Knowledge that Transforms

MODELS WHICH INCORPORATE both uncertainty and the dynamic behavior of economic agents are difficult to analyze.2 Moreover, even when a solution is obtained, it can seldom be simply stated and rarely lends itself to straightforward interpretations. An example of an appealingly understood result is a turnpike theorem, which states that if the planning horizon is distant then the optimal policy can be approximated by a wealth-independent policy. Our paper develops an analogous result in a stochastic intertemporal model of portfolio selection. In fact, we obtain necessary and some sufficient conditions for a turnpike. The problem considered in this essay is that of an investor-a von NeumannMorgenstern expected utility maximizer-who invests for a finite horizon and consumes only his terminal wealth. At the beginning of the first period the investor allocates his wealth, w, among various assets, and at the end of the first

[In the context of regression models with stochastic explanatory variables, the exact sampling distribution of the omitted variable (OV) estimator is derive. We show that stochastic regressors present the problem of larger variance for the OV estimator than in the nonstochastic case, and derive conditions under which omission may be better under a minimum mean square error criterion. Since the errors-in-variables problem can be interpreted as a specification error problem with stochastic regressors, we also consider the issue of MSE dominance of the proxy-variable estimator over the OV estimator.]

[An example is given of a sequence of labor managed economies with decreasing efficiency sizes for which a free entry Cournot equilibrium fails to exist.]

This paper considers the null hypothesis that the errors on a regression equation form a random walk. By using the standard Durbin-Watson assumptions, we derive three test statistics that are uniformly most powerful against the alternative hypothesis that the errors are being generated by the stationary first order Markoff process. Unfortunately, the tabulated lower and upper bounds are too wide apart and so we compare the powers of the three tests using simulated as well as economic data. It is then recommended that the Imhof routine should be attached to standard regression programs to calculate the exact limit of the Berenblut-Webb statistic.

THIS PAPER BELONGS to that part of economic dynamics of which the consumption turnpike theorems are typical results. However, rather than the usual formulation of the problem as a mathematical programming problem, we study it in the framework of dynamic equilibrium models which were first studied in [9]. In [9] we considered finite equilibrium trajectories for which the technology as well as demand functions were assumed constant in time. Here a more general model will be described. It permits changing technology and demand functions and pays more attention to the exploration of the asymptotic properties of infinite trajectories. We define the class of efficient equilibrium trajectories and prove that, under certain conditions, infinite trajectories in this class converge to each other. Finite trajectories (which are always efficient) may differ essentially from them only at the beginning and at the end of the planning period. For a stationary model a strong turnpike theorem follows from these considerations. It is shown that nonefficient equilibrium trajectories are characterized by fast growth of prices and high levels of production. At the same time, the consumption, as a rule, goes to zero. Here we present conditions which imply the uniqueness of efficient trajectories and the absence of nonefficient ones. For the special case in which the equilibrium model is equivalent to an optimization model, efficient equilibrium trajectories are strongly optimal.

[In the axiomatic theory of n-person bargaining, we show that there is a unique solution possessing properties: efficiency, symmetry, invariance under utility transformations, independence of irrelevant alternatives other than ideal point, and individual monotonicity on comparable domains. The solution obtained both extends and modifies the solution characterized by Kalai and Smorodinsky which is also known as Raiffa's solution, and is given a characterization as the lexicographic maxmin solution up to a normalization of utilities. The result can be translated to provide an axiomatic derivation of the Rawlsian lexmin choice function with a suitable redressing.]

Economic theorists have interpreted the "efficient markets hypothesis" to assert that equilibrium asset prices reveal all decision-relevant information in the market. This paper establishes conditions on investors' utility functions of future wealth which are necessary for the efficient markets hypothesis to be satisfied and be robust to slight perturbations of endowments and the joint distribution of current information and future asset values. The main result states that over the relevant range of future wealth values, there are three possible cases: (i) all investors are risk-neutral; (ii) modulo a change in the wealth origin, each investor has constant relative risk aversion with the same constant for all investors; or (iii) all investors have constant absolute risk aversion.

ARMAX systems in structural specification are considered. Topological and geometric properties of the parameter space and of the parameterization which are important for the properties of the estimators, regardless of their special form, are investigated and the specification of the maximum lag lengths is discussed.

We consider optimal capital accumulation in a nonlinear activity analysis model in which production and primary resource supplies are affected by a stationary stochastic process of exogenous shocks; the optimality criterion is the sum of discounted expected future social utilities. Under various neoclassical conditions on technology and preferences, (i) there exists an optimal policy of investment and consumption expressible as a continuous time-invariant function of the capital stocks and the history of stochastic shocks, and (ii) there is a stationary stochastic process of capital stocks that is consistent with the optimal policy.