Should Firms Be Required To Pay For Vocational Training?

SHOULD FIRMS BE REQUIRED TO PAY FORVOCATIONAL TRAINING?�

Margaret Stevens

Failure in the training market may result from credit constraints and other capital marketimperfections, deterring potential trainees, or labour market imperfections creating externalbene®ts for ®rms. This paper presents a model of a training market affected by both problems,and examines their impact, and the impact of various policy measures, on the welfare ofworkers and ®rms. It is shown that there is a rationale for imposing training costs on ®rms,irrespective of the cause of under-investment. However, training levy schemes in which the levydepends upon the wage bill are shown to address capital market imperfections only.

Policy-makers in several countries have attempted to increase investment invocational training by imposing a training levy on ®rms. In the United King-dom a policy of this type operated between 1964 and 1982. For each of 28industries, an Industrial Training Board was given statutory powers to raise alevy from the ®rms within the industry, and redistribute it in the form of grantsto those ®rms deemed to train their employees to an appropriate level. In1971 France instituted a similar policy requiring employers to spend a certainpercentage of payroll costs on training. The required percentage has graduallybeen raised, standing now at 11

2%, and the system continues to operate withlittle political controversy. In contrast, the very similar Australian TrainingGuarantee Scheme faced strong opposition from employers' organisations andwas suspended in 1994, after only four years.1

The supposed economic rationale for such intervention is that trainingcreates external bene®ts for other ®rms. A ®rm will be deterred from investingsuf®ciently in training because trained workers might leave, and the ®rmwould then be unable to capture the bene®ts. A mechanism is needed toensure that ®rms cannot free-ride by `poaching' skilled labour from other®rms. But this argument has found little favour with economists in recentyears, and few have defended the use of levy schemes.

Perfectly competitive markets ensure optimal investment in training asfollows. Provided that the skills are `general'2 (Becker, 1962) they can betraded in a competitive labour market: a generally-trained worker is paid hismarginal product, and thus receives the full return from the training invest-ment. Moreover, he is fully informed about the expected return, and canborrow at a competitive interest rate in order to ®nance the investment. The

The Economic Journal, 111 ( July), 485±505. # Royal Economic Society 2001. Published by BlackwellPublishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA.

[ 485 ]

� I would like to thank participants in seminars at the Universities of Oxford and Stirling for usefulcomments on an earlier version of this paper, and two anonymous referees for extensive and helpfulsuggestions.

1 See Finegold and Crouch (1994) for discussion of levy schemes in these and other countries.Greenhalgh (1999) describes the current French system in detail. Green et al. (1999) discuss the use oftraining levies and workplace regulation in Korea, Singapore, and Taiwan.

2 Speci®c skills will not be considered in this paper; although investment in speci®c training may besub-optimal (due to a hold-up problem, for example) there are fewer compelling arguments for publicintervention.

decision as to whether to undertake training is his alone; even if training takesplace `on-the-job' the ®rm is involved only passively, as the supplier of thetraining which the worker demands, and the worker pays by accepting lowerwages during the training period. The ®rm will not invest in training, since itcannot obtain a return. But optimal investment follows from the decisions ofrational workers.

There are two principal theoretical explanations for failure in the marketfor vocational training. One is that potential trainees do not invest in trainingbecause of capital market problems: they cannot borrow against humancapital, or insure against associated risks. The second is that the skilled labourmarket is not perfectly competitive, so that the wage is not equal to themarginal product of the worker. Then, both the worker and the ®rm where hetrains may obtain part of the expected return to a training investment, so theywill share the costs. However, if it is possible that the worker will move to analternative ®rm that will pay him a wage below marginal product, thisconstitutes an external bene®t which will lead to under-investment.

These market failure arguments seem to suggest that a training levy can bejusti®ed if the cause of under-investment is an imperfectly competitive labourmarket, but is inappropriate if the problem originates in the capital market. Inthis paper I investigate this proposition, and explore the impact of differenttypes of training policy.

I construct a model of the market for vocational training allowing for bothlabour and capital market imperfections. A policy of requiring ®rms toincrease training expenditure beyond their private choice is a ®rst-bestresponse to under-investment caused by labour market imperfections, and canalso be a second-best response to problems originating in the capital market.While this provides a rationale for imposing training costs on ®rms, a levyscheme does not necessarily have that effect; if the ®rm's liability to train isassessed as a proportion of wages, the scheme acts instead like a trainingsubsidy ®nanced by a tax on wages. I show that such a policy addresses capitalmarket problems only.

1. Explanations for Training Market Failure3

Having demonstrated the absence of external bene®ts to general training,Becker (1962) concluded that under-investment in general skills must be dueto the credit constraints facing trainees. Human capital cannot normally beused as security for a loan. The source of the problem is the asymmetries ofinformation and associated moral hazard that make it infeasible to writecomplete loan contracts. A related problem (Layard et al., 1995; Hamilton,1987) is the uncertainty in the return to a training investment (due, forexample, to shocks to the demand for particular skills), and the lack ofinsurance against such risks.

Becker's analysis presumes that the labour market for generally skilled

3 See Booth and Snower (1996), Bishop (1997) and Stevens (1999) for more extensive discussion.

486 [ J U L YT H E E C O N O M I C J O U R N A L

# Royal Economic Society 2001

workers is perfectly competitive. Stevens (1994; 1996) and Acemoglu (1997)both show that an imperfectly competitive labour market may cause under-investment in training. In Stevens' models the market for skilled workers isoligopsonistic ± due to mobility costs and the nature of the skills, skilledworkers have a limited number of potential employers. Acemoglu's model hasmany employers but search frictions in the skilled labour market. In bothmodels the effect of imperfect competition is that a worker may move aftertraining to an employer who can pay him a wage lower than productivity,although his skills are useful in all ®rms ± training has external bene®ts forthese ®rms, so the incentive to invest in training is too low. This has beendescribed (Booth and Snower, 1996; Stevens, 1996; Booth and Zoega, 1999) asa `poaching externality' (although the term can be misleading, as discussedbelow).

More precisely, the externality arises when training increases the actual orpotential monopsony rents of future employers. Stevens (1996) argues thattraining has this effect because ®rms are differentiated in their skill require-ments and so skilled workers have a reduced set of potential employers.Similarly, in a search market, it may take longer to ®nd an appropriate skilledjob than an unskilled one ± this is the assumption adopted in the modeldeveloped in Section 2 below. In the frictional labour market in Acemoglu's(1997) model, the wage is assumed to be an exogenous fraction of the worker'soutput, so all ®rms obtain higher rents from trained workers.

Acemoglu and Pischke (1999a,b) argue that imperfect competition in thelabour market is a necessary condition for ®rms to invest in `technologicallygeneral' training; with a perfectly competitive labour market, ®rms will notinvest even if trainees are severely credit-constrained (see also Stevens, 1996).Firms have an incentive to invest whenever training `compresses the wagestructure' ± that is, raises productivity more than the market wage. Theysuggest several types of labour market distortion with this feature; in most butnot all of these, training compresses the external wage structure as well as thewage structure in the training ®rm, and hence has potential bene®ts forexternal ®rms.4

One example of wage compression (Chang and Wang, 1996; Acemoglu andPischke, 1998) occurs as a result of an information asymmetry, when outside®rms cannot observe workers' skills or ability. The wage is reduced by adverseselection. Firms obtain no external bene®ts in equilibrium: in this respectthese models differ from the oligopsony and search models. Nevertheless, thelevel of training is too low. At the equilibrium, the worker and ®rm will not

4 As noted above, this is sometimes described as a poaching externality, yet for some of theirexamples, Acemoglu and Pischke suggest that poaching is not a problem, even when the external wagestructure is compressed. They are using the term `poaching' in a stronger sense, to mean the adoptionby ®rms of a strategy of poaching skilled workers instead of training. In Stevens (1994), Chang andWang (1996) and Acemoglu (1997) there is a poaching externality in the weaker sense that investmentin training is too low because workers may (whether or not they do so in equilibrium) move to other®rms who will bene®t from the training, and who might therefore be seen as `poachers'. In equilibriumit can happen (as in Acemoglu, 1997) that all ®rms both invest in training and employ workers trainedin other ®rms.

2001] 487S H O U L D F I R M S B E R E Q U I R E D T O P A Y


increase their investment because if they did so, external ®rms would bene®t.Acemoglu and Pischke demonstrate that this information asymmetry can bebene®cial when no training would otherwise occur because trainees areseverely credit-constrained. By diverting part of the return from worker to ®rm,it gives ®rms an incentive to invest. Other types of labour market imperfectioncan be expected to act similarly.

It is dif®cult to assess the practical signi®cance of the externality problem.There are plausible arguments that training reduces labour market competi-tion, but we have no direct evidence to support them (although the ®ndingthat ®rms do pay for general training (Acemoglu and Pischke, 1998) constitu-tes indirect evidence). Surveys of employers' attitudes to training and poachingare hard to interpret. A ®nding that employers are deterred from providingtraining because they may lose workers to other ®rms is consistent with acompetitive labour market ± it does not necessarily constitute evidence of anexternality. On the other hand a survey by the Confederation of BritishIndustry (1997) found that employers believe themselves to provide trainingwhich is highly transferable, but nevertheless increases the likelihood ofretaining employees by instilling `greater organisational commitment'. TheCBI interpreted this as evidence against a poaching problem, but it doessuggest that training increases the labour market power of employers, in whichcase there may be under-investment due to an externality.

Bishop (1997) discusses other explanations for training market failure:information problems, distortions arising from the tax system, and networkexternalities. However, it is under-investment arising from capital marketimperfections and/or externalities between ®rms that has been the basis ofcalls for large-scale public intervention in the training market (for example,Chapman, 1993; Layard et al., 1995), and which is therefore the focus of thispaper.

The objective is to construct a simple and tractable `supply and demand'model of a training market affected by both types of problem. This can be usedto clarify the differing impact of capital and labour market imperfections ontraining, to examine the interaction between them, and to explore the impactof policy. In particular, the model allows us to analyse the effects of policies onthe welfare of workers and ®rms separately, which (as explained in the nextsection) is not possible in most existing models of training, but is importantfor the political implications of training policy.

2. The Model

Consider a particular skill, which is of potential value to many ®rms. There is acontinuum of workers, initially unskilled and not attached to ®rms, withproductivity normalised to zero, who have identical productive characteristicsbut may differ in their disutility of training. The disutility of the jth worker isD( j) where D9( j) > 0.

Suppose that workers possessing this skill are one of many possible inputs toproduction. There is a continuum of ®rms, differing in technology and the



choice of other inputs. If ®rm i wishes to use this particular skill, it must incuran investment cost E(i), where E9(i) > 0. Thus E(i) is an entry cost to theskilled labour market (although it may be negative, representing a bene®t ofentry). Having incurred this cost, all ®rms have identical production functionsf (Ni) where Ni is the mass of skilled workers employed, and f 9 . 0, f 0 < 0,with constant labour demand elasticity

jåj � ÿ f 9(Ni)

Nif 0(Ni)> 1:

The speci®cation of the technology is unusual, so deserves some comment.The aim is to capture in a simple way5 two possible features of the skilledlabour market which are not present in most training models. First, thedemand for skilled labour may be downward-sloping, so that when skilledworkers are scarce the wage will be higher. Second, heterogeneity in entry costsallows for infra-marginal ®rms to earn rents from training and employingskilled workers. This makes it possible to consider the `welfare' of ®rms,without arbitrarily ®xing the number of ®rms ± otherwise, with homogeneityand entry, all ®rms make zero pro®ts in equilibrium, and are indifferent topolicy decisions.

In general, the welfare of ®rms and workers must depend on the elasticity ofthe entry of each group to the market. Existing models of training assumeeither that the populations of ®rms and workers are ®xed (inelastic), or free(perfectly elastic) entry by one group only, so that the other group necessarilyobtains all the rents. The speci®cation here, with E9 and D9 > 0, is moregeneral and includes free-entry of either group as a special case, although werequire either E9 . 0 or D9 . 0 to close the model.

There are two periods, a training period and an employment period. In the®rst period ®rm i chooses whether to enter, and if so, how many workers totrain. If it trains Ti workers the cost of training is C(Ti): C9 . 0, C 0 > 0.

Unskilled workers are perfectly mobile between ®rms, and will wish to trainin the ®rm where the expected utility of training is highest (provided that netutility is positive after allowing for the disutility of training). This means thatthe training market is effectively competitive. In the second period ®rmscompete for the services of the skilled workers. The skilled labour market isimperfectly competitive: skilled workers care about the non-wage character-istics of jobs, and take time to ®nd a preferred job, and this gives ®rms somewage-setting power. Thus the model has the characteristic of wage-compression(Acemoglu and Pischke (1999a) discussed above): the effect of training is toraise productivity more than the wage.

Workers' decisions are affected by capital market imperfections, which aremodelled very simply, as follows. All agents are risk-neutral, and there is nodiscounting between periods. Firms maximise the sum of expected pro®ts overthe two periods, and can borrow and save at a zero interest rate. Workers

5 The alternative would be a more complete general equilibrium model, with capital and skilled andunskilled labour in the production function, together with heterogeneity of the production functionitself.



maximise the sum of utility, but have no initial resources so must borrow to®nance training, and face an interest rate r > 0 on loans. It is possible toextend the model to allow for the effect of uncertainty on risk-averse workers(Stevens, 1999); the effects of increasing uncertainty on training decisions aresimilar to the effects of increasing r . Here, for simplicity, we represent thedegree of capital market imperfection by the single parameter r .

We will look for a symmetric equilibrium in which every ®rm that enterstrains the same number, T , of workers. The ®rst step is to analyse the skilledlabour market assuming that a mass m of ®rms has entered the market, that®rm k has trained Tk workers, and that all other ®rms have trained T workers.

2.1. The Skilled Labour Market

The labour market is subject to frictions, which give ®rms some market power.At the start of period two ®rm i sets wage W i . Frictions arise because skilledjobs differ in non-wage characteristics, and each worker must search for a jobthat suits him.

We will suppose that the worker knows the wage and non-wage character-istics in the ®rm where he trained, but inspecting an alternative ®rm takes timeç < 1, and all search must take place within a time interval of unit length atthe start of the second period. So the worker takes a random sample ofn � 1=ç alternative ®rms,6 then chooses the best of the n � 1 ®rms available tohim. Thus ç represents the degree of labour market friction. As ç approacheszero the worker samples all ®rms.

The non-wage characteristics of ®rm i are represented by a random variableyi � U[0, h], independent across ®rms, and the worker's utility from a job in®rm i is:

U (W i , yi) � W iyi:

His realisation of yi is independent of the realisation for any other worker. Wechoose h � (n � 2)=(n � 1) to normalise the expected maximum value of yi

in the sample to be one. This means that yi captures the worker's assessmentof the non-wage utility in ®rm i relative to the pleasantest job he can expect to®nd by sampling n � 1 ®rms.

Suppose that ®rm k has trained Tk workers and sets a wage W k , and that allthe other ®rms (except possibly for a set of ®rms of mass zero) have eachtrained T workers and set a wage W . To ®nd the equilibrium wage-settingstrategies we ®rst determine the supply of labour to ®rm k.

Consider a worker who samples ®rm k, and n other ®rms. He prefers ®rm kif W kyk . Wyi for all the other ®rms, i, in his sample. So the probability, P , thathe prefers ®rm k depends on the relative wage wk � W k=W , and is given by:

P(wk) � 1

h

� h

0F n(wkyk)dyk

6 More precisely n � int(1=ç), but for the derivation of the labour market equilibrium we will simplyassume that 1=ç is an integer.



where F is the uniform distribution function. Evaluating this:

P(w) �

ç

1� çw1=ç if w < 1,

ç

1� ç1� 1

ç1ÿ 1

w

� �" #if w . 1:

8>>><>>>: (1)

Firm k is sampled by all the workers that it trained, together with a mass nT ofthose trained in other ®rms ± that is by Tk � T=ç workers. Hence the supplyof labour to ®rm k is:

Nk � P(wk)çTk � T

ç

� �: (2)

The market is monopsonistically competitive: each ®rm faces an upward-sloping labour supply function but its choice of wage does not affect any other®rm. As the search friction ç approaches zero, it can be veri®ed from (1) and(2) that the ®rm's labour supply becomes perfectly elastic at the market wageW . If the ®rm trains the same number of workers as all other ®rms, T , and setsthe market wage, it can expect to recruit T skilled workers. However, traininggives workers a degree of attachment to the training ®rm because they knowthe job characteristics there, but have to search for alternatives. Hence, when çis high, workers trained by ®rm k have a signi®cant effect on its own supply ofskilled labour, but when the labour market becomes more competitive the®rm's hold over its own workers diminishes ± in the limit, all ®rms compete onequal terms for all workers.

It helps to simplify the analysis if we linearise the labour supply functionaround the market wage. The function P(w) given by (1) is continuous, withcontinuous ®rst derivative, so we avoid having to treat the two segments of thefunction separately by using an approximation valid for w close to 1 (that is, inthe neighbourhood of the symmetric equilibrium):

P(w) � ç

1� ç1� 1

ç(w ÿ 1)

� �and hence replacing (2) by the labour supply function:7

Nk � 1� 1

ç(wk ÿ 1)

� �çTk � T

ç� 1

� �: (3)

Now consider the ®rm k's choice of wages. It chooses W k to maximise pro®tsin the skilled labour market, Øk :

Øk � f (Nk)ÿ W kNk

taking the market wage W as given. The ®rst order condition is:

f 9(Nk) � (1� ç)W k (4)

7 This step is convenient because it avoids some additional analysis needed to allow for thediscontinuity in the second derivative of P , but it is not essential for evaluating the equilibrium: withoutit, we obtain the same qualitative results.



where Nk is given by (3). Putting Tk � T and W k � W in (4) gives thecorresponding condition for ®rms that have trained T workers and set a wageW :

f 9(T ) � (1� ç)W : (5)

So, in a symmetric equilibrium in which almost all ®rms have trained Tworkers, the market wage W is determined by (5). If ®rm k has trained adifferent number of workers Tk , it sets a different wage W k determined by (4).Clearly, all ®rms set a wage below marginal product when the search friction çis positive.

2.1.1. The ®rm's private bene®t from training

Consider the effect of the ®rm's own training, Tk , on its second-period pro®twhen wages are optimally chosen, Ø�k (Tk). By the envelope theorem the effectacting through wages disappears, so:

dØ�kdTk

� [ f 9(Nk)ÿ W k]@Nk

@Tk: (6)

The bene®t from training an additional worker is the difference between thewage and the marginal product, multiplied by the probability of keeping theworker after training. At the symmetric equilibrium when all ®rms have trainedT workers:

dØ�kdTk

� ç

1� ç

� �2

f 9(T ): (7)

Clearly the marginal bene®t of training depends on the existence of frictions,and disappears as ç! 0.

2.1.2. The worker's expected utility in the skilled labour market

A worker who has trained in ®rm k samples n other ®rms and works in the onethat gives him highest utility. Let U e

k be his expected utility in the skilledlabour market. At the equilibrium described by (4) and (5):

U ek �

��max(W kyk , Wy)g n(y)g 1(yk)dy dyk (8)

where g n( y) � ny nÿ1=hn is the density function of the maximum of the non-wage characteristics variable in a sample of n ®rms. Evaluating the integral(see Appendix):

U ek �

W

(ç� 1)21� 2ç� ç2w1�(1=ç)

k

h iif wk < 1,

W

2(ç� 1)(1� 2ç)wk � 1

wk

� �if wk > 1:

8>><>>: (9)

At the symmetric equilibrium when all ®rms have trained T workers:



U ek � W � f 9(T )

1� ç: (10)

But if ®rm k trains a different number of workers, this affects the wage there,and hence the worker's utility. Differentiating (9) with respect to W k , and (4)with respect to Tk , we obtain the overall effect of the ®rm's training on theworker's utility. Evaluated at the symmetric equilibrium, this is:

@U ek

@Tk� @U e

k

@W k

dW k

dTk� ÿ ç

1� ç

� �3 f 9(T )

(1� çjåj)T: (11)

So from (10), the worker's expected utility is equal to the equilibrium wage,which approaches the competitive wage as ç! 0. From (11), when ç. 0, theworker would bene®t if the ®rm reduced the number of other trainees, sincethis would raise the skilled wage in that ®rm, and hence his expected utility.

Note that the result that expected utility equals expected wage arises becausethe worker's utility is dependent on the non-wage characteristics of ®rmsrelative to what he can expect given his sample size, so expected non-wageutility does not increase as the sample size increases. Hence frictions do notcause allocative inef®ciency in the labour market. This allows us to focus onthe effects of labour market frictions on training decisions only, and to clarifythe extent to which training policy can improve the outcome given the existenceof frictions ± clearly training policy cannot help to allocate the worker to hisbest job if the worker is unable to inspect all the possible jobs. The alternativespeci®cation, in which the absolute level of non-wage characteristics deter-mines utility, is algebraically more complex but gives the same qualitativeresults.

2.2. The Training Market

In the ®rst period each ®rm that has entered chooses its training programme,then trainees evaluate the training offered by ®rms and decide whether totrain, and if so, where. Speci®cally, ®rm k chooses the number of trainees Tk ,and the price of training Pk . Since the productivity of unskilled workers andtrainees is normalised to zero, this is equivalent to setting a trainee wage of(ÿPk).8

When the number of trainees in each ®rm has been decided, trainees canform an expectation U e

k of their utility in the skilled labour market if they trainin ®rm k. This depends on the wages that they expect each ®rm to set, whichin turn depends on the number of trainees in each ®rm. Workers must borrowto ®nance training, and repay the loan in the second period at interest rate r .

8 Note that we are ruling out training contracts in which the ®rm sets a fee to be paid by the workerif he leaves after training. Such contracts are not normally legally enforceable, although the Britishgovernment did consider changing the law (Employment Department et al., 1992). They can beexpected to reduce the externality problem, but would not, in the present model, eliminate it. In thesecond period, ®rms would make different offers to workers trained inside and outside the ®rm, butthe search friction would still give ®rms some labour market power over workers trained elsewhere.



Hence the net second-period expected utility for any worker choosing to trainin ®rm k is:

uk � U ek ÿ (1� r)Pk (12)

(provided that Pk > 0).9 Since there are many ®rms and workers, and allworkers who choose to train will wish to do so at the ®rm offering the trainingpackage with the highest level of second-period utility, the training market iseffectively competitive. However the ®rms are not price-takers; rather, theymust offer the market level of expected future utility, uk � u.

Hence ®rm k chooses Tk and Pk to maximise its two-period pro®t, subject tothe constraint that the combined effect of these decisions is to provide utilityu. To ®nd the symmetric equilibrium, assume that all other ®rms choose thesame price, P , and quantity, T , giving utility u. Then the problem for ®rm k is:

maxPk ,Tk

Ø�(Tk)� PkTk ÿ C(Tk) subject to U ek ÿ (1� r)Pk � u: (13)

The ®rst-order condition is:

dØ�dTk

� Pk ÿ C9(Tk)� Tk

1� r

@U ek

@Tk� 0 (14)

where dØ�=dTk and @U ek=@Tk are given by (7) and (11). In equilibrium

Tk � T and Pk � P so the ®rm's optimal choice satis®es:

P ÿ C9(T )� ç

1� ç

� �2

f 9(T )ÿ ç3

(1� r)(1� ç)3(1� çjåj) f 9(T ) � 0: (15)

On the demand-side, the expected future utility for trainees is:

u � f 9(T )

1� çÿ (1� r)P

(P > 0) and workers will wish to train if their individual disutility of training isless than u. In equilibrium, when m ®rms each train T workers, the disutilityof the marginal worker equals u:

f 9(T )

1� çÿ (1� r)P � D(mT ): (16)

Finally, ®rms enter the market until the two-period pro®t is zero for themarginal ®rm:

f (T )ÿ f 9(T )

1� çT � PT ÿ C(T ) � E(m): (17)

Equations (15) and (16) can be regarded as the ®rm's supply function and themarket demand function for training, although some care is required in this

9 In the following analysis we ignore the case in which the equilibrium price set by ®rms is strictlynegative. This is straightforward to analyse, but occurs only if both labour and capital marketimperfections are very high.



interpretation since it is utility, not price, that is taken as given by ®rms. Thenumber of ®rms, and hence market supply, is determined by (17).

Consider now the effects of capital and labour market frictions on the supplyand demand for training. Looking ®rst at the supply function (15), note thatwhen ç � 0 the ®rm supplies training at marginal cost. As in Stevens (1996)and Acemoglu and Pischke (1999a), when the labour market is competitive®rms will not invest in training even if workers are credit-constrained (r . 0).The third term in (15) represents an increase in training supply due to labourmarket frictions (ç. 0). The ®rm will ®nance part of the cost of trainingbecause it has a positive probability of keeping the worker at a wage belowmarginal product.

There is a secondary, negative, effect of ç on training supply, represented bythe fourth term in (15). In the presence of frictions, a ®rm that reduces thequantity of training below that of its competitors raises the expected wage of itsworkers and hence the price that trainees will pay. Thus labour marketfrictions give ®rms some derived power in the training market, tending toreduce training supply. This effect is most severe when there is a perfect capitalmarket (so that trainees are able to pay more), but is always outweighed by theprimary effect ± that is, the sum of the third and fourth terms in (15) ispositive. But it means that in the presence of labour market frictions, creditconstraints do tend to increase the supply of training.

The effects of capital and labour market imperfections on the demand fortraining (16) are more straightforward. Credit constraints reduce demandbecause they raise the effective price. Labour market frictions reduce theexpected bene®t for trainees, and hence demand.

In summary, imperfections in capital and labour markets increase the ®rm'ssupply of training and reduce market demand. In the next section we examinethe overall effect on equilibrium training and welfare, allowing also for theentry decisions of ®rms.

2.3. Welfare and Comparative Statics

The demand function (16) and supply functions (15) and (17), togetherdetermine the equilibrium number of trainees per ®rm, T�(r , ç), the numberof ®rms m�(r , ç), and the price of training.

The welfare of ®rms and workers at the market equilibrium is representedby producer surplus and `worker surplus' respectively:

Ù f (m�) ��m�

0[E(m�)ÿ E(i)]di, (18)

Ùw(m�T�) ��m�T�

0[D(m�T�)ÿ D( j)]dj : (19)

Ùf and Ùw are increasing functions of m� and m�T� respectively.



2.3.1. First-best outcome

If there is perfect competition in the labour and capital markets, (r � ç � 0),we have the ®rst-best training outcome:

f 9(Tf )ÿ C9(Tf ) � D(mf Tf ),

f (Tf )ÿ C(Tf ) � TD(mf Tf )� E(mf ), (20)

P � C9(Tf ); W � f 9(Tf ):

Workers pay the full marginal cost of training, and reap the full return in theform of enhanced wages.

2.3.2. Comparative statics: labour market imperfections

Differentiating (15) to (17) with respect to ç (see appendix A.2.) gives:

If r � 0,@(m�T�)

@ç, 0;

@m�@ç

is ambiguous: (21)

For r sufficiently high,@(m�T�)

@ç. 0 and

@m�@ç

. 0: (22)

With a perfect capital market (or for small r , by continuity), labour marketfrictions decrease the quantity of training. They decrease demand and increasesupply, but the decrease in demand always dominates the increase in supply.The intuition is simple: frictions reduce the wage, raising the return to trainingfor ®rms and lowering it for workers. But a worker loses whether or not hechanges ®rm after training, whereas his training ®rm gains only if the workerstays, which he does with probability less than one. In other words, there is anexternal bene®t to outside ®rms. The overall effect on ®rm welfare is ambig-uous: they lose from the decline in the supply of skilled workers, but gaindirectly from the lower wage.

However, (22) shows that labour market imperfections can bene®t bothworkers and ®rms, by mitigating the effects of capital market problems. Whendemand for training is already low because of credit constraints, an increase infriction and consequent reduction in the wage has little effect on demand.Then the increase in supply outweighs the fall in demand, and the overalleffect on training is positive.

These results illustrate the discussion of employers' attitudes in Section 1above. It is when labour market frictions are high that employers are notdeterred from paying for training by the fear of losing the trained workers.The employer does not perceive training as a problem (although correspond-ingly he may perceive a dif®culty of recruiting skilled workers). So frictionsincrease supply. But, if there are no credit constraints, the increase in supply isalways outweighed by a fall in demand, so the overall effect of frictions is toreduce equilibrium training. The joint return to training for the ®rm and thetrainee falls, because some of the bene®t accrues to external ®rms. On theother hand, when demand is already low due to capital market imperfections,



the net effect of labour market frictions can be positive. There is still anexternality ± investment in training is lower than it would be if the bene®ts toother ®rms were taken into account ± but there is more training than wouldoccur without frictions.

2.3.3. Comparative statics: capital market imperfections

Similarly, differentiating (15) to (17) with respect to r gives (see appendixA.3.):

@(T�m�)@ r

, 0 and@m�@ r

, 0 provided that C9(T�) .ç

1� ç

� �2

f 9(T�): (23)

When there are no labour market frictions, credit constraints decrease trainingin the obvious way: they reduce demand and have no effect on supply. Inthe presence of frictions credit constraints also increase supply (by limiting the®rm's incentive to exploit the worker's future attachment and push up theprice); however (23) tells us that the decrease in demand normally dominates,reducing training. Speci®cally, it states that credit constraints cannot increasethe welfare of ®rms or workers unless labour market frictions are so high, andthe equilibrium quantity of training per ®rm is so low, that the second-periodmarginal private bene®t to the ®rm of training a worker is greater than themarginal cost of training.

2.3.4. Summary of the effects of labour and capital market imperfections

Labour market frictions reduce the demand for training and increase thesupply. With a perfect capital market the demand effect dominates. Whentrainees are credit constrained the effect on demand is smaller, so that labourmarket imperfections may increase training and the welfare of both workersand ®rms.

Credit constraints reduce the demand for training. In the presence of labourmarket frictions they can have a positive effect on supply; however the supplyeffect is likely to be small, and the overall effect of credit constraints istherefore to reduce training and welfare.

Finally in this section, note that although increases in ç or r can sometimesincrease training, the equilibrium total quantity m�T� is always lower than®rst-best in the presence of either type of imperfection. An outline proof isgiven in the appendix.

3. Policy

Consider a policy-maker who wishes to mitigate the effects on training oflabour and capital market imperfections. His objective is to raise the welfare of®rms and/or workers. In this section, we use the model developed in Section 2to look ®rst at the effects of regulating the training offered by ®rms, and then



at the use of subsidies; ®nally, we examine the impact of a training levyscheme.

3.1. Regulation of Firms' Training

Suppose that the policy-maker can set the amount of training in each ®rm thatenters the market for skilled labour. We will assume that he does not regulateskilled or trainee wages: these will be determined in the markets. He sets Tsubject to the training demand function (16) and the entry condition for ®rms(17), over-riding the ®rm's supply function (15). Eliminating price from (16)and (17), the policy-maker's constraint is therefore:

E(m)� TD(mT )

1� r� f (T )ÿ C(T )ÿ WT 1ÿ 1

1� r

� �where W � f 9(T )

1� ç:

(24)

From (18) and (19):

dÙ f

dT� mE9(m)

dm

dTand

dÙw

dT� mTD9(m) m � T

dm

dT

� �, (25)

from which it is clear that the optimal level of T for workers is higher than theoptimal level for ®rms. Differentiating (24) gives:

1

m

dÙ f

dT� 1

m(1� r)

dÙw

dT� f 9(T )ÿ C9(T )

ÿ W � TdW

dT

� �1ÿ 1

1� r

� �ÿ D(mT )

1� r(26)

which represents the constraint on the policy-maker's ability to raise welfare bysetting T . Evaluating the right-hand side of (26) at the private optimum(T�, m�) we obtain:

1

m

dÙ f

dT� 1

1� r

dÙw

dT

� ��T�T�m�m�

�ç f 9(T�)(1� ç)2

� ç3 f 9(T�)(1� ç)3(1� r)(1� çjåj)

ÿ TdW

dT1ÿ 1

1� r

� �: (27)

The three terms in (27) represent three positive effects on welfare of raisingtraining above the ®rms' private choice. The ®rst term represents the gain,when there are labour market frictions, from internalising the bene®ts oftraining to other ®rms. This is the difference between wage and marginalproduct, multiplied by the probability that the worker will move to a different®rm. The second term is the gain from preventing ®rms from trying to raisetheir own training price by reducing training relative to other ®rms. This termis most signi®cant when ç is high and r is low.

The third term is a price effect. When the number of trainees rises theskilled wage falls, bene®ting ®rms. With a perfect capital market this would be



exactly offset by a fall in the price trainees are prepared to pay. But whentrainees are credit-constrained there is a smaller effect on the price, leading toa net increase in welfare.

Clearly the distribution of welfare gains between ®rms and workers dependson the elasticity of supply of ®rms and trainees to the market, E9 and D9respectively. In the case of a perfectly elastic supply of trainees, for example,trainees obtain no surplus, and the ®rms obtain all of the bene®t of the policy.

From (25) we can see that if ®rm welfare rises, worker welfare does so too.Hence a rise in Ùf is necessary and suf®cient for a Pareto improvement.Rewriting (27):

dÙ f

dT

��T�T�m�m�

�sgn ç f 9(T�)(1� ç)2

� ç3 f 9(T�)(1� ç)3(1� r)(1� çjåj)

ÿ TdW

dT1ÿ 1

1� r

� �ÿ mTD9(mT )

1� r: (28)

Firm welfare rises provided that the three gains identi®ed above are not offsetby the last term in (28), which is the increase in utility that is required toattract further trainees into the market. If r is high and/or the disutility oftraining does not increase much at the margin, then this term is small and wehave a Pareto improvement.

The last two terms of (28) may be combined as follows:

dÙ f

dT

��T�T�m�m�

�sgnç f 9(T�)(1� ç)2

� ç3 f 9(T�)(1� ç)3(1� r)(1� çjåj)� T

dP

dTÿ dW

dT

� �(29)

where P is the demand price of training de®ned by (16). From this formula-tion, we can say that a suf®cient condition for a Pareto improvement is that thefall in the skilled wage is greater than the rise in the trainee wage.

Note that ®rms may gain from being required to increase the supply oftraining above their private choice, even when the cause of the problem is inthe capital market ± when it is the trainees who are investing too little. Theintuition is as follows. Credit constraints ¯atten the training demand function.Trainees will not pay a high price for training, but when the price is low manyworkers are willing to train without the need for further price reductions.Hence, ®rms can gain collectively from raising training if the improvement inthe supply of skilled labour (the fall in the wage) outweighs the fall in the priceof training along the demand function. Firms cannot act individually toincrease training because they would lose trainees to other ®rms.

Clearly this policy cannot achieve the ®rst-best outcome (Tf , mf ) whenr . 0 ± it cannot prevent some dissipation of welfare in the imperfectlycompetitive capital market. When r � 0, the ®rst-best outcome does lie on thepolicy-maker's constraint (24) and maximises the sum of worker and ®rmwelfare; however, the policy optimum depends on the relative weight assignedto the welfare of ®rms and workers.

In summary, if there is signi®cant under-investment due to labour and/or



capital market imperfections, a policy of requiring ®rms to ®nance an increasein training will produce a Pareto improvement, provided that the supply oftrainees is not too steeply sloping. If the supply of trainees is inelastic, theremay be a transfer of welfare from ®rms to workers.

3.2. Subsidy

3.2.1. A subsidy ®nanced by taxing ®rms' pro®ts

It is straightforward to see that this is exactly equivalent to the policy ofregulation analysed in the previous section. The policy-maker can over-ride the®rm's supply decision either directly, by regulating the quantity, or indirectlyby manipulating the incentive to train.

3.2.2. A subsidy ®nanced by taxing wages

Suppose that the policy-maker gives a subsidy sP , where P is the price paid to®rms, so that (1ÿ s)P is paid by trainees, and sets a tax on skilled wagessuf®cient to raise the required revenue at the new equilibrium. This changesthe demand function (16) to:

f 9(T )

1� çÿ [1� r(1ÿ s)]P � D(mT ) (30)

(provided that 0 < s < 1) with no effect on the supply equations (15) and(17). Clearly this is equivalent to reducing the interest rate on loans to workers;with s � 1, the policy-maker can fully release the credit constraints. With thevery simple model of capital market imperfections used here, this policymimics the operation of a perfect capital market.

However, it can do nothing to mitigate under-investment due to labourmarket imperfections. This result is not model-speci®c: a training subsidy®nanced by a tax on skilled wages simply redistributes the worker's incomeacross periods. With a perfect capital market this would have no effect at all,since the worker could redistribute income costlessly himself by borrowing orsaving. In general, the best that can be done via such a policy is to boostdemand to the level that would occur with a perfect capital market. A highertax and subsidy would simply induce workers to save.

From the comparative statics results of 2.3.3 we can see that, at the privateequilibrium, reducing the effective interest rate r facing workers would in-crease the welfare of both ®rms and workers, except possibly when ç is highand r is already low.

3.3. A Training Levy Scheme

In a training levy scheme the policy-maker sets the level of resources that the®rm is required to spend on training. At ®rst sight this appears to be equivalentto regulating training. However (in the schemes instituted in the United



Kingdom, France, and other countries) the ®rm's liability to spend on trainingis assessed as a proportion of its total wage bill. Assuming that all employeesare affected equally, the effect is that each employee receives some subsidisedtraining, ®nanced by a proportional tax on his own wages spread over thewhole period of employment. We have analysed this policy in Section 3.2.2: asubsidy ®nanced by taxing wages affects the demand function and not thesupply function, and alleviates under-investment due to capital market imper-fections only. Thus, if operated in this way, a levy scheme does not address theproblem of external bene®ts to other ®rms arising from labour marketfrictions; for this, training liability should depend on pro®ts, not wages.

3.4. Policy Conclusions

The above analysis clari®es the important distinction between two types ofpolicy: demand-side policies (such as loans to trainees, and training subsidies®nanced through wage taxation) which affect the demand function only, andsupply-side policies (taxation of pro®ts, or regulation) affecting the trainingsupplied by ®rms. Demand-side policies can only alleviate capital marketproblems, in which case they will normally increase the welfare of both workersand ®rms. Supply-side policies are ®rst-best only for problems arising in thelabour market, but can raise welfare irrespective of the source of under-investment. They deliver a Pareto improvement if the supply of potentialtrainees is suf®ciently elastic; otherwise there may be a transfer of welfare from®rms to workers.

Perhaps surprisingly, training levy schemes (as normally operated) are ademand-side policy, effective only against capital market problems. Previousdiscussion of training levies in the economics literature has supposed preciselythe opposite: that they are an inappropriate intervention if capital marketimperfections are the main source of training market failure (Lees andChiplin, 1970; Layard et al., 1995) but can be justi®ed when there areexternalities between ®rms (Jones, 1988; Chapman, 1993; Booth and Snower,1996; Stevens, 1996).

The present model does not allow us to make distinctions between differenttypes of demand-side and supply-side policy. To go further, we would need amore detailed model of the source of capital market imperfections: forexample, if trainees' decisions are affected by risk and uncertainty loans maynot be equivalent to a subsidy ®nanced through wage taxation. Perhaps moreimportantly, we should allow for the limited information available in practiceto the policy-maker, which will affect his ability to redress capital marketproblems, and his choice between taxation and regulation of ®rms.10 Whenimplementing any policy designed to raise the level of training the policy-maker faces a monitoring problem to ensure that the resultant training is of anappropriate quantity and quality.

10 Here, the issues are similar to those arising in environmental policy, as in the classic treatment ofWeitzman (1974).



Should ®rms be required to pay for vocational training? The model allows usto draw the following conclusions. First, if, due to labour market imperfections,training allows ®rms to earn signi®cant rents from the employment of skilledworkers, it is appropriate to make ®rms bear higher training costs (by, forexample, taxing pro®ts). Second, imposing training costs on ®rms could be asecond-best policy, raising the welfare of ®rms and workers, even when thecause of underinvestment lies in the capital market. Third, contrary toappearances, training levy schemes do not `make ®rms pay' ± they affect thedecisions of trainees, not ®rms. But if, in spite of this, the question isinterpreted as meaning `Are levy schemes a good idea?' we can say that theycould be an appropriate response to under-investment arising from capitalmarket imperfections, whose effectiveness in practice should be comparedwith other demand-side policies such as loans.

Nuf®eld College, Oxford

Date of receipt of ®rst submission: March 1999Date of receipt of ®nal typescript: November 2000

Appendix

A.1. Derivation of (9):

Equation (8) can be written:

U ek

W� wk

��wk x . y

xg n( y)g 1(x)dy dx ��

wk x , y

yg(y)dy dx:

When wk < 1 this is:

U ek

W� wk

� h

0xg 1(x)

�wk x

0g n(y)dy

� �dx �

� h

0g 1(x)

� h

wk xyg n( y)dy

" #dx

� n

h n�1

� h

0wk x

�wk x

0y nÿ1dy �

� h

wk xyn dy

!dx:

Evaluating this, using h � (n � 2)=(n � 1), gives the ®rst line of (9). For wk > 1 thecalculation is similar, but we integrate in reverse order (with respect to x ®rst, then y).

A.2. Comparative statics for ç

Equilibrium is determined by (15), (16) and (17). Using (15) de®ne the supply price:

Ps(T , r , ç) � C9(T )ÿ ç

1� ç

� �2

f 9(T ) 1ÿ á

(1� r)

� �where á(ç) � ç

(1� ç)(1� çjåj) :

Differentiating (16) and (17), after substituting P � Ps, gives:



A@T

@ç� T 2 D9

@m

@ç� ÿ Tf 9(T )

(1� ç)2[1ÿ (1� r)ã]

B@T

@çÿ E 9(m)

@m

@ç� ÿ Tf 9(T )

(1� ç)2(1ÿ ã)

where:

A � (1� r)T@Ps

@Tÿ Tf 0(T )

1� ç� mTD9 . 0

and

B � T@Ps

@Tÿ Tf 0(T )

1� ç� â f 9(T ) . 0;

â(ç, r) . 0; ã(ç, r) � á

1� rf[2(1� r)ÿ 3á](1� çjåj)� áçjåj(1� ç)g:

Solving:

@m

@ç�sgn

A(1ÿ ã)ÿ B[1ÿ (1� r)ã],

@(mT )

@ç�sgn

(A ÿ mTD9)T (1ÿ ã)ÿ (BT � mE9)[1ÿ (1� r)ã]:

It can be veri®ed that 0 , ã, 1, and that for r suf®ciently large, 1ÿ (1� r)ã, 0.These expressions can then be signed for the cases r � 0 and high r .

A.3. Comparative Statics for r

Similarly:

A@T

@ r� T 2 D9

@m

@ r� ÿKT

where

K (T , ç) � C9(T )ÿ ç

1� ç

� �2

f 9(T ),

and

B@T

@ rÿ E 9(m)

@m

@ r� ÿT

@Ps

@ r. 0:

Solving:

@m

@ r�sgn

A@Ps

@ rÿ BK

and

@(mT )

@ r�sgn

(A ÿ mTD9)T@Ps

@ rÿ (BT � mE9)K

and K . 0 is suf®cient for both derivatives to be negative.



A.4. To prove that m�T�, mf Tf

Introduce another parameter, t 2 [0, 1], into the supply function:

Ps(T , r , ç) � C9(T )ÿ ç

1� ç

� �2

f 9(T ) 1ÿ tá

(1� r)

� �and consider the equilibrium m�T�(r , ç, t). As in A.2., it is straightforward to showthat

@(mT )

@ t, 0 8r , ç:

Also, when t � 0, A.2. and A.3. can be modi®ed to show

@(mT )

@ r, 0 8ç,

and when r � 0,

@(mT )

@ç, 0:

Applying these results:

m�T� � m�T�(r , ç, 1) , m�T�(r , ç, 0) , m�T�(0, ç, 0) , m�T�(0, 0, 0) � mf Tf :

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Should Firms Be Required To Pay For Vocational Training?

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