[Excerpt] This chapter proposes tests of various notions of equality of opportunity and applies them to intergenerational income data for the United States and Britain. Agreement is widespread that equality of opportunity holds in a society if the chances that individuals have to succeed depend only on their own efforts and not on extraneous circumstances that may inhibit or expand those chances. What is contentious, however, is what constitutes "effort" and "circumstances." Most people, we think, would say that the social connections of an individual's parents would be included among circumstances: equality of opportunity is incomplete if some individuals get ahead because they have well-connected parents. This and other channels through which circumstances affect income opportunities in an intergenerational context are discussed in Section 2. Section 3 then formulates four, increasingly stringent criteria for equality of opportunity. In Section 4, we turn to an empirical implementation of these criteria to test for equality of opportunity in the United States and Britain. The results, presented in Section 5, provide only the weakest of support for equality of opportunity in the United States and no support at all in Britain. Concluding remarks are presented in Section 6.