Hector Chade Publications

We analyze a multidimensional screening model in which a principal offers a menu of quality-price pairs to a consumer with multiple dimensions of private information and a quasilinear utility function. We derive necessary conditions for optimality, and use them to provide insight into optimal exclusion, positive trade, and screening. We then recast the problem in terms of incremental quality levels and prices, the so-called demand-profile approach (DPA). Under DPA, the problem decouples across increments and can be solved one at a time. We provide novel conditions under which DPA recovers the solution to the full problem exactly or approximately, and which make the necessary conditions sufficient for optimality: essentially, valuations must be sufficiently correlated across quality increments. Applied to empirical estimates of demand for health insurance, we show that DPA is approximately valid, and we apply it to understand equilibrium outcomes in a monopoly insurance market.

We study infinitely repeated games with observable actions, where players have present-biased (so-called beta-delta) preferences. We give a two-step procedure to characterize Strotz–Pollak equilibrium payoffs: compute the continuation payoff set using recursive techniques, and then use this set to characterize the equilibrium payoff set U(beta,delta). While Strotz–Pollak equilibrium and subgame perfection differ here, the generated paths and payoffs nonetheless coincide.

We then explore the cost of the present-time bias. Fixing the total present value of 1 util flow, lower beta or higher delta shrinks the payoff set. Surprisingly, unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set U(beta,delta) is not separately monotonic in beta or delta. While U(beta,delta) is contained in payoff set of a standard repeated game with smaller discount factor, the present-time bias precludes any lower bound on U(beta,delta) that would easily generalize the beta = 1 folk-theorem.

Keywords: Beta-delta preferences, Repeated games, Dynamic programming, Strotz–Pollak equilibrium

JEL Classification: C73

We introduce and solve a new class of “downward-recursive” static portfolio choice problems. An individual simultaneously chooses among ranked stochastic options, and each choice is costly. In the motivational application, just one may be exercised from those that succeed. This often emerges in practice, such as when a student applies to many colleges.

We show that a greedy algorithm finds the optimal set. The optimal choices are “less aggressive” than the sequentially optimal ones, but “more aggressive” than the best singletons. The optimal set in general contains gaps. We provide a comparative static on the chosen set.

Keywords: College application, Submodular optimization, Greedy algorithm, Directed search

JEL Classification: C61, D83, J64