## Income, Schooling and Ability

A Summary for the EC406 class so its not im my usual format…

 Topic: Returns to Education Income, Schooling and Ability: Evidence from a New Sample of Identical Twins O. Ashenfelter & C. Rouse, QJE Vol. 113 No. 1 (1998) Key Findings An extra year of schooling increases earnings by 9% Relevant Theory One of the key challenges for estimating returns to education is that ability levels differ by individual, and as ability is unobserved and can only be proxied for on a rough basis this biases OLS results. IV techniques have been used with a varying degree of success, but one other line of attack is to look at twins. Essentially the argument runs that identical twins are identical in terms of their ability due to their shared genetic makeup. Therefore the schooling investments made by genetic twins should be the same apart from random deviations that are not related to the determinants of schooling choices (ability etc.) Empirical Strategy Generalised Least Squares and Fixed Effects Model. Specification Y1j = βS1j + θ[(S1j + S2j)/ 2] + λXj + Vj + ε1j           (1) And Y2j = βS2j + θ[(S1j + S2j )/ 2] + λXj + Vj + ε2j           (2)   Where Y is log wage for twin 1 or 2 of family j. S is schooling indexed similarly. X is a vector of covariates that determine wages across families but not within families (race, age etc.). The average education of the family is added (S1j + S2j / 2) as this controls for what they term family ability (i.e. what you inherit thanks to the conditions under which the twins grew up). Vj is then the innate ability of the individual which is the same across both equations as the twins are assumed to be identical.   This specification can then be estimated using GLS, and this will allow for an estimation of the family ability, but not the innate ability which remains in the error term. However, as innate ability is equal across specifications subtracting (1) from (2) will difference away the innate ability and a fixed effects model estimates:   Y2j-Y1j = β [(S2j –S1j)/2] + (ε2j– ε1j)                          (3)   The advantage of (3) is that innate ability is differenced away at the cost of being able to estimate family ability. Additionally, (3) is reliant on the fact that there is no difference in the ability within twins. Any deviation in ability will create biased estimates of β.   There are well documented problems with measurement error in self-reported units of education, which is exacerbated in first differenced equations (see lecture notes for more on this including proofs). Thus in the paper they implement an IV strategy to deal with the reported errors. That is they ask not only for self-reported units of education, but they also ask the twin how many years of education were attained by their sibling. They then use the responses of one to instrument for the amount of education of the other. This eliminates the person specific element of the measurement error. Data Data are drawn from 700 interviews collected at a twins fair in Ohio where the emphasis is on similarity so everyone tend to be identical, and dressed the same etc. The data are in panel format from 1989-1993, and if respondents were interviewed more than once, their answers were averaged. Main Table So column (1) reports the GLS estimation of aroun 0.1 log points increase in wages for each year of education. Column (2) reports the fit of the equations (I have no idea what that means), Column (3) reports three stage least sqaures which in a nutshell uses the IV strategy to cope with measurement error before moving on to the GLS. Column (4) reports the first difference estimator, which reduces significantly to 0.7 suggesting that innate ability is important for determining both years of education and subsequent earnings. The coefficient is restored to around 0.9  in column (5) when the IV strategy is implemented to cope with the measurement error. Columns (6) – (10) do the same process but controlling for a host of family level covariates. Critique It may well be thought that twins do in fact differ in innate ability. Whilst they attempt to control for family ability by using the average level of education attained by the twins, this is an incredibly rough approximation, and is probably not fine enough to capture how twins may experience different learning environments. They do also control for who was born first, which is good as it is often said that the first born is heavier and this determines life chances. From the summary statistics presented at the front of the paper it is clear that the twins interviewed differed positively from the population at large in terms of earning, employment, and education. Thus this sample is not hugely representative, and it may be hard to generalize the results to the population at large. Policy Implications Increasing access to education can improve wage opportunities based presumably on productivity increases for the better educated. When I Grow Up, I Want To Be: The type of person who knows what the hell GLS is.