Knowing the degree of substitutability between schooling groups is essential to understanding the role of human capital in income differences and to assessing the economic impact of such policies as schooling subsidies, immigration systems, or redistributive taxes. We derive a lower bound for...

Central bank balance sheet expansion is financed by commercial banks. It involves not just a substitution of liquid central bank reserves for other assets held by commercial banks, but also a counterpart alteration in commercial bank liabilities, such as in short-term deposits issued to finance...

This paper considers the problem of making inferences about the effects of a program on multiple outcomes when the assignment of treatment status is imperfectly randomized. By imperfect randomization we mean that treatment status is reassigned after an initial randomization on the basis of...