2. Suppose that you are interested in estimating the following earnings regression: lOgI/Vi = o + lEDUi + Ui' where for individual i, Wl- is annual earnings, EDUi is the years of education, 50 and [1 are unknown parameters, and Ul- is an unobserved random variable, where i = 1,. . . , n. Here, UL- may include an unobserved individual ability that may be related with earnings and education. The sample is restricted to males born in the same year. The OLS estimate of 1 is 5'1 = 0.09 with a standard error of 0.03. (3) Suppose that one is interested in estimating the correlation between lo gWi and EDUi. Determine whether the following is true or false. Explain why. In View of the estimated value of [$1, lo 9W,- and E DU,- are positively correlated. (b) Now suppose that one is interested in estimating the return to education, that is the causal e'ect of education on log earnings. Suppose that all individuals in the sample have twin brothers and we know earnings and education for all twin brothers. Suggest a method for estimating the return to education using data on twins. Explain why an estimate based on your suggested method can be a better estimate for the realm to education than the OLS estimate. (c) Now suppose that Ui = ,BZABILITYi + Vi, where ABILITYi is an unobserved ability for individual i, [32 is an unknown parameter, and Vi is uncorrelated with E DU, and ABILITYi. Instead of observing ABILITYi, suppose that an IQ test score, denoted by I Q, is an observed measurement of ABILITYi. Assume that IQ: = ABILITYi + Q, where Si is uncorrelated with ABILITY, and EDUi. Would you estimate the return to education consistently by running an OLS regression of logWi on a constant term, EDUi, and I Q? Explain briey. ((1) Now suppose that two types of test scores are available, say an IQ test (IQ,) and a different cognitive test (C T,- ). Suggest a method for estimating the return to education using data on two test scores. Explain why an estimate based on your suggested method can be a better estimate for the return to education than the OLS estimate in part (c)