This paper is concerned with costs of capital in mathematical programming formulations of the problem of capital budgeting under capital rationing. It shows that there is a serious error in the method outlined by previous authors for converting the shadow prices from the solution of the dual into measures of the firm's marginal internal opportunity rates. In addition to demonstrating that the traditional approach leads to erroneous and nonsensical results, this paper presents a correct procedure for determining these rates.

[The purpose of this paper is to amend some of Hannan's [6] identification results for ARMAX models and to discuss identification in ARMAX models when identities are present. In addition, we briefly discuss how the ARMAX results can be adapted to obtain identification conditions for dynamic simultaneous equations models with autoregressive disturbances.]

A simple test for heteroscedastic disturbances in a linear regression model is developed using the framework of the Lagrangian multiplier test. For a wide range of heteroscedastic and random coefficient specifications, the criterion is given as a readily computed function of the OLS residuals. Some finite sample evidence is presented to supplement the general asymptotic properties of Lagrangian multiplier tests.

For a general vector linear time series model we prove the strong consistency and asymptotic normality of parameter estimates obtained by maximizing a particular time domain approximation to a Gaussian likelihood, although we do not assume that the observations are necessarily normally distributed. To solve the normal equations we set up a constrained Gauss-Newton iteration and obtain the properties of the iterates when the sample size is large. In particular we show that the iterates are efficient when the iteration begins with a VN- consistent estimator. We obtain similar results to the above for a frequency domain approximation to a Gaussian likelihood. We use the asymptotic estimation theory to obtain the asymptotic distribution of several familiar test statistics for testing nonlinear equality constraints.