[Defining each good (factor) in each different country as a distinct good (factor), one can use Scarf's algorithm to solve general equilibrium problems for a trading world. The dimension of such problems grows very fast with the number of goods (factors) and countries, making computations extremely costly. Here we present a method for solving general equilibrium problems for a trading world which can be applied to a class of problems, and which requires considerably less computation time than the direct application of Scarf's algorithm.]
If the liquidity trap is viewed as a property of the aggregate demand for money (or liquid assets), it can be generated from the agents' microeconomic behavior only in special cases, even in the presence of the Keynesian assumption of inelastic expectations. On the other hand, in an economy where a central bank intervenes by open market operations, short run equilibrium interest rates on long term bonds tending to zero are associated with short run equilibrium money stocks which tend to infinity, once the Keynesian assumption of inelastic expectations is made.
derived and discussed by these authors, with the exception of Diewert, treats time as continuous; the index is an integral over time. Empirical work has proceeded by calculating discrete annual changes, which are then used to obtain an approximation to the continuous index. Even when the object of the calculation is the estimation of total factor productivity over a very long time, annual data on output, inputs, and factor shares are used. However, detailed data are frequently not available annually. For example, much of the detailed data on labor inputs are available only from the Census of Population, which is taken every 10 years. The question studied in this paper is whether or not a reasonable approximation to the continuous Divisia index can be calculated using data from only the beginning and end of a long period of time. Our answer is favorable. We derive a suitable approximation, calculate bounds on its errors, and suggest that in the usual cases these errors are likely to be small. We then calculate the growth in total factor productivity in the American economy from 1909 to 1958 using the conventional method based on annual changes and compare it to our approximation based on data for 1909 and 1958 only. The two calculations give almost exactly the same result. We conclude that in most cases the data for intervening years are superfluous. This conclusion makes it possible to make detailed and accurate calculations of the growth in total factor productivity from one decennial census
[A choice function, which maps each set of alternatives in a domain of feasible sets into a non-empty subset of itself (called the choice set), is said to be representable by a weak order if some weak order on the alternatives has maximum elements within each feasible set, all of which are in the choice set of that feasible set. A Partial Congruence Axiom ("every non-empty finite collection of feasible sets has an alternative which is in the choice set of every feasible set in the collection which contains that alternative") is shown to be necessary and sufficient for weak order representability when all choice sets are finite. A stronger form of partial congruence is proved to be necessary and sufficient for weak order representability when the number of feasible sets is countable, regardless of the cardinalities of the choice sets. The general case of arbitrary cardinalities for the domain and the choice sets is presently unsettled.]
[This paper provides an existence proof of an oligopolistic equilibrium which solves some difficulties in the construction of a consistent descriptive model of imperfect competition.]
[We suggest a frequency-domain class of instrumental variables estimators for all of part of an open, linear system of differential equations. While the estimators have similar statistical properties to those of [6] they seem preferable computationally in those situations in which they can be used. The estimation procedure consists of two basic steps, the first of which we describe as consistent and the second, efficient. We discuss the possible instruments that can be used. This type of procedure, like that of [6], could also be used to efficiently estimate discrete time systems, under weak conditions on the residuals.]
[This paper is concerned with Fisher's tests for index numbers. In particular, uniqueness and inconsistency theorems are proved. Beyond that, Fisher's system of tests is weakened considerably. Without any regularity assumption (such as differentiability or continuity) it is shown that every subset of the system of weakened tests is consistent while the whole system is inconsistent. The question of how far the whole system must be weakened to obtain a consistent set of tests is also considered.]
This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.