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].

[All over the world economists are busy evaluating major road proposals and other transport projects. But this work is largely confined to rural areas because the methods used are inappropriate for evaluating big transport schemes in towns, where traffic congestion is a dominating consideration. This paper discusses congestion as an economic problem of demand and supply, expressed as simple functions of the cost of travel, in time and money, to the road user. Road expansion in congested cities often seems to achieve nothing but more congestion. This paper demonstrates how this arises as a process of market equilibrium, and how one can assess the benefits of the road expansion in this situation. The paper then considers how the evaluation of road schemes would be affected if direct road pricing were introduced into cities as a means of controlling congestion.]

[The Ramsey model of optimal capital accumulation is reconsidered under the additional restriction that gross investment must be nonnegative. An effective characterization of the optimal solution in open-loop form is obtained. It is shown, however, that in general no restriction can be placed on the number of intervals in which the non negativity constraint is binding.]

Contents: Some formulations of mathematical programming under risk Chance-constrained programming as a model of decision making under risk The creation of excess resources under risk Portfolio selection Capital budgeting under risk Chance constrained programming as a problem in calculus of variations Applications of the variational formulation to a production problem.