We investigate a method for extracting nonlinear principal components. These principal components maximize variation subject to smoothness and orthogonality constraints; but we allow for a general class of constraints and multivariate densities, including densities without compact support and...

We make the case for the U.S. government to issue a new security with a coupon tied to the United States’ current dollar GDP. This security might pay, for example, a coupon of one-trillionth of the GDP, and we propose the name "Trill" be used to refer to this new security. This new debt...

This paper examines circumstances under which subjectivity enhances the effectiveness of inductive reasoning. We consider a game in which Fate chooses a data generating process and agents are characterized by inference rules that may be purely objective (or data-based) or may incorporate...

These notes are provided to describe many of the problems encountered concerning both structure and behavior in specifying what is meant by the solution to a game of strategy in matrix or strategic form. In the short term in particular, it is often reasonable for the individual to accept as...

This forthcoming chapter in the Handbook of Income Distribution (eds., A. Atkinson and F. Bourguignon) summarizes the literature on equality of opportunity. We begin by reviewing the philosophical debate concerning equality since Rawls (sections 1 and 2), present economic algorithms for...

Why did evolution not give us a utility function that is offspring alone? Why do we care intrinsically about other outcomes, such as food, and what determines the intensity of such preferences? A common view is that such other outcomes enhance fitness and the intensity of our preference for a...

We analyze the welfare consequences of a monopolist having additional information about consumers' tastes, beyond the prior distribution; the additional information can be used to charge different prices to different segments of the market, i.e., carry out "third degree price discrimination." We...