Topic 3 - Empirical and policy aspects of demand for labourProfessor Christine Greenhalgh

P Cahuc and A Zylberberg (2004) Labor Economics, Chapter 4: Labor Demand, part 2.Griliches, Z., 1969. Capital–skill complementarity. Review of Economics and Statistics 51, pp. 465–468.T Boeri and J van Ours (2008) The Economics of Imperfect Labor Markets, Chapter 2: Minimum Wages. A Manning (2003) Monopsony in Motion, Chapter 12: The Minimum Wage and Trade Unions.H Robinson (2002) ‘Wrong side of the track? The impact of the minimum wage on gender pay gaps in Britain’, Oxford Bulletin of Economics and Statistics, Vol. 64 (5), December.

Demand for labour input – maximising profit by minimising costs of production π(Y) = P(Y).Y - C( W, R, Y) P = price of output (can vary with output if not perfectly

competitive output market);Y = level of output chosen to maximise profit; W = wage per unit of employment; R = cost per unit of capital KProfit maximising output is where price equals a mark-

up factor times marginal cost of productionSize of mark-up depends on output price elasticity

Mark-up = 1 if product market is perfect competitionMark-up is > 1 if imperfect competition

Optimal combination of inputs is when each factor is used so that its marginal productivity equals the profit mark-up times its factor cost

Derivation of an empirical demand function for labour (1)

• Decide on production function (summary of technological possibilities) against which firms have to maximise profits

• Specify nature of product and factor markets to decide whether prices are seen as constant (competitive) or changing with quantities (not competitive)

• Write down conditions for max. profits and derive the demand for labour

• Examples of production functions are Cobb-Douglas (considered restrictive as σ =

1) CES (constant elasticity of factor substitution but with values of σ other than 1)

• This approach permits estimation of unconditional demand for labour (any output may be chosen)

Derivation of an empirical demand function for labour (2)

• Alternative approach avoids choice of specific production function and specifies directly a cost function

• Cost function has to have properties considered reasonable for case of cost minimisation in choice of inputs for a given output

• Examples given in Cahuc and Zylberberg are Leontief & Translog functions

• These cost functions permit the elasticity of substitution to vary with wages and with share of input in total costs

• The cost function approach permits estimation of the conditional demand for labour, given a known level of desired output

Elasticity of demand for labour L = f (W, R) or L = f (W, R, Y)

ηLW = unconditional elasticity: how much does demand vary if wage rate changes

and choice of profit maximising output also changes?

ηLW|Y = conditional elasticity: how much does demand vary if wage rate changes but output is kept constant?

Conditional elasticity reflects the possibility of factor substitution between inputs of capital and labour

ηLW = ηLW|Y + ηLY.ηYW

Unconditional ηLW is sum of substitution and scale effects

Scale effect is multiple of output elasticity of demand for labour and elasticity of output w.r.t. the wage rise

Empirical values for demand elasticitiesCahuc & Zylberberg quote Hamermesh (1993)

Unconditional ηLW = 1.0

Conditional ηLW|Y = 0.3

It can also be shown that:

ηLW|Y = - (1- s) σ

where s is share of labour in total cost and σ is the elasticity of substitution of labour and capital

Given conditional elasticity of 0.3 and known share of labour of 0.7 in most advanced countries thenelas. of substitution σ = 1.0

Implications of these estimates• Unit value of unconditional elasticity implies the

wage bill is constant along the demand curve• This suggests a fairly large rate of trade-off

between jobs and wage rises for union bargaining (in right to manage model)

• Large trade-off for government with imposition of minimum wages in competitive markets

• Large difference between conditional and unconditional elasticity means that the scale effect is a significantly big component of the adjustment to any wage cost increase

• Unitary elasticity of substitution means that Cobb-Douglas production function is an acceptable approximation for analysing aggregate production

Adjustments in the short and long run with asymmetric costs

Distinguish between no. of workers and hours per worker in labour demand

• Changing employment incurs hiring or firing costs (which are not equal, thus asymmetric)

• Changing hours of work incurs payment of overtime hours or compensation for short time

Distinguish between workers on permanent contracts and those on temporary contracts

• Temporary workers generally have lower claims to redundancy pay

• Some temporary workers are hired at higher hourly rates e.g. agency staff

Empirical evidence on adjustment• Over the business cycle hours per worker adjust

more than no. of workers => labour hoarding• This phenomenon reflects higher adjustment

costs for workers than for hours• In the US: hiring costs > firing costs• In France: firing costs > hiring costs• Net impact on jobs/unemployment of rise in

hiring and firing costs is difficult to estimate:– Rise in hiring costs is expected to reduce

demand for workers– Rise in firing cost encourages labour hoarding– Expected profit per worker is reduced by

increase in firing costs so this reduces hiring

Relative adjustment rates for temporary and permanent staff

Evidence for Spain: Benito and Hernando in Oxford Bulletin Econ. Stat. 70(3) June 2008

Data 1985-2001 - rapid rise in share of temp. staff from 9% mid 80s to 20% by 2001

• Wage elasticity of demand all workers = - 0.4• Wage elasticity for permanent workers = - 0.0• Wage elasticity for temporary workers = - 2.1 • Output elasticity of demand all workers = 0.18• Output elasticity for permanent workers = 0.11• Output elasticity for temporary workers = 0.63

Capital-skill complementaritySource: Griliches 1969

Divide workers into two types –

skilled S and unskilled N

As before capital K has price of R

Wage of skilled worker is Z, unskilled is W

How do relative demands for skilled and unskilled change if W, Z or R change?

Hypotheses: σNK > σSK as the unskilled are

more easily substituted for capital than skilled

and

σKN> σSN as capital is more easily substitutable

than is skilled labour with unskilled

Empirics of capital-skill complementarityGriliches shows that the relative demands for

factors can be expressed by the following two functions:

(1) S/N = f (W/Z, R/Z)with signs of coefficients +ve and –ve

Rise in W/Z causes normal relative price effect (switch to cheaper substitute)

Rise in R/Z shows bigger switch from K to N than from K to S, so S/N falls

(2) S/K = f (W/Z, R/Z)with signs of coefficients –ve and +ve

Rise in W/Z causes bigger switch between K and N than between S and N, so S/K falls

Rise in R/Z gives normal relative price effect

Estimates and implications of capital-skill complementarity

• Griliches’ estimates using two databases for the US in 1950s and 1960s confirm the signs of all four coefficients

What are the implications?• Suppose capital becomes cheaper through time,

for example due to innovation in producer durables, then R/Z falls

• In (2) this will cause production to become more capital intensive even relative to skilled workers

• But in (1) this will cause the demand for skilled workers to rise relative to the demand for unskilled workers

• See next lecture for more on this topic

Theory - Minimum wages, labour demand and supply

Competition v. Monopsony • Minimum wages (MW) in perfectly competitive labour markets -

face immediate trade-off of jobs and wages along the demand curve

• Under Monopsony (or Oligopsony) standard model shows can be some increase in employment instead(MW creates horizontal supply curve with constant MC)

• To maximise employment under Monopsony MW is set at the competitive market wage

• Any higher MW faces trade-off along demand curveAdditional theory relating to labour market frictions • Reactions to rise in wage can be increased labour supply, more

intensive job search and a fall in turnover• Also efficiency wage theory suggests rise in productivity of

those in work leading to higher employment

Employment as minimum wage rises

Employment

On Supply Curve On Demand Curve

Minimum Wage = Minimum Wage = Minimum WageMonopsony Wage Competitive Wage  

Empirical studies of effects of minimum wages (quoted in Boeri and van Ours)

• UK – Stewart Economic Journal (2004) found no adverse effects on low wage employment

• Problem that his study was too early? (UK MW was set at very low rates in 1999-2001)

• US – Card and Krueger AER (1994) compared workers in fast food in New Jersey and Pennsylvania

• Found NJ employment in these establishments rose when MW was increased in this state

• Suggests there was monopsony despite rapid turnover in this sector (or efficiency wage effect reduced turnover)

• EU – Dolado et al. Economic Policy (1996)• Mainly found negative effects on employment • Effects in Europe worse for young people

Minimum wages in G5 countries (2005)Note - Germany has no national minimum wage Approx. 70% of its workers are covered by wages set in collective bargaining agreements In all four countries in table MW coverage is 100%

Country Minimum Wage to Average Production Worker’s Wage (%)

Min Wage per hour in Euros

(PPP exch. rates)

France 52 7.51

Japan 40 4.15

UK 39 6.40

US 31 3.48

UK National Minimum Wage- rates since 1999

Age group   22+yrs      18-21yrs    16-17yrs

Apr-99       £3.60          £3.00          noneJun-00       £3.70          £3.20          noneOct-01       £4.10          £3.50          noneOct-02       £4.20          £3.60          noneOct-03       £4.50          £3.80          noneOct-04       £4.85          £4.10          £3.00Oct-05       £5.05          £4.25          £3.00Oct-06       £5.35          £4.45          £3.30Oct-07       £5.52          £4.60          £3.40Oct-08      £5.73       £4.77        £3.53

•  

Changes in Minimum Wage rates

Age group   22+yrs      18-21yrs    16-17yrs∆ 99-08 59% 59%

∆ 99-04 35% 37%∆ 04-08 18% 16% 18% 

Adjusting for inflation –Real rise since 1999 in Adult Min Wage is +31%Next increase is due 1st October 2009 Announcement expected in week of 11th May

Questions for policy now• Having raised MW by > 30% in a decade should its

real rate remain constant now?• Index linking could avoid MW rising above the

competitive wage for low-paid workers• In the present severe recession has the competitive

real wage fallen? (Seems likely)• If so should the real value of MW be reduced to

maximise employment?• Might be sensible to keep nominal rates constant or

even reduce them given near zero inflation• Implies trade-off between equity for the employed

and for the unemployed

Minimum wages and gender equalityRobinson article in Ox. Bull. Ec. & Stats. 2002

• Many women work in part-time jobs with low wages• Expect MW to affect women more than men• Can we observe Male-Female wage differential

falling when UK MW began?Study by Robinson (2003) compares evidence for

period 1995 to 2000 (MW intro. was April 1998)• Robinson uses data from UK Labour Force Survey

which is very large database • Able to track changes at all points in wage

distribution• Problem here (as with Stewart) that this was the

period of very low level of MW

Gender pay gaps in hourly wages – raw and adjusted for characteristics

Men and women adults; characteristics include region, industry, marital, education,union, temporary

Comparison hourly rates for adults in 3rd quarter

Robinson Table 3

Raw gap Adjusted gap

1997 -0.308 -0.160

1998 -0.323 -0.177

1999 -0.303 -0.171

2000 -0.277 -0.145

Findings MW and gender wage gap• Gender pay gap rose between 1997 and 1998 but

fell again from 1998 to 1999• No net change over two years in raw gap, but a

rise in gap adjusted for characteristics 1997-99• Gender pay gaps (raw and adjusted) then fell

between 1999 and 2000 by 2.6 & 3.2 (log) points respectively

• Simulation results show a rise in MW would raise F/ M gender pay ratio by 3 points from 73.7 at £3.60 to 76.5 at £5.00

• This rise in MW has now happened so = good news for low paid women?

• But what trade off with jobs? Back to labour demand curve!