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Transcript of Labor Economics Stepan Jurajda Office #2 (2 nd floor) CERGE-EI building (Politickych veznu 7)...
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Labor Economics
Stepan JurajdaOffice #2 (2nd floor) CERGE-EI building
(Politickych veznu 7)[email protected]
Office Hour: Tuesdays after class
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Introduction
• Consider the distribution of wages:
What can explain why some people earn more than others?
(based on exposition by Alan Manning)
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Overall Distribution of Hourly Wages in the
UK – trimmed (£1 to £100 per hour)
0.2
.4.6
.8D
ensi
ty
0 1 2 3 4 5lnwages
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Models of Distribution of Wages
• Start with perfectly competitive model• Assumes labour market is frictionless so a single
market wage for a given type of labour – the ‘law of one wage’ (note: this assumes no non-pecuniary aspects to work so no compensating differentials)
• ‘law of one wage’ sustained by arbitrage – if a worker earns CZK100 per hour and an identical worker for a second firm earns CZK90 per hour, the first employer could offer the second worker CZK95 making both of them better-off
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The Employer Decision (the Demand for Labour)
• Given exogenous market wage, W, employers choose employment, N to maximize:
• Where F(N,Z) is revenue function and Z are other factors affecting revenue (possibly including other sorts of labour)
( , )F N Z WN
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• This leads to familiar first-order condition:
• i.e. MRPL=W
• From the decisions of individual employers one can derive an aggregate labour demand curve:
( , )F N ZW
N
( , )d dN N W Z
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The Worker Decision(the Supply of Labour)
• Assume the only decision is whether to work or not (the extensive margin) – no decision about hours of work (the intensive margin)
• Assume a fraction n(W,X) of individuals want to work given market wage W; there are L workers. X is other factors influencing labour supply.
• The labour supply curve will be given by:•
( , )sN n W X L
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Equilibrium
• Equilibrium is at wage where demand equals supply. This also determines employment.
• What influences equilibrium wages/employment in this model:– Demand factors, Z– Supply Factors, X
• How these affect wages and employment depends on elasticity of demand and supply curves
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What determines wages?
• Exogenous variables are demand factors, Z, and supply factors, X.
• Statements like ‘wages are determined by marginal products’ are a bit loose
• True that W=MRPL but MRPL is potentially endogenous as depends on level of employment
• Can use a model to explain both absolute level of wages and relative wages. Go through a simple example:
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A Simple Two-Skill Model
• Two types of labour, denoted 0 and 1. Assume revenue function is given by:
• You should recognise this as a CES production function with CRS
(1/ )
0 1(1 )Y A N N
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• Marginal product of labour of type 0 is:
• Marginal product of labour of type 1 is:1
(1/ ) 111 0 1
1 1
(1 ) (1 ) (1 )Y Y
N A N NN N
1(1/ ) 11
0 0 10 0
(1 )Y Y
N A N NN N
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• As W=MPL we must have:
• Write this in logs:
• Where σ=1/(1-ρ) is the elasticity of substitution• This gives relationship between relative wages
and relative employment
1
01
0 1
(1 ) NW
W N
1 0 1 0( )n n d w w
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A Simple Model of Relative Supply
• We will use the following form:
• Where ε is elasticity of supply curve. This might be larger in long- than short-run
• Combining demand and supply curves we have that:
• Which shows role of demand and supply factors and elasticities.
1 0 1 0( )n n s w w
1 0
d sw w
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Data from the US
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What about unemployment?
• As defined in labor market statistics (those who want a job but have not got one) does not exist in the frictionless model.
• Anyone who wants a job at the market wage can get one (so observed unemployment must be voluntary).
• Failure of this model to have a sensible concept of unemployment is one reason to prefer models with frictions.
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Before we go there, a reminder
• Unemployment has different definitions (ILO, registered)
• US-EU unemployment gap used to be different
• An unemployment rate does not mean much without an employment rate
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The Distribution of Wages in Imperfect Labour Markets
• Discuss a simple variant of a model of labour market with frictions – the Burdett-Mortensen 1998 IER model. Here, MPL=p with perfect competition but with frictions other factors are important.
• Frictions are important: people are happy (sad) when they get (lose) a job. This would not be the case in the competitive model.
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Labour Markets with frictions, cont.
• Assume that employers set wages before meeting workers (Pissarides assumes that there is bargaining after they meet. Hall & Krueger: 1/3 wage posting 1/3 bargained.)
• L identical workers, get w (if work) or b.• M identical CRS firms, profits= (p-w)n(w).
There is a firm distribution of wages F(w).• Matching: job offers drawn at random
arrive to both unemployed and employed at rate λ; exog. job destruction rate is δ.
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Labour Markets with frictions, cont.
• Unemployed use a reservation wage strategy to decide whether to accept the job offer or wait for a better one (r=b).
• 1. steady state unempl.: Inflow = Outflow: δ(1-u) = λ[1-F(r)]u + 2. In equilibrium F(r)=0 (why offer a wage below r? – you’ll make 0 profits) => equilibrium u= δ / (δ+λ).
• Employed workers quit: q(w)= λ[1-F(w)]
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Labour Markets with frictions, cont.• In steady state, a firm recruits and loses
the same number of workers: [δ+q(w)]n(w)=R(w)= λL/M[u+(1-u)N(w)] where N(w) is the fraction of employed workers who are paid w or less.
• Derive n(w): firm employment and profit. Next, get equilibrium wage distribution F(w) & average wage E(w).
• EQ: all wages offered give the same profit (π=(p-w)n(w) higher w means higher n(w).) + no other w gives higher profit.
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• Average wage is given by:
• So the important factors are– Productivity, p– Reservation wage, b– Rate of job-finding, λ and rate of job-loss, δ– i.e. a richer menu of possible explanations
• But, also equilibrium wage dispersion (even when workers are all identical; a failure of the ‘law of one wage’) so luck also important.
• Perfect competition if λ/δ=∞. Frictions disappear. Competition for workers drives w to p (MP).
p bE w
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Institutions also important
• Even in a perfectly competitive labour market institutions affect wages/emplmnt
• Possible factors are:– Trade unions– Minimum wages– Welfare state (affects incentives, inequality)
Example: higher unempl. benefit increases the wage share and reduces inequality, but it also increases the unempl. rate thus making the distribution of income more unequal.
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Stylized Facts About the Distribution of Wages
• There is a lot of dispersion in the distribution of ‘wages’
• Most commonly used measure of wages is hourly wage excluding payroll taxes and income taxes/social security contributions
• This is neither reward to an hour of work for worker nor costs of an hour of work to an employer so not clear it has economic meaning
• But it is the way wage information in US CPS, EU LFS is collected.
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Overall Distribution of Hourly Wages in the UK - Untrimmed
0.2
.4.6
.8D
ensi
ty
-2 0 2 4 6lnwages
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Overall Distribution of Hourly Wages in the
UK – trimmed (£1 to £100 per hour)
0.2
.4.6
.8D
ensi
ty
0 1 2 3 4 5lnwages
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Overall Distribution of CZ Hourly Wages1Q2006: median: 105CZK, 5th percentile: 55CZK, 95th: 253
0.2
.4.6
.81
Den
sity
4 6 8 10Log of hourly wage rate
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Comments
• Sizeable dispersion (there is also much dispersion in firm-level productivity)
• Distribution of log hourly wages reasonably well-approximated by a normal distribution (the blue line)
• Can reject normality with large samples
• More interested in how earnings are influenced by characteristics
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The Earnings Function
• Main tool for looking at wage inequality is the earnings function (first used by Mincer) – a regression of log hourly wages on some characteristics:
• Earnings functions contain information about both absolute and relative wages but we will focus on latter
ln w x
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Interpreting Earnings Functions
• Literature often unclear about what an earnings function meant to be:– A reduced-form?– A labour demand curve (W=MRPL)?– A labour supply curve?
• Much of the time it is not obvious – perhaps best to think of it as an estimate of the expectation of log wages conditional on x
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An example of an earnings function – UK LFS
• This earnings function includes the following variables:– Gender– Race– Education– Family characteristics (married, kids)– (potential) experience (=age –age left FT education)– Job tenure– employer characteristics (union, public sector, employer size)– Industry– Region– Occupation (column 1 only)
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An example of an earnings function – UK LFS all all men women
female -0.175 -0.202 0 0
-0.008 -0.008 0 0
black -0.04 -0.052 -0.136 -0.032
-0.032 -0.034 -0.056 -0.042
indian -0.057 -0.072 -0.046 -0.115
-0.03 -0.032 -0.043 -0.047
pakistan -0.127 -0.098 -0.086 -0.144
-0.052 -0.055 -0.073 -0.084
bengali -0.26 -0.178 -0.206 -0.104
-0.089 -0.095 -0.116 -0.172
chinese -0.093 -0.053 -0.025 -0.033
-0.091 -0.097 -0.162 -0.116
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Education variables
all all men women
degree 0.286 0.507 0.484 0.489
-0.011 -0.01 -0.015 -0.012
A' level 0.082 0.113 0.098 0.094
-0.009 -0.01 -0.014 -0.013
no quals -0.059 -0.105 -0.127 -0.087
-0.01 -0.011 -0.017 -0.014
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Family Characteristics
all all men women
married + kids 0.111 0.121 0.201 0.015
-0.011 -0.012 -0.018 -0.017
married+no kids 0.107 0.128 0.159 0.079
-0.011 -0.012 -0.018 -0.016
single+kids -0.02 -0.022 -0.103 -0.045
-0.016 -0.017 -0.029 -0.02
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Experience/Job Tenureall all men women
experience/10 0.231 0.264 0.31 0.213
-0.011 -0.012 -0.018 -0.016
experience/10 squared -0.046 -0.054 -0.058 -0.051
-0.002 -0.002 -0.003 -0.003
tenure/10 0.145 0.191 0.161 0.225
-0.011 -0.012 -0.017 -0.018
tenure/10 squared -0.02 -0.026 -0.02 -0.036
-0.004 -0.004 -0.005 -0.006
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Employer Characteristics
all all men women
union -0.014 -0.043 -0.091 0.018
-0.008 -0.008 -0.012 -0.011
whether work in public sector 0.031 0.021 -0.054 0.063
-0.012 -0.013 -0.02 -0.016
ln employer size 0.051 0.051 0.07 0.033
-0.003 -0.003 -0.005 -0.004
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Industry (selected relative to manufacturing)
all all menwome
n
g:wholesale, retail trade -0.158 -0.123 -0.071 -0.142
-0.014 -0.013 -0.019 -0.019
h:hotels & restaurants -0.209 -0.232 -0.21 -0.237
-0.022 -0.023 -0.04 -0.028
i:transport & communication 0.001 -0.016 -0.017 0.038
-0.014 -0.015 -0.018 -0.027
j:financial intermediation 0.192 0.271 0.342 0.217
-0.017 -0.018 -0.026 -0.024
k:real estate, renting 0.048 0.107 0.12 0.12
-0.014 -0.015 -0.02 -0.022
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Region (selected relative to Merseyside)
all all men women
inner london 0.277 0.309 0.312 0.369
-0.028 -0.03 -0.047 -0.043
outer london 0.222 0.249 0.253 0.317
-0.025 -0.027 -0.042 -0.038
rest of south east 0.149 0.175 0.234 0.185
-0.022 -0.024 -0.038 -0.035
south west 0.034 0.03 0.069 0.068
-0.024 -0.026 -0.04 -0.037
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Occupation (relative to craft workers) – only 1st column
1 managers and administrators
0.4
6 personal, protective occupations
0.002
-0.015 -0.017
2 professional occupations
0.447
7 sales occupations
0.025
-0.017 -0.019
3 associate prof & tech occupations
0.263
8 plant and machine operatives
-0.04
-0.016 -0.015
4 clerical,secretarial occupations
0.041
9 other occupations
-0.129
-0.015 -0.017
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Stylized facts to be deduced from this earnings function
• women earn less than men• ethnic minorities earn less than whites• education is associated with higher earnings • wages are a concave function of experience,
first increasing and then decreasing slightly• wages are a concave function of job tenure• wages are related to ‘family’ characteristics• wages are related to employer characteristics
e.g. industry, size• union workers tend to earn more (?)
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The same stylized facts for CZ(1) (2) (1) (2)
Female -0.24 -0.26 Industry relat. to Agriculture
Educ. Relat. to Primary Mining 0.26 0.32
Apprenticeship 0.08 0.07 Manufacturing 0.21 0.21
Secondary w/ GCE 0.34 0.32 Utilities 0.39 0.36
College and University 0.82 0.82 Construction 0.22 0.21
Post-graduate 1.04 1.04 Retail 0.10 0.08
Age 0.04 0.04 Hotels 0.07 0.15
Age squared -0.04 -0.04 Transport 0.25 0.25
Part-time -0.05 -0.05 Banks 0.54 0.63
Firm size (employment) 0.06 0.07 RealEstate+R&D. -0.02 -0.03
Firm size squared -0.02 0.04 Other Services 0.12 0.11
_const 3.49 3.48
Trade unions 0.004
N 1m 0.5m
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The variables included here are common but can find many others sometimes included
• Labour market conditions – e.g. unemployment rate, ‘cohort’ size
• Other employer characteristics e.g. profitability• Computer use- e.g. Krueger, QJE 1993• Pencil use – e.g. diNardo and Pischke, QJE 97• Beauty – Hamermesh and Biddle, AER 94• Height – Persico, Postlewaite, Silverman, JPE
04• Sexual orientation – Arabshebaini et al,
Economica 05
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Raises question of what should be included in an earnings function
• Depends on question you want to answer• E.g. what is effect of education on earnings –
should occupation be included or excluded?• Note that return to education lower if include
occupation• Tells us part of return of education is access to
better occupations – so perhaps should exclude occupation
• But tells us about way in which education affects earnings – there is a return within occupations
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Other things to remember
• May be interactions between variables e.g. look at separate earnings functions for men and women. Return to experience lower for women but returns to education very similar.
• R2 is not very high – rarely above 0.5 and often about 0.3. So, there is a lot of unexplained wage variation: unobserved characteristics, ‘true’ wage dispersion, measurement error.
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Problems with Interpreting Earnings Functions
• Earnings functions are regressions so potentially have all usual problems:– endogeneity e.g. correlation between job tenure and
wages– omitted variable e.g. ‘ability’– selection – not everyone works e.g. the earnings of
women with very young children
• Tell us about correlation but we are interested in causal effects and ‘correlation is not causation’