unemployment statistics of different countries are often not comparable. The basic idea, however, is that an unemployed individual is someone who wants to work but cannot find a suitable job at the wages, and with the condition, they are willing to accept. • Even when the economy is in a business cycle upturn we do not observe a zero level of unem- ployment. Friedman referred to the level of unemployment consistent with a constant rate of wage and price inflation (and constant inflationary expectations) as the natural rate. • Minimum wages (or mandatory disequilibrium award wages) will result in structural unemploy- ment for the least skilled workers by both contracting the demand for unskilled labor and, tem- porarily at least, increasing the supply of workers willing to work at the legal minimum wage. Similarly, if trade unions (or labor court judges) are more effective at raising real wages in some SD w w N unemployed 135 industries than they are in others, there will be queues for the plum union jobs and these will be measured as unemployment. • Equilibrium explanations of the natural rate of unemployment, and variations around that natural rate, also often rely on incomplete information. Relative demand or technology shifts lead to a loss of employment at some firms, but a demand for labor at others. Workers who lose employ- ment will in general find it desirable to search before accepting a new job. Measured unemploy- ment levels typically correspond to the number of people actively looking for a job. • Labor economists have elaborated on these models in various ways to obtain a better description of labor markets. The models have been tested using quite sophisticated econometric techniques to cope with the non-linearities and have performed reasonably well when tested on microeco- nomic data. 2. A Model of Job Search • Assume a worker can either search or work but not both. Assume he allocates his time between search and work to maximize the expected present value of his earnings stream. Let his discount factor be β . Assume that each time he searches he draws a wage independently from the distri- bution φ (w). If he searches we assume he earns nothing this period and if the current job offer is not accepted this period it cannot be recalled at a later date. • Let V(w) = expected present value of a worker with wage offer w who behaves optimally. If he works at the wage w he gets w + β w + β 2 w +… = w/(1- β ) (1) If he doesn't work he gets 0 this period, draws w' from φ and behaves optimally from there. So 138 and (10) We can do various comparative static exercises with this expression for the reservation wage by differentiating with respect to the parameters of interest. • Note that we can rewrite the expression (10) for the reservation wage β (1 - Φ ( )) + - β = (11) so that (12) • The individual can work at or attempt to get another job at the differential w - by searching. The right hand side of (12) equals the discounted expected gain from searching and this must equal the reservation wage at the margin. • One implication of the model is that the availability of unemployment benefits will tend to ex- tend the period of search by reducing search costs below the foregone wage. It has been argued, for example, that the introduction of unemployment benefits into the UK in the 1920's was one factor contributing to the historically high unemployment in that country at that time. • If current wage offers convey information about future wage offers, we get more complicated dynamics. The reservation wage will in general change over time. This will also happen if the horizon of the individual is finite. w A 1 β–( ) β 1 βΦ w( )– -------------------------- w'φ w'( ) w'd w ∞ ∫= = w w w w w β w'φ w'( ) w'd w ∞ ∫ w β 1 β– ----------- w w–( )φ w( ) wd w ∞ ∫= w w w 139 • We have taken φ as fixed in the above analysis. Why does this distribution persist over time? One answer is that it takes time and other resources to arbitrage across markets. Furthermore, if relative demands or production technologies are continually changing the opportunities for arbi- trage are also changing. An alternative interpretation of φ as the productivity of the match be- tween workers and firms also would result in a distribution of φ which persists. The productivity of different matches seems to be an important element in search models. This has been pursued in the work of Jovanovic and others. • The assumption that the worker either works or searches was imposed on the model. In practice, search occurs on the job. Taking a wage cut and searching for a better job while working seems to dominate the above strategy unless the marginal value of leisure and/or unemployment com- pensation is high. One way to derive a dichotomous model endogenously might be to suppose employers take the individual's previous wage as a signal of his ability. This would impose a cost to taking a wage cut on the current job before searching. It might also be more expensive to go to interviews and fill out and file applications if still working. That is, search costs might be low- er if you're unemployed. Finally, taking a wage cut and staying employed while searching may not be a feasible option if the firm has some lumpiness in production so that at lower levels of output the additional workers are unprofitable at any wage acceptable to the worker. The work by Hansen and others has studied the effect of fixed costs, either for the firm or the worker, on employment relationships. The fixed costs could include for example the fixed costs of getting to work and getting started. With such fixed costs, it is not optimal to reduce work hours of each employee when desired output falls. Reducing the number of employees is preferable. The em- ployees laid off would be offered unemployment benefits and for the period the benefits last, will search for a new job. 3. Implicit Contract Theory and Involuntary Unemployment • Another strand of the literature has focused on explicit or implicit wage contracts, which are a means for firms and workers to share risks. In effect the firms insure workers, but in return have 140 the right to lay-off workers when they face an unfavorable demand for their output. A conse- quence of the insurance is that real wages and employment are less variable than they would be in a spot labor market, and one can explain ex-post involuntary unemployment and the availabil- ity of private unemployment insurance. • The basic hypothesis underlying the contract models is that firms are less risk averse than work- ers. A justification for this assumption might be that human capital is non-marketable and there- fore allows for less risk sharing for workers than can be achieved in capital markets for firms' assets.1 • Assume a firm has the production function f(n) with f′ > 0, f″ < 0, and n the level of employment of homogeneous labor. Assume the firm is competitive and able to sell all it wants in period t at the real price pθ, θ = 1,2 representing two states of the world. Assume p1 > p2. Assume the firm and its workers share a common view of the probabilities of the two states emerging and denote these π1 and π2. Denote by wθ the real wage paid by the firm in state θ. The firm's profits in state θ are then given by pθf(nθ) - wθnθ (13) • Assume all workers are identical and possess an indirect utility function which is concave in the real wage and hours of employment V = g(wθ, L) g1 > 0, g11 < 0, g2 ≥ 0, g22 ≤ 0. (14) Suppose hours of work are fixed institutionally (this might be derived by assuming preferences or technology is convex - such as in the fixed costs model examined by Hansen). Assume that if 1. To quote Azariadis: “Employers possess substantial information about the status of each employee, control a supervisory apparatus which monitors current job performance, and enjoy superior access to financial mar- kets. It is sensible, therefore, for firms to underwrite the insurance policies their employees are unable to place directly and, in effect, to become in part financial intermediaries, shifting risk from owners of human capital to owners of financial capital.” 143 (26) (27) (28) Then from (27) (29) The concavity of U and U′ > 0 imply − Ψ(w, r) > w − r (30) so that (29) implies p2f′(n2) < r (31) • If workers derive no utility from additional leisure when unemployed r = 0 and f′(n2) > 0 yields a contradiction. Therefore, if r = 0 we must have n1 = n2 and the workers bear no risk – the risk neutral firm provides complete insurance. On the other hand, if r is large enough that p2f′(n2) < r we can have n1 > n2 and there will be layoffs in state 2. • Observe that Ψ(w, r) is the risk premium workers have to be paid to accept the chance of unem- ployment in state 2. When this risk premium plus the value of marginal product p2f′(n2) falls short of w (the wage workers have to be paid in state 2) everyone is better off on average if fewer than n1 work in state 2. This reduction in employment is achieved by temporary layoffs rather than wage cuts. π1p1f′ n1( ) π1w– π2 n2U w( ) n1U′ w( ) --------------------– π2 n2U r( ) n1U′ w( ) --------------------+ 0= p2f′ n2( ) w– U w( ) U′ w( ) --------------- U r( ) U′ w( ) ---------------–+ 0= v π1U w( ) π2 n2 n1 ---- U w( ) π2 n1 n2– n1 ----------------U r( )+ += p2f′ n2( ) w– 1 U′ w( ) --------------- U w( ) U r( )–[ ] Ψ w r,( )≡–= 144 • Returning to the case n1 > n2, (26) implies (32) so the real wage the firm pays in both periods is between the values of the marginal physical product of labor in the two periods. The situation is illustrated in the diagram below. Here the values with superscript 0 denote the outcomes we would observe in a spot market. In a spot labor market we would have real wages (33) and levels of employment (34) where and (35) • Thus in the case n1 > n2 we have n2 > . In the contract market the value of the marginal product of labor is equated to the marginal private cost of leisure w − Ψ(w, r) < r so the level of employ- ment is higher in the low demand state. The firm insures the workers by providing less wage vari- ability and less employment variability than would occur in a spot market. Of course, the workers pay a premium for this insurance in the form of wages below the value of their marginal product in the state of high demand. p1f′ n1( ) w π2n2 π1n1 ---------- U w( ) U r( )–[ ] U′ w( ) ----------------------------------- w>+= w w 0 if θ 1= r if θ 2=   = n n1 0 n1= if θ 1= n2 0 if θ 2=      = w 0 p1f′ n1 0( )= p2f′ n2 0( ) r= n2 0 145 • We would have measured unemployment of n1 - n2 in state 2 in the contract model. Notice, how- ever, that the measured unemployment would in fact be higher if the market were a spot market. In that case, measured unemployment in state 2 would be n1 - . Also observe that if the spot market does not have unemployment in state 2, neither does the contract market. • The key implication of this model is that some inflexibility of real wages across different states of demand might well be consistent with a competitive model. The mere observation of such real wage inflexibility does not necessarily imply we cannot obtain an explanation consistent with individual maximizing behavior mediated by competitive markets. The model does not, howev- er, explain high employment variability – the variation in employment is less in the contract model than it would be in a spot labor market. • Now we can ask whether the unemployment in state 2 is involuntary. Given state 2, unemploy- ment is ex-post involuntary - individuals would rather work at the wage w than collect the lower sum r which represents the value of non-market activity. On the other hand, the contract itself is freely arrived at and unemployment resulting from it is ex-ante voluntary. Furthermore, to pre- w0 w r n2 0 n2 n1 = n 0 n2 0 148 • According to the standard analysis, the costs of a minimum wage include both the net value of the lost employment opportunities and the net value of the lost output from firms. There may also be losses associated with the increased unemployment as individuals spend more time and other resources searching for the limited jobs available at the legal minimum wage. Losses in current employment may also have future costs as individuals who are denied valuable work experience suffer a reduction in future productivity. Time out of the work force can also produce a deterio- ration in previously acquired work skills. Some individuals displaced from the sectors covered by a minimum wage take jobs in uncovered sectors at a reduced wage rate. The opportunity to find work in occupations that aren’t covered by the minimum wage lessens the adverse impact of the law on overall levels of employment. Some of the effects of the minimum wage are, how- ever, spread from the covered to the uncovered sectors as workers in the latter sectors suffer de- clines in their real wages. In addition, since the marginal product of labor is higher in the covered than the uncovered sectors, the value of output could be increased by transferring labor back to the covered sectors. Some of the efficiency costs of the minimum wage will therefore take the form of an inefficient allocation of labor across the different sectors of the economy. • However, the standard analysis cannot explain why so many employers appear to be able to pay the legally prescribed minimum wage (and other “award wages”) without greatly reducing em- ployment. In the standard analysis, it is only through a reduction in employment that the margin- al product of workers can be increased to equal the legally prescribed minimum real wage. • The following figure illustrates the distribution of wages following the imposition and enforce- ment of a minimum wage as predicted by the standard theory. Any individual whose marginal product after the minimum is imposed is less than the minimum would lose his job. 3 The reduc- tion in employment following the imposition of a minimum wage generally raises the marginal 3. Some individuals with a marginal product less than the legal minimum wage before the minimum is im- posed will keep their jobs and be paid the minimum. However, we would expect the demand curves for a nar- rowly defined skill category of labor to be quite elastic. A legal minimum real wage of w0 would therefore eliminate most jobs with a marginal product less than w0 before the imposition of the minimum wage. 149 products of labor and shifts the wage distribution to the right, particularly for low wages where most of the employment changes are concentrated. Thus, the post-minimum distribution is not merely a truncated version of the pre-minimum distribution. Nevertheless, we would expect the post-minimum distribution to be a truncated version of a “smooth” distribution. • In practice, the imposition and effective enforcement of a minimum wage leads to a large num- ber of workers receiving the minimum as illustrated in the following figure. Furthermore, a change in the minimum wage shifts the mass of workers receiving the minimum. proportion marginal product & real wage legal minimum unemployed 150 • Similarly, the distribution of wages in many European economies has noticeable peaks at various award wage levels. Many workers in different industries, or parts of the country, receive exactly the same wage. 4 In a deregulated labor market, the wages paid for similar jobs in different in- dustries or different locations would be related since the employers are drawing on a common labor pool. However, the marginal products of workers in a particular job classification are likely to vary from one industry to the next. Even in the same industry, different employers use differ- ent technologies, so the marginal products of workers nominally doing the same job are likely to differ. Finally, similarly classified jobs in different industries or locations are likely to have dif- ferent non-pecuniary characteristics. This would also lead to wage variations as workers and firms competed on the attractiveness of the overall employment opportunity and not just wage rates. In summary, in a free and competitive labor market we would expect to see a smooth dis- tribution of wages within a particular job category rather than the high degree of uniformity char- acteristic of European wage distributions. 4. As with the simple minimum, however, the award wage is non-binding in some cases and the firms make over-award payments. proportion marginal product & real wage legal minimum 153 ply effort, he must be compensated by higher wages if he is to remain equally satisfied as e in- creases. Hence, the indifference curves are positively sloped in (w,e) space. The concavity of these indifference curves follows from the assumption of decreasing marginal utility of wages and increasing marginal disutility of effort. As e increases, larger increases in w are required to compensate for a given increase in e. • In an unconstrained market equilibrium, the chosen wage and effort level will maximize the worker’s utility for a given level of firm profits as at (w*, e*). The particular levels of firm profits and worker utility at the equilibrium (the split of the rents between the employer and the employ- ee) depend on the trade-off between enforced effort and worker surplus as alternative means of increasing productivity. • Now suppose the firm and the worker are forced to negotiate in the context of a minimum wage law specifying that the worker must be paid a (real) wage w0 per hour. The firm can pay the high- er minimum wage by increasing the amount of effort of the employee, but the deal between the employer and employee is no longer efficient. It does not make either the firm or the worker as effort real wage iso-profit locus indifference curves w* e* 154 well off as they could be given the technology. • If the exogenously imposed minimum is too high, there may be no level of e that would enable the employer to pay w0 and earn a profit. The minimum wage would then produce unemploy- ment as in the standard analysis. 5 Alternatively, the employer might have to increase e so much that the worker is worse off than his “reservation level” of utility, U0. Unemployment would again increase as workers leave their current job to search for an alternative they believe will yield higher utility. For some unskilled workers, the relevant alternative might be long term un- employment and accompanying benefits or unemployment insurance payments. The indiffer- ence curve corresponding to utility level U0 intersects the zero profit locus for the firm at wmax. Any exogenously imposed real wage between w* and wmax would not lead to unemployment, or efficiency losses as usually measured. 5. In the short run, the firm only needs to cover its operating costs to remain in business. It may be willing to earn less than a competitive rate of return on its capital stock for a short period of time so long as it expects to be able to earn more than the competitive return on its capital at some time in the future. The firm may be reluctant to lay off employees to cover a temporary decline in profits when it has invested in a relationship with those employees. effort wage π* w* e* U* π=0 w0 U0 wmax maximum wage unconstrained wage = w0 155 • The model can also explain why minimum wages are more likely to reduce the employment of younger workers. These workers have accumulated fewer firm-specific skills and therefore are probably earning fewer “rents” from their current job than more established workers. There would be less of a difference between the utility level and U0 for these workers. Wages could not be increased as much above w* before utility declined below U0. • To allow for changes in hours of work and the number of employees in addition to effort levels, we need an algebraic formulation of the model. The additional freedom the firm has to vary hours of work and the number of employees would enable it to adjust to an even larger range of exogenously imposed real wages without going out of business. In so far as the firm reduces the number of employees, however, a change in the minimum wage will produce a fall in employ- ment. We might identify this fall in employment with “layoffs” rather than “quits” (when U falls to U0) or “bankruptcies” (when firm profits fall to zero). The key difference between this more general model and the simple model with fixed employment and hours, however, is that a reduc- tion in total hours worked is now an alternative to an increase in e as a method of raising the mar- ginal product of labor to equal w0. If the increase in the real wage together with the change in hours worked by each employee raises utility, and if e does not increase too much, then the utility of those individuals who keep their jobs can rise. We can restore the proposition from the stan- dard analysis that the imposition of the minimum wage may be favored by a union representing unskilled workers when it raises the utility of those who keep their jobs. This is only likely to happen, however, in those cases where the minimum wage reduces total hours worked, and therefore imposes high efficiency losses as conventionally measured.