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Bayesian Limited Information Analysis of the Simultaneous Equations Model

Econometrica 1976 44(5), 1045
[This paper presents a Bayesian analysis of a single equation from a simultaneous equations system. The analysis is carried out under "limited information" because no prior information (other than a list of endogenous and exogenous variables) is introduced on the parameters of the remaining equations in the in the system. These parameters are integrated out analytically. The equation of interest may or may not be identified by means of exact a priori information; probabilistic prior information is equally acceptable. The prior density is either of the non-informative or the natural conjugate type. The kernel of the posterior density for the regression coefficients is a ratio of t kernels. The existence of posterior moments is ascertained. This approach is applied for illustrative purposes to Tintner's model of the meat market.]

On the Role of Separability Assumptions in Determining Impatience Implications

Econometrica 1976 44(1), 67
The impatience implications of continuous time utility indicators are interesting to the extent that they differ from the discrete time results. The class of tFaditional integral utility indicators are considered and impatience implications are shown to depend on the dif- ferent convergence implications of the continuous time case. The stronger separability assumptions of continuous time utility indicators allow a weakening of compactness assumptions often required to demonstrate impatience. presence of impatience. Specific separability assumptions were invoked by Koopmans (8) and Koopmans, Diamond, and Williamson (9) in order to demonstrate the presence of impatience in problems involving choice over an infinite program horizon. From a paper by Diamond (4) one,can infer much of the relationship between separability assumptions and impatience implications. Diamond employed several intertemporal non-complementary assumptions to demonstrate eventual impatience for a case in which the consumption space was not compact in the topology of the norm. The use of non-complementary axioms seems justifijable as their economic implications are straightforward while those of compactness assumptions are not immediately obvious.2 Moreover the natural extension of Diamond's first axiom to all time periods yields a condition equivalent to the independence assumption employed by Debreu (3) in representing preferences by an additive function. Consequently, this paper analyzes separable utility indicators directly for impatience implications; the analysis considers the continuous time case as it subsumes the discrete time analog. However the discrete time case will be discussed in order to facilitate analogy construction.

Pricing in a Dynamic Model with Saturation

Econometrica 1976 44(6), 1153
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.