DANS CE MODELE, on considere un agent economique seulement. Celui-ci dispose d'un actif de montant c0 et cherche 'a I'affecter au mieux, mettons en totalite sur k placements pendant une periode definie assez courte. Les taux d'interet qui correspondent 'a chaque sorte de placement sont, pour la periode 'a venir en question, aleatoires-objectifs soit (X1, . . ,Xk).1 Designons par (b1,.. ., bk) ou Yk bi = 1 et bi >0 une affectation de co envisagee par cet agent. Le montant d'actif en fin de periode est actuellement aleatoire et donne par l'equation

[It is known that there is a one-to-one correspondence between stationary ARMAX and state space models. In order to estimate these it is necessary first to identify and further, having identified, to choose parameters. This paper discusses the properties a system of identification and parameterization might be desired to have in relation to various examples of identification. It also constructs a (known) canonical state space form (identification) out of the constants needed to specify the corresponding ARMAX form. It is argued that what is here called "simple identification" will be the best basis for identification even though some structures cannot be identified in this manner.]

[This paper considers an income maximizing life cycle model of human capital accumulation with the objective of simultaneous estimation of the parameters of the model from observations of the age-earnings profile. The earnings profile, which is a solution to the optimal control problem, is nonlinear and therefore was estimated by nonlinear least squares. The parameter estimates are all quite precise (in the standard error sense) and seem to be intuitively reasonable. The results given here suggest that optimal control models can be verified by direct estimation of the solution.]

[In this paper, we propose a procedure based on the use of the Moore-Penrose inverse of matrices for deriving unique indirect least squares (ILS) estimates of the structural parameters in the overidentified case. The procedure makes use of all reduced form estimates in deriving the unique structural estimates. The estimator is shown to be consistent. We derive the relationship between this estimator, the two stage least squares (2SLS) estimator, and instrumental variables (IV) estimators. We also derive the asymptotic distribution of the proposed estimator, and extend the procedure to a full information ILS estimator (FILS). The results of sampling experiments are summarized.]

WE CONSIDER A MICROECONOMIC growth model in which a certain product or service, supplied and consumed period by period, becomes more valuable to a consumer-objectively or subjectively-as its use becomes widespread, up to some level of saturation. A reasonable example might be the rental of communication facilities. Taking the standpoint of the producer, we ask for that schedule which maximizes the present value of the profit stream. We show that the solution to this problem differs considerably from that given by profit maximization in each individual period (sometimes termed myopic): it calls for lower prices to the consumer. As such, it provides some quantitative justification for practical policies of pricing for development. Its intuitive explanation is that lower prices (i.e., larger outputs) in the initial stages speed the buildup of demand to its saturation value; the larger profits realizable on larger volume are thereby brought foward in time and increase their contribution to the discounted stream. This effect, being independent of the shape of demand or cost curves, may be attributed to growth alone. It suggests that growth potential, when properly perceived and utilized, can yield a mutual gain to the producer and consumers, since the latter benefit not only from lower prices, but also from the fact that the value of the product to them, which is assumed to increase with higher use, likewise rises more rapidly.

The paper develops a simple iterative procedure for deriving linear decision rules which provide the optimal control policy for a stochastic dynamic linear system. The procedure works for a quadratic objective function with any time horizon up to and including infinity, either with or without time discounting. The role of target variables is conisidered and there is a discussion of the results which ensue if these targets are incompatible, that is, if they do not satisfy the underlying structural model. The paper concludes with some consideration of the convergence and other properties of the controlled system. THIS PAPER DEVELOPS a simple iterative method for deriving linear decision rules which provide the control policy for a stochastic dynamic linear system which is optimal for a quadratic criterion. The basic theory in economics was developed by Holt, Simon, Theil, Phillips, and others2 in the fifties and has recently been extended by Aoki [1], Chow [2 and 3], and Turnovsky [10]. The method described here is similar to that used by Chow [3] where the dynamic structure of the model is used to develop a suitable iterative procedure. This procedure is computationally simple, of low dimensionality, and may be applied to a system with any number of lags, irrespective of whether it is stable or unstable. For economic applications, the underlying system would typically be an econometric model in reduced form which has either been specially estimated as a completely linear model or has been suitably linearized. In Section 2 of the paper we derive a general procedure for solving an infinite horizon quadratic programming problem, proving both its convergence and optimality properties. In Sections 3 and 4 we discuss how this procedure may be adapted to solve finite and infinite horizon stochastic control problems and demonstrate some properties of the optimal path. Since the method produces an analytically explicit solution we are enabled to develop some further convergence properties of the infinite horizon, optimal path in Section 5. The specific control problem to be discussed in this paper is one of the following

[A specialization of the Edgeworth type formulae due to Chambers [4] to approximate the marginal distribution of an econometric estimator is presented, and its application to improvement of the use of asymptotic limits in significance testing is discussed. Appendices discuss the validity of Nagar approximations to estimator moments, the exact distribution of the instrumental variable estimator, the Edgeworth approximations for 3SLS and FIML estimators, and the use of Monte Carlo procedures for assessing the appropriate probability to attach to a given significance test.]

[Economists as yet have relatively little evidence concerning the sign of the net cross-price effect in a family model of labor supply. Part of the problem is attributable to a lack of quality data for nonlabor income. In this paper I derive a simple indirect test which does not require accurate estimates of income effects and apply it to data from the National Longitudinal Survey.]

[Ostroy and Starr [3] have recently shown how money (a good which may be traded although it satisfies no excess supply/demand) allows decentralized achievement of competitive equilibrium allocations via a round of bilateral trades. Following Jevons [1], monetary exchange is here defined as any trade which decreases the utility of any participant. The consequences of this alternative definition for the Ostroy/Starr thesis are investigated and generalized to cover the case where exchange takes place multilaterally (instead of just bilaterally).]