We provide an axiomatic foundation for decision making in a complex environment. We do not assume that the decision maker has complete structural knowledge of the environment. Instead the agent knows the set of actions he can take, he formulates preferences directly on the actions, and chooses according to these preferences. On the basis of experience he modifies these preferences according to a systematic procedure. Our axioms are imposed on this procedure, rather than directly on the choice itself. The axioms consists of a group of natural structural restrictions and a group of independence axioms. Our main result is an axiomatic foundation for a set of simple adaptive learning procedures which include the replicator dynamic.
This paper considers a generalized method of moments (GMM) estimation problem in which one has a vector of moment conditions, some of which are correct and some incorrect. The paper introduces several procedures for consistently selecting the correct moment conditions. The procedures also can consistently determine whether there is a sufficient number of correct moment conditions to identify the unknown parameters of interest. The paper specifies moment selection criteria that are GMM analogues of the widely used BIC and AIC model selection criteria. (The latter is not consistent.) The paper also considers downward and upward testing procedures. All of the moment selection procedures discussed in this paper are based on the minimized values of the GMM criterion function for different vectors of moment conditions. The procedures are applicable in time-series and cross-sectional contexts. Application of the results of the paper to instrumental variables estimation problems yields consistent procedures for selecting instrumental variables.
An exponentially small departure from the common knowledge assumption on the number T of repetitions of the prisoners' dilemma already enables cooperation. More generally, with such a departure, any feasible individually rational outcome of any one-shot game can be approximated by an equilibrium of a finitely repeated version of that game. The departure from common knowledge is small in the following sense:(1) the players know T with precision +/-K; (2) with probability 1 - epsilon, the players know T precisely; moreover, this knowledge is mutual of order epsilon T; and (3) the deviation of T from its finite expectation is exponentially small.
Vector AutoRegressions (VARs) have now become the most popular tool of Time Series analysis amongst econometricians. Unfortunately, little is known about the analytic finite-sample properties of parameter estimators for such systems. The asymptotic analysis of VARs published to date does not address questions regarding the influence of the number and nature of the system's variates on parameter estimates. Clearly, both questions will have repercussions on the way VARs are used, and we intend to address them here.We consider the implications of varying the dimensions of VARs on the biases of Maximum Likelihood and Least Squares Estimators (MLE and LSE, respectively). In the purely nonstationary case (k-dimensional random walk), estimator biases are approximately equal to the dimension of the system (k) times the univariate bias, even when the variates are generated independently of each other. We show that the variance too increases with the dimension of the system, hence also raising the Mean Squared Error (MSE) of the estimator. When some stable linear combinations exist, the biases are generally smaller and are asymptotically proportional to the sum of the characteristic roots of the VAR. One source of such combinations is meaningful economic relations that are represented by the cointegration of some of the components of the VAR. Adding economically-irrelevant variables to a VAR is thus shown to have more serious negative consequences in integrated time series than in classical ergodic or cross section analyses. The findings strengthen the case for parsimonious modelling and for the reduction step of the general-to-specific marginalization method. They also support the use of seasonally unadjusted data whenever possible.
A dynamic search framework is developed to analyze the intertemporal labor force participation behavior of married women, using longitudinal data to allow for a rich dynamic structure. The sensitivity to alternative distributional assumptions is evaluated using linear probability and probit models. The dynamic probit models are estimated using maximum simulated likelihood (MSL) estimation, to overcome the computational difficulties inherent in maximum likelihood estimation of models with nontrivial error structures. The results find that participation decisions are characterized by significant state dependence, unobserved heterogeneity, and negative serial correlation in the error component. The hypothesis that fertility decisions are exogenous to women's participation decisions is rejected when dynamics are ignored; however, there is no evidence against this hypothesis in dynamic model specifications. Women's participation response is stronger to permanent than current nonlabor income, reflecting unobserved taste factors.
When players have identical time preferences, the set of feasible repeated game payoffs coincides with the convex hull of the underlying stage- game payoffs. Moreover, all feasible and individually rational payoffs can be sustained by equilibria if the players are sufficiently patient. Neither of these facts generalizes to the case of different time preferences. First, players can mutually benefit from trading payoffs across time. Hence, the set of feasible repeated game payoffs is typically larger than the convex hull of the underlying stage-game payoffs. Second, it is not usually the case that every trade plan that guarantees individually rational payoffs can be sustained by an equilibrium, no matter how patient the players are. This paper provides a simple characterization of the sets of Nash and of subgame perfect equilibrium payoffs in two-player repeated games.
This paper extends the classic two-armed bandit problem to a many-agent setting in which N players each face the same experimentation problem. The main change from the single-agent problem is that an agent can now learn from the current experimentation of other agents. Information is therefore a public good, and a free-rider problem in experimentation naturally arises. More interestingly, the prospect of future experimentation by others encourages agents to increase current experimentation, in order to bring forward the time at which the extra information generated by such experimentation becomes available. The paper provides an analysis of the set of stationary Markov equilibria in terms of the free-rider effect and the encouragement effect.
In this paper, we structurally estimate a sequential model of high school attendance and work decisions. The estimates imply that youths who drop out of high school have different traits than those who graduate, e.g., they have lower school ability and/or motivation, lower expectations about the rewards from graduation, and a comparative advantage at jobs that are done by non-graduates. We also found that working while in school reduces school performance. However, policy experiments indicate that even a complete prohibition on working would have a limited impact on the high school graduation rates of white males.
We derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be the solution of such a problem. If the maintained assumptions include free disposal and monotonicity, then we obtain a complete characterization of all optimal policy and optimal value functions. This is the case, e.g., in the standard aggregative optimal growth model.