Stephen M. Goldfeld

Some Tests for Homoscedasticity

Abstract Two exact tests are presented for testing the hypothesis that the residuals from a least squares regression are homoscedastic. The results can be used to test the hypothesis that a linear [ratio] model explains the relationship between variables as opposed to the alternative that the ratio [linear] specification is correct. The first test is parametric and uses the F-statistic. The second test is nonparametric and uses the number of peaks in the ordered sequence of unsigned residuals. In conclusion, the results of some experimental calculations of the powers of the tests are discussed.

The demand for money

Publisher Summary The relation between the demand for money balances and its determinants is a fundamental building block in most theories of macroeconomic behavior. The demand for money is a critical component in the formulation of monetary policy, and a stable demand function for money has long been perceived as a prerequisite for the use of monetary aggregates in the conduct of policy. The repeated breakdown of existing empirical models in the face of newly emerging data has fostered a vast industry devoted to examining and improving the demand for money function. This process has been aided by a growing arsenal of econometric techniques that has permitted more sophisticated examinations of dynamics, functional forms, and expectations. These techniques have also provided researchers with a wide variety of diagnostic tests to evaluate the adequacy of particular specifications. The chapter reviews underlying theoretical models to re-examine measurement and specification issues such as the definition of money and the appropriate scale and opportunity cost variables. It discusses the estimation issues, criticisms, and modifications in the partial adjustment model.

Budget constraints, bailouts, and the firm under central planning

Abstract Motivated by the notion of the soft budget constraint, we develop two models of an enterprise that can obtain bailouts from the state when its operating profit is negative. The models allow for uncertainty both in production and in the extent to which the enterprise can obtain subsidies. We derive the optimal factor inputs and show, via both theorems and illustrative calculations, how the availability of bailouts increases the demand for factor inputs. The dependence of this increase on the features of the bailout process is also characterized.

Output targets, the soft budget constraint and the firm under central planning

Abstract The paper considers the case of an expected profit maximizing firm which has an output target imposed on it by central planners and which may receive (partial) bailouts if its operating profit is negative. The model contains several sources of uncertainty. The paper compares the amounts of input use in the pure bailout case, the pure output target case, the bailout-with-output-target-case and the standard competitive case both theoretically and with numerical experiments.

Money Demand: The Effects of Inflation and Alternative Adjustment Mechanisms

The paper first reconciles a variety of specification tests for partial adjustment money demand models and points out a fundamental identification problem which makes it impossible to distinguish between the real and nominal partial adjustment models if inflation has an independent effect on the long-run demand for money. The paper also finds that empirical estimates of simple partial adjustment models have some undesirable properties and then considers the shortand long-run effects of inflation in a more general distributed lag model.

Some properties of the simple disequilibrium model with covariance

Abstract This paper investigates two difficulties that arise in disequilibrium models with non-zero covariances between demand and supply errors. The nature of these difficulties is demonstrated analytically and some preliminary observations are made about their practical, computational significance.

Econometric modelling with non-normal disturbances

Abstract This paper analyzes a general class of non-normal density functions (dubbed Sargan densities) in the context of the ordinary regression model and the simple one-market disequilibrium model. Use of the normal density in disequilibrium models is unwieldy, especially for multimarket models, since the application of maximum likelihood methods requires numerical evaluation of multiple integrals. These difficulties are avoided with the Sargan densities, and based on both asymptotic results and limited sampling experiments, these densities appear to offer a promising alternative to the normal in disequilibrium models.

NONLINEAR SIMULTANEOUS EQUATIONS: ESTIMATION AND PREDICTION*

Abstract : The small sample properties of certain estimators of the coefficients of systems of simultaneous nonlinear equations are investigated. Sampling experiments are used in connection with two specific nonlinear models. The estimating methods investigated comprise direct least squares, various forms of two-stage least squares and full-information maximum likelihood. The relative performances of the various methods are evaluated on the basis of informal comparisons of their respective mean absolute errors and root mean square errors and also by more formal tests of significance. Direct least squares is found to be, as expected, the worst estimating method. The other two methods are rather more comparable with full-information maximum likelihood holding the edge for both theoretical and experimental reasons. (Author)

Uncertainty, bailouts, and the Kornai effect

Abstract We investigate the effects of bailouts on a firm with negative profits. The production function is Cobb-Douglas and the firm experiences both revenue and cost uncertainty. The effect of bailouts on input demand depends on the technology, the variances of the random variables and the correlation between them.

Single-market disequilibrium models: Estimating and testing

Abstract The present paper investigates several issues of estimation and hypothesis testing in the context of a single-market disequilibrium model. The paper attempts to shed light on the following four questions: (1) What are the small-sample properties of the maximum likelihood estimator in various disequilibrium models? (2) How can one test the hypothesis of equilibrium vs. disequilibrium? (3) Can one reasonably estimate the unobservable demand and supply quantities from observable data? and (4) What are the consequences of using an equilibrium model instead of a disequilibrium one, or of using a misspecified disequilibrium model? Each of these questions is examined with the aid of sampling experiments.