PARETO IMPROVING MINIMUM WAGE LAWS

PARETO IMPROVING MINIMUM WAGE LAWS

KEVIN LANG’

By increasing the expected wage in low skill iobs, a minimum wage law can reduce the incentive for low skill workers to imitate high skill workers in the signalling process. The gain from reduced investment in the signal can more than offset the loss from unemployment among low skill workers so that total output increases. Moreover, with an appropriate poll tax on workers to compensate owners of capital, the law can make all workers and owners of capital better o f f .

I. INTRODUCTION

The standard theorems of welfare economics imply that any form of price- fixing (such as minimum wage laws) causes inefficiencies. In this paper, I show that if education serves as a signal, a minimum wage law can lead to a pareto improvement. In essence, by increasing expected income in low skill jobs, a minimum wage law can reduce the incentive for low skill workers to “imitate” high skill workers in the signalling process. The gains from reduced investment in the wasteful signal may outweigh the costs of unemployment. Section one presents the theorems in terms of a simple model. The main theorem is proved for a more general model in section two.

II. A SIMPLE MODEL

I begin by considering a simple model in which there are just two types of workers and two types of jobs used to produce a single numeraire good.

Assumptions

A l ) Workers choose schooling in order to maximize the expected value of their earnings minus costs of education. A2) In primary jobs, type one workers have constant value of marginal product v 1 and type two workers have marginal product equal to zero. A3) In secondary jobs, value of marginal product is identical for all workers and is a declining function of the number of workers employed

where N is the number of workers employed in secondary jobs.

In order to ensure that workers always prefer primary jobs, I further

*University of California, Irvine. I would like to thank Art De Vany, William Dickens, Stephen Erfle, Henry Farber, Amihai Glazer, Shulamit Kahn, David Levine, and an anonymous referee for useful comments and suggestions.

145 Economic Inquiry Vol. XXV, January 1987, 145-158

146 ECONOMIC INQUIRY

assume that type one workers are always more productive in primary than secondary jobs.

A4) 0 1 >%(O)

Under assumptions (Al) -(A4), if firms could distinguish between the two types of workers, type one workers would be employed in primary jobs and would receive higher wages than type two workers, all of whom would be employed in secondary jobs. Consequently, type two workers would try to pretend that they were type one workers and obtain primary jobs.

If worker type is not directly observable, educational attainment may serve as a signal provided that education is less costly for type one workers [Spence 19731. Thus I assume

A5) The cost of s years of schooling for type one and type two workers is given by cIs and c2s with c1 < c2.

Assumption (A5) is a necessary condition for a signalling equilibrium. Two additional assumptions ensure that a signalling equilibrium exists and that it is unique.

A6) L , / L 2 < (c2 - cl) /c l where L , and L z are the numbers of type 1 and type 2 workers.

Assumption A6 is a technical assumption which ensures the existence of an equilibrium. When the number of high skill workers is large relative to the number of low skill workers, a Nash equilibrium may not exist. A6 pre- vents this difficulty from arising by assuming a sufficiently large concentra- tion of low skill workers. A number of alternative assumptions would also ensure the existence of an equilibrium, but they are generally more difficult to present without an extensive discussion of the sorting literature. The reader may wish to substitute the more direct assumption that a unique equilibrium exists in which the two types of workers obtain different levels of education.

A7) Firms can observe education costlessly, know the educational cost functions and productivities of the two types of workers, but not individuals’ types. Workers know their type and educational cost function.

The information structure assumed in A7 implies that f&ms do not need to experiment with wage offers or to monitor the productivity of workers ex post to determine the effectiveness of the sorting mechanism. A realistic assumption would be that firms observe actual productivity only with a long lag.

Since A2-A4 ensure that type one workers are always more productive in the primary sector and type two workers are always more productive in the secondary sector, a “reasonable” sorting equilibrium should match worker and job types. A5-A7 ensure that this is, in fact, the equilibrium. These

LANG: MINIMUM WAGE 147

assumptions are relaxed at the cost of considerable mathematical complexity in section two.

Under assumptions Al-A7, in equilibrium, type one workers are employed in primary jobs, receive a wage equal to v l , while type two workers are employed in secondary jobs at a wage equal to v z ( L z ) . In order for type two workers not to imitate type one workers, the cost to type 2 workers of obtaining the educational credential for primary jobs must be at least as great as the difference between primary and secondary wages. For a sorting equilibrium, educational attainment must satisfy

for type 1 workers and s: = 0 for type 2 workers. We are now in a position to consider the central results of this paper. The

intuitive argument for the results is as follows. If a minimum wage is imposed above the equilibrium in the secondary sector but below the primary sector wage and demand for secondary labor is inelastic, the expected wage in secondary employment must rise. Therefore, the expected difference between primary and secondary wages falls. The equilibrium signal for type one workers falls. Reduced investment in the signal by type one workers increases primary output; at the same time the minimum wage causes unemployment in the secondary sector, which reduces secondary output. The net result may be increased output depending on the cost of signalling and the elasticity of demand.

THEOREM 1. Under assumptions A1 -A7, there exist values of the elasticity of demand for secondary labor such that a minimum wage law increases output.

as output net of education costs where q is secondary output, tV2 is the number of workers employed in the secondary sector and w2 is the secondary wage. Note that if there is a minimum wage, the number of workers employed in the secondary sector, N,, is less than the number of type 2 workers, L,. Since there is unemployment in the secondary sector and all workers are identical in the secondary sector, secondary jobs are allocated randomly. Workers entering the secondary sector do not necessarily receive we but instead receive an expected wage ( w 2 N 2 / L 2 ) . Thus, s: depends on the expected wage in secondary jobs.

From (1) and (2)


(4) dQ/dwz = ( d q / d N , ) ( d N z / d ~ z ) + clL,Nz/(Lzcz)

+ ( d N z / d ~ z ) ~ ~ L , w z / ( L z c z ) .

When d Q / d w , is positive, a minimum wage infinitesimally above the equilibrium secondary wage increase the net value of output. Without the minimum wage, that is evaluated at the market clearing wage, the supply of type 2 workers ( L , ) equals demand ( N , ) . Workers are hired until dq /dN, equals the wage, w2. Substituting and rearranging terms, a small increase in w2 caused by a minimum wage will increase net output when

(5) Ed > - c lL , / ( c lL , + CZL2)

where c d is the elasticity of demand for secondary workers ( d N 2 / d w 2 ) / (w2/N2) . Since the right hand side is strictly negative, for any values of c , ; c2. L , and L,, there will always be some (negative) values of the elasticity of demand such that condition (5) holds. QED

COROLLARY 1. I f the primary sector ( L , ) is very large relative to the secondary sector ( L 2 ) , a minimum wage law increases output if and only if it reduces investment in education.

Proof. If the primary sector is very large relative to the secondary sector condition (5) requires the elasticity of demand to be greater than minus one. A small increase in the minimum wage increases the expected secondary wage if and only if the elasticity of demand is greater than minus 1. s: decreases if and only if the expected secondary wage increases. Hence, with the primary sector very large relative to the secondary, the conditions for s: to decrease and output to increase are identical.

Intuitively, when the secondary sector is small relative to the primary sector, the unemployment cost of a minimum wage is negligible. Therefore, a minimum wage law will increase or decrease output depending on whether it reduces or increases investment in the wasteful signal.

This corollary suggests that we may be able to evaluate the desirability of a minimum wage law by examining its effect on educational attainment. However, it should be noted that when the primary sector is large relative to the secondary sector, assumption A6 is likely to be violated, so that a Nash equilibrium does not exist. The corollary would continue to hold if an alternative equilibrium concept such as reactive equilibrium [ Riley 19791 were used.

Although minimum wage laws which increase output make type 1 workers better off by reducing their education cost and type 2 workers better off by increasing their expected wage, they reduce profits by increasing the secondary wage. The fact that output increases, however, suggests that with suit- able lump sum transfers, capitalists as well as workers could be made better off. However, since government cannot distinguish among workers, it must tax each worker equally. In this case it is not self-evident that it will not have to “overtax” one type of worker in order to compensate capitalists. The next


theorem gives the condition under which a combination of lump sum taxes and a minimum wage law can lead to a pareto improvement relative to the equilibrium with no minimum wage law.

THEOREM 2. Under assumptions Al-A7, with appropriate lump sum transfers, a minimum wage law infinitesimally above the market clearing wage in the secondary sector constitutes a pareto improvement if

( l + c d ) > cZLZ/(cl(Ll+LZ)).

Proof. Since there is no change in primary wages or employment, the only effects on profits are from changes in secondary wages and employment. Since firms choose the number of secondary workers to maximize profits (i.e., they set adaN, equal to zero), a small change in the number of workers employed has only a second order effect on profits. Thus the only factor affecting profits is the increased wage which reduces profits by Lz . The lump sum tax per worker necessary to cover this profit reduction is therefore LZ/(Ll +Lz)*

Consider the conditions under which the after tax expected secondary wage rises due to the minimum wage. There are two parts, an increase in the expected wage and a direct decrease due to the lump sum tax. Differen- tiating the expected ( N z w z / L 2 ) wage gives the first part (before subtracting the tax)

(6) dE(Wz)/dwz = 1 + Ed > 0.

Subtracting the tax and rearranging terms gives

(7) c d > -LI/(LI +Lz)

which is a weaker condition than (5 ) . Thus whenever (5 ) is satisfied, (7) is also satisfied.

For type 1 workers to be better off, the savings on educatim must exceed the lump sum tax.

(8) or

c ldso /dwz - L z / ( L l + L z ) > 0

(9) cl(l+cd)/Cz - L$/(L,+LZ) >o. Rearranging terms proves the theorem. QED

COROLLARY 2. I f the primary sector is large relative to the secondary sector, a minimum wage law with appropriate lump sum transfers constitutes a Pareto improvement i f and only i f it reduces investment in education.

The proof parallels that of corollary 1 and is not provided here.

111. A MORE GENERAL MODEL

The significance of the results in this paper depends on two factors- whether the results of the simple model hold under more realistic assump-


tions and whether the conditions for a minimum wage to be welfare improving are actually met. The basic result does not depend on the highly restrictive model used to simplify the mathematics. With many types of workers and many types of jobs, low skilled workers will be matched with those jobs in which skill is least important.

In this section, I maintain the assumption that there is a set of jobs in which skill level does not affect output. There is also a set of jobs in which skill level does affect output although the effect of skill on output may vary among these jobs. Workers who signal high ability will be employed in those jobs in which ability most increases output. This assumption is reasonable in the light of the findings of Dickens and Lang [1985]. They show that there are two sectors of the labor market, one in which there are substantial returns to education and experience and one in which there are no returns to these variables.

If demand for workers in low skill jobs is sufficiently inelastic, a minimum wage law will increase the attractiveness of these jobs by increasing the expected wage. Low skill workers will therefore have less of an incentive to pretend they are more skilled workers. The level of education required to signal each skill level will decline. Again reduced expenditure on the signal can outweigh the cost of education. This result does not depend on education being a pure signal. Education can both increase productivity and serve as a signal. This section develops a theorem similar to theorem 1, for this more general case. Readers who are not interested in the details of the proof cqn skip to the conclusion without much loss of content.

Assumptions about Firms ( B l ) There is a single competitive firm producing according to the tech- nology

(10) where p is the infinite vector of achieved skill (productivity) levels of each type of worker employed, N is the vector giving the distribution of employed workers by innate ability and k is capital. The price of output is 1.

The elements of N are denoted by N ( a ) where a denotes innate ability. It is important to note that there is a distinction in the model between achieved skill or productivity ( p ) and innate ability (a ) . For concreteness, it may be useful to think of Q as IQ. N(100) would then be the number of employed workers with an IQ of 100; p would be their productivity after whatever education they choose to obtain. While it turns out to be true in the model that all workers with the same innate ability attain the same productivity, this is an equilibrium condition rather than an identity, and it is important to maintain the distinction.

(B2) Workers may be assigned to either of two types of jobs, primary jobs in which marginal productivity varies with skill level, p , and secondary jobs in which marginal productivity is the same for all workers. For simplicity

4 = 4 (P, N, k)


the scale of p is defined so that it equals marginal productivity if employed in a primary sector job.

Assumptions about Workers (B3) Workers’ skill levels (and hence, their marginal products) depend on their innate ability and their schooling

(11) p = p (s,a), ap/as L. 0, ap/aa > 0, a2p/asaa 2 0.

The positive cross partial derivative ensures that higher ability workers gain at least as much as lower ability workers from any particular year of schooling.

(B4) The cost of schooling depends on the level of schooling obtained and innate ability

(12)

schooling is cheaper for high ability workers.

(B5) Innate ability, a, is distributed continuously over the range [ a , , ~ ’ ] .

Assumptions about lnf ormation (B6) Workers know their innate ability and skill functions and, hence, their skill level perfectly. (B7) Firms do not observe ability or skill level but can observe education costlessly. (B8) There are no contingent contracts. Workers cannot be offered a wage contingent on their productivity.

Assumptions about the Nature of Equilibrium The above assumptions are consistent with the existence of a signalling

equilibrium. Workers use education to signal their productivity and em- ployers use education to screen workers. However, it should be noted that education is not assumed to be a pure signal: assumption (B3) allows schooling to increase productivity. However, since there are cost advantages for high innate ability workers, education can simultaneously serve as a signal.

The nature and uniqueness of equilibrium in this type of model can be shown to depend on the nature of the “game being played” [Riley 1979; Stiglitz and Weiss 1983; Weiss 19831. For example, it depends on who “plays” first, workers or firms, and what expectations firms have about workers who play “disequilibrium” strategies. It therefore seems appropriate to specify an equilibrium which is consistent with a variety of posited games although it may not be a unique equilibrium for each particular game. The actual game being played need not be specified. The signalling equilibrium to be con- sidered is one where:

(B9) In the absence of a minimum wage law markets for all skill classes clear. The unemployment rate is zero.

c = c(s,a) - c(s) - a, a d a a < 0.

The negative cross partial derivative implies that any particular year of


(B10) Workers are paid their marginal product. Recall that in the secondary sector, all workers have the same marginal product. In the primary sector education is strictly increasing with respect to ability. (B11) The individual of lowest ability (a) in the primary sector is indifferent between primary and secondary employment and earns the secondary sector wage.

In the equilibrium described by (B9)-(Bll), the primary sector is in a standard sorting equilibrium, the secondary sector is in competitive equilibrium and firms cannot profitably make offers which cause workers to shift between sectors. This equilibrium is not the only conceivable equilibrium. Simple Nash behavior is insufficient to rule out violations of (B10) and (B11). However, the equilibrium is in accord with standard models in the literature [Riley 1979 Weiss 1983; Stightz and Weiss 19841.

Assumptions (Bl)-(Bll) imply that there will be a wage schooling profile in the primary sector which depends on the secondary sector wage since the lowest paid worker in the primary sector receives the secondary wage:

w = w(s, w,)

where w, is the secondary sector (or minimum) wage. It should be noted that w does not depend on innate ability (a) since ability is not observed directly. Ability affects wages only through the signal, s.

Similarly, the amount of schooling individuals obtain will depend on their innate ability and the wage profile and thus on their ability and the secondary wage

(14) s = s(a, 20,).

Since in equilibrium each worker is paid his marginal product (assumption B10)

(15) P (S (a, wm), a) = 4 s (a, Wm), wm),

where for convenience w is now used only for primary sector wages.

dary sector wage (assumption B11) Since the individual of lowest ability in the primary sector earns the secon-

(16) W(S(a,wrn),wm) = w m *

Since the lowest ability worker in the primary sector is just indifferent between primary and secondary employment

where N , and L, are the demand and supply of secondary workers and therefore the right hand side of (17) is the expected secondary sector wage. It should be noted that if the minimum wage is the market clearing wage, N , equals L,. Under these circumstances, combining (16) and (17) reveals that the assumptions require that, in the absence of an effective minimum wage,

LANC: MINIMUM WAGE 153

the lowest innate ability worker in the primary sector obtains infinitesimal education.

We are now in a position to prove a more general version of theorem 1. The intuition behind the proof is similar to the intuition in the previous section.

If a minimum wage is imposed, unemployment will result in the secondary sector. The expected wage in secondary sector work may increase or decrease depending on the elasticity of demand for labor in that sector. If the expected wage decreases, the more productive workers who otherwise would have entered the secondary market will choose to remain in school in order to enter the primary market with productivity above the minimum wage. On the other hand, if the expected secondary sector wage increases, some less productive workers who otherwise would have entered the primary market, will decide not to get any education and instead enter the secondary labor market.

Since education is affected in both cases and education serves to signal productivity, minimum wage laws will affect all primary market workers. In the case where minimum wage laws cause low productivity workers to obtain more education than they would have otherwise, minimum wage laws force slightly higher productivity workers to also increase their educational attainment (relative to the no minimum wage equilibrium) in order to signal their greater productivity. In this way, the equilibrium level of educational attainment under minimum wage laws is higher for all primary market workers. Similarly, if the laws cause some workers who would otherwise have entered the primary market to enter the secondary market (and hence not obtain education), all workers in the primary sector will get less education.

In the case where all workers get more education, increased investment in the signal exacerbates the productivity loss due to unemployment. However, if minimum wage laws decrease educational investment, reduced over- investment may wholly or partially offset lost output due to unemployment. If demand for secondary labor is relatively inelastic and the primary sector is large relative to the secondary sector, minimum wage laws are, in fact, likely to increase total output, despite their effect on unemployment. This is demonstrated formally below.

THEOREM 3. Under assumptions B1-B11, there exist values of the elasticity of demand for secondary labor and the ratio of primary to secondary labor such that a minimum wage law increases output net o f education costs.

Proof. The proof proceeds as in the simpler case. We differentiate output net of education costs with respect to the minimum wage and rearrange terms to express the condition that net output increase in terms of the elasticity of demand.


Define Q = q ( p , N , k) -Jaf c(s, t ) L ( t ) dt as output net of education costs, where L is the number of workers with a given innate ability level. Then,

d Q / d w , = i o a i a q / a N ) ( a N / d w , ) d t

a. +/ ( a q / a p ) (ap /as ) (as /aw , )Nd t

- ~ o a ~ a c / a s ) ( a s / a w . ) L dt

ao

where arguments of functions are dropped for convenience. The derivation of equation (18) is best understood by remembering that differentiation of Q is performed with respect to each element of an infinite vector and “sum- ming” these effects. Thus the first expression represents the integral of the derivatives of q with respect to each element of N; the second expression represents the derivative of q with respect to each element of p . p is not affected directly by the minimum wage. However, the minimum wage will affect the amount of education obtained and hence, productivity. There are N ( a ) employees of type a. Hence the effect on p must be multiplied by N ( a ) . The third expression is derived by taking the derivatives of the costs of education. Note that the supply of workers with a given level of innate ability (L(a) ) is fixed and is not a function of the secondary wage.

Equation (18) can be simplified by noting that aq /aN is the value of the marginal product since the price of output equals 1. Since by assumption workers are paid the value of their marginal products, the first term reduces to the integral of w ( a N / a w , ) . Since N is the number of employed workers, the change in N with respect to the minimum wage is zero for workers who remain in the primary sector or shift to the primary sector. In fact, the change in employment is just the negative of the change in secondary sector unemployment which in turn is just minus the change in demand plus the change in supply. Workers in the secondary sector and the marginal worker in the primary sector all earn w , by assumption (B11). Consequently, the first and fourth terms of (18) reduce to

(19) w m (NI -L: ) where N: and L: are the change in the demand and supply of secondary workers, respectively.

Since only primary workers obtain education, the second and thud ex- pressions are integrated only over primary sector workers. The variable p has been normalized to equal marginal productivity in primary sector jobs; therefore, a q / a p equals 1. Equation (18) can therefore be written

(20) d Q / d w , = w,(N:-L:) + ( a p / a s - ac /as ) (as /aw , )N( t ) dt. la- Net output will increase if the secondary sector wage is increased slightly


provided (20) is positive. In the absence of a minimum wage law, the supply of secondary labor ( L , ) equals the demand ( N , ) . Equation (20) becomes

N , ( E d - t , ) + (ap/as - ac/as)(as/aw,)N(t) dt > 0 (21) la- where Ed and E , are the elasticities of secondary labor demand and supply with respect to the secondary sector wage, respectively.

If the primary sector is large relative to the secondary sector, the second term will dominate the first term. Since, with educational signalling, the cost of education exceeds its effect on output, the second term will be negative if and only if minimum wage laws reduce educational attainment. Therefore if the primary sector is large relative to the secondary sector and minimum wage laws reduce education attainment, such laws will increase total output. However, since the elasticities, adaw,, and the relative sector sizes are inter- related, this must be demonstrated more formally.

The critical terms to be derived are as/aw, and c,. It is shown in the appendix that

(22) (ap/as - ac/as)(as/aw) 2 (1 + Ed - E , ) A(U)

where A(a) is a positive weight and that

(23) 8 = (1 +c d r ) 6 I S / ( 1 -r+‘?% I S )

where r = (ap/as)/(aw/as), = w,L(g)/(L,(ap/aa)). is the “impact elasticity of supply’’-when the minimum wage is raised,

the number of workers who are insufficiently productive to obtain primary sector employment at the education levels associated with the old minimum increases. Therefore the supply of secondary workers would increase. c I S is the elasticity of supply with respect to the minimum wage if education levels do not change. r is the proportion of the wage increase from education which is due to increased productivity. It can be viewed as measuring the importance of the human capital effect of education relative to the signalling effect. If T equals 1, there is no signal; if r equals 0, education does not increase productivity.

Given (22) and (23), a sufficient condition for (21) to hold, i.e., for a minimum wage law to increase output net of education costs is

R =J‘A(t)N(t)dt/(N, 0 + where R is a weighted proportion of workers employed in the primary sector. R is strictly greater than zero. Since r is nonnegative and less than one and the impact elasticity is positive, the denominator of (2.4) is positive. Condition (24) therefore requires that the numerator be smaller than


some positive value. This can always be fulfilled for sufficiently small t d and

COROLLARY 3. I f the primary sector is very large relative to the secondary sector, a minimum wage law increases output if and only if it reduces inoest- ment in education. The proof parallels that of corolIary 1 and is not presented here.

CIS. QED

IV. CONCLUDING REMARKS

In the fuller model as in the simple model, a minimum wage law can be welfare improving and will tend to be if a) it reduces education and b) if the primary sector (where skill differences exist) is large relative to the secondary sector (where skill differences are small or nonexistent).

Dickens and Lang [ 19851 provide evidence that about nine-tenths of adult male workers are in the primary sector. Thus the critical issue is whether minimum wage laws reduce investment in education. Unfortunately, evidence regarding the effect of minimum wage laws on education is mixed. Time-series studies [Mattila 1978;1979] have shown that education is increased by statutory minima, while cross-section studies [Ehrenberg and Marcus 1979; Cunningham 19811 have obtained the opposite result. Thus we must remain agnostic regarding the effect of minimum wage laws on education and even more so on total output.

This paper also suggests avenues for empirical research to assess the significance of signalling models of education in the labor market. Since the model implies that a minimum wage law should affect the educational attainment of workers who would earn more than the minimum wage even in its absence, the effects of minimum wage laws could be used to measure the importance of educational signalling. A similar approach is used by Lang (1986) to analyze the effects of compulsory school attendance laws under the human capital and signalling hypotheses.

APPENDIX

Derivation of Equation (22) From (15) and (17),

(25) P(s(a,wrn),a) = C ( S ( a , w m ) , a ) + (Ns/Ls)wrn. Differentiating with respect to w, gives

(26) ( d p / d s ) ( d d d w , ) = ( W a s ) (dddw,) + (( N:/L , ) - ( N , L : ) / L ; ) w ,

+ N J L , . Evaluated at the equilibrium secondary sector wage (N ,=L , )


(27) (ap/as - ac/as)(as/w,) = 1 + E d - E,.

Equation (27) gives adaw, evaluated at a. We can show that as/aw, is more negative for higher values of a. Differentiating (15) first with respect to w, and then with respect to a gives

(28) (a2p/asaa)(as/aw,) + (ap/as - aw/as)(a2s/aw,aa) = o The first term in (28) is nonpositive if as/aw, is negative. Since aw/as is greater than ap/as, a2s/aw,an is nonpositive. It therefore follows from (26) and (28) that

(29) adaw, 1 ( 1 + Ed - E,)/(ap(g)/as - ac(g)/as)

Multiplying both sides of (29) by ap (a)/& - ac(a)/as gives equation (22).

Derivation of Equation (23) From (15) and (16),

(30) P(s(a,wm), w,) = w,.

(31)

(32) dg/dw, = [l - (ap/as)(i + E d - €,)/(ap/as - aw/as)]/(dp/da)

(33) E , = (dg/dw,)L(g)w,/L,

dg/dw, = [l - (ap/a~)(ds/dw,)]/(dp/da) Substituting (27) into (31) gives:

But,

Multiplying both sides of (32) by L(g)w,/L, and rearranging terms yields equation (23).

REFERENCES

Cunningham, James. “The Impact of Minimum Wages on Youth Unemployment, Hours of Work, and School Attendance: Cross-sectional Evidence from the 1960 and 1970 Cen- suses,” in The Economics of Legal Minimum Wages, edited by S. Rottenberg. Washington, D.C.: American Enterprise Institute, 1981,88-123.

Ehrenberg, Ronald and Alan Marcus. “Minimum Wage Legislation and the Educational Out- comes of Youth in Research in Labor Economics, Vol. 111, edited by R. Ehrenberg. Greenwich, Conn.: JAI Press, 1979.

Dickens, \\.‘illiam T. and Kevin Lang. “A Test of Dual Labor Market Theory.” American Eco- nomic Review, September 1985,792-805.

Lang, Kevin. “Human Capital vs. Sorting: The Effects of Compulsory Attendance Laws.” Quar- terly Journal of Economics, August 1986, 609-24.

Mattila, J. Peter. “The Impact of Minimum Wages on Teenage Schooling and on the Part- Time/Full-Time Employment of Youths” in The Economics of Legal Minimum Wages, edited by S. Rottenberg. Washington, D.C.: American Enterprise Institute, 1981, 61-87.

-. “Youth Labor Markets, Enrollments, and Minimum Wages,” Proceedings of the Thirty- First Annual Meeting of the Industrial Relations Research Association, August %-31,1978, 1 3 - 4 0 ,


Riley, John. “Informational Equilibrium.” Econometrica, March 1979,331-59. Spence, Michael A. “Job Market Signaling.” Quarterly Journal of Economics, August 1973,

Stightz, Joseph and Andrew Weiss. “Sorting Out the Differences Between Screening and Sig-

Weiss, Andrew. “A Sorting-cum-Learning Model of Education.” Journal of Political Economy,

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