Policy Analysis (using examples from Labor Economics)

1. Policy Analysis (using examples from Labor Economics) Stepan Jurajda Office #333 (3rd floor) CERGE-EI building (Politickych veznu 7) stepan.jurajda@cerge-ei.cz Office Hour: Tuesdays after class

2. Introduction • Consider the distribution of wages: What can explain why some people earn more than others? How can we learn from data or models?

3. Overall Distribution of Hourly Wages in the UK - Untrimmed

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

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

6. 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.

7. 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

8. 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

9. 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

10. 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)

11. An example of an earnings function – UK LFS

12. Education variables

13. Family Characteristics

14. Experience/Job Tenure

15. Employer Characteristics

16. Industry (selected relative to manufacturing)

17. Region (selected relative to Merseyside)

18. Occupation (relative to craft workers) – only 1st column

19. 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 (?)

20. The same stylized facts for CZ

21. 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

22. 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

23. 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.

24. 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.

25. 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

26. 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)

27. 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:

28. 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:

29. 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

30. 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:

31. 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

32. Marginal product of labour of type 0 is: • Marginal product of labour of type 1 is:

33. 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

34. 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.

35. Data from the US

36. 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.

37. 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

40. 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.

41. 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.

42. 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)]

43. 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.

44. 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).

45. 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.