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Background • Acquiring education is an investment in the sense that one givers up something now (you could be working in McDonalds and not paying fees) in the hope of getting more back in the future. • For that, reason education is often described as ‘human capital’, the title of a famous book by Gary Becker. • like all investments, how the future gain compares to the current sacrifice is critical in determining whether education is a good investment or not.
The Individual Decision to Acquire education • Assume earnings if have s years of (post-compulsory) schooling is W(s) • Assume only cost of education is forgone earnings – no direct cost • Assume everyone lives for ever • PDV of s years of education is:
The education decision (cont) • Taking logs this can be written as: • The first order-condition can be written as: • i.e. acquire education up to the point where the increase in log earnings is equal to the rate at which future earnings are discounted
Equilibrium • Suppose all individuals identical • Suppose require different levels of education in equilibrium • Then must be the case that • Is equalized for different levels of s • Think of including years of education on RHS of earnings function – coefficient on s is measure of r – rate of return to education
Estimates of rate of return to education • For US a typical OLS estimate from an earnings function is about 8% • Other countries are a bit different • Suggests education a very good investment – few other investments offer an 8% real return.
Estimates of rate of return to education for other countriesTrostel, Walker, Woolley, Labour Economics 2002)
A puzzle • If rate of return to education is so high, why aren’t more people acquiring education • Possible answers: • Liquidity constraints • Bias in OLS estimate so rate of return not really that high • Heterogeneity in the returns to education
Liquidity Constraints • In perfect capital market r should be rate of interest • But if imperfect capital market may be much higher. • Why might it be higher – hard to borrow money against human capital as no collateral
Bias in OLS estimate • Why might OLS estimate be biased? • Most common answer is ‘ability bias’ • Ability has effect on wages independent of education but is positively correlated with schooling and typically not controlled for in regression. • Suppose true model is:
But a is omitted from regression so estimate: • Standard formula for omitted variables bias gives us that: • So that OLS estimate biased upwards if a and s are positively correlated (as is very likely)
Solutions to Omitted Ability Bias Problems • Put in better controls for ‘ability’ e.g. use of IQ tests etc • Twin studies • Instrumental Variables
Better Controls for Ability • a sensible idea though it is generally easier said than done. • But there are some data sets (e.g. the US National Longitudinal Survey of Youth – NLSY) which do have the results of tests given to people before they finish compulsory schooling. • When these variables are included in an earnings regression the measured rate of return to education does fall. • But one problem with this is that education itself may be measured with error which leads to an attenuation bias. • This attenuation bias may get worse if controls for ability are included, a point we have discussed in this course
Twin studies • Pioneered by Taubman (AER, 1976) • Simple model for earnings of twin 1 and twin 2 in pair i • Cannot estimate by OLS as s may be correlated with a • but assume that identical twins have a1i=a2i
Take differences: • Now regressor uncorrelated with error so estimate will be consistent • Estimate from twins studies typically suggest lower rate of return to education than OLS – suggestive of ability bias
Problems with Twin Studies • Do identical twins really have identical ability – identical genes but perhaps not everything in the genes • Measurement error problems – measurement error leads to attenuation bias, measurement error like to be bigger in Δs than s as identical twins tend to have similar levels of schooling – see notes for details • Similar to point made in panel data section – within twin estimates like fixed effect estimates
The Instrumental Variable Approach • Basic Idea of IV in this context – find instrument(s) correlated with s but uncorrelated with a • A number of studies have used different instruments • quarter of birth (Angrist-Krueger QJE 91) • proximity to a college (Card) • Changes in minimum school leaving age (Harmon-Walker AER 95) • month of birth (del Bono and Galindo-Rueda) • Often find higher estimates than OLS
Look at one in more detail (del Bono an dgalidno-Rueda) • The idea – until 1977 UK compulsory schooling laws allowed those in a school cohort born between 1st Sept and 31st January to eave school at Easter and not take exams. • This had the effect of reducing the probability of getting an academic qualification for those born before February
Comment • Note: use employment as outcome variable as do not have large enough sample size to estimate precise wage effects • So cannot use results directly to compute rate of return to education • But idea should be clear
Heterogeneity in Returns to education (Card, JOLE 1999) • Uses idea that there is likely to be heterogeneity in both return to school and the cost of schooling (the discount rate)
What does IV estimate when returns are heterogeneous • This is a surprisingly complicated question • Angrist-Imbens LATE tells us that it picks up the average returns for education for those whose behaviour is altered by the instrument • Unlike IV estimate for homegenous case this means estimate will vary with the instrument • This issue comes up in other areas where IV is increasibly popular
Card’s conclusions on returns to education • Average rate of return probably only slighlty below OLS estimate • There is some variation in return to education with observable factors • IV estimates tend to be bigger than OLS estimates probably because the interventions exploited pick up the returns for a group for whom it is large
Other issues in the returns to education • Have focused on quantity of schooling but quality and type of schooling also important – e.g. what is effect of class sizes • Why does education raise earnings – two main models • Raises human capital • Acts as a signal (Spence)