The Impact of Youth Unemployment Policy

Filges, Trine; Larsen, Birthe Working Paper The Impact of Youth Unemployment Policy Working paper, No. 8-2001 Provided in Cooperation with: Department of Economics, Copenhagen Business School (CBS) Suggested Citation: Filges, Trine; Larsen, Birthe (2001) : The Impact of Youth Unemployment Policy, Working paper, No. 8-2001, Copenhagen Business School (CBS), Department of Economics, Frederiksberg, https://hdl.handle.net/10398/7639 This Version is available at: https://hdl.handle.net/10419/208448 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/3.0/ The Impact of Youth Unemployment Policy¤ Trine Filges y and Birthe Larsen z December 6, 2001 Abstract This paper examines the impact on unemployment, unemployment distribution, wages and welfare of Youth Unemployment Programmes (YUPs). The aim of YUP is to increase the number of young people acquiring skills. We assume that the YUPs are a complete success and consequently analyse what happens when the number of skilled workers increases relatively to the number of unskilled workers. The results depend on the productivity of the skilled workers when employed in the unskilled sector relatively to the productivity of the unskilled worker. Keywords: Skill, unemployment, search JEL classications: J18, J38, J68 1. Introduction Reduction of high European unemployment rates has been of great concern to the politicians in the European countries throughout the nineties. In many countries, this concern has resulted in policy attempts in order to ght the problem. Di¤erent policies have been used and a shift from passive unemployment policy, generally, simply in the form of unemployment insurance paid to unemployed workers towards active labour market policy has been initiated in many countries. For example, Nickell and Van Ours (2000) analyses the Dutch and British cases. Both countries have experienced a large drop in unemployment during the nineties. Denmark has experienced an even larger fall in unemployment during the same period. We therefore give a short description of the policy implemented ¤ Comments from participants at the European Economic Association Conference, Lausanne 2001, are gratefully acknowledged. y Centre for Research in Social Integration and Marginalization and the Danish National Institute of Social Research, Herluf Trolles Gade 11, DK-1052 Copenhagen K, E-mail address: tif@s.dk, Phone: +45 3348 0926, Fax: +45 3348 0833 z Centre for Research in Social Integration and Marginalization and Copenhagen Business School, Department of Economics, Solbjerg Plads 3, DK-2000 Copenhagen F. E-mail address: [email protected] in Denmark in the nineties, even though some of the same elements may be found in the policy conducted in other countries. In Denmark in 1996 a reform directed towards the unemployed, low-educated youth was implemented, the Youth Unemployment Programme (YUP). The aim of this reform was to improve the employment possibilities for unemployed, loweducated youth by motivating them to undertake an education. 1 The motivation was the fact that the unemployment rate of skilled workers was (and still is) less than the unemployment rate of unskilled workers in Denmark, and this ordering has been present in more than twenty years. Groes and Holm (1999) analyse the unemployment rates in Denmark dependent upon educational level for the period 1980-1998. The unemployment rate of skilled workers is below the average. This ordering has been the same throughout the period, and there is evidence of further polarization: the unemployment rate of non-skilled workers keeps increasing, whereas they expect bottleneck problems for higher educated workers. In this paper we analyse the long-term e¤ects on unemployment, wages and welfare of the YUP. Furthermore, we consider distribution e¤ects of the YUP. We set up a search model distinguishing between skilled and unskilled workers. We do not model the decision to acquire skills, rather we assume that an exogenous fraction of the labour force has already acquired skills. 2 Consequently, workers are either skilled or unskilled. There are two sectors, a skilled sector where there is a minimum skill requirement and an unskilled sector without any skill requirements. Unskilled workers cannot be hired in the skilled sector whereas skilled workers can be hired in both the unskilled and the skilled sector. This denition of skills enables us to distinguish between skilled jobs and unskilled jobs and skilled workers and unskilled workers. We assume that skilled workers search for jobs in both sectors as the value of employment in the unskilled sector is higher than the value of being unemployed. The assumption that workers search for jobs in both sectors is also found in Gautier (2001) and Albrecht and Vroman (2000). Furthermore it is in accordance with real life behaviour of skilled workers in Denmark. In 1998, 30 percent of the workers who are employed in the unskilled sector are skilled workers according to the Danish Ministry of Labour (2000). We assume that workers can direct their search, i.e., they know whether they apply for a skilled job or an unskilled job. Firms, however, do not know ex ante which type of workers applies for the vacancy. The motivation behind these assumptions is that it is not di¢cult for a rm to inform about the skill requirements for a job, but they cannot ex ante exclude some workers from applying for the job. 1 Young insured persons, less than 25 years, without any formal education beyond secondary school, and who have been unemployed for 6 months during the last 9 months, are given an o¤er of 18 months specially designed vocational education. This o¤er contains an incentive to undertake ordinary education or to nd a job since unemployment benets are cut by 50 percent while in the special education programme. Refusal to participate in the special education programmes is followed by a sanction, it will result in a total loss of unemployment benets. 2 See Filges and Larsen ( 2001 ) for an analysis of the decision to acquire skills. 2 Consequently, skilled workers search for jobs in both sectors whereas unskilled workers, knowing they are unemployable in the skilled sector, search for jobs in the unskilled sector only. The wage paid in the skilled sector is higher than the wage o¤ered in the unskilled sector. This implies that skilled workers prefer to work in the skilled sector and consequently, they search for jobs in the skilled sector while employed in the unskilled sector. 3 We assume that the YUP is a complete success in the sense that it actually increases the relative number of workers acquiring skills. Consequently, we analyse the long-term e¤ect of the YUP by considering an exogenous increase in the number of skilled workers relative to the number of unskilled workers. Usually, in standard search models, the unemployment rate of a specic worker group is not a¤ected by the number of workers in the group. In the present model, however, a larger fraction of skilled workers implies that the unemployment rate of skilled workers as well as the unemployment rate of unskilled workers are a¤ected. The results depend on the marginal productivity of the skilled worker while employed in the unskilled sector relatively to the productivity of the unskilled worker. If the marginal productivity of a skilled worker employed in the unskilled sector relative to the marginal productivity of an unskilled worker is lower than a threshold, ¯ ¤ , where in general ¯ ¤ is greater than 1;then the e¤ects are as follows. A larger fraction of skilled workers implies that the unemployment rate of skilled workers as well as the unemployment rate of unskilled workers increases. The positive e¤ect on the unemployment rates is due to the assumption that unemployed skilled workers search for jobs in both the skilled and the unskilled sector. The YUP also induces a negative e¤ect on the total unemployment rate. This results from the movement of workers from the high unemployment group, the unskilled workers, to the low unemployment group, the skilled workers. Hence, the net e¤ect of the YUP on the total unemployment rate is ambiguous. Similarly, there is both a negative and a positive welfare e¤ect. Increasing the relative number of skilled workers implies moving workers from the group giving rise to the lowest welfare to the group of workers giving rise to the highest welfare, thereby inducing an increase in total welfare. However, the YUP has a negative impact on the total welfare rate in the economy. Consequently, the total welfare e¤ect of the YUP is ambiguous. Considering wage e¤ects we show that wages in the unskilled sector decreases due to the YUP. Concerning distribution e¤ects, we show that the YUP induces a more unequal wage and unemployment distribution. Initially, the wage rate in the skilled sector is higher than wages in the unskilled sector. The YUP worsens this unequal wage distribution. Likewise, unemployment of the unskilled workers is initially higher than unemployment of the skilled workers. The YUP worsens the unequal unemployment distribution too. When the marginal productivity of the skilled worker employed in the unskilled sector crosses the threshold ¯ ¤ then these ndings are somewhat modied. 3 This information structure is also found in Gautier ( 2001 ) . 3 In this case, we may see a decrease in wage dispersion and the unemployment rates of both skilled and unskilled workers as well as an increase in the welfare rate of the economy. Our contribution should be compared to two related papers. Gauthier (2001) has been written parallel with our paper and do have some similarities to our paper. However, in his paper wages are only functions of exogenous parameters. Our paper has wages as functions of transition rates as these are important for workers fall back position. We can therefore study impacts of a change in the fraction of skilled workers on wages and wage distribution. Furthermore, we can consider impacts on welfare. Saint-Paul (1996) perform a similar experiment as we do, but in a more restrictive model, in the sense that there is a xed number of jobs in the economy and workers employed in the unskilled sector do not search on-the-job. The paper is organized as follows. The model is presented in Section 2.In Section 3, the equilibrium is described and Section 4considers the e¤ects of YUP. The last section concludes. 2. The model In this section we set up the model to analyse the long-term e¤ects on unemployment, wages and welfare of YUP. We do not model the decision to acquire skills, rather we assume that an exogenous fraction of the labour force has already acquired skills. Consequently, the labour force consists of workers who are either skilled or unskilled. In order to focus on the long term impact of the YUP, we analyse the consequences of an exogenous increase in the number of skilled workers. There are two sectors, sector 1is the skilled sector and supplies jobs only to skilled workers. Sector 2, is the unskilled sector and supplies jobs to both skilled and unskilled workers. The marginal product in sector 1is higher than in sector 2. Skilled workers, however, prefer to work in sector 1as the marginal product is higher than in sector 2and consequently the wage paid is also higher than the wage o¤ered in sector 2. 2.1. Workers Let ¡ E j i and ¡ U i denote the expected present values of lifetime utilities of being employed and unemployed, respectively. Subscript i=S; N denotes skilled respectively unskilled workers and j=1;2denotes which sector the worker is employed in. The lifetime utilities of a skilled worker are then: r¡ E 1 S =w 1 s ¡t+q ( ¡ U S ¡¡ E 1 S );(2.1) r¡ U S =b¡t+p 1 ( ¡ E 1 S ¡¡ U S )+p 2 ¡¡ E 2 S ¡¡ U S ¢;(2.2) 4 r¡ E 2 S =w 2 s ¡t+p 1 ¡¡ E 1 S ¡¡ E 2 S ¢¡q¡¡ E 2 S ¡¡ U S ¢;(2.3) where bis the unemployment insurance, ris the discount rate and qis an exogenous fraction of currently employed workers leaving their jobs. The wage rate of a skilled worker working in sector 1is denoted w 1 s ,andw 2 s isthewagerateofa skilled worker employed in sector 2.tis a lump sum tax paid by all workers. p 1 is the transition rate of skilled workers into employment in sector 1and p 2 is the transition rate of workers into employment in sector 2. Note that unemployed skilled workers search for a job in both sector 1and sector 2, and that skilled workers employed in sector 2search for a job in sector 1. The lifetime utilities of unskilled workers are: r¡ E 2 N =w 2 n ¡t+q ( ¡ U N ¡¡ E 2 N );(2.4) r¡ U N =b¡t+p 2 ( ¡ E 2 N ¡¡ U N );(2.5) where w 2 n is the wage rate of an unskilled worker employed in sector 2.Notethat the transition rates of skilled and unskilled workers into employment in sector 2 are equal. Hence, as argued below, we assume that skilled and unskilled workers compete for jobs in sector 2on equal terms. 2.2. Firms Firms supply jobs dependent upon the wage and their hiring costs. Firms supply one job each. Let ybe the marginal product of a skilled worker in sector 1,ay, a<1,whereay > b, is the marginal product of an unskilled worker in sector 2, nally, a¯y is the marginal product of a skilled worker working in sector 2, a¯ < 1and a¯y > b.Hence,wehavethat b<min (a¯y; ay). Note, that we assume that the skills of skilled workers do not imply that they necessarily are able to produce more than unskilled workers when working in the unskilled sector. Only when the skilled workers are employed in the skilled sector do they make use of their skills and consequently are able to produce at their maximum. We do not restrict ¯to be larger or smaller than one, only less than 1 a . The empirical evidence on this issue is mixed (see Büchel 2000 for a survey) and the intuition is as follows. If ¯=1 , that is, a skilled worker employed in sector 2has the same marginal productivity as an unskilled worker employed in sector 2.This assumption implies that for example, when working as a cleaner, it does not matter for the marginal product whether you are able to control a crane or not. The number of u¤ removed in a day is the same. On the other hand, when controlling a crane it surely matters for the marginal product whether you are trained to do that or not. If ¯>1;the skilled worker is more productive than the unskilled workers, while employed in sector 2. This may happen, for example, in the tourist sector, where some knowledge of language may be an advantage even in unskilled kind of jobs, or it may happen if skilled workers have a higher 5 level of job satisfaction or better health status. The case of ¯<1, corresponds to the situation where skilled workers when performing unskilled kind of jobs are so bored and frustrated that it negatively inuences their level of job satisfaction and health status and consequently lowers their productivity. 4 The expected present values of a lled job in sector j,j=1;2,¡ J j ;and of a vacant job, ¡ V j , are determined by the equations: r¡ J 1 =y¡w 1 s ¡q(¡ J 1 ¡¡ V 1 );(2.6) r¡ V 1 =¸ 1 ¡¡ J 1 ¡¡ V 1 ¢¡k; (2.7) r¡ J 2 ¡w 2 n ¢=ay ¡w 2 n ¡q(¡ J 2 ¡w 2 n ¢¡¡ V 2 );(2.8) r¡ J 2 ¡w 2 s ¢=ay¯ ¡w 2 s ¡ ( p 1 +q) ( ¡ J 2 ¡w 2 s ¢¡¡ V 2 );(2.9) r¡ V 2 =¸ 2 ( ¸ N ¡ J 2 ¡w 2 n ¢+ ( 1¡¸ N )¡ J 2 ¡w 2 s ¢¡¡ V 2 )¡k; (2.10) where ¸ j ,j=1;2, is the rms transition rate, and ¸ N is the probability that the worker searching for a job in sector 2is unskilled. The direct cost associated with job supply is given by k. Free entry implies that jobs are supplied as long as it is protable, i.e. until ¡ V i =0:Using this condition and combining equations (2.6)-(2.7), respectively (2.8)-(2.10) gives two equations to determine the rms transition rates: ¡k+¸ 1 y¡w 1 s r+q=0;(2.11) ¡k+¸ 2 µ¸ N µay ¡w 2 n r+q¶+ ( 1¡¸ N )µay¯ ¡w 2 s r+q+p 1 ¶¶ =0:(2.12) 2.3. Matching and Unemployment The work force is divided into two groups according to skills. We normalize the total labour force to one. The number of workers who have acquired skills is given by ¤and the number of unskilled workers is 1¡¤.E j i ,i=S; N; and j=1;2, denotes the number of workers of type iemployed in sector j,andU i ,i=S; N, denotes the number of unemployed workers of type i.Theowsofworkersis illustrated in Figure 2.1. In steady state, inows are equal to outows. The equations determining equilibrium unemployment for unskilled and skilled workers, employment for skilled workers employed in sector 1and in sector 2and total numbers are: p 2 U N =qE 2 N ; 4 A number of US studies show that overqualied workers have a lower level of job satisfaction and more health problems and consequently have higher rates of shirking or absenteeism than correctly allocated workers, see Büchel 2000. 6 ES1 U S US @ p1 ES2 ES2 @ q US @ p2 EN2 UN @ p2 EN2 @ q UN ES1 @ q ES2 @ p1 Figure 2.1: Labour Market Flows ( p 1 +p 2 )U S =q¡E 1 S +E 2 S ¢; p 1 ¡U S +E 2 S ¢=qE 1 S ; p 2 U S = ( q+p 1 )E 2 S ; U N +E 2 N =1 ¡¤; U S +E 1 S +E 2 s =¤: The number of workers in each of the categories is then given by: E 1 S =p 1 q+p 1 ¤;(2.13) E 2 S =p 2 q+p 1 U S ;(2.14) U s =¤ q q+p 1 +p 2 ;(2.15) E 2 N = ( 1¡¤) p 2 q+p 2 ;(2.16) U N = ( 1¡¤) q q+p 2 :(2.17) The unemployment rates are both increasing in the separation rate, q,and decreasing in the transition rate p 2 . In addition the unemployment rate of skilled workers decreases with p 1 . The employment rates all decrease with the separation rate, q. In addition, the employment rate of skilled workers in sector 1increases with the transition rate p 1 and the employment rate of unskilled workers in sector 2increases with the transition rate p 2 . The employment rate of skilled workers 7 employed in sector 2increases with the transition rate p 2 and decreases with the transition rate p 1 . The employment prospects of skilled workers are better than for unskilled workers, see equation (2.15) and (2.17): U N 1¡¤>U S ¤: Furthermore, the rate of skilled workers employed in skilled jobs is higher than the rate of unskilled workers employed in unskilled jobs if the transition rate into jobs in sector 1is higher than the transition rate into jobs in sector 2: p 1 >p 2 )E 1 S 1¡¤>E 2 N ¤:(2.18) We will only consider parameter values for which the employment rate of skilled workers in skilled jobs is higher than the employment rate of unskilled workers in unskilled jobs. This is denitely the most realistic situation. Groes and Holm (1999) nd that the unemployment rate for unskilled workers in Denmark has been above average, whereas the unemployment of skilled workers has been below average, throughout the period 1980-1998. Furthermore, the philosophy behind the YUP is to increase the employment prospects of young people by motivating them to undertake an education. If the inequality in (2.18) is reversed the YUP does not make any sense. The number of matches formed in sector 1, respectively, sector 2,isgivenby the matching functions: x j (V j ;fS j )=pV j pfS j ,j=1;2;(2.19) where V j is the number of vacancies in sector j,andfS j is the total number of workers searching for a job in sector jmeasured in e¢ciency terms. fis a measure of the workers search e¢ciency. Note that the number of matches has positive rst order derivatives in V j and fS j , negative second order derivatives, positive cross partial derivatives and is homogenous of degree one in V j and fS j . Pissarides 86 and Blanchard and Diamond 89 provide empirical justication for the Cobb-Douglas matching function with equal exponents. The workers transition rate, p j ,j=1;2;is equal to the number of matches divided by the number of searchers. The rms transition rate is equal to the number of matches divided by the number of vacancies. We measure the transition rates in terms of labour market tightness, µ j . Labour market tightness is a measure of how tight the market is, and is given by vacancies relative to the number of searchers in e¢ciency terms. The transition rates become: p j =fpµ j ;¸ j =³pµ j ´ ¡ 1 ,µ j =V j fS j ;j=1;2:(2.20) 8 concerning their job search into sector 1increases, tending to increase skilled workers bargaining power. The impact on sector 1 wages is therefore ambiguous. Consider next the case where ¯>¯ ¤ . The transition rate into employment in sector 2increases corresponding to wage decreases for the workers employed in this sector. Symmetrically we have a decrease in the transition rate into sector 1, again inducing an ambiguous impact on sector 1 wages. 4.2. Wage dispersion In the previous section we have shown that sector 2 wages decrease (increase) for ¯<¯ ¤ (¯>¯ ¤ ) and the impact on sector 1 wages is ambiguous, following an increase in the fraction of skilled workers. In this section we evaluate what happens to wage dispersion, both between unskilled and skilled workers and inbetween sector 1 and sector 2 workers. Wage dispersion between unskilled and skilled workers employed in sector 2 is dened as WD 2 =w 2 n ¡w 2 s 6 0for ¯ 5 ¯ 1 ; where ¯ 1 >1is dened in equation (2.28). Wage dispersion between skilled workers employed in sector 1and unskilled workers is positive: WD sn =w 1 s ¡w 2 n >0: Finally, wage dispersion between skilled workers employed in sector 1and 2 is positive: WD ss =w 1 s ¡w 2 s >0: Proposition 4.2. When the fraction of skilled workers increases, ¤increases, wage dispersion between skilled workers in sector 1 and unskilled workers increases (decreases) for ¯<¯ ¤ (¯ ¤ <¯<¹ ¯) @WD sn @ ¤ >0¡ @WD sn @ ¤ <0¢, wage dispersion in-between skilled workers increases (decreases) for ¯<¯ ¤ (¯ ¤ <¯) @WD ss @ ¤ >0¡ @WD ss @ ¤ <0¢;and the sign of the change in wage dispersion between sector 2 workers is indeterminate. Proof. Di¤erentiating wage dispersion with respect to ¤we obtain: @WD 2 @¤=dw 2 n d¤¡dw 2 s d¤; @WD sn @¤=dw 1 s d¤¡dw 2 n d¤; @WD ss @¤=dw 1 s d¤¡dw 2 s d¤: 15 Substituting for the derivatives gives: @WD 2 @¤=µdx dp 2 (ay ¡b)¡dw 2 s dp 2 ¡dw 2 s dp 1 @p 1 @p 2 ¶@p 2 @¤; @WD sn @¤=µdw 1 s dp 1 @p 1 @p 2 +(a¯y ¡b)@x 3 @p 2 ¡dx dp 2 (ay ¡b)¶@p 2 @¤; @WD ss @¤=µdw 1 s dp 1 @p 1 @p 2 +(a¯y ¡b)@x 3 @p 2 ¡dw 2 s dp 2 ¡dw 2 s dp 1 @p 1 @p 2 ¶@p 2 @¤: Using a¯ < 1;a<1;and @p 1 @p 2 <0it is shown in Appendix Dthat the sign of the second derivative is positive for ¯<¯ ¤ and negative for ¯ ¤ <¯<¹ ¯; where ¹ ¯is determined by the equation: a¯y ¡b ay ¡b= ( p 1 +2 ( r+q)) ( p 2 +2 ( r+q+p 1 )) 2 2 ( r+q+p 1 ) ( p 2 +2 ( r+q)) 2 ; and the sign of the last derivative is positive for ¯<¯ ¤ and negative for ¯>¯ ¤ . For ¯<¯ ¤ we then have the following. Both wages of sector 2 decrease and we cannot determine which of the two wages decreases the most. Wage dispersion in-between skilled workers employed in sector 1 and unskilled workers will increase. Hence, even if the wage rate for skilled sector 1 workers should decrease, it decreases less than the wage rate received by unskilled workers. Wage dispersion in-between skilled workers employed in the two sectors increases for ¯<¯ ¤ . The shift of workers from the unskilled to the skilled labour force induces a more unequal wage distribution. The intuition is here that both skilled workers negotiating wages in sector 1 and sector 2 are equally a¤ected by the fall in the transition rate into employment in sector 2, whereas the higher transition rate into sector 1 employment tends to increase sector 1 wages. For ¯>¯ ¤ the transition rate into sector 2 increases with ¤.Inthiscase,wage dispersion in-between skilled workers employed in sector 1 and unskilled workers will decrease if ¯<¹ ¯and wage dispersion in-between skilled workers employed in the two sectors decreases. 4.3. Unemployment Considering unemployment, we rst consider the impact on the unemployment rates for skilled and unskilled workers when increasing the number of skilled workers relative to the number of unskilled workers. Proposition 4.3. When the fraction of skilled workers increases, ¤increases, unemployment rates for skilled and unskilled workers increase (decrease), d ( U S = ¤ ) d ¤ > 0(<0); d ( U N = ( 1 ¡ ¤ ) ) d ¤ >0(<0)for¯<¯ ¤ ; ( ¯>¯ ¤ ). 16 Proof. Di¤erentiating the two unemployment rates with respect to ¤we obtain: d(U S =¤) d¤=¡ U S ³ dp 1 dp 2 jp 1 (p 2 )+1 ´ (p 1 +p 2 +q) dp 2 d¤;(4.1) d(U N =(1 ¡¤)) d¤=¡U N (p 2 +q) dp 2 d¤;(4.2) where we showed above (see equation (3.1)) that: ¡1<@p 1 @p 2 jp 1 (p 2 )<0)@p 1 @p 2 jp 1 (p 2 )+1>0;8¯>0: The net e¤ect on both unemployment rates of increasing the number of skilled workersispositivefor¯<¯ ¤ . The unemployment rate of unskilled workers increases because the value of employing a job with a skilled worker is less than the value of lling the job with an unskilled worker. When the number of skilled workers increases relative to the number of unskilled workers the probability of employing a skilled worker in sector 2increases. This implies that fewer vacancies are supplied in the unskilled sector and the unemployment rate consequently increases. Symmetrically, when ¯>¯ ¤ the value of employing a skilled worker is higher in sector 1, implying a higher vacancy supply and thus lower unemployment. Considerthecasewhere¯<¯ ¤ . Concerning the unemployment rate of skilled workers, there is a positive as well as a negative e¤ect. The positive e¤ect is directly due to a fall in the number of vacancies supplied in the unskilled sector. The negative e¤ect arises because the transition rate into employment in the skilled sector, p 1 , increases. The transition rate, p 1 , is not directly dependent upon p 2 . The e¤ect works through the wage of skilled workers employed in the skilled sector. As the value of unemployment decreases due to the lower transition rate into employment in the unskilled sector, this tends to decrease the wage of skilled workers employed in the skilled sector (c.i.f. proposition 4.2). The lower wage implies that the value of having a lled job in the skilled sector increases, implying that more vacancies are supplied. The net e¤ect on the unemployment rate is unambiguously positive. When ¯>¯ ¤ , the result is the reverse: higher p 2 and lower p 1 resulting in lower unemployment for skilled workers, U S . Consequently, the unemployment rates of both skilled and unskilled workers increase for ¯<¯ ¤ ,areuna¤ectedfor¯=¯ ¤ and decrease for ¯>¯ ¤ as a result of the larger fraction of skilled workers. Furthermore, it can be shown that the larger fraction of skilled workers harms the unskilled workers the most when ¯<¯ ¤ , as the increase in the unemployment rate is higher for unskilled workers than for skilled workers. For ¯>¯ ¤ , the decrease in unskilled unemployment is larger than the decrease in skilled unemployment: 17 d(U S =¤) d¤¡d(U N =(1 ¡¤)) d¤ =qdp 2 d¤Ã1 (q+p 2 ) 2 ¡ dp 1 dp 2 jp 1 (p 2 )+1 (q+p 1 +p 2 ) 2 !<0 =0 >0 for8 < : ¯<¯ ¤ ¯=¯ ¤ ¯>¯ ¤ Wethereforehavetheresult: Proposition 4.4. A larger fraction of skilled workers induces a more unequal unemployment distribution for ¯<¯ ¤ , has no impact for ¯=¯ ¤ and a more equal unemployment distribution for ¯>¯ ¤ : Another interesting thing to consider is the number of skilled workers employed in sector 2. The higher unemployment rate of skilled workers will tend to increase the rate of skilled workers employed in the unskilled sector and the lower vacancy supply in sector 2will tend to decrease this rate. The net e¤ect can be shown to be negative. We obtain the result. Proposition 4.5. The rate of skilled workers employed in sector 2 decreases (una¤ected/increases), d ( E 2 S = ¤ ) d ¤ <0(=0 = >0)for¯<¯ ¤ (¯=¯ ¤ = ¯>¯ ¤ ). Proof. Di¤erentiating E 2 S = ¤with respect to ¤we have: d ( E 2 S = ¤) d¤=U S q+p 1 0 @¡ p 2 ³ @p 1 @p 2 jp 1 ( p 2 )+1 ´ @p 2 d ¤ q+p 1 +p 2 + @p 2 d ¤ ( q+p 1 )¡p 2 @p 1 @p 2 jp 1 ( p 2 ) @p 2 d ¤ q+p 1 1 A Rewriting the equation we get: d ( E 2 S = ¤) d¤=U S ( q+p 1 ) @p 2 d¤µ¡@p 1 @p 2 jp 1 ( p 2 )µp 2 q+p 1 +p 2 +p 2 q+p 1 ¶+q+p 1 q+p 1 +p 2 ¶; showing that the net e¤ect is negative for ¯<¯ ¤ and positive for ¯>¯ ¤ . The last thing to consider in this section is the impact on the total unemployment rate. The total unemployment rate in the economy is given by: U=U S +U N U S +U N +E 2 S +E 1 S +E 2 N =U S +U N : We can conclude the following: Proposition 4.6. The impact on total unemployment following an increase in the number of skilled workers is ambiguous for ¯<¯ ¤ and negative for ¯¸¯ ¤ . 18 Proof. The e¤ect of increasing the relative number of skilled workers on total unemployment is: dU d¤=µU S ¤¡U N 1¡¤¶¡@p 2 d¤µµ@p 1 @p 2 jp 1 (p 2 )+1 ¶U S p 1 +p 2 +q+U N p 2 +q¶; where the rst parenthesis contain a negative value and the last, squared, parenthesis contain a positive value. As @p 2 d ¤ <0(¸0)for¯<¯ ¤ (¯¸¯ ¤ )the net e¤ect is ambiguous for ¯<¯ ¤ and negative for ¯¸¯ ¤ . As the unemployment rate of skilled workers is less than the unemployment rate of unskilled workers: U S ¤ ¡ U N 1 ¡ ¤ <0, the sum of the rst two terms is negative. Hence, moving workers from the high unemployment group to the low unemployment group obviously decreases the total unemployment rate. The last term is the sum of the e¤ects on the skilled and unskilled workers unemployment rates respectively. As they are both positive for ¯<¯ ¤ , these e¤ects contribute to an increase in the total unemployment rate. In this case, the total e¤ect is thus ambiguous. For ¯>¯ ¤ both unemployment rate decreases, consequently, unemployment decreases. To conclude, we have two distinct cases. When ¯<¯ ¤ ,whathappenswhen the relative number of skilled workers increases is that, although the chance of getting a job in the skilled sector increases, p 1 increases, it is not enough to outweigh the fall in the transition rate into employment in the unskilled sector, p 2 . Hence, the unemployment rates of both skilled and unskilled workers increase. The only positive e¤ect on total employment is the movement of workers from the high unemployment group to the low unemployment group. Furthermore, initially, the employment prospects of an unskilled worker is worse than for a skilled worker. As the unemployment rate of unskilled workers increases more than the unemployment rate of skilled workers, the relative position of an unskilled worker in terms of employment prospects worsen. The larger fraction of skilled workers induces a more unequal unemployment distribution. When ¯>¯ ¤ , the transition rate into sector 2increases, thereby both unemployment rates and total unemployment decreases. Furthermore, the decrease in unemployment for unskilled workers is larger than the decrease in unemployment for skilled workers, inducing a more equal unemployment distribution. However, in this case there will be a larger fraction of skilled workers employed in sector 1. 4.4. Welfare In this section we examine the impact on welfare from an increase in the fraction of skilled workers. Given all workers pay a lump sum tax the government budget constraint is given as: b ( U s +U N )=t¡E 1 S +E 2 S +E N +U S +U N ¢=t: 19 The welfare function is derived to be: W=W 1 S +W 2 S +W 1 N ; where W 1 S =E 1 S y¡V 1 k=p 1 q+p 1 ¤µy¡kqp 1 f¶; W 2 S +W 2 N =E 2 N ay +E 2 S a¯y ¡V 2 k =¤ qp 2 (q+p 1 +p 2 )(q+p 1 )µa¯y ¡kp 2 f(q+p 1 )¶ + ( 1¡¤) p 2 q+p 2 µay ¡kqp 2 f¶; using the government budget constraint to eliminate taxes and unemployment insurance. W 1 S is welfare associated with sector 1 and W 2 S +W 2 N is welfare associated with sector 2. Welfare is increasing in employment and productivity and decreasing in vacancy costs. It can be shown that: W 1 S ¤>W 2 S ¤,W 1 S ¤>W 2 N 1¡¤if p 1 >p 2 (4.3) W 2 N 1¡¤>W 2 S ¤if p 1 >p 2 and ¯<~ ¯(4.4) where ~ ¯>¯ ¤ is dened by the equation: a¯y ¡b ay ¡b=(p 2 +2(q+p 1 )) (p 2 +2q) p 1 +q qµ1+ b ay ¡b¶=0 , = p 1 ( p 1 +p 2 +2q) ( p 2 +2q) q ( p 2 +q) ( p 1 +p 2 +q) ( p 1 +q): The welfare rate concerning skilled workers employed in the skilled sector, sector 1, is the highest. In general the welfare rate concerning unskilled workers is higher than the welfare rate concerning skilled workers employed in sector 2. However, when skilled workers employed in sector 2 have a much higher productivity than an unskilled worker, this higher productivity may compensate for the higher risk of separation connected to this worker and consequently the welfare rate of unskilled workers is less than the welfare rate of skilled workers employed in sector 2. Considering an increase in the relative number of skilled workers, we can show the following: Proposition 4.7. The total welfare e¤ect of increasing the number of skilled workers is ambiguous for ¯<¯ ¤ and positive for ¯¸¯ ¤ . 20 Proof. Di¤erentiating the welfare equation with respect to the fraction of skilled workers, ¤,weobtain: W 1 S ¤+W 2 S ¤¡W 2 N 1¡¤+¤@(W 1 S =¤) @¤+(1¡¤) @(W 2 N =(1 ¡¤)) @¤+¤@(W 2 S =¤) @¤;(4.5) where: @(W 1 S =¤) @¤=dp 1 dp 2 dp 2 d¤µy¡kqp 1 f¡(q+p 1 )p 1 k f¶q (q+p 1 ) 2 ;(4.6) @(W 2 N =(1 ¡¤)) @¤=q ( q+p 2 ) 2 µay ¡kp 2 q f¡(q+p 2 )kp 2 f¶dp 2 d¤;(4.7) @ ( W 2 S = ¤) @¤=q q + p 1 ¡ p 2 dp 1 dp 2 q + p 1 + p 2 ³ a¯y q + p 1 ¡ kp 2 f ´¡p 2 ³ a¯y ( q + p 1 ) 2 dp 1 dp 2 + k f ´ q+p 1 +p 2 dp 2 d¤:(4.8) Using the equilibrium condition equations (2.23) and (2.24) and the equations for wages in equilibrium (see Appendix A), we can show that: @ ( W 1 S = ¤) @¤=dp 1 dp 2 dp 2 d¤ 1 ( q+p 1 ) 2 µbq + ( a¯y ¡b)qp 2 p 2 +2 ( q+p 1 )¶ 6 0for ¯ 5 ¯ ¤ ; @ ( W 2 N = ( 1¡¤)) @¤=bq ( q+p 2 ) 2 dp 2 d¤ 5 0for ¯ 5 ¯ ¤ ; @ ( W 2 S = ¤) @¤= qµb¡p 2 b ( q + p 1 ) 2 + ( 3 ( q + p 1 ) 2 + p 2 ( p 2 +4 ( q + p 1 ) ) ) a¯y ( q + p 1 ) 2 ( p 2 +2 ( q + p 1 ) ) dp 1 dp 2 ¶ ( q+p 1 +p 2 ) 2 dp 2 d¤ 5 0for ¯ 5 ¯ ¤ : Using ¡1< dp 1 dp 2 <0and p 1 >p 2 wecanestablishthat: ¤@(W 1 S =¤) @¤+ ( 1¡¤) @(W 2 N =(1 ¡¤)) @¤+¤@(W 2 S =¤) @¤ 5 0for ¯ 5 ¯ ¤ Hence, the total welfare rate e¤ect is negative for ¯<¯ ¤ and positive for ¯>¯ ¤ . Furthermore the sum of the rst three terms in (4.5) is positive if p 1 >p 2 : W 1 S ¤+W 2 S ¤¡W 2 N 1¡¤>0: Welfare associated with sector 1increases (decreases), whereas welfare associated with sector 2decreases (increases) for ¯<¯ ¤ (¯>¯ ¤ ). The total e¤ect of a larger fraction of skilled workers on the welfare rate, the sum of the welfare rates, is negative (positive) for ¯<¯ ¤ (¯>¯ ¤ ). As welfare associated with sector 1 is higher than welfare associated with sector 2, the movement of people from the group of unskilled workers to the group of skilled workers induces an increase in total welfare. Consequently the e¤ect of YUP on welfare is ambiguous (positive) for ¯<¯ ¤ (¯¸¯ ¤ ) in a way similar to the impact of YUP on unemployment. 21 5. Evaluation In this papers set up, analytic results concerning the e¤ects on total unemployment and welfare from increasing the relative number of skilled workers can not be derived. Consequently, in this section, simulations are carried out in order to determine the total unemployment and welfare e¤ects. In the baseline case, the exogenous variables of the model are set at the following values: a=0:75 b=0:45 y=1 r=0:06 q=0:08 k=0:20 f=0:40 ¤=0:60 The marginal productivity of an unskilled worker is set to 75 percent of the marginal productivity of a skilled worker occupying a skilled job. This value is chosen in order to achieve an unemployment rate dispersion between unskilled and skilled workers in the same order of magnitude as in Denmark in the late nineties. The benet level is set at 0:6ay =0:45, which is in accordance with conditions in Denmark. The relative number of skilled workers in the baseline projection is set at 0:60, which is equal to the level in Denmark in the late nineties. The value of fand the ow cost of keeping a vacancy open are chosen in order to achieve a value of the total unemployment rate in the same order of magnitude as in Denmark in the late nineties. The baseline projection is carried out, assuming that skilled workers are respectively equally, more and less productive when performing unskilled jobs than unskilled workers. The results of the simulations are shown in Table 1 below. ¯=1 ¯=1:25 ¯=0:75 ¤=0:6¤=0:7¤=0:6¤=0:7¤=0:6¤=0:7 p 1 0:8558 0:8590 0:8041 0:8080 0:8969 0:8984 " ¤ p 2 0:5403 0:5077 0:5773 0:5557 0:5092 0:4676 # ¤ U0:0841 0:0798 0:0815 0:0765 0:0866 0:0826 # U s ¤ 0:0542 0:0553 0:0547 0:0554 0:0538 0:0553 " ¤ U n 1 ¡ ¤ 0:1290 0:1361 0:1217 0:1259 0:1358 0:1461 " ¤ U n ¤ ¡ U s 1 ¡ ¤ 0:0748 0:0808 0:0670 0:0704 0:0819 0:0908 " ¤ E 2 s ¤ 0:0313 0:0299 0:0357 0:0347 0:0281 0:0264 # ¤ w 1 s 0:9401 0:9399 0:9437 0:9434 0:9372 0:9371 # w 2 s 0:6320 0:6304 0:7508 0:7491 0:5173 0:5166 # ¤ w 2 n 0:6988 0:6967 0:7010 0:6997 0:6968 0:6938 # ¤ w 1 s ¡w 2 n 0:2413 0:2432 0:2427 0:2437 0:2404 0:2433 " ¤ W 1 s ¤ 0:8832 0:8834 0:8803 0:8805 0:8852 0:8852 " ¤ W 2 s ¤ 0:0156 0:0153 0:0244 0:0240 0:0880 0:0088 # ¤ W 2 n 1 ¡ ¤ 0:6345 0:6304 0:6384 0:6362 0:6306 0:6245 # ¤ W0:7930 0:8182 0:7982 0:8240 0:7886 0:8132 " Table 1 : Simulation results for ¯ =1 ;¯ =0 : 75 ;¯ =1 : 25 . 22 Inthebaselinecasethevalueof¯ ¤ is equal to 1.602. ¯ ¤ is the critical value of the relative productivity of skilled workers performing unskilled jobs. Hence, only if skilled workers are 60 percent more productive in unskilled jobs compared to unskilled workers, the results in Table 1 will be reversed (except the e¤ects on total unemployment, U; and total welfare, W). Inthecasewhere¯=1 , that is, all workers are equally productive when performing unskilled jobs, the total unemployment rate is 8:41%, the unskilled unemployment rate is 12:9% and the skilled unemployment rate is 5:42%.The e¤ects of increasing the relative number of skilled workers from 60 percent to 70 percent is the same in all three cases and is shown in the last column. The e¤ect on the endogenous variables where analytic results were obtained in the previous sections is marked with a *. In all three cases the unemployment rates of both skilled and unskilled workers increase as a result of more workers acquiring skills. Unemployment of the unskilled workers is initially higher than unemployment of the skilled workers and the unequal unemployment distribution worsens. The increased unemployment rates of both worker groups tend to increase the total unemployment rate. However, the negative e¤ect on the total unemployment rate due to the movement of workers from the high unemployment group, the unskilled workers, to the low unemployment group, the skilled workers outweighs the positive e¤ect. Hence, the net e¤ect on total unemployment of YUP is negative. Similar to the unemployment e¤ect, there is a negative and a positive welfare e¤ect. The YUP has a negative impact on the total welfare rate in the economy. However, welfare associated with the skilled sector is higher than the welfare rate associated with the unskilled sector. Hence, moving workers from the group giving rise to the lowest welfare to the group of workers giving rise to the highest welfare, induces an increase in total welfare. Wages of the unskilled as well as the skilled sector decrease. Initially, wages in the skilled sector is higher than wages in the unskilled sector. As the skilled sector wage reduction is very small the unequal wage distribution worsens. As mentioned above the threshold value of ¯is 1.602 in the baseline case. Hence, if skilled workers are 60 percent more productive in unskilled jobs compared to unskilled workers, the analytic results, marked in Table 1 with a *, will be reversed. However, ¯will never reach this level as the upper limit to ¯is given by 1 a =1:333 3. In order to evaluate how likely it is that ¯reaches the threshold value ¯ ¤ , we have changed the parameter values in the baseline projection one by one, until ¯ ¤ is less than the upper limit 1 a . The results are shown in Table 2 below: 23 ¯ ¤ a¯ ¤ U U s ¤ U n 1 ¡ ¤ b ay baseline 1:602 1:201 0:0841 0:0542 0:1290 0:60 f=0:1 1:002 0:752 0:1750 0:1172 0:2620 0:60 b=0:65 1:281 0:961 0:1363 0:0765 0:2259 0:87 a=0:60 1:588 0:953 0:1093 0:0600 0:1832 0:75 k=0:75 1:485 1:114 ¡¡¡0:60 y=0:70 1:273 0:955 0:1597 0:0917 0:2616 0:86 q=0:50 1:296 0:972 0:4524 0:3510 0:6044 0:60 r=0:45 1:312 0:984 0:1206 0:0769 0:1861 0:60 Table 2: Impact on results changing the parameter values one by one. The parameter change as compared with the baseline case is given in the rst column. Note that the upper limit of ¯ ¤ is given by the inequality a¯ ¤ <1. In the baseline projection the restriction is binding. Likewise, the restriction is binding when increasing the ow cost of keeping a vacancy to its maximum (k<min ( a¯y; ay)). The values of unemployment is therefore not shown in this case. In general, inspection of Table 2 leads to the conclusion that in order to have a non-binding restriction on ¯ ¤ the equilibrium values of the unemployment rates have to be very high, especially the unskilled unemployment rate has to be unrealistic high. Decreasing the relative productivity of unskilled workers, a, produces the lowest unemployment rates. However, in this case only if skilled workers are more than 58 percent more productive performing unskilled jobs compared to unskilled workers, the analytic results, marked in Table 1 with a *, will be reversed. The realism of this scenario is doubtful. 6. Conclusion We have analyzed the wage, welfare and distribution e¤ects of YUP by considering an increase in the number of skilled workers, keeping constant the total number of workers. In our set up, where skilled workers search for jobs in both the skilled and the unskilled sector (sector 1 and sector 2), we have shown that the YUP do benet the workers who participated in the programme. However, in terms of unemployment, wages, wage dispersion and welfare, the results depend on the productivity of a skilled worker while employed in the unskilled sector relatively to the separation rate of this worker. This is the case as the skilled worker while performing an unskilled job, search on the job for a skilled job giving him or her a higher wage. Thereby the skilled worker separates more frequently from an unskilled job than the unskilled worker. We derive a condition under which both skilled and unskilled workers are better o¤ or worse o¤ in the sense that their probability of obtaining a job in the 24 dp 2 dp 1 =¡dª=dp 1 dª=dp 2 = ¡³ d¸ N dp 1 ³ ay ¡ w 2 n r + q ¡ a¯y ¡ w 2 s r + q + p 1 ´¡ ( 1 ¡ ¸ N ) r + q + p 1 ³ dw 2 s dp 1 + a¯y ¡ w 2 s r + q + p 1 ´´ d¸ N dp 2 ³ ay ¡ w 2 n r + q ¡ a¯y ¡ w 2 s r + q + p 1 ´¡ ¸ Nay ¡ w 2 n r + q + ( 1 ¡ ¸ N ) a¯y ¡ w 2 s r + q + p 1 p 2 ¡ dw 2 n dp 2 ¸ N r + q ¡ dw 2 s dp 2 1 ¡ ¸ N r + q + p 1 We can show that this slope is greater than ¡1. As shown above the denominator is negative. Hence, if the inequality: d¸ N dp 1 µay ¡w 2 n r+q¡a¯y ¡w 2 s r+q+p 1 ¶¡ ( 1¡¸ N ) r+q+p 1 µdw 2 s dp 1 +a¯y ¡w 2 s r+q+p 1 ¶(C.7) ¡d¸ N dp 2 µay ¡w 2 n r+q¡a¯y ¡w 2 s r+q+p 1 ¶+¸ Nay ¡ w 2 n r + q + ( 1¡¸ N ) a¯y ¡ w 2 s r + q + p 1 p 2 +dw 2 n dp 2 ¸ N r+q+dw 2 s dp 2 1¡¸ N r+q+p 1 >0; holdswehavethat: dp 2 dp 1 jp 2 ( p 1 )>¡1: For ¯<¯ ¤ we have: By use of equation (C.3), (C.6) and (B.1) we know that: µd¸ N dp 1 ¡d¸ N dp 2 ¶µay ¡w 2 n r+q¡a¯y ¡w 2 s r+q+p 1 ¶+¸ Nay ¡ w 2 n r + q p 2 +dw 2 n dp 2 ¸ N r+q>0 And as p 1 >p 2 we have that ³ dw 2 s dp 2 ¡ dw 2 s dp 1 ¡ a¯y ¡ w 2 s r + q + p 1 + a¯y ¡ w 2 s p 2 ´>0. Hence, for ¯<¯ ¤ we have established that: dp 2 dp 1 jp 2 ( p 1 )>¡1: For ¯>¯ ¤ we can show the following: p 2 +2 ( r+q+p 1 ) p 2 +2 ( r+q)<a¯y ¡b ay ¡b<T B p 2 +2 ( r+q+p 1 ) p 2 +2 ( r+q))dp 2 dp 1 jp 2 ( p 1 )>¡1: (C.8) 31 where T B = ¸N ( 1 ¡ ¸N ) p 2+ q + 2 ¸N ( p 2+ r + q ) p 2( p 2+2( r + q )) ¸N ( 1 ¡ ¸N ) p 2+ q ¡ 2 ( 1 ¡ ¸N ) ( r + q + p 1) p 2( p 2+2( r + q + p 1)) >1. The rst inequality in equation (C.8) denes ¯ ¤ and the second inequality denes ^ ¯Hence if ¯<^ ¯where ¯ ¤ <^ ¯, we have established that: dp 2 dp 1 jp 2 (p 1 )> ¡1. D. Appendix D The equations for the change in wage dispersions are: @WD 2 @¤=dw 2 n d¤¡dw 2 s d¤;(D.1) @WD sn @¤=dw 1 s d¤¡dw 2 n d¤;(D.2) @WD ss @¤=dw 1 s d¤¡dw 2 s d¤:(D.3) Sign of @WD 2 @ ¤ We have that @WD 2 @¤=dw 2 n d¤¡dw 2 s d¤=µdx dp 2 ( ay ¡b)¡dw 2 s dp 2 ¡dw 2 s dp 1 @p 1 @p 2 ¶@p 2 @¤; which has the same sign as ¡r+q (p 2 +2(r+q)) 2 (ay ¡b)+ ( r+q+p 1 ) (p 2 +2(r+q+p 1 )) 2 (a¯y ¡b)+dw 2 s dp 1 @p 1 @p 2 : which has an ambiguous sign for all ¯. Sign of @WD sn @ ¤ We have that equation (D.2) is: @WD sn @¤=µdw 1 s dp 1 @p 1 @p 2 + ( a¯y ¡b)@x 3 @p 2 ¡dx dp 2 ( ay ¡b)¶@p 2 @¤; which for ¯<¹ ¯has the same sign as ¡ @p 2 @ ¤ . ¹ ¯is determined by the equation: a¯y ¡b ay ¡b= ( p 1 +2 ( r+q)) ( p 2 +2 ( r+q+p 1 )) 2 2 ( r+q+p 1 ) ( p 2 +2 ( r+q)) 2 : It can be shown that ¯ ¤ <¹ ¯: 32 Hence we the following: @WD sn @¤>0if ¯<¯ ¤ ; @WD sn @¤<0if ¯ ¤ <¯<¹ ¯: Otherwise the sign is indeterminate. 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