[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.]
PAYROLL AND PROGRESSIVE INCOME taxes play an enormous role in the American fiscal system. It is therefore of some importance to know the extent to which they influence work incentives. The purpose of this study is to present some econometric evidence on the effects of taxes on married women, a group of growing importance in the American labor force.2 A testable model of labor supply is developed which permits statistical estimation of a coefficient of tax perception. Unlike previous models of labor supply, it allows for the possibility that the wage may depend on the number of hours worked. Contrary to much of the literature, the results of this paper strongly suggest that marginal tax rates do have an important impact on labor force behavior. This section reviews briefly the past thought on this problem. Section 2 develops a model to explain work decisions when an individual faces a whole set of wagehour combinations, rather than a given wage independent of the number of hours he works. In Section 3 this model is modified to permit an explicit test of whether or not taxes affect individuals' labor supply decisions. Estimation problems are discussed at length, and the empirical results are presented. A concluding section contains a summary and suggestions for future research.
In a multiplicative model it is usual to assume that the logarithm of the disturbance variable is normally distributed with unknown variance a2 and with a mean which is either zero or - la2 according to the viewpoint taken of the object of the model. It is shown that, for each of several estimation criteria, the two assumptions lead to precisely the same point estimators of the exponents of the explanatory variables in the model and of the conditional mean, median, and mode of the dependent variable for specified values of the explanatory variables. An improved form is also given of the estimator of the conditional mean proposed by Teekens and Koerts [8]. A MULTIPLICATIVE MODEL is one in which a dependent variable is hypothesized to be proportional to the product of powers (unknown) of two or more explanatory variables. Such models arise in many areas; an important example of such a model in econometrics is the Cobb-Douglas production function. Observations will deviate from the theoretical model because of the presence of a disturbance variable. It is customary to include this variable as a multiplicative factor in the model and to assume that its logarithm is normally distributed with a mean which may be either zero or minus half its variance, the choice being dependent upon the viewpoint taken regarding the purpose of the model. We show that the choice does not affect the standard point estimators of the exponents (elasticities) of the explanatory variables in the model nor the standard estimators, including that proposed by Teekens and Koerts [8], of the conditional mean, median, and mode of the dependent variable.
[The static aspect of the Le Chatelier-Samuelson principle in the local version is fully characterized in an extremum formulation with differing systems of auxiliary constraints. The local characterization results in an interesting finding. With the systems of effective constraints which restrict only as man involved variables as the number of constraints, the variations of an extremum system, as consequences of changes in parametric indices of exogeneous conditions, will be only quantitative. With the systems of effective constraints which restrict more or all the involved variables, however, the consequential variations will be qualitative as well as quantitative. Necessary and sufficient conditions are investigated for constrained saddle points to exhibit a generalized Le Chatelier-Samuelson principle. An economic argument along the lines of demand theory is that the generalized principle among constrained demands is established if and only if the Jacobian of the constrained demands with effective constraints exhibits a dominant complementarity for the new constraint with its coefficients non-negative. The Marshallian conjectures about short run and long run are extensively discussed and rigorously proved with the results.]
[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.]