This paper develops approximations of the Gram-Charlier type to the cumulative distribution function of the instrumental variables estimator on classical assumptions. In the special case where there are only two endogenous variables in the estimated equation, exact values of the cumulative distribution function are computed by numerical integration and compared with the approximations. Although the error in the approximation depends critically on the parameters of the stochastic model, the approximation is good for the special case even for small sample size over a wide range of values of the parameters. THIS PAPER was originally conceived as a study of the finite sample distribution of two stage least squares estimates. Since it was found that the distribution of a more general class of instrumental variables estimates can be discussed in the same way with a trifling complication of the algebra, the paper was modified to cover these estimates. The basic approach is somewhat similar to that of Nagar [15], since it involves expanding the formulae for the estimator as a series of terms of 0(1), O(T-+), O(T- 1), O(T- 1+), etc., and from this a similar expansion is found for the cumulative probability of the form

In this paper, a continuous time model for a monopoly firm of the Evans' type, encompassing operations, investments, and output prices, is formulated as an optimal control problem. In the model the objective of the firm is to maximize, subject to various constraints, the integral of production profits less interest and investment costs over a finite decision-making interval, plus the value of the capacity at the end of the period. The state variables are capacity, debt, and output price; the controls are the scale of operation, rate of purchase of new capacity, and rate of change of the output price. Final capacity, price, and debt are control parameters. There are several inequality constraints. Using results in control theory, the optimal controls are characterized for a model basically linear in structure. It shows that the one case suggested by Evans for further analysis is a trivial problem. These results are interpreted using the properties of the value equation. In addition, the control model is formulated alternatively as a mathematical programming problem. Solutions may then be computed by published algorithms.

Reviews the book "Topics in Managerial Accounting," by L.S. Rosen.