An important purpose in pooling time-series and cross-section data is to control for individual-specific unobservable effects which may be correlated with other explanatory variables, e.g. latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions. Using instrumental variables and the time-invariant characteristics of the latent variable, we derive: 1. (1) a test for the presence of this effect and for the over-identifying restriction we use; 2. (2) necessary and sufficient conditions for identification of all the parameters in the model; and 3. (3) the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within-groups estimator. We calculate efficient estimates of a wage equation from the Michigan income dynamics data which indicate substantial differences from within-groups and Balestra-Nerlove estimates — particularly a significantly higher estimate of the returns to schooling.

Linear time series models have come to dominate the macroeconomic literature on rational expectations and equilibrium business cycle theory. But the explicit solution of such models has generally required strong restrictions upon the exogenous process of stochastic shocks (e.g., temporal independence) as well as upon the values of various demand and supply elasticities. This paper exhibits a solution technique, the method of z-transforms, which does not require one to impose such restrictions. The value of this method is illustrated by applying it to completely characterize the symmetric, stationary, rational expectations equilibria of a naive linear model of land speculation. This approach also permits systematic study of the informationally asymmetric equilibria of the model. THIS PAPER develops a method for analyzing rational expectations (RE) equilibria in linear economic models. The methods I shall discuss usually enable one to determine whether or not a given model has a RE equilibrium and, if one exists, to exhibit an explicit expression for the stochastic process of equilibrium prices. The techniques apply to linear models driven by stationary processes of exogenous random shocks

[Agents are assumed to have smooth preferences with natural boundary conditions. For large regular economies, satisfying an indeconposability conditions, it is shown that core allocations and competitive allocations converge to each other with a rate inversely proportional to the number of agents m. To the extent that the indecomposability condition is harmless, 1/m can be regarded as the normal rate of convergence. However, if indifference surfaces are allowed to have kinks, 1/m cannot be regarded as normal. This is treated in Part II [6].]

The situation in which a principal-agent relationship is repeated finitely many times (T) is formulated as a sequential game.For any Pareto-optimal cooperative arrangement in the one-period game that dominates a one-period Nash equilibrium, and any positive number epsilon, there exists for every sufficiently large T a (noncooperative) epsilon equilibrium of the T-period game that yields each player an average expected utility that is at least his expected utility in the one-period cooperative arrangement, less epsilon.

[If independent observations x are drawn from the distribution located at @m, f (x; @m)=c"3 exp[-g(x -@m)], and if g is symmetric and strictly convex, then the maximum likelihood estimate of μ lies between the smallest and largest folded sample observations. If the distribution has fatter tails than a normal distribution, then the maximum likelihood estimate lies between the smallest and largest means of trimmed subsamples. If the distribution is assumed to be symmetric and unimodal, the centers of tight clusters of observations can be maximum likelihood estimates. If observations are not independent, then there is no bound: given any example any number is a maximum likelihood estimate for some sampling distribution. Stationary is not sufficient to bound the estimate between the minimum and maximum observations.]

We consider economies with preferences drawn from a very general class of strongly convex preferences, closely related to the class of convex (but intransitive and incomplete) preferences for which Mas-Colell proved the existence of competitive equilibria [13]. We prove a strong core limit theorem for sequences of such economies with a mild assumption on endowments (the largest endowment is small compared to the total endowment) and a uniform convexity condition. The results extend corresponding results in Hildenbrand's book [8]. The proof, which is based on our earlier result for economies with more general preferences [2], is elementary.