Knowledge that Transforms

Peter Schmidt, On the Difference Between Conditional and Unconditional Asymptotic Distributions of Estimates in Distributed Lag Models with Integer-Valued Parameters, Econometrica, Vol. 41, No. 1 (Jan., 1973), pp. 165-169

This paper analyzes the problem of inducing the members of an organization to behave as if they formed a team. Considered is a conglomerate-type organization consisting of a set of semi-autonomous subunits that are coordinated by the organization's head. The head's incentive problem is to choose a set of employee compensation rules that will induce his subunit managers to communicate accurate information and take optimal decisions. The main result exhibits a particular set of compensation rules, an optimal incentive structure, that leads to team behavior. Particular attention is directed to the informational aspects of the problem. An extended example of a resource allocation model is discussed and the optimal incentive structure is interpreted in terms of prices charged by the head for resources allocated to the subunits.

THE USE OF the geometric distributed lag in economics is widespread. The Liviatan [6] method for estimating its parameters is simple and provides consistent estimates. Moreover, it can be used to provide initial estimates for more sophisticated techniques [2]. Not much is known about the statistical properties of these estimators, especially their small sample properties. We do know that their asymptotic efficiencies are inferior to most alternatives [1], and recently Nagar and Gupta [7] have provided approximations to the small sample biases. The purpose of this note is to derive a simple way of displaying the Liviatan estimators which makes their nature clear and which allows the small sample distribution of one of them to be easily deduced. The main result is that the estimator of the parameter which defines the geometric distributed lag is a ratio of two ordinary least squares estimators. With this and the assumption that the error terms form a sequence of independent, identically distributed normal variables, it is possible, using the work of Geary [4], to derive the small sample distribution of this estimator. This result forms the main part of this note, which concludes with a brief discussion of the problem of setting confidence limits along the lines suggested by Fieller [3].

This paper deals with similarities and differences in the equations defining the full information maximum likelihood and three stage least squares estimators. It shows that the twp sets of equations are similar, the difference being that the two estimators purge the jointly dependent variables differently. Hence, even if three stage least squares is iterated, it will not give an estimator which is the same as the maximum likelihood one. On the other hand, it is quite apparently asymptotically equivalent to full information maximum likelihood. A number of other results are also obtained.

This paper reports on some mathematical and analytical properties of a static nonlinear model of a national economy or, more generally, of a multisectored economy. The model is a nonlinear version of the well-known linear input-output model of Leontief. Conditions are given for the nonlinear model to be workable in the sense that (i) there is a unique nonnegative vector of output production levels for each nonnegative final-demand vector, and (ii) the vector of output levels depends in a certain reasonable manner on the finaldemand vector. Attention is also focused on several other properties of the model of economic interest. For example, it is shown that propositions completely analogous to the LeChatelier-Samuelson principle in both the weak and strong forms for workable Leontief systems are valid within the context of the nonlinear model.

The paper compares the power of two tests for serial correlation in regression models with lagged dependent variables, recently suggested by Durbin, with that of the likelihood ratio test by means of two sets of Monte-Carlo experiments-one in which the exogenous series is taken to be the quarterly GNP series for the USA and the other in which the exogenous series is generated by a known autoregression.