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### Policy Analysis (using examples from Labor Economics)

Stepan Jurajda

Office #333 (3rd 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?

How can we learn from data or models?

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

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.

Comments

- Wage 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?

(More on models of wage determination later)

- 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 (more on that later when we model the labor market), measurement error.

Problems with Interpreting Earnings Functions

- Earnings functions are regressions so potentially have all usual problems:
- endogeneity (correlation between job tenure & wages)
- omitted variable (‘ability’)
- selection – not everyone works (women with children)
- Tell us about correlation but we are interested in causal effects and ‘correlation is not causation’
- In this course, we’ll consider empirical identification strategies that get at causality.
- In economics, we need models to interpret data. Some wage modelling follows.

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 (recall the empirical stylized fact of low R2).
- 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.

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