J. Tinbergen, Tjalling C. Koopmans, Jacob Marschak, Francois Divisia, Jacques Rueff, B. Chait, La loi de divergence: Discussion, Econometrica, Vol. 17, Supplement: Report of the Washington Meeting (Jul., 1949), pp. 124-128

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional cointegrating regressions where the regressor is an integrated time series, it is shown here that inverse and ill-posed inverse problems do not arise. Remarkably, nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving simple useable asymptotics in practical work. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series. The methods may be applied to a wide range of empirical models where functional estimation of cointegrating relations is required.

We prove existence of equilibrium in a continuous-time securities market in which the securities are potentially dynamically complete: the number of securities is at least one more than the number of independent sources of uncertainty. We prove that dynamic completeness of the candidate equilibrium price process follows from mild exogenous assumptions on the economic primitives of the model. Our result is universal, rather than generic: dynamic completeness of the candidate equilibrium price process and existence of equilibrium follow from the way information is revealed in a Brownian filtration, and from a mild exogenous nondegeneracy condition on the terminal security dividends. The nondegeneracy condition, which requires that finding one point at which a determinant of a Jacobian matrix of dividends is nonzero, is very easy to check. We find that the equilibrium prices, consumptions, and trading strategies are well-behaved functions of the stochastic process describing the evolution of information. We prove that equilibria of discrete approximations converge to equilibria of the continuous-time economy.

This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported. Copyright The Econometric Society 2006.

[We consider an economy in which agents may or may not communicate with each other. Coalitions can form only between linked agents. We consider two cases: agents must communicate directly to be in the same coalition or in the second case indirectly. We consider the communication to be random. The economy may then be represented by a stochastic graph; the admissible coalitions are then stochastic and thus so is the core of an economy. We demonstrate that if the probability that agents are linked with each other does not tend to zero too fast as this number increases, then the probability that a coalition will form and block any non-Walrasian allocation tends to one, as the number of agents goes to infinity.]

Estimators obtained by maximizing a likelihood function are studied in the case where the true p.d.f. does not necessarily belong to the family chosen for the likelihood function. When such a procedure is applied to the estimation of the parameters of the first order moments, it is possible to prove a necessary and sufficient condition for its consistency. Asymptotic normality is shown as well as the existence of a lower bound for the asymptotic covariance matrix. It is also seen that this bound can be reached if consistent estimates are available for the parameters of the second order moments. Finally, a necessary and sufficient condition for the consistency if the pseudo maximum likelihood estimation of the first and second moments is given.

A solution method and an estimation method for nonlinear rational expectations models are presented in this paper.The solution method can be used in forecasting and policy applications and can handle models with serial correlation and multiple viewpoint dates.When applied to linear models, the solution method yields the same results as those obtained from currently available methods that are designed specifically for linear models.It is, however, more flexible and general than these methods.The estimation method is based on the maximum likelihood principal.It is, as far as we know, the only method available for obtaining maximum likelihood estimates for nonlinear rational expectations models.The method has the advantage of being applicable to a wide range of models, including, as a special case, linear models.The method can also handle different assumptions about the expectations of the exogenous variables, something which is not true of currently available approaches to linear models.

We study the joint design of dynamic incentives and performance feedback for an environment with a coarse (all‐or‐nothing) measure of performance, and show that hiding information from the agent can be an optimal way to motivate effort. Using a novel approach to incentive compatibility, we derive a two‐phase solution that begins with a “silent phase” where the agent is given no feedback and is asked to work non‐stop, and ends with a “full‐transparency phase” where the agent stops working as soon as a performance threshold is met. Hiding information leads to greater effort, but an ignorant agent is also more expensive to motivate. The two‐phase solution—where the agent's ignorance is fully frontloaded—stems from a “backward compounding effect” that raises the cost of hiding information as time passes.

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that when each agent's signal space is finite, the agents will commonly learn the value of the parameter, that is, that the true value of the parameter will become approximate common knowledge. The essential step in this argument is to express the expectation of one agent's signals, conditional on those of the other agent, in terms of a Markov chain. This allows us to invoke a contraction mapping principle ensuring that if one agent's signals are close to those expected under a particular value of the parameter, then that agent expects the other agent's signals to be even closer to those expected under the parameter value. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.

This paper develops a nonparametric theory of preferences over one's own and others' monetary payoffs. We introduce ?more altruistic than? (MAT), a partial ordering over such preferences, and interpret it with known parametric models. We also introduce and illustrate ?more generous than? (MGT), a partial ordering over opportunity sets. Several recent studies focus on two-player extensive form games of complete information in which the first mover (FM) chooses a more or less generous opportunity set for the second mover (SM). Here reciprocity can be formalized as the assertion that an MGT choice by the FM will elicit MAT preferences in the SM. A further assertion is that the effect on preferences is stronger for acts of commission by FM than for acts of omission. We state and prove propositions on the observable consequences of these assertions. Finally, empirical support for the propositions is found in existing data from investment and dictator games, the carrot and stick game, and the Stackelberg duopoly game and in new data from Stackelberg mini-games.