The diversification discount (multiple segment firm value below the value imputed using single segment firm multiples) is commonly thought to be generated by agency problems, a lack of transparency, or lackluster future prospects for diversified firms. If multiple segment firms have lower uncertainty about mean profitability than single segment firms, rational learning about mean profitability provides an alternative explanation for the diversification discount that does not rely on suboptimal managerial decisions or a poor firm outlook. Empirical tests which examine changes in firm value across the business cycle and idiosyncratic volatility are consistent with lower uncertainty about mean profitability for multiple segment firms.

The topic of this paper is inference in models in which parameters are defined by moment inequalities and/or equalities. The parameters may or may not be identified. This paper introduces a new class of confidence sets and tests based on generalized moment selection (GMS). GMS procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative. The power of GMS tests is compared to that of subsampling, m out of n bootstrap, and “plug-in asymptotic” (PA) tests. The latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size (in a uniform sense) for the moment inequality/equality model. GMS tests are shown to have asymptotic power that dominates that of subsampling, m out of n bootstrap, and PA tests. Subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of PA tests.