Policy analysis using examples from labor economics
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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. Introduction. Consider the distribution of wages:

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Policy Analysis (using examples from Labor Economics)

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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


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 - Untrimmed


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)


An example of an earnings function – UK LFS


Education variables


Family Characteristics


Experience/Job Tenure


Employer Characteristics


Industry (selected relative to manufacturing)


Region (selected relative to Merseyside)


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


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 same stylized facts for CZ


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.


Data from the US


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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