# Job security and job search in more than one labor market.

I. INTRODUCTION

A person looking for a new job faces a choice not only of which jobs to accept, but where to search for a job. In this connection, differences in job security across sectors of the economy would appear to be a major concern of many workers. However, job security has not found a commensurate place in the literature on job search, largely due to the single-sector orientation of standard search models. This paper analyzes the optimal search behavior of unemployed workers who may search in two distinct labor markets or sectors of the economy. It is shown that the optimal policy assigns the same reservation wage but different search intensities in each sector.

The search literature has generally assumed that a worker searches for a job in a single labor market. Jobs differ from each other once found, but while searching all jobs look the same to a worker until an offer is made. In this context, jobs with higher layoff rates have been shown to induce higher, lower, or no different reservation wages than similar jobs with lower layoff rates, depending upon the specifics of the models, which are not compelling. Examples include Burdett and Mortensen |1980~, Hey and Mavromaras |1981~, Ioannides |1981~, Sargent |1987~, and Wright |1986; 1987~. Despite our intuitions, these studies provide no strong suggestion that a worker will be more likely to become employed in a type of job which offers greater job security, all else equal. It is otherwise in a multi-sector world. While the reservation wages associated with the two sectors of the economy are equal despite differences in layoff rates, a worker will search more intensively in the sector with a lower layoff rate.

II. THE MODEL

The model is simple. The worker maximizes his expected wealth in a continuous-time, stationary environment over an infinite time horizon. There are two sectors, A and B. Each is characterized by a (permanent) layoff rate, an offer-arrival rate, and a wage-offer distribution. The model generalizes the standard search paradigm and generalizes easily to N sectors. Accordingly, familiar derivations will be omitted. They can be found in Fallick |1990~. An unemployed worker may search for a job in either or both of the sectors simultaneously. He pays search costs depending upon how much he searches in total. The worker may not search while employed, and there is no possibility of being recalled to a previous job.

The worker may move from unemployment to employment in either sector by receiving and accepting a wage offer from that sector. Wage offers from sector j, j = A,B, are random variables drawn independently from a constant, exogenous distribution function |F.sup.j~(w). Offers expire immediately if not accepted. An employed worker may move from employment in either sector to unemployment by being laid off. Every job in a sector has the same layoff rate. An employed worker never quits. (It would never be optimal to quit anyway.)

Assume that the instantaneous probability of receiving a job offer from sector j is equal to ||Alpha~.sub.j~|Sigma~(|s.sub.j~), where ||Alpha~.sub.j~, the "offer-arrival rate," is the exogenous instantaneous probability that an offer from sector j arrives during the period. The term ||Alpha~.sub.j~ is constant over time. The term |Sigma~(|s.sub.j~) is a function of the "intensity" with which the worker searches in sector j while unemployed. Normalize the total amount of search intensity available at any one time to unity, so that |s.sub.A~ + |s.sub.B~ |is less than or equal to~ 1. Let |Sigma~(|center dot~) be an increasing concave function with |Sigma~(0) = 0, |Sigma~(1) = 1, |Sigma~|prime~(0) = |infinity~ and |Sigma~|prime~(1) = 0. The instantaneous probability of a permanent lay-off from a job in sector j is ||Lambda~.sub.j~. There is a constant marginal cost of searching, c. Assume that job offers and layoffs are generated by constant Poisson processes. In standard fashion, the instantaneous probability of receiving more than one offer simultaneously vanishes.

In this stationary environment, the elements of the optimal strategy are stationary. Denote the reservation wage for jobs in sector j by |Mathematical Expression Omitted~. The hazard rate for transitions from unemployment to employment in sector j at time t is |Mathematical Expression Omitted~. The hazard rate for transitions from employment in sector j to unemployment is ||Lambda~.sub.j~.

Let |V.sup.j~(w) be the expected present discounted value, with discount rate r, of current and future income as viewed from time zero if the worker were employed in sector j at wage w. Let |V.sup.u~ be the analogous quantity for unemployment. Assume that the unemployed worker chooses a search strategy so as to maximize |V.sup.u~. The worker chooses |s.sub.j~ and |Mathematical Expression Omitted~ subject to the transition rates above and the constraint that |s.sub.j~ |is greater than or equal to~ 0. The dynamic program can be written as

|Mathematical Expression Omitted~

(2) |V.sup.j~(w) = (w + ||Lambda~.sub.j~|V.sup.u~)/(r+||Lambda~.sub.j~) j = A, B.

The first-order conditions for the search intensities are

|Mathematical Expression Omitted~

III. RESERVATION WAGES

It seems reasonable that a higher probability of being laid off (less job security) in a sector would make jobs there less attractive to a prospective employee and therefore raise the reservation wages for that sector relative to the other sector. This consideration led Topel |1984~ and Murphy and Topel |1987~ to look for compensating differentials for unemployment risk. In the present model, however, such differentials do not arise. Combining (1) with (2) yields

(4) ||w.sup.r~.sub.B~ = ||w.sup.r~.sub.B~ = |w.sup.r~ = r|V.sup.u~.

The reservation wages for jobs in the two sectors are equal, despite the fact that the layoff rates, offer-arrival rates, and offer distributions differ. "Because the worker is indifferent between employment (at the reservation wage) and unemployed search, the possibility of being laid off in the future is of no consequence in a stationary environment."(1)

Substituting the value functions out of (1) yields the fundamental reservation wage equation

|Mathematical Expression Omitted~

This specification is a generalization of the standard reservation wage equation expressed by Mortensen |1986~. Differentiating (7) demonstrates that d|w.sup.r~/d||Alpha~.sub.j~ |is greater than~ 0, d|w.sup.r~/d||Lambda~.sub.j~ |is less than~ 0, d|w.sup.r~/dc |is less than~ 0, and any first-order stochastic improvement in |F.sup.j~(w) increases the common reservation wage, j = A,B. An increase in the layoff rate in either sector decreases the common reservation wage, since it is less worthwhile to wait for a higher paying job if that job is likely to end shortly.

IV. SEARCH INTENSITIES

In the two-sector search model, the search intensities are of primary interest. After eliminating the value functions, (3) becomes

|Mathematical Expression Omitted~

From (6), it is clear that if the two sectors were identical in all other respects, then a worker would search more intensively in the sector with a larger offer-arrival rate, a lower layoff rate, or a superior wage-offer distribution. The optimal search intensities in the two sectors can be shown, by differentiating (6), to respond to changes in these attributes in a similar fashion.

The main point is that, all else equal, the optimal amount of search is greater in the sector with the lower layoff rate. Moreover, an increase in the layoff rate in either sector decreases the optimal amount of search in that sector and increases the optimal amount of search in the other sector. Thus the relative search intensities do adjust to disparities and changes in the layoff rates, in contrast to the reservation wage.(2) Thus a worker will be faster to find and take a job in a sector with a lower layoff rate. This provides a compelling reason that a worker will be more likely to enter a job which offers greater security, all else equal.

1. Burdett and Mortensen |1980, 653~. See also Wright |1987~. Modifications, such as introducing costs to making transitions between unemployment and employment, can upset this result.

2. One could imagine this giving rise to something akin to compensating differentials if employers in sectors with layoff rates see fit to improve their wage-offer distribution in order to attract more search activity. Burdett and Mortensen |1980~ present a related situation, in which a firm with a higher layoff rate must pay a higher wage if it wants to dissuade its employees from engaging in on-the-job-search.

REFERENCES

Burdett, K., and D. Mortensen. "Search, Layoffs, and Labor Market Equilibrium." Journal of Political Economy, August 1980, 652-72.

Fallick, B. C. "Job Security and Job Search in More Than One Labor Market." Manuscript, UCLA, October 1990.

Hey, J., and K. Mavromaras. "The Effect of Unemployment Insurance on the Riskiness of Occupational Choice." Journal of Public Economics, December 1981, 317-41.

Ioannides, Y. "Job Search, Unemployment and Savings." Journal of Monetary Economics, May 1981, 355-70.

Mortensen, D. "Job Search and Labor Market Analysis," in Handbook of Labor Economics, vol. II, edited by O. Ashenfelter and R. Layard. Amsterdam: Elsevier Science Publishers BV, 1986, 849-919.

Murphy, K., and R. Topel. "Unemployment, Risk, and Earnings: Testing for Equalizing Wage Differences in the Labor Market," in Unemployment and the Structure of Labor Markets, edited by K. Lang and J. Leonard. New York: Blackwell, 1987.

Sargent, T. Dynamic Macroeconomic Theory. Cambridge, Mass.: Harvard University Press, 1987.

Topel, R. "Equilibrium Earnings, Turnover, and Unemployment: New Evidence." Journal of Labor Economics, October 1984.

Wright, R. "Job Search and Cyclical Unemployment." Journal of Political Economy, February 1986, 38-55.

-----. "Search, Layoffs, and Reservation Wages." Journal of Labor Economics, July 1987, 354-65.

A person looking for a new job faces a choice not only of which jobs to accept, but where to search for a job. In this connection, differences in job security across sectors of the economy would appear to be a major concern of many workers. However, job security has not found a commensurate place in the literature on job search, largely due to the single-sector orientation of standard search models. This paper analyzes the optimal search behavior of unemployed workers who may search in two distinct labor markets or sectors of the economy. It is shown that the optimal policy assigns the same reservation wage but different search intensities in each sector.

The search literature has generally assumed that a worker searches for a job in a single labor market. Jobs differ from each other once found, but while searching all jobs look the same to a worker until an offer is made. In this context, jobs with higher layoff rates have been shown to induce higher, lower, or no different reservation wages than similar jobs with lower layoff rates, depending upon the specifics of the models, which are not compelling. Examples include Burdett and Mortensen |1980~, Hey and Mavromaras |1981~, Ioannides |1981~, Sargent |1987~, and Wright |1986; 1987~. Despite our intuitions, these studies provide no strong suggestion that a worker will be more likely to become employed in a type of job which offers greater job security, all else equal. It is otherwise in a multi-sector world. While the reservation wages associated with the two sectors of the economy are equal despite differences in layoff rates, a worker will search more intensively in the sector with a lower layoff rate.

II. THE MODEL

The model is simple. The worker maximizes his expected wealth in a continuous-time, stationary environment over an infinite time horizon. There are two sectors, A and B. Each is characterized by a (permanent) layoff rate, an offer-arrival rate, and a wage-offer distribution. The model generalizes the standard search paradigm and generalizes easily to N sectors. Accordingly, familiar derivations will be omitted. They can be found in Fallick |1990~. An unemployed worker may search for a job in either or both of the sectors simultaneously. He pays search costs depending upon how much he searches in total. The worker may not search while employed, and there is no possibility of being recalled to a previous job.

The worker may move from unemployment to employment in either sector by receiving and accepting a wage offer from that sector. Wage offers from sector j, j = A,B, are random variables drawn independently from a constant, exogenous distribution function |F.sup.j~(w). Offers expire immediately if not accepted. An employed worker may move from employment in either sector to unemployment by being laid off. Every job in a sector has the same layoff rate. An employed worker never quits. (It would never be optimal to quit anyway.)

Assume that the instantaneous probability of receiving a job offer from sector j is equal to ||Alpha~.sub.j~|Sigma~(|s.sub.j~), where ||Alpha~.sub.j~, the "offer-arrival rate," is the exogenous instantaneous probability that an offer from sector j arrives during the period. The term ||Alpha~.sub.j~ is constant over time. The term |Sigma~(|s.sub.j~) is a function of the "intensity" with which the worker searches in sector j while unemployed. Normalize the total amount of search intensity available at any one time to unity, so that |s.sub.A~ + |s.sub.B~ |is less than or equal to~ 1. Let |Sigma~(|center dot~) be an increasing concave function with |Sigma~(0) = 0, |Sigma~(1) = 1, |Sigma~|prime~(0) = |infinity~ and |Sigma~|prime~(1) = 0. The instantaneous probability of a permanent lay-off from a job in sector j is ||Lambda~.sub.j~. There is a constant marginal cost of searching, c. Assume that job offers and layoffs are generated by constant Poisson processes. In standard fashion, the instantaneous probability of receiving more than one offer simultaneously vanishes.

In this stationary environment, the elements of the optimal strategy are stationary. Denote the reservation wage for jobs in sector j by |Mathematical Expression Omitted~. The hazard rate for transitions from unemployment to employment in sector j at time t is |Mathematical Expression Omitted~. The hazard rate for transitions from employment in sector j to unemployment is ||Lambda~.sub.j~.

Let |V.sup.j~(w) be the expected present discounted value, with discount rate r, of current and future income as viewed from time zero if the worker were employed in sector j at wage w. Let |V.sup.u~ be the analogous quantity for unemployment. Assume that the unemployed worker chooses a search strategy so as to maximize |V.sup.u~. The worker chooses |s.sub.j~ and |Mathematical Expression Omitted~ subject to the transition rates above and the constraint that |s.sub.j~ |is greater than or equal to~ 0. The dynamic program can be written as

|Mathematical Expression Omitted~

(2) |V.sup.j~(w) = (w + ||Lambda~.sub.j~|V.sup.u~)/(r+||Lambda~.sub.j~) j = A, B.

The first-order conditions for the search intensities are

|Mathematical Expression Omitted~

III. RESERVATION WAGES

It seems reasonable that a higher probability of being laid off (less job security) in a sector would make jobs there less attractive to a prospective employee and therefore raise the reservation wages for that sector relative to the other sector. This consideration led Topel |1984~ and Murphy and Topel |1987~ to look for compensating differentials for unemployment risk. In the present model, however, such differentials do not arise. Combining (1) with (2) yields

(4) ||w.sup.r~.sub.B~ = ||w.sup.r~.sub.B~ = |w.sup.r~ = r|V.sup.u~.

The reservation wages for jobs in the two sectors are equal, despite the fact that the layoff rates, offer-arrival rates, and offer distributions differ. "Because the worker is indifferent between employment (at the reservation wage) and unemployed search, the possibility of being laid off in the future is of no consequence in a stationary environment."(1)

Substituting the value functions out of (1) yields the fundamental reservation wage equation

|Mathematical Expression Omitted~

This specification is a generalization of the standard reservation wage equation expressed by Mortensen |1986~. Differentiating (7) demonstrates that d|w.sup.r~/d||Alpha~.sub.j~ |is greater than~ 0, d|w.sup.r~/d||Lambda~.sub.j~ |is less than~ 0, d|w.sup.r~/dc |is less than~ 0, and any first-order stochastic improvement in |F.sup.j~(w) increases the common reservation wage, j = A,B. An increase in the layoff rate in either sector decreases the common reservation wage, since it is less worthwhile to wait for a higher paying job if that job is likely to end shortly.

IV. SEARCH INTENSITIES

In the two-sector search model, the search intensities are of primary interest. After eliminating the value functions, (3) becomes

|Mathematical Expression Omitted~

From (6), it is clear that if the two sectors were identical in all other respects, then a worker would search more intensively in the sector with a larger offer-arrival rate, a lower layoff rate, or a superior wage-offer distribution. The optimal search intensities in the two sectors can be shown, by differentiating (6), to respond to changes in these attributes in a similar fashion.

The main point is that, all else equal, the optimal amount of search is greater in the sector with the lower layoff rate. Moreover, an increase in the layoff rate in either sector decreases the optimal amount of search in that sector and increases the optimal amount of search in the other sector. Thus the relative search intensities do adjust to disparities and changes in the layoff rates, in contrast to the reservation wage.(2) Thus a worker will be faster to find and take a job in a sector with a lower layoff rate. This provides a compelling reason that a worker will be more likely to enter a job which offers greater security, all else equal.

1. Burdett and Mortensen |1980, 653~. See also Wright |1987~. Modifications, such as introducing costs to making transitions between unemployment and employment, can upset this result.

2. One could imagine this giving rise to something akin to compensating differentials if employers in sectors with layoff rates see fit to improve their wage-offer distribution in order to attract more search activity. Burdett and Mortensen |1980~ present a related situation, in which a firm with a higher layoff rate must pay a higher wage if it wants to dissuade its employees from engaging in on-the-job-search.

REFERENCES

Burdett, K., and D. Mortensen. "Search, Layoffs, and Labor Market Equilibrium." Journal of Political Economy, August 1980, 652-72.

Fallick, B. C. "Job Security and Job Search in More Than One Labor Market." Manuscript, UCLA, October 1990.

Hey, J., and K. Mavromaras. "The Effect of Unemployment Insurance on the Riskiness of Occupational Choice." Journal of Public Economics, December 1981, 317-41.

Ioannides, Y. "Job Search, Unemployment and Savings." Journal of Monetary Economics, May 1981, 355-70.

Mortensen, D. "Job Search and Labor Market Analysis," in Handbook of Labor Economics, vol. II, edited by O. Ashenfelter and R. Layard. Amsterdam: Elsevier Science Publishers BV, 1986, 849-919.

Murphy, K., and R. Topel. "Unemployment, Risk, and Earnings: Testing for Equalizing Wage Differences in the Labor Market," in Unemployment and the Structure of Labor Markets, edited by K. Lang and J. Leonard. New York: Blackwell, 1987.

Sargent, T. Dynamic Macroeconomic Theory. Cambridge, Mass.: Harvard University Press, 1987.

Topel, R. "Equilibrium Earnings, Turnover, and Unemployment: New Evidence." Journal of Labor Economics, October 1984.

Wright, R. "Job Search and Cyclical Unemployment." Journal of Political Economy, February 1986, 38-55.

-----. "Search, Layoffs, and Reservation Wages." Journal of Labor Economics, July 1987, 354-65.

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Author: | Fallick, Bruce Chelimsky |
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Publication: | Economic Inquiry |

Date: | Oct 1, 1992 |

Words: | 1629 |

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