Levy-Grant-Schemes in Vocational Education

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1 Levy-Gran-Schemes n Vocaonal Educaon Sefan Bornemann Munch Graduae School of Economcs Inernaonal Educaonal Economcs Conference Taru, Augus 26h, 2005

2 Sefan Bornemann / MGSE Srucure Movaon and Objecve Leraure Revew Smple Model Prvae Opmum Socal Opmum Levy-Gran-Schemes Summary and Conclusons # 2

3 Sefan Bornemann / MGSE Movaon Why sudy levy-gran-schemes for vocaonal educaon? Recen polcy debae o couner lack of apprenceshp ranng n Germany by nroducng a levy-gran-scheme Dscussons on levy-fnanced connuous educaon Incenves schemes for on-he-job ranng n several ndusral counres, e.g. UK, DK, NL, F # 3

Recen polcy debae o couner lack of apprenceshp ranng n Germany by nroducng

4 Sefan Bornemann / MGSE Objecve Economc analyss of levy-gran-schemes Cenral quesons: 1. Why do frms provde cosly apprenceshps ha offer mosly general ranng? 2. Do posve spllovers arse causng under-provson? 3. Can levy-gran-schemes ncrease ranng and mprove overall welfare? # 4

Why do frms provde cosly apprenceshps ha offer mosly general ranng?

5 Sefan Bornemann / MGSE Leraure revew Poachng (Pgou 1912) Non-ranng frms benef by employng sklled workers Posve exernaly under-provson Human capal heory (Becker 1962) Tranng frm does no oban reurns from general ranng. Worker receves full reurns hrough hgher wage. If frm provdes ranng, worker pays by nal wage cu No exernaly ranng effcen # 5

Tranng frm does no oban reurns from general ranng.

6 Sefan Bornemann / MGSE Leraure revew (con d) Emprcally, frms subsanally fnance general ranng. Ne coss of apprenceshps (e.g. Bardeleben u.a. 1994) Human capal heory and mperfec labor markes Frcons reduce wage arbrage Marke wage below margnal produc of ranng frm Rens from employmen provde ranng ncenves Non-ranng frms benef from urnover Posve exernaly under-provson # 6

labor markes Frcons reduce wage arbrage Marke wage below margnal produc of ranng frm Rens

7 Sefan Bornemann / MGSE Leraure revew (con d) Exsng explanaons Asymmerc nformaon (e.g. Kaz/Zderman 1990) Technologcal complemens (e.g. Franz/Soskce 1995) Search frcons (e.g. Sevens 1994) Machng frcons (e.g. Burde/Smh 1996) Labor marke nsuons (e.g. Acemoglu/Pschke 1998) Research gap Polcy assessmen? Formal analyss of ncenve schemes lackng (Franz 1985, Alewell/Rcher 1999, Bosch 2004) # 7

g. Acemoglu/Pschke 1998) Research gap Polcy assessmen?

8 Smple Model Tranng perod Poachng perod Frm offers w o arac workers and rans A + 1 apprences Workers ake job wh hghes ne wage Workforce N + 1 = N Frm offers wage w o arac worke Workers ake job wh hghes ne wage A # 8 Sefan Bornemann / MGSE

wage Workforce N + 1 = N + + 1 Frm offers wage w o arac

9 Sefan Bornemann / MGSE Smple Model Basc se-up Wage compeon n frms, ={1 n}, wh homogeneous echnology v consan margnal produc of labor Frconal labor marke workers evenly dsrbued n a crcular cy workers ncur commung coss δ wh he dsance o work # 9 Tranng perfecly general wh convex coss c (A ) reveals an apprences locaon preference

workers evenly dsrbued n a crcular cy workers ncur commung coss δ wh he dsance o

10 Smple Model Basc se-up (Con d) Ne wage w = w δθ q Labor supply ncreasng n he wage (Labor-lesure-rade-off) N N ( w ) wh > 0 w Apprences parcpaon consran ( ) 0 ρ E w + w a # 10 Sefan Bornemann / MGSE

11 Smple Model Hoellng-Crcle (n=4) q 1 θˆ 1,2 q 4 q 2 q 3 # 11 Sefan Bornemann / MGSE

12 Smple Model Segmen whn Hoellng-Crcle w w w ( q ) δ θ w 1 δ ( q + θ ) w + 1 # 12 Sefan Bornemann / MGSE q ˆ θ, + q Frm Frm +1

13 Smple Model Poachng Perod Arbrage condon for ndfferen worker ( ˆ ) ( ˆ ), , + 1 w δ θ q = w δ q θ Indfferen worker ˆ θ, + 1 q + q w w = 2 2 Frms share of workforce ˆ θ 1, , + 1 ˆ ˆ 1 1 γ = f( θ) dθ = θ θ = + 2w w w ( ), + 1 1, ˆ n 2δ θ # 13 Sefan Bornemann / MGSE

w = 2 2 Frms share of workforce ˆ θ 1, + 1 + 1, + 1 ˆ ˆ 1 1 γ = f( θ)

14 Smple Model Poachng Perod Wage offer problem of frm wages decrease profs wages ncrease share of sklled workforce maxπ w + 1 ( ) = v w γ N Reacon funcons δ n { } 2v w + 4w + 4w 2 = 0 = 1... n # 14 Sefan Bornemann / MGSE

γ N + 1 + 1 + 1 + 1 + 1 Reacon funcons 1 + 1 + 1 1 + 1 1 + 1 1 δ 1

15 Smple Model Poachng Perod Opmal wages Opmal worker shares Opmal profs w = w = v π + 1* + 1* + 1 j γ = γ j = n δ 1 nn δ n = π j = N # 15 Sefan Bornemann / MGSE

1* + 1 j γ + 1 + 1 1 = γ j = n δ 1 nn δ n +

16 Smple Model Tranng Perod Decson problem of frm ( ) δ arg max ρ n nn + v w γn waa c( A) w, A fuure profs presen profs ranng coss foc = v w + δ 4w 1 + 4w+ 1 2 n = w δ 1 = ρ n n+ w = A * a c( A ) 0 0 # 16 Sefan Bornemann / MGSE

profs ranng coss foc = 1 1 1 1 2v w + δ 4w 1 + 4w+ 1 2 n =

17 Smple Model Tranng Perod Equlbrum wage * δ w = v n Tranng condon δ 1 ρ n n reurn o frm ρ δ 1 * n n wa c( A ) δ * 4 n c A + ρ( v ) = ( ) reurn o worker = margnal cos # 17 Sefan Bornemann / MGSE

wa c( A ) + 1 5 δ * 4 n c A + ρ( v ) = ( ) reurn

18 Smple Model Welfare n symmerc case Welfare problem W = profs + ne wages ranng coss W = ρw + W c ( A ) + 1 ( + 1 δ ) + 1 ( + 1 δ ρ ) W = ρ v 4n N + v 4n N c( A) welfare n +1 welfare n Socally opmal ranng ρ = + 1 δ ( v 4n) c( A ) socal reurn from ranng margnal ranng coss # 18 Sefan Bornemann / MGSE

v 4n N c( A) welfare n +1 welfare n Socally opmal ranng ρ = + 1 δ ( v 4n)

19 Smple Model Posve spllovers and under-provson Prvaely opmum ρ ( + n 1 δ δ v ) = c ( A ) 1 * n n 4n Socal opmum ρ ( + 1 δ ) ( v = c ) A 4n Posve exernaly A > A * # 19 Sefan Bornemann / MGSE

20 Smple Model Reurns from ranng Reurn o worker w ( ) ( ρ ) δ R = ρe w = v 4 n Reurn o ranng frm R f = ρ δ 1 n n Prvae reurns ( + 1 n 1 ) δ δ R = R + R = ρ v prv w f n n 4n Socal reurns socal ( + 1 ) δ R = ρ v 4n # 20 Sefan Bornemann / MGSE Posve exernaly δ X = R R = n 1 socal prv ρ n n

R = R + R = ρ v prv w f n n 4n Socal reurns socal ( + 1 ) δ R = ρ v 4n #

21 Smple Model Exernaly c X = R socal n 1 δ ρ n n R = R + R R w prv w f # 21 Sefan Bornemann / MGSE * A A A

22 Incenve Schemes Pgouvan Subsdy c R socal z = n 1 ρ n δ n R prv # 22 Sefan Bornemann / MGSE * A A A

23 Sefan Bornemann / MGSE Exensons Heerogeneous frms Wage heerogeney Hgher ranng n more producve frms Opmal subsdy a funcon of fuure producvy levels Allow for capal nvesmen. Exernaly dsors capal nvesmen. Opmal subsdy also depends on capal nvesmen # 23

24 Levy-Gran-Schemes Basc Idea Frms ranng quoa α Scheme β = A N gran, f α ˆ > α = levy, f α ˆ < α Budge consran leves = grans + admnsrave coss # 24 Sefan Bornemann / MGSE

25 Levy-Gran-Schemes Dealed scheme proposal ( 10 BerASchG) gran = za z ˆ α N A levy = pn + p ˆ α β ( ˆ ) Nz ˆ α α f α > α = p ( ˆ ) N ˆ α α f α < α ˆ α # 25 Sefan Bornemann / MGSE Smplfed Scheme ( ˆ ) ˆ β = Nz α α = zα N + za= τn + za τ

26 Levy-Gran-Schemes Essenally, an employee ax o fnance subsdes Frm s ne paymen β = τn za Budge consran β ( τn za ) 0 = = # 26 Sefan Bornemann / MGSE

27 Levy-Gran-Schemes Decson problem of frm wh scheme ( ) a δ arg max ρ n nn + v w γ N w A c ( A ) + β w, A fuure profs ranng coss scheme presen profs foc = v w + δ 4w 1 + 4w+ 1 2 n 2τ = w δ 1 = ρ n n w = A # a c( A ) 0 0 # 27 Sefan Bornemann / MGSE

28 Levy-Gran-Schemes Equlbrum wage * δ w = v n τ Tax fully shfed ono wages of exsng workforce Tranng condon ρ + = δ 1 # n n z wa c( A ) reurn o frm reurn o worker margnal cos Tranng ncreases n he subsdy A # >A * # 28 Sefan Bornemann / MGSE

29 Levy-Gran-Schemes Governmen s decson problem ( + 1 δ ) + 1 ( δ ) max W = ρ v 4n N (.) + v 4n N (.) c( A) z, τ socal welfare n +1 s.. za τ N = 0 socal welfare n ranng coss τ, z # 29 Sefan Bornemann / MGSE

30 Levy-Gran-Schemes Resuls Ne welfare effec ambguous ( ) 1 ( ) W + δ A δ N w A = ρ v 4n z v 4n c + w τ z = z z= 0 welfare gan from ranng welfare loss from axaon ranng coss 0 Specfable effecs + nernalzes exernaly dsoron from labor ax ( dsoron from unform subsdy) # 30 Sefan Bornemann / MGSE

31 Sefan Bornemann / MGSE Exensons Analyze parcular ncenve schemes (Gasskov 1994). Tranng funds Levy schemes Levy-exempon schemes Dfferences n ax base and subsdy dsrbuon # 31

32 Sefan Bornemann / MGSE Summary and Conclusons In frconal labor markes frms provde and parally fnance vocaonal ranng, vocaonal ranng s underprovded because of posve spllovers on oher frms. Levy-gran-schemes represen ax-subsdy-sysems subsdze ranng by axng presen workforce welfare effecs are heorecally ambguous Gven hgh labor coss, alernave polces warraned # 32

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