One of the most important current questions in economic analysis is whether or not labor markets clear in the short run. To answer this, it is necessary to be able to distinguish between restricted and unrestricted behavior by consumers supplying labor. This paper investigates the forms of preferences which lie behind linear models of labor supply, and derives the functional forms for commodity demands which accompany them, both with and without quantity restrictions in the labor market. Simple linkages between restricted and unrestricted demands are also considered as is the question of perfect aggregation over consumers in the presence of quantity restrictions.
and where tl, 2, ... , n-k is a set of independent standard normal variates. The significance points of dM, dL, and du may be evaluated by the methods of Imhof [3] and Pan [8]. Savin and White [9] have noted that Koerts and Abrahamse's [5, pp. 159-160] FORTRAN implementation of Imhof's procedure fails to converge when the significance point is near A1. This defect is easily remedied by replacing Imhof's lower bound for the inverse of the truncation error by
This paper examines some implications of the observation that the same Lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses. A characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification, and the consequences for finite sample power properties are examined by Monte Carlo experiments.
IT IS WELL KNOWN that in an econometric model, under general assumptions, the ex-post forecast error (conditional on predetermined variables) can be decomposed into the sum of two independent terms; the former is the component due to error in estimated coefficients, while the latter depends on the random error terms. The asymptotic covariance matrix of the first component can be analytically derived through intermediate computation of the covariance matrix of restricted reduced form coefficients. However, in the case of overidentified models, this may lead to a great increase in the problem's dimensions, the number of reduced form parameters being larger (often much larger) than the number of structural parameters. This intermediate step is, however, unnecessary; this note discusses a straightforward analytic derivation of the desired matrix directly from the estimated structural parameters, without any increase in the dimensions of the problem, thus facilitating the computation even for medium to large econometric models. Let
MANY PROBLEMS IN MACROECONOMICS, both of closed and open economies, are analyzed by means of expenditure and money demand functions. The properties of these functions play a major role in the derivation of results in these investigations. Although specifiers of such functions have in mind optimizing behavior by economic agents, explicit derivation of their properties from optimizing behavior is seldom undertaken. In many cases in which they are undertaken, it is assumed that utility depends on real money balance (e.g. [2]), an assumption which many find undesirable. There have been recently attempts to deal with macroeconomic issues by explicitly modeling the role of money in the economy thus avoiding the need to model it as an argument of the utility function-and by explicitly using optimizing behavior of economic agents (e.g. [3,5,6]). However, in those cases either the expenditure and money demand functions were characterized for steady states (e.g. [5,6]), or they were not derived because they were not required [3]. In this paper I derive an expenditure and a money demand function which arise from a problem of optimal allocation of consumption over time in which all payments are made in the form of money, there are liquidity constraints, and money is the only asset. Utility is derived only from consumption. These functions can be used to investigate macroeconomic problems as demonstrated
The purpose of this paper is to construct an abstract model of a society in which each member can cooperate with others by forming a coalition, but at the same time can be influenced by the members outside the coalition. A new concept of equilibrium, called here a social coalitional equilibrium, is proposed, and a sufficient condition for its existence provided. The social coalitional equilibrium may be considered a synthesis of the Nash equilibrium (a noncooperative solution concept) and the core (a cooperative solution concept). The paper provides a broadly applicable mathematical tool for proving existence of equilibrium for models of labor-managed market economies. THE PURPOSE OF THE PRESENT PAPER is to construct an abstract model of a society in which each member can cooperate with others by forming a coalition, but at the same time can be influenced by the members outside the coalition. A new concept of equilibrium, called here a social coalitional equilibrium, is proposed, and a sufficient condition for its existence provided. A coalition structure is endogenously determined in equilibrium. When the model is suitably specified, it describes noncooperative behavior of the members, and the social coalitional equilibrium is reduced to the Nash equilibrium. Given another extreme specification, the model is reduced to a cooperative game without sidepayments in characteristic function form, and the set of social coalitional equilibria corresponds precisely to the core. The need for study of the present model arose originally out of the author's recent investigation of labor-managed market economies, both the socialistic version and the capitalistic version, in [10, 11, 12]. Indeed, the model and the concept of social coalitional equilibrium were obtained by abstracting and generalizing the formal aspect of those studies. The socialistic labor-managed market economy has long been the object of study of various authors; see, e.g., Vanek [19]. The capitalistic labor-managed market economy seems to reflect the institutional aspect of the modern capitalistic society better than the economies formulated by other available general equilibrium models. It differs, for example, from the standard private ownership economy of Arrow and Debreu [1] (see also Debreu [6, Sec. 5.5]) in that (i) the ownership and control of a firm are separated; (ii) no particular firm is given a priori, but instead, the list of potential firms is given as a primitive datum; and (iii) the behavioral principle of the economic agents involves both noncooperative behavior and cooperative behavior. Because of the above feature (ii), any general equilibrium model of this economy has to formulate the economic mechanism that underlies the formation of firms in equilibrium. As
[The theoretical validity of consumer surplus analysis at the level of the individual agent is shown to be independent of the assumption that individual preferences are transitive. With or without transitive preferences, consumer surplus can be calculated as an appropriate area to the left of compensated demand functions. Without transitive preferences consumer surplus cannot be interpreted as a money index of utility change nor does it have an exact willingness to pay interpretation; rather it must be interpreted as a hypothetical compensation payment. Without transitive preferences the measurement of consumer surplus using ordinary demand functions to approximate compensated demand functions must rely on a heuristic rule to the effect that the "inconsistency effect" of a price change is small since full duality between ordinary and compensated demand functions does not (generally) hold.]