The construction of tests of model specification is considered from a general point of view. The results are applied to testing the serial independence of the disturbances in a regression model where some of the regressors are lagged dependent variables. It is shown that the asymptotic distribution of the lag-1 serial correlation coefficient calculated from the least-squares residuals differs from that of the coefficient calculated from the true disturbances. A consequence of this is that tests of serial independence based on the residuals from regression on fixed regressors are invalid when applied to models containing lagged dependent variables even when the null hypothesis of serial independence is true. Tests which are asymptotically valid for the large-sample case are suggested.

This article shows how to transform residuals from regression on an arbitrary set of k regressors to a set of values having the same joint distribution as the residuals from regression on a different set L of k regressors. Let d′ denote the value of the statistic <tex-math>$\Σ (z_t-z_t-1)^2/\Σ z_t^2$</tex-math> calculated from these values. It is shown that for a suitable choice of L the distribution of d′ is the same as that of <tex-math>d_U</tex-math>, the significance values of which are tabulated in [1].

A Monte Carlo experiment is carried out to examine the small sample properties of ordinary least squares, indirect least squares, Hoch's, and Klein's estimates of the parameters of the Cobb-Douglas production function.A perfectly competitive model of firms irn a single industry is considered in nine situations which differ in the behavior of the disturbances, the variability of inputs, and the position of the average firm.In each case 200 samples of size 20 anld 200 samples of size 100 were obtained to approximate the sampling distribution of the various estimators.

The problem dealt with in this article is whether we can indicate, with the help of measured economic concepts, the rate of savings--as a function of time--which maximizes utility over time. The author believes that his attempt has been unsuccessful, but hopes that the nature of the difficulties encountered may be of some help in future attempts to solve this problem. A problem regarding the most important decision to be taken for any development program.

Stimulated by Fleming's study on a related subject, the author compares four methods to eliminate balance of payments disequilibria between high-employment countries forming a closed group: (i) "discriminatory" import duties and subsidies, (ii) "discriminatory" duties only or the corresponding quantitative restrictions, (iii) nondiscriminatory duties, and (iv) devaluation or income adaptation. For each an "optimum version" is defined and chosen; they are compared as to (a) the loss in international trade and (b) the distribution of the "direct burden" between the countries (defined as the short-run loss in real expenditure). A number of rather specific simplifications are introduced, all tending to make the case as symmetric as possible with regard to countries and commodities. As a consequence of the high-employment hypothesis and of absence of production substitution, problems of optimum allocation of resources are ruled out; the approach is a short-run one. Only policies (i) and (iv) show no loss of trade, whereas the others do; but in the case of devaluation the "direct burden" is relatively heavier for the deficit countries than in the other three cases.