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### Labor Economics

Stepan Jurajda

Office #2 (2nd floor) CERGE-EI building

(Politickych veznu 7)

Office Hour: Tuesdays after class

Introduction

- Consider the distribution of wages:

What can explain why some people earn more than others?

(based on exposition by Alan Manning)

Overall Distribution of Hourly Wages in the UK – trimmed (£1 to £100 per hour)

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

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)

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:

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:

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

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:

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

Marginal product of labour of type 0 is:

- Marginal product of labour of type 1 is:

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

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.

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.

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

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.

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.

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)]

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.

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).

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.

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.

Overall Distribution of Hourly Wages in the UK – trimmed (£1 to £100 per hour)

Overall Distribution of CZ Hourly Wages1Q2006: median: 105CZK, 5th percentile: 55CZK, 95th: 253

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

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

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

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)

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 (?)

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

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

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.

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’

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