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Recent studies debate how the unobserved dependence between the monetary return to college education and selection into college can be characterised. This paper examines this question using British data. We develop a semiparametric local instrumental variables estimator for identified features of a flexible correlated random coefficient model. These identified features are directly related to the marginal and average treatment effect in policy evaluation. Our results indicate that returns to college systematically differ between actual college graduates and actual college non-graduates. They are on average higher for college graduates and positively related to selection into college for 96% of the individuals. The dependence between selection into college and returns to college education is strongest for individuals with low math test scores at the age of 7, individuals with less educated mothers, and for working-class individuals

College education and wages in the U.K.: estimating conditional average structural functions in nonadditive models with binary endogenous variables