Knowledge that Transforms

This paper presents three sets of results about equilibrium bias of technology. First, I show that when the menu of technological possibilities only allows for factor-augmenting technologies, the increase in the supply of a factor induces technological change relatively biased toward that factor—meaning that the induced technological change increases the relative marginal product of the factor becoming more abundant. Moreover, this induced bias can be strong enough to make the relative marginal product of a factor increasing in response to an increase in its supply, thus leading to an upward-sloping relative demand curve. I also show that these results about relative bias do not generalize when more general menus of technological possibilities are considered. Second, I prove that under mild assumptions, the increase in the supply of a factor induces technological change that is absolutely biased toward that factor—meaning that it increases its marginal product at given factor proportions. The third and most important result in the paper establishes the possibility of and conditions for strong absolute equilibrium bias—whereby the price (marginal product) of a factor increases in response to an increase in its supply. I prove that, under some regularity conditions, there will be strong absolute equilibrium bias if and only if the aggregate production function of the economy fails to be jointly concave in factors and technology. This type of failure of joint concavity is possible in economies where equilibrium factor demands and technologies result from the decisions of different agents.

This paper considers issues related to estimation, inference, and computation with multiple structural changes that occur at unknown dates in a system of equations. Changes can occur in the regression coefficients and/or the covariance matrix of the errors. We also allow arbitrary restrictions on these parameters, which permits the analysis of partial structural change models, common breaks that occur in all equations, breaks that occur in a subset of equations, and so forth. The method of estimation is quasi-maximum likelihood based on Normal errors. The limiting distributions are obtained under more general assumptions than previous studies. For testing, we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes. Structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present. For computation, an algorithm for an efficient procedure is proposed to construct the estimates and test statistics. We also introduce a novel locally ordered breaks model, which allows the breaks in different equations to be related yet not occurring at the same dates.

When two parties have different prior beliefs about some future event, they can realize gains through speculative trade. Can these gains be realized when the parties' prior beliefs are not common knowledge? We examine a simple example in which two parties having heterogeneous prior beliefs, independently drawn from some distribution, bet on what future action one of them will choose. We define a notion of "constrained interim-efficient" best and ask whether they can be implemented in Bayesian equilibrium by some mechanism. Our main result establishes that as the costs of unilaterally manipulating the bet's outcome become more symmetric across states, implementation becomes easier. In particular, when these costs are equal in both states, implementation is possible for any distribution.

This paper develops and applies some new results in the theory of monotone comparative statics. Let f be a real-valued function defined on Rl and consider the problem of maximizing f(x) when x is constrained to lie in some subset C of Rl. We develop a natural way to order the constraint sets C and find the corresponding restrictions on the objective function f that guarantee that optimal solutions increase with the constraint set. We apply our techniques to problems in consumer, producer, and portfolio theory. We also use them to generalize Rybcsynski's theorem and the LeChatelier principle.

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Rationalizability is a central solution concept of game theory. Economic models often have many rationalizable outcomes, motivating economists to use refinements of rationalizability, including equilibrium refinements. In this paper we try to achieve a general understanding of when this multiplicity occurs and how one should deal with it. Assuming that the set of possible payoff functions and belief structures is sufficiently rich, we establish a revealing structure of the correspondence of beliefs to sets of rationalizable outcomes. We show that, for any rationalizable action a of any type, we can perturb the beliefs of the type in such a way that a is uniquely rationalizable for the new type. This unique outcome will be robust to further small changes. When multiplicity occurs, then we are in a “knife-edge” case, where the unique rationalizable outcome changes, sandwiched between open sets of types where each of the rationalizable actions is uniquely rationalizable. As an immediate application of this result, we characterize, for any refinement of rationalizability, the predictions that are robust to small misspecifications of interim beliefs. These are only those predictions that are true for all rationalizable strategies, that is, the predictions that could have been made without the refinement.

Consider a two-person intertemporal bargaining problem in which players choose actions and offers each period, and collect payoffs (as a function of that period's actions) while bargaining proceeds. This can alternatively be viewed as an infinitely repeated game wherein players can offer one another enforceable contracts that govern play for the rest of the game. Theory is silent with regard to how the surplus is likely to be split, because a folk theorem applies. Perturbing such a game with a rich set of behavioral types for each player yields a specific asymptotic prediction for how the surplus will be divided, as the perturbation probabilities approach zero. Behavioral types may follow nonstationary strategies and respond to the opponent's play. In equilibrium, rational players initially choose a behavioral type to imitate and a war of attrition ensues. How much should a player try to get and how should she behave while waiting for the resolution of bargaining? In both respects she should build her strategy around the advice given by the "Nash bargaining with threats" (NBWT) theory developed for two-stage games. In any perfect Bayesian equilibrium, she can guarantee herself virtually her NBWT payoff by imitating a behavioral type with the following simple strategy: in every period, ask for (and accept nothing less than) that player's NBWT share and, while waiting for the other side to concede, take the action Nash recommends as a threat in his two-stage game. The results suggest that there are forces at work in some dynamic games that favor certain payoffs over all others. This is in stark contrast to the classic folk theorems, to the further folk theorems established for repeated games with two-sided reputational perturbations, and to the permissive results obtained in the literature on bargaining with payoffs as you go. Copyright The Econometric Society 2007.

This paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression, or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified. Failure to account for misclassification is shown to result in attenuation bias in the estimated treatment effect. An identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect. A discrete instrument suffices for nonparametric identification.

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In this paper, we generalize the notion of Pareto-efficiency to make it applicable to environments with endogenous populations. Two efficiency concepts are proposed, P-efficiency and A-efficiency. The two concepts differ in how they treat potential agents that are not born. We show that these concepts are closely related to the notion of Pareto-efficiency when fertility is exogenous. We then prove versions of the first welfare theorem assuming that decision making is efficient within the dynasty. We discuss two sets of sufficient conditions for noncooperative equilibria of family decision problems to be efficient. These include the Barro and Becker model as a special case. Finally, we study examples of equilibrium settings in which fertility decisions are not efficient, and classify them into ones where inefficiencies arise inside the family and ones where they arise across families.