WAGE AND UNEMPLOYMENT

Accordingly, we return to the relation of unemployment to the bargaining- determined wage. How much, indeed, would we expect the wage zt to vary with changes in the rate of unemployment? Recall that zt has three components (equation A11.9k in the appendix to Chapter 11 and A14.3b in the appendix to this chapter):

For an employee whose second-best alternative is to seek other employment, supposing the search for new employment is successful, the payoff of the new job will have the same components. Moreover, if the job search fails in the current period, the individual may obtain employment in a future period. Similarly, if he remains in his present employment, he can expect remuneration in future periods, which will comprise the same three components, along with some probability of disemployment in the future periods. These sequences of expected future remuneration could be quite complex, but we are concerned here with the response to changes in unemployment in the current period, so we let the expected discounted value of remuneration in future periods, conditional on separation from the current job, be a constant Z1. We let the expected discounted value of remuneration in future periods conditional on continuation in the job for the current period be a constant Z2. Let the probability of re-employment in the current period bep, y* the net share of the surplus to be expected in that case, and g* the expected value of the compensation for effort in the new job. Suppose further that there is a fixed cost, g, of entering the labor market. This might be a resource cost such as the cost of travel to attend interviews. It might also be a subjective fixed cost. Surveys of self-assessed quality of life indicate that the unemployed are less happy than those who are employed at the same income (for example, Frey, 2008). Then this subjective fixed cost is a component of g. Thus, a rational agent then will leave the job if

That is, the rationality constraint yt $ wt is equivalent to That is,

Assume for simplicity that Z1 = Z2. Then (14.5) becomes That is,

Thus,

With V the coalitional surplus in the present job net of the outside options of all members of the coalition. This will be illustrated by a numerical example. For simplicity and for comparability with received theory, assume that all employees have the same outside option y* = z* - g* - w;, g(h) = g*, and that there are n employees. Then

As p varies from zero to one pip varies from 0 to 0.5 and ppp varies from 1 to 0.5. Thus, the first term is a constant with respect top, the last varies directly with p, and the middle term varies inversely with p, provided pz* > g.

As a first approximation, let the overall average p be the ratio of the number of job openings, J, to the number unemployed, U. This may oversimplify - some job openings will be filled directly by transfers from other jobs, without a period of unemployment, and some openings may indeed not be available to the unemployed, for example. Further, Chapter 12 has proposed a different measure. Nevertheless, for simplicity and comparability with the received literature, and preliminarily, posit

Job openings as a proportion of unemployment

Figure 14.1 Job openings as a proportion of unemployment

Taking data on the level of job openings in the United States for 2001-2014 from the JOLTS project of the Bureau of Labor Statistics and data on unemployment levels from the Bureau of Labor Statistics for the same period, we see the quotient as plotted in Figure 14.1. On the one hand, the quotient varies between 0 and 1 and so may, without contradiction (at least in this period) be interpreted as a probability. On the other hand, it varies over most of that range in a highly countercyclical way. Thus it would seem that, by identifying this quotient with the probability of quick re-employment, we err in the direction of exaggerating the impact of cyclical variations on the computed wage, rather than in the opposite direction.

For a numerical example, suppose that 1in = 1/2, z* = 42,500, g* = 35,000, and l (V* — wA — g i^bw) = 1000 and g = 5000. Note that In = 0.5, would imply that employees as a group obtain about half of the surplus: if l is the same for all employees, then they receive exactly half. Then we obtain the calculated values for zi in four contrasting periods as shown in Table 14.1.

We see that the projected value of z varies only slightly as the unemployment rate fluctuates from its lows to its highs over “the great recession.” The variation is less than 2 percent. The quotient J/U and the predicted

Table 14.1 Computed wage payments

Period

Average unemployment rate

Average quotient

Computed wage

2002-2005

5.6

0.439459449

46144.85541

2006-2008

5.008

0.561981044

46349.20262

2009-2011

9.28

0.200062587

45625.16298

2010-2014

7.6

0.331186084

45932.96334

Thepredicted wage and the quotient J/U

Figure 14.2 Thepredicted wage and the quotient J/U

wage are plotted together in Figure 14.2 with the predicted wage expressed as a proportion of 100,000 for comparability.

A reason for this result is that g*, the compensation for the disutility of effort, is relatively large by comparison with z*, the expected wage conditional on re-employment, and z. Since the individual’s bargaining share, y ,, is net of this compensation, and the compensation recurs in the case of re-employment, it reduces the impact of J/U on the predicted wage. To illustrate this, consider a second example with z* = 40,000, g* = 0, g = 0, and 1i (V*wA — g , [ gw,) =40,000. Then we have Table 14.2 and Figure 14.3 by contrast with Table 14.1 and Figure 14.2. While the variation in the wage from the low to high points in 2002-2014 does not appear large by comparison with that of J/U, it is in the range of 9 percent, about five times as great as the previous example.

Table 14.2 Computed wage payments in an alternative example

Period

Average unemployment rate

Average quotient

Computed wage

2002-2005

5.6

0.439459449

46105.89551

2006-2008

5.008

0.561981044

47195.7473

2009-2011

9.28

0.200062587

43334.20255

2010-2014

7.6

0.331186084

44975.80448

The predicted wage and the quotient J/U in the alternative example

Figure 14.3 The predicted wage and the quotient J/U in the alternative example

It appears that the application of bargaining theory to the determination of wages in search-and-matching models has overlooked a key question: what proportion of the wage is compensation for the disutility of effort? If that proportion is large, then the model does not predict any considerable countercyclical variation of wages with unemployment. We note that the compensation for effort depends on the structure of production, and not on the employee’s outside option. In a more complex model, there might be other components of employee compensation that depend on the persistent structure of production rather than on the employees’ outside option, and this result probably is more valuable as an instance of that dependence than as a complete theory of wages. The question should be, to what extent are wages determined by the structure of production

Two measures of the probability of re-employment

Figure 14.4 Two measures of the probability of re-employment

rather than by the employee’s outside option? The evidence that real wages are sticky suggests that wages are primarily determined by the persistent structure of production.

All in all, the prediction that the wage would fluctuate countercyclically is weakly supported if at all. If the bargaining model is somewhat more realistically complex, and in particular includes a component of the wage that compensates for efficient effort, then the predicted countercyclical fluctuation in wages could be very slight, if not indeed negligible.

Thus far we have used the ratio J/U as the probability of prompt reemployment in determining the individual employee’s outside option and thus wage. Suppose instead we adopt the index p = [1 — (1 — U)J ] suggested by the search model of section 12.2.1. A preliminary examination of the two probability expressions suggests that there will be little difference, but that this substitution would further reduce the responsiveness of the wage to unemployment. This is suggested by Figure 14.4, which compares the two estimates of the probability of re-employment.

Then, replacing J/U with the index, we have Table 14.3 in place of Table 14.1, and in place of Figure 14.2 we have Figure 14.5.

It seems that the bargaining hypothesis cannot be dismissed on the grounds that the wage does not vary proportionately with the rate of unemployment.

Table 14.3 Computed wage payments

Period

Average unemployment rate

Average index

Computed wage

2002-2005

5.6

0.354234575

45980.90809

2006-2008

5.008

0.425803662

46119.90436

2009-2011

9.28

0.180904544

45574.46814

2010-2014

7.6

0.281289003

45823.25982

The probability of re-employment and the predicted wage in a third example

Figure 14.5 The probability of re-employment and the predicted wage in a third example

 
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