A reconsideration of the Angrist-Krueger analysis on returns to education

In this paper we reconsider the analysis of the effect of education on income by Angrist and Krueger (1991). In order to account for possible endogeneity of the education spell, these authors use quarter of birth to form valid instruments. Angristand Krueger apply a classical method, two-stage least-squares (2SLS), and consider results for data sets on individuals from all states of the US. In this paper the research by Angrist and Krueger is extended both in a methodological and an empirical way. Classical as well as Bayesian methods are used. Bayesian results under the Jeffreys prior are emphasized, as these results are valid in finite samples and because in the instrumental variables (IV) regression model the Jeffreys prior is in a certain sense, truly, non-informative. Further, it is considered how results vary between subsets of the data corresponding to regions of the US. Finally, some assumptions of Angrist and Krueger are investigated and it is examined if one could still obtain usable results if some assumptions are dropped. Our main findings are: (1) The Angrist-Krueger results on returns to education for the USA are almost completely determined by data from a few Southern states; (2) The conclusion of Bound, Jaeger and Baker (1995), that the instruments of Angrist and Krueger give hardly any usable information concerning the causal effect of education on wages, is too strong. A model of Angrist and Krueger (or a slightly modified version) can give usable information on the causal effect of education on income in the Southern region of the US; (3) The instruments for education that are based on quarter of birth are stronger for people with at most 8 or at least 14 years of education than for people with 9-13 years of education. This suggests that quarter of birth does not only affect the number of completed years of schooling for those who leave school as soon as the law allows for it, as these persons usually have completed 9-13 years of education. Therefore, if one intends to increase the understanding of the working of the quarter-of-birth instruments, it is a better idea to focus on differences between states in school entry requirements and/or compulsory schooling laws for children of age 5-7 than to concentrate on the differences in compulsory schooling laws for students of age 16-18.