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This article was downloaded by: [University of Illinois Chicago] On: 08 December 2014, At: 21:45 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Applied Economics Letters Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/rael20 Macroeconomic implications of search theory for the labour market Sanjiv Ranjan Das a a Graduate School of Business Administration , Harvard University , Soldiers Field, Boston, MA, 021 63, USA Published online: 02 Nov 2006. To cite this article: Sanjiv Ranjan Das (1997) Macroeconomic implications of search theory for the labour market, Applied Economics Letters, 4:12, 719-723, DOI: 10.1080/758528714 To link to this article: http://dx.doi.org/10.1080/758528714 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

Macroeconomic implications of search theory for the labour market

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Page 1: Macroeconomic implications of search theory for the labour market

This article was downloaded by: [University of Illinois Chicago]On: 08 December 2014, At: 21:45Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Applied Economics LettersPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/rael20

Macroeconomic implications of search theory forthe labour marketSanjiv Ranjan Das aa Graduate School of Business Administration , Harvard University , Soldiers Field,Boston, MA, 021 63, USAPublished online: 02 Nov 2006.

To cite this article: Sanjiv Ranjan Das (1997) Macroeconomic implications of search theory for the labour market,Applied Economics Letters, 4:12, 719-723, DOI: 10.1080/758528714

To link to this article: http://dx.doi.org/10.1080/758528714

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) containedin the publications on our platform. However, Taylor & Francis, our agents, and our licensors make norepresentations or warranties whatsoever as to the accuracy, completeness, or suitability for any purposeof the Content. Any opinions and views expressed in this publication are the opinions and views of theauthors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should notbe relied upon and should be independently verified with primary sources of information. Taylor and Francisshall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, andother liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relationto or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial or systematicreproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in anyform to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Macroeconomic implications of search theory for the labour market

Applied Economics Letters, 1997, 4, 7 19-723

Macroeconomic implications of search theory for the labour market

SANJIV RANJAN DAS

Graduate School of Business Administration, Harvard University, Soldiers Field, Boston, MA 02 1 63. USA

Received 26 September 1996

'While the usual job search problem is a microeconomic one, this paper applies labour market data to a standard search model to extract macroeconomic implications. A theoretical relationship between the minimum wage, subsistence wage and reservation wage is posited and found to be violated in the data. The paper raises several issues of public policy. It finds that the minimum wage offered is low. It provides a measure of the 'quality' of the labour market, and discusses how it may be improved, by increasing the minimum wage, reducing bargaining between the supply and demand sides of the labour market, and curbing wage volatility.

I. INTRODUCTION

Search problems have been analysed extensively in micro- economics. In this paper, the job search issue is analysed in a macroeconomic context. Using macroeconomic data, we analyse the efficacy of public policy using a simple search model.

The theory of search was pioneered by McCall (1970) and Stigler (1961). The classic application of search theory models the behaviour of a job seeker who faces a choice between accepting a current offer of employment or holding out for a better one in the future. Entering the job market frequently is costly (in time, effort and reputation), hence opting for a current job offer effectively precludes the job seeker from accepting a suboptimal job, and then continuing to search. This makes the problem interesting.

The paper models analytically and numerically the typical search problem using data from the labour environment. A model is developed and solved using numerical procedures. Several different variables affect the job seeker's search decision: the distribution of wages in the labour market, amount of the dole (subsistence wage), the horizon of time for which the dole is provided, and the rate of interest.

The results obtained have public policy implications pertaining to (i) the level of the minimum wage in the economy, (ii) the choice of the amount of the dole, and (iii) the 'quality' of the labour market. In the rest of the paper, we will examine the nature of the relationship between the search process, employment, minimum wage and the dole. Using a

simple search model, we will use labour market data to infer the job-seeker's reservation wage, examine the effect of various economic variables on the search choice, and estimate the average period a worker will remain unemployed.

11. RESERVATION WAGE, SUBSISTENCE WAGE AND MINIMMUM WAGE

The solution to the search problem provides a reservation wage (W,), the wage below which the job seeker would refuse existing job offers and prefer to wait for a better offer. Wages each period ( w ) are a random draw from the distribution of wages in the economy, and a job offer is accepted only if w > w,.

In this study, we apply search modelling to the entire class of unemployed people in the labour force. Government regulation of the labour market involves the setting of the dole (or sub- sistence wage, W,), and fixing the minimum wage (W,).

Accurate establishment of the subsistence and minimum wage levels is critical for the productive use of the available labour force. The dole represents a drain on the resources of society, as it is the maintenance costs of supporting possibly productive labour in future periods.1 Policy makers would attempt to minimize this cost. Accurate establishment of the minimum wage ensures maximization of productivity and labour welfare.

Assessment of the current labour market policy is embodied in the following proposition:

'It may be argued that such money may able better spent creating employment opportunities anyway, rather than support unproductive labour

1350-585 1 O 1997 Routledge

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S. R. Das

Proposition 1: Relationship of the Reservation Wage, Table 1 . Wage data by industry: descriptive statistics

Minimum Wage and Subsistence wage: Industry 1985 1986 1987 1988 Average

In an eficient labour market, the following relationship must hold: Mining 519.93 525.8 1 531.70 539.33 529.19

Construction 464.46 466.75 480.44 493.08 476.18 Transportation 450.30 458.64 471.58 484.18 466.18

w, < w, < wm Wholesale trading 35 1.74 358.1 1 365.76 378.71 363.58 Retail trading 174.64 176.08 178.70 183.62 178.26 -

proof: ~t must be true that W, < wm, for else no one would Finance insurance 289.02 304.30 316.90 326.33 309.14 Services work at the minimum wage. W., < W, for if the dole were Lumber

256.75 265.85 275.93 290.47 272.25 327.98 336.10 341.04 346.98 338.03

greater than the reservation wage, there is no incentive to go Furniture 282.50 296.91 306.80 3 12.84 299.76 off the dole, as it is costly to enter the labour market, and the Stone and glass 412.30 423.69 433.58 442.88 428.11 dole which is higher than the reservation wage offers no Precious metals 484.3 1 496.93 514.61 529.74 506.40 - - incentive to do so, ~ f f ~ ~ t i ~ ~ l ~ , the solution to the search Fabrication material 400.61 408.04 416.00 429.89 413.64

Machinery problem revolves around accepting the first offer which Electrical

427.04 439.71 452.38 469.03 447.04 384.08 395.65 404.09 415.33 399.79

exceeds the reservation wage, and since the dole already ,does Motor vehicles 541.45 541.86 543.48 568.34 548.78

so, no one would be seeking work! Finally, W, < Wm, for if Instrumentation 375.97 388.27 402.41 414.17 395.21

W, > Wm no one would work at the minimum wage. Misellaneous 287.62 298.98 305.74 313.99 301.58

Of course, jobs are not in infinite supply at the minimum wage W,. Therefore, even though Wm > W,, it does not mean that a person will be able to find work. Ideally, W,, should be equal to W,, so that finding a minimum wage job does not result in perceived underemployment. As we shall see later in this paper, the relationship between the minimum wage and the reservation wage is one indication of the 'quality' of the labour market.

111. DATA

manufacturing Food Tobacco Textile Apparel Paper Printing Chemical Petrol Rubber Leather

Mean 377.17 388.06 400.82 412.58 394.66 Standard deviation 108.09 109.88 114.15 118.98 112.46 Skewness -0.543 0 . 4 8 3 -0.524 -0.495 -0.528 Kurtosis 0.034 -0.013 0.004 0.052 0.003

Using data, from the Social Security Bulletin, Anrzual Statistical Supplement for the period 1985-88, we compute the reservation wage (W,) and examine if the inequality in Proposition 1 holds. The choice of this period is useful since the minimum wage was constant through this period. Solving the search problem requires the wage distribution facing the job seeker each period (assumed to be a week). We assume that the wage distribution available to the marginal job seeker is drawn from the bottom tier of the labour market. Hence, wage data is drawn from the manufacturing and non-super- visory sectors. Implicit in the analysis is (i) that the job seeker is indifferent to the type of industry he gets to work in, and (ii) that he is capable of accepting and undertaking employment in a wide spectrum of jobs. The former assumes that he is actively seeking work, i.e. in immediate need of a job, and the latter assumption is based on the fact that the analysis applies to the lower segment of the job market, i.e. the relatively unskilled sector. Source data is provided in Table 1.

The mean wage (per week) is $394.66, with a standard deviation of $1 12.46. Skewness is mildly negative, while excess kurtosis is small. We assume that the wage distribution is roughly normal. Other relevant statistical data is provided in Table 2. This table contains data on the minimum wage, interest rates, and the dole (subsistence wage).

IV. MODEL

A standard job search model is employed. The job seeker faces a wage (w E (0, w ) ) distribution, with probability density function f (w) , and probability distribution function F ( w ) = Prob(wage < w). w is an upper bound on the wage distribution, and w < CQ. The distribution of w is assumed to be time-homogenous. The job seeker solves an optimal stopping (dynamic programming) problem, which may be expressed by the usual Bellman equation:

v(wt) = max [ - ( 1 - 0 ) ' c + a ~ " v ( w t + ) d F ( w r + ) I where c is the dole, and the intertemporal discount factor is CY = &. r being the interest rate per period. t indexes the time period, the time interval being one week. v(w) is the value function for the problem, i.e. the value to infinity of future wages when the optimal choices are made by the decision maker. The solution to the problem consists of finding the reservation wage (decision rule) for the job seeker at which the value function is optimized.

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Search theory for labour market

Table 2. Wage data by industry: descriptive statisric.s

Item 1985 1986 1987 1988 Average

Unemployment insurance ($MM) 98.20 100.20 103.70 106.90 102.25 Weekly subsistence wage ($) - - - - 139.74 Federal minimum wage ($/hour) 3.35 3.35 3.35 3.35 3.35 Average production worker wages ($/hr) 9.54 9.73 9.91 10.18 9.84 Average production worker h/week 40.50 40.70 4 1 .OO 41.00 40.80 Wage per week ($) 386.37 396.01 406.3 1 417.38 401.52 Treasury bill rates (9% per annum) 7.73 6.17 5.44 6.48 6.45

Source: Social Securit). Bulletin-Annual Statistical Supplement, 1989.

The job seeker either accepts the current wage offer or rejects it, and holds out to the next period. If he accepts, he then receives a perpetuity in the amount of &. If he does not accept the job offer, he receives c and the future expected value of jobs given by the expected value of the optimal policy v ( ~ , + ~ ) next period. The reservation wage W, is the point at which he will be indifferent between the above two choices. If w > W,, then v(w) = This means that in the range w >_ W,, v(w) is an increasing, linear function of w. And if w < W,, then v(w) is a constant function because it must be at least a function of the reservation wage. Therefore, v(w) = &. These arguments lead to a simplification of the Bellman equation. At the point of indifference (w = W,), it must be that

Since w = Wr.Vw < W,, the expression above simplifies even further to

Wr dF(wt+~) (I - t e )

w wt-t I +QL, (I-U, dFw,+ I

which is rewritten as

Solving this equation for W,, provides us the job seeker's reservation wage given the dole, interest rates and the wage distribution. The above equation does not admit an analytical solution for W,, and is solved using numerical methods.

Mean unemployed waiting time Computing the solution to Equation 1 provides the reservation wage W,. The job seeker rejects a job with probability y, where y = f: dF(w). Therefore, if a person accepts a job after n peribds (weeks), the probability of such an event is

y(n), where y(n) = (1 - y)y(np') The mean waiting time is then simply computed as follows:

OC 1 MWT = E n y ( n ) =-

n=O ( 1 -Y)

V. RESULTS AND CONCLUSIONS

Numerical implementation Using the available data, we computed the reservation wage and mean waiting times for the period 1985-88. The reservation wage from the model is found to be $649 per week, and the mean unemployed waiting time is approxi- mately 7.5 weeks. The dole is $139.74 per week and the annual interest rate used for discounting is taken to be 6.45%. (See Table 2).

The graphs in Figures 1 to 4 depict the values of reservation wages and mean wait times for ranges of the mean wage, standard deviation of mean wage, dole and interest rate levels. The reservation wage is increasing in the mean wage (see Figure 1). The mean wait time increases for low levels of the mean wage and then declines. This is because, at low wage levels it is worth waiting for a better offer as the mean wage is less attractive relative to the dole. As the mean wage moves into higher ranges, it becomes more costly to forego job offers, as they are more attractive relative to the dole. Therefore the mean wait time demonstrates a rising and then falling curve as a function of the mean wage level.

Figure 2 is a plot of W, and MWT as a function of the variability (a) in the mean wage. The reservation wage increases at first with increasing variability of the mean wage, as it increases the likelihood of a better offer. However, beyond a point, as a increases, it is possible that higher variability means several worse offers as well, and is not desirable, and hence reduces the reservation wage. Analo- gously, the mean wait time displays the same increasing and then declining behaviour as a function of a.

Figure 3 portrays the response of the two measures to the level of the dole. Since increases in the dole makes the value of waiting for better offers greater, it is natural that both the

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Page 5: Macroeconomic implications of search theory for the labour market

0 4 C 0 200 250 300 350 400 450 500 550 600

Mean Wage

Fig. 1 Reservation wages and mean wait times for varying wage levels. This graph depicts the variation in W, and MWTfor a range of mean wages. Reservation wages are expressed in terms of dollars per week and the mean wait time is in units of weeks.

(- ) Reservation wage; (+) Mean wait time.

reservation wage and the mean wait time are increasing functions of the dole. By and large, sensitivity of the measures to the dole is weak, which hints at the fact that the level of the subsistence wage is not a critical element of labour policy. In Figure 4, we see the variation in the reservation wage and mean wait time to changes in the interest rate. The reservation wage decreases in the interest rate, as the cost of waiting goes up. However, the level of sensitivity to this variable is very low. It is even lower for the mean wait time.

Analysis We now evaluate Proposition 1. The reservation wage is at a level above that of the minimum wage and subsistence wage. We find that W , = W,, < W,. This violates Proposition 1. The minimum wage per week works out to be $136.68 (3.35 per h x 40.80 hlweek), which is approximately the same as the dole per week, $139.74. This is even more surprising as an unemployed person may not be able to obtain 40 h of work per week. Hence, little incentive exists for the unemployed to work at the minimum wage as the dole is an equivalent or better option. This will lead to people seeking minimum wages only after the period of availability of the dole runs out.

One may well ask why people work at the minimum wage when their reservation wage is higher. There are two reasons

S. R. Das

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500 1 I I I t I I 1 0 50 60 70 80 90 100 110 120 130 140 150

Sigma

Fig. 2 Reservation wages and mean wait times for varying wage .starzdard deviations. This graph depicts the variation in W,. and MWT for a range of wage level standard deviation (uncertainty around wage offers). Reservation wages are expressed in terms o f dollars per week and the mean wait rime is in units of weeks.

(- ) Reservation wage; (+) Mean wait time.

for this. One, the analysis here concerns the average worker, and it is possible to envisage a range of workers facing varied wage distributions. Hence, the lower tier of wage distributions may be more in line with the minimum wages observed. However, this still means that on average the minimum wage is out of line with the wage distributions observed. Two, people may still work at the minimum wage because they substitute it for the dole when their period on the dole runs out.

Moreover, the average period for which the dole is provided is about 15 weeks. The model shows that the mean wait time is optimally 7.5 weeks. Hence, the period for the dole spans the mean wait time.

There is a great difference between the minimum wage and the reservation wage. This is indicative of three things. One, the level of involuntary unemployment; two, the quality of the labour market in terms of fairness of wages; and three, the relative bargaining power between the suppliers of jobs and job seekers. We can therefore define a measure of labour market quality (LMQ) as follows:

w m LMQ = - w,

Intuition shows that the quality of the labour market may be thought of as increasing in the LMQ statistic. Ideally, in a good

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Search theory for labour market 723

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U a b a a O - N O b U a b m a O - N O b m

- ~ ~ ~ ~ . - ~ ~ ~ ~ N N N N N N

Dole Interest Rate

Fig. 3. Reservation wages and mean wait times for varying Fig. 4. Reservation wages and mean wait times for varying interest subsistence wage (dole) levels. This graph depicts the variation in rate levels. This graph depicts the variation in W, und MWT for a W, and MWT for a range of subsistence wages. Reservation wages range of interest rates. Reservation wages are expressed in terms o f are expressed in terms o f dollars per week and the mean wait time is dollars per week and the mean wait time is in units of weeks. in units of weeks. (- ) Reservation wage; (a) Mean wait time.

(- ) Reservation wage; (+) Mean wait time.

quality labour market LMQ should be at least greater than or equal to 1 , so as to be in consonance with Proposition 1 . The policy maker can improve LMQ in two ways: increase W , or reduce W,.. W,. is affected by the location parameter of current wages being offered in regular jobs. If this can be lowered, then LMQ may be raised. One of the reasons that W, is high is because people who are employed are able to demand higher wages. Reduction of bargaining power amongst unions may actually improve the quality of the labour market. Another way to reduce W, is to reduce wage volatility u below current levels. Whether wage volatility can be managed via macro- economic policy is an open issue.

Raising W,,, may be brought about by increasing the willingness of labour market suppliers to pay more at the margin (i.e. a reduction in their bargaining power). This they may do, if the need to sustain the high wages of currently employed labour is reduced. In addition, raising the produc- tivity of labour via education and retraining will raise the threshold levels employers are willing to pay, and will raise the level of LMQ. Therefore, across the board reduction in bargaining power for both the suppliers and demanders of jobs will improve the quality of the labour market. Existing employed people also gain when they lose their jobs.

Conclusion We conducted an analysis of the labour market using search theory and some easily observable aggregate data. Using an analytical model of the optimal policy followed by the job seeker, and with data from the labour market, we computed the reservation wage, and mean unemployed wait time. Our established null hypothesis regarding the relationship between the minimum wage, subsistence wage and reservation wage was found to be violated.

The analysis raises several issues of public policy. It suggests that the minimum wage offered is low. We provide a measure of the quality of the labour market, and discuss how it may be improved, i.e. (i) by increasing the minimum wage, (ii) reducing the bargaining between the supply and demand sides of the labour market, and (iii) attempting to reduce wage volatility.

REFERENCES

McCall, J. (1970) Economics of information and job search, Quarterly Journal of Economic, 84(1), 113-26.

Stigler, G. (1961) The economics of information, Journal of Politicai Economy, 69(3), 2 13-25.

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