[This paper derives the asymptotic distribution of restricted and unrestricted reduced form estimators and compares their asymptotic efficiency. It also shows that the same techniques yield the asymptotic distribution of dynamic multipliers.]
THE DYMULT (dynamic multipliers) program is designed to calculate impact, interim, and total multipliers of a simple linear simultaneous equations model with lags. Builders of an aggregate econometric model have often concentrated on the validity of signs and magnitudes of the estimated regression coefficients of each structural equation and neglected to check the stability conditions of the system, which could be a symptom of specification errors in the model. The DYMULT program checks the stability conditions of the system of equations and calculates the impact, interim, and total multipliers. The matrix form of a simple lag linear simultaneous equations model can be written as follows:
The various conditions for non-intransitivity of majority rule formulated over the past decade have been concerned with choices over arbitrary, usually finite, sets of discrete alternatives. In many economic and other social choice problems, however, the possible choices constitute a point set in some appropriately defined multi-dimensional commodity or policy space. It is shown that in problems of this kind, when voter preferences can be represented by quasi-concave, differentiable utility functions, the various equilibrium conditions for majority rule are incompatible with even a very modest degree of heterogeneity of tastes, and for most purposes are probably not significantly less restrictive than the extreme condition of complete unanimity of individual preferences.
[A distributed lag estimator is developed here from Bayesian priors regarding the"smoothness" of the lag curve. "Smoothness" priors of the dth degree are represented by a normal density function with zero mean of the difference of order d + 1 of the coefficients, where d will usually be one to zero. Such probabilistic priors, which do not imply any parametrization of the lag curve, are, it is contended here, a more accurate representation of the kind of prior knowledge that has led many researchers to use the polynomial distributed lag estimation procedure, and other parametrization procedures, in the past. The estimator developed here is, moreover, very simple in its implementation. All that is needed is any least squares regression program.]