Empirical Strategies and Labour Supply PDF

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EMPIRICAL STRATEGIES AND LABOUR SUPPLY Much of the time we will want to explore whether x causes y e.g. Does an extra year of schooling (x) increase wages (y)?. Problem: Causation vs Correlation

Basic OLS Regression ✦

We want to estimate the relationship between x and y

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Parameter 𝛃 causal effect of x on y?

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ONLY if regression makes sense

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AND if x is uncorrelated with 𝛆 (else we have endogeneity)

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Numerical example: Suppose there are 100 unemployed: 50 of them are motivated, 50 are not (motivation is unobserved)

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Without job training, all motivated would find a job

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All 100 are offered voluntary job training, and only the motivated go (Why? Because they are motivated)

Does an extra year of schooling increase wages? • Strong positive relationship between wages and years of schooling • If you ran a regression of: ln(wagei) = 𝛂 + 𝛃*schooling + 𝛆i • The coefficient on schooling would be 0.10 i.e. a 10% return to one extra year of schooling What is the problem with this regression? • Lots of things correlated with both wages and years of schooling (e.g. family background, ability etc). • Returns to schooling (the so-called parameter of interest) will be biased because of these missing variables. • To see this, consider the relationship between a measure of ability and both years of schooling and wages • AFQT score is positively correlated with both wages and years of schooling, if we leave it out of the equation the coefficient on years of schooling will be biased upward • Adding AFQT drops returns to schooling by 40% to 0.06.

What to do? •Control for as much as possible in the regression •But what about unobserved things? •Look at wages and schooling among twins (same family background, same genetics) •But if twins are so similar, why do they differ in years of schooling?

BEST CASE - Random Assignment • How would you design a perfect experiment? • Take a random sample of kid • Some get “treatment” of more schooling • “Control” group doesn’t get more schooling • Since assignment to “treatment” and “control” group is random, there would be no relationship between years of schooling and any individual ability, family background etc (assuming full compliance with the experiment). • Return to a year of schooling = average wage of treatment group minus average wage of control group. • This estimate is called the population Average Treatment Effect (ATE).

Difference-in Difference • How do you estimate the effect of a policy on an outcome variable? • Typically policy is binding for some (treatment) but not for others (control) • First difference:

Dtreat = Ytreat , after - Ytreat, before Dcontrol = Ycontrol ,after - Ycontrol ,before • First equation might naivety be interpreted as the policy effect • BUT: maybe outcome would have changed in the absence of the policy • Diff-in-diff:

b = D treat - D control • Example: Consider the introduction of a welfare program that provides a tax credit to a certain group of workers to encourage them to work. Suppose single mothers are given a credit over a range of annual wage income (treatment group) while single women without children are not eligible (control group). We can observe the labour supply of both groups of women both before and after the policy is introduced. • Suppose we found that the labour participation rate of single mothers rose substantially. The problem is that perhaps the economy was doing really well at the time and this was the cause, not the policy. • Fortunately in this example we have the control group. If we compare their labour force participation at the same time we can control for economic conditions. But the control group are not necessarily the same as the treatment group before the welfare program was introduced, so we need to control for pre-treatment differences i.e. we need to examine the difference in the change in labour force participation between the two groups • So we estimate the difference-in-difference to control for all this: After Before After Before b = (LFPTreated - LFPTreated - LFPControl ) - (LFPControl )

Instrumental Variables • Another way of thinking about the problem is to ask if there is some other variable that is related to x but that we are sure is not related to y. • Why might this help? Suppose we could observe a variable z that had a direct effect on x but that z had no effect on y (other than through x). So we have two equations:

yi = α + β xi + ui xi = δ + λ zi + ν i • Then we could use the variation in x caused by the variation in z to estimate the effect of x on y.! This is the Instrumental Variable (IV) regression of x on y using z as the instrument. z is a valid instrument provided (i) z is uncorrelated with the error term u and (ii) z is correlated with the regressor x.

• A well-known example of such an approach uses the time of year in which an individual is born. In the US, children born early in the year start school at an older age and so can leave school with less years of schooling than those born later in the year. • Kid A born in January 1990, kid B born August 1990 • Both start school in Sept 1996 – but kid A is 6yr 8mths old and kid B is 6yr 1mths old! • Suppose compulsory schooling laws require kids to remain in school until they reach 17 Then • Kid A can leave in Jan 2007 with 10yrs 4mths schooling while • Kid B can leave in Aug 2007 so receives 10yrs 8mths schooling. So • → month (or quarter) of birth (z) is correlated with years of schooling (x) but it is hard to see how z has any direct effect on wages (y) • Evidence suggests that the IV estimate of years of schooling using quarter of birth as an instrument produces about the same estimate of returns as does basic OLS.

• Another Example: Suppose you wanted to know whether military veterans earn more or less than otherwise identical non-veterans • Problem is that being a veteran is generally correlated with lots of things that also affect wages – the same problem • Angrist (1990,! AER) proposes using the Vietnam draft lottery as an instrument to get round the problem. During the Vietnam war, young men were conscripted into the US Army on the basis of a random lottery. If your age group was due for conscription, you got a lottery number at the start of the year and government started at lottery number 1 and conscripted everyone they needed by working up the lottery numbers. • So a low lottery number (z) is strongly correlated with being a veteran (x) but again it is hard to see how z has any direct effect on wages (y).

How do we interpret the IV estimate? • The IV estimate works by capturing the fact that some people can be induced/forced into receiving the treatment (e.g. an extra year of schooling) because of the instrument. In the previous examples, some kids who want to leave school as quickly as possible get more education than others because of the interaction of month of birth and compulsory school laws and some kids are forced to become soldiers because they got a low lottery number. • But unlike the random assignment example, the coefficient we estimate with IV only gets the return to schooling for those who are induced/forced into receiving the treatment • This is called the Local Average Treatment Effect (LATE) and may or may not be very interesting. This compares with the population Average Treatment Effect (ATE) that we identify in the random assignment example.

Regression Discontinuity • The regression discontinuity idea is based on looking at individuals who did and did not get the treatment (e.g. an extra year of schooling) based on some rule or policy over which they have no control or at least limited control – so conceptually like IV. • For example, suppose you were only allowed to stay on for an extra year of schooling if you got more than 50% in a final year exam. Then people who get 49% don’t get the extra year and those who get 51% do. But it seems reasonable to argue that such people are very similar and so likely to have the same ability, family background etc. • So comparing the future wages of those who got 49% on the exam with those who got 51% on the test (and therefore got the extra year of schooling) would give a good estimate of the returns to the extra year of schooling.

• An example of the regression discontinuity approach for wages and years of schooling is given in Oreopoulos (2006) • In 1947, the school leaving age in the UK was raised from 14 to 15. !Individuals had no control over this policy and so kids who only wanted to get educated up to age 14 could do so if they were born before 1933 but had to stay until 15 if they born in 1934 or later. • This produced a noticeable jump in the average age of school leaving – the regression discontinuity schooling chart. Remember that this didn’t need to be the case – it could have been that virtually all kids were already staying on to age 15 before the policy change. The fact that they weren’t makes the policy change a very effective regression discontinuity. • What about the effect on wages? The same type of chart shows the wage effect – wage chart. • The return to schooling is then just calculated by comparing the mean wage and schooling levels around the discontinuity

Labour Supply Neoclassical model of labour supply: Individual receives utility from both consumption and leisure U = f(C, L)

(1)

Of course, you need to work (give up L) to enjoy consumption UC > 0, UCC < 0 UL > 0, ULL < 0

Indifference Curve

Budget Constraint

Properties

• The budget constraint that an individual faces is given by:

• Downward sloping (because UC and UL are both assumed positive) • Higher indifference curves yield higher utility • Indifference curves do not intersect • Indifference curves are convex to the origin (what is relatively scarce is more highly valued) • Marginal rate of substitution: -MUL/MUC

C = wh + V (2) where w is the hourly wage rate , h are the hours of work and V is non-labour income (e.g. interest on savings, asset price gains etc.). Note that if we define total hours in the period (e.g. a week) as T, then T=h+L

(3)

• We can use (2) and (3) to rewrite the budget constraint as: C = (wT + V) - wL • This gives the budget line which is downward sloping in consumption-leisure space and has a gradient to -w

The Hours Decision ‣An individual chooses a consumption/leisure bundles that maximises utility (1) subject to the budget constraint (3) ‣The solution requires that the slope of the budget line be equal to the slope of the indifference curve at the optimal bundle ‣This requires:

UL =w Uc

An Increase in non-labour income V ‣ With the wage rate held constant, the budget line has a parallel shift up when V rises. Remember that the slope of the budget line is given by –w so doesn’t change. ‣ If leisure is a normal good (i.e. increases in income increase consumption of the good), the income effect of a rise in V reduces

EMPIRICAL EVIDENCE - Imbens, Rubin and Sacerdote (2001) “Estimating the Effect of Unearned Income on Labor Earnings, Savings and Consumption: Evidence from a Survey of Lottery Players”, American Economic Review 1) Aim of paper • Testing whether changes in V (unearned income) affect labour-leisure choices (and savings and consumption) • Most papers have just looked at the correlation between unearned income and labour supply (e.g. hours worked). • Problem is again that there are likely other things that are correlated both with unearned income and labour supply that we cant observe (e.g. work ethic, family etc.) 2) Methodology and Data • Identification strategy of Imbens et al is to use winnings on the Massachusetts lottery from the mid-1980s. Such winnings are of course completely random and so provide exogenous variation in unearned income. However the group of people choosing to play the lottery are not random • They have data on 237 winners (of which 43 are big winners – a prize of at least $2million, paid in annual instalments over 20 years) and 259 non-winners. The non-winners are people who took part in the lottery but did not win • They surveyed everyone and asked questions about background (e.g. education, age, marital status), earnings, savings, consumption and assets. They also got permission to access social security records so that reliable earnings records before and after the lottery wins were available. • For the winners, the difference in average earnings over the six postlottery years and the six pre-lottery years is -$1,877 and for the nonwinners the average change is $448. Given a difference in average prize of $55,000 for the winner/ nonwinners comparison, the estimated marginal effect is (- 1,877 448)/(55,000 - 0) =!-0.042 (SE 0.016). • Big fall in annual earnings for big winners at time of prize and the fall is sustained over the subsequent years

BASIC RESULT -EFFECT ON EARNINGS

BASIC RESULT - EFFECT ON WORKING • Big fall in probability of working for big winners at time of prize and again the fall is sustained over the subsequent years

3) Problems with paper • Sample is quite small and non-response is very large – under 50% replied to the survey. Different behaviour between responders and non-responders? • Extreme comparison – workers had average wages of $16,000 and big winners suddenly got at least an extra $100,000 per year – generalizable to more normal non-labour income shocks?

A Rise in the Wage Rate ‣ Suppose the wage rate increases. This now rotates the budget line and makes it steeper. ‣ The effect on hours of work now depends on the combination of two effects: the income effect and the substitution effect ‣ If the income effect dominates, hours of work fall. If the substitution effect dominates, hours of work rise Income Effect Dominates ‣Income effect moves us from P to Q (reducing hours worked), substitution effect moves us from Q to R (increasing hours worked). ‣Final result is fall in hours from P to R as income effect larger than substitution effect. Substitution Effect Dominates

effect smaller than substitut

Labour Force Participation Decision ‣ The previous model focused on hours supplied (the intensive margin) ‣ Probably the more important aspect of labour supply is the decision as to whether to participate in the labour market at all (the extensive margin) ‣ The reservation wage is defined as the wage offer that makes the individual just indifferent between participating and not participating ‣The individual does not participate at the low wage, does work at the high wage and the reservation wage is given by the slope of the indifference curve at the endowment point.

Deriving the Labour Supply Curve • The labour supply curve of an individual plots the relationship between hours of work and wage rates for that person.

Aggregate Labour Supply Curve is obtained by adding up every individual Labour Supply Curve

• It is derived from plotting the hours worked for a set of different wage rates curve-budget line diagram • For normal wage rates we e effect to dominate and the slope upward • It is possible that for high w effect dominates and the la negative slope – perhaps ju

Backward-Bending Sup wage rate (the slope of the labour supply curve) • σ = percentage change in hours worked divided by percentage change in wage rate • σ less than 1 is inelastic as hours of work respond proportionately less than changes in wages and vice versa

POLICY: A Cash Grant ‣ Suppose the government offers a cash grant to a group of individuals (e.g. single parent families) if they do not work but that the grant is immediately withdrawn if the person works. ‣ Unsurprisingly such a welfare scheme unambiguously reduces labour force participation ‣ Note that this is not because of a poor work ethic among the recipients, but because the incentives to work have been reduce ‣ A cash grant raises potential non-labour income and so shifts the endowment point from the origin (assume no non-labour income initially) to G. ‣ The worker has more utility at G than at P and so drops out of the labour market. ‣ The reservation wage has risen for this worker.

POLICY: Working Tax ‣ In the UK this is called the Credit (EITC). The idea is would otherwise not find it worth working ‣ The aim is therefore to encourage some non-workers to join the labour force ‣ The program works by introducing various ‘kinks’ in the budget constraint. This can produce a complex set of income and substitution effects depending on exactly where you are on the budget constraint. The Budget Constraint under EITC

EMPIRICAL EVIDENCE - Eissa and Liebman (1996) “Labor Supply Response to the Earned Income Tax Credit”, Quarterly Journal of Economics 1) Aim of paper • The 1986 Tax Reform Act in the US expanded the Earned Income Tax Credit (EITC). • The paper seeks to explore the effect of the change on the labour force participation and hours of work of single women with children

2) Methodology and Data • Identification comes from the fact that the EITC is only paid to those workers with a child. So if we compare the labour market outcomes of single women with children and single women without children before and after the 1986 Tax Reform Act we can estimate the effect of the policy change (diff-in-diff). • Focusing on single women avoids problems of joint labour supply decisions within a household. • The authors have data from a large representative US household survey that has information before and after the reform on participation, hours worked, wages and children.

3) Problems with paper • Usual question with a diff-in-diff approach – is the EITC policy change the only thing that changed in 1986 that affected the labour supply of women with children relative to women without children. This is likely to be problematic because the EITC change was part of a very broad Tax Reform Act. • It would be more illuminating if we had detailed data on exact earnings before and after the EITC change so that we could examine how the labour supply responses varied depending on the position on the kinked budget line....