[This paper discusses the constraints on a dynamic equation represented by the possibility of factoring out an autoregressive error specification from a general lag structure. A suitable Wald test is defined and applied to a practical case.]
IN THE LATE 1960's, Richardson [18] and Sawa [20] derived the exact distribution of the two-stage least squares (2SLS) estimator in a structural equation (of a simultaneous system) that contained two endogenous variables and an arbitrary number of degrees of overidentification. Their results refer to the 2SLS estimator of the coefficient of the endogenous variable included on the right hand side of the equation and were obtained under the classical assumptions (to use the term employed by Sargan [19]) of normally distributed disturbances and nonrandom exogenous variables. Very little exact finite sample theory has been published so far for estimators in structural equations containing more than two endogenous variables. Basmann et al. [4] extract the joint probability density function (p.d.f.) of the 2SLS estimator in a just identified equation containing three endogenous variables. Basmann [3] quotes a result due to Richardson for the same set up but with an 2 arbitrary number of degrees of overidentification . In Basmann's notation, this last result characterizes the subclass
This paper discusses the properties of parallel preference structures and their potential usefulness in empirical research. The parallel structure can accommodate arbitrarily flexible substitution properties and linear or nonlinear income-consumption curves, with the linear form representing a special case of the Gorman polar form. The global properties are distinctive in that indifference loci are parallel surfaces, identical in shape and scale at all utility levels. These properties are potentially appropriate for models of family labor supply but are less suitable for applications to production over a wide range of output. Alternative parameterizations and estimation forms are discussed and the model is shown to provide a basis for interpretation of models of labor supply estimated by Professors Ashenfelter and Heckman. PARALLEL PREFERENCE STRUCTURES are characterized by indifference surfaces that are identical in shape and scale, each being a translation of a basic surface along parallel income-consumption curves. The purpose of this paper is to discuss the properties of parallel structures and their potential usefulness in models of labor supply and commodity demand. Limited applications in production analysis are also discussed but are not the primary focus of the paper. In their most tractable form, with linear income-consumption curves, parallel 2 structures are a special case of the Gorman polar form. A suitably parameterized cost or expenditure function for a linear parallel structure provides a second order point approximation to an arbitrary general cost or expenditure function. By that criterion, a variety of simple versions of the parallel structure are on roughly equal footing with other flexible functional forms employed in recent demand, produc
We construct a general equilibrium model of international trade where each government agent has a system of tariffs as his strategic variables. Our general equilibrium model follows recent contributions allowing incompleteness and intransitivity of consumer preferences. Government agents are assumed to have incomplete information on the preferences of domestic consumers and the availability of commodities. The behavior of each government agent is to choose a system of tariffs to maximize the estimated preferences of domestic consumers with a constraint on an estimated availability of commodities. We introduce an equilibrium concept so that (a) estimated preferences and an estimated available set of commodities are compatible with an observed state of the world economy and (b) a consumption bundle intended by each government agent coincides with a consumption bundle chosen by its domestic consumers. Our major goal is to provide the existence of such an equilibrium.
[In a broad class of situations not covered by the Gibbard-Satterthwaite Theorem it is shown that one cannot design a strategy-proof choice mechanism which attains Pareto optimal outcomes. The results are shown to be genetic in character--i.e., any nonmanipulable mechanism will attain nonoptimal outcomes virtually everywhere--and they cover, in particular, certain problems of allocating public and private goods. The analysis is carried out in transferable utility environments, and makes extensive use of the mechanisms recently introduced by Groves.]
The purpose here is to make explicit the sense in which two dynamic processes, due to Malinvaud and others (whose solutions determine an efficient allocation for a given economy), are related to the gradient projection method known in the nonlinear optimization literature. The connections we establish derive from simple observations on first order characterizations of efficient allocations; they also lead to the formulation of another process, that applies to a classical welfare maximization problem; finally, they provide a common basis for an a priori justification of each of the three processes involved, which supplements the intrinsic properties that they can be shown to have.
In this paper we discuss the (Pareto) optimal provision of a public good (desirable or undesirable) in an intergenerational model of an economy, where regeneration is an endogenous decision variable of the households in the economy. We show that in addition to providing desirable public goods and/or levying the well known Pigouvian taxes on polluting industries, a government must subsidize households who are consuming a desirable public good and tax consumers who are consuming an undesirable public good (pollution). In addition, we show that there is a public rate of return, distinct from the market rate of return, that should be used by the government for the evaluation of investments in public goods. This public rate of return is smaller than the market rate of return in a growing economy and larger than the market rate of return in a declining economy. We investigate biases in both the public and market rates of return, as well as in other parameters which characterize the economy, as a result of nonoptimal governmental behavior. We discuss the question of how to aggregate biases due to different public goods. 1. INTRODUCTION THE RENEWED INTEREST in the interrelationship between household behavior and economic growth has recently been emphasized by the contributions of Nerlove [15] and of Razin and Ben Zion [17], both of which offer an intergenerational model of population growth. In this paper we follow the lead of Razin and Ben Zion but add to the economy a public good (desirable or undesirable) and a government whose function is to insure the (Pareto) optimal provision of this public good. We assume a homogeneous population with respect to tastes, abilities, and initial endowments and thus we address only efficiency considerations.
[This paper is concerned with giving general conditions for the validity of a approximation to a distribution function by means of the weighted sum of a set of Chi-squared distribution functions. The conditions are very similar to those of [3]. The approximation is illustrated by an example of its use.]
This paper builds a formal theory of consumer behavior under imperfect information when goods are described by multiple characteristics which vary in their degree of "observability." An optimal strategy for the consumer is shown to exist. In general, this strategy is shown to involve both inspection (sampling to observe general characteristics of goods) and evaluation (consumption of goods to observe specific characteristics). Comparative statics of the optimal strategy are also analyzed.