R. Harkema

Maximum likelihood estimation of sum-constrained linear models with insufficient observations☆

Abstract A maximum likelihood procedure for estimating sum-constrained linear models is presented, which seems to provide a good balance between excessive observational requirements on the one hand and an unduly restrictive specification of the contemporaneous covariance matrix on the other.

Some evidence on the performance of size correction factors in testing consumer demand models

Abstract Simulation experiments with the Rotterdam model show that restricting the covariance matrix and using its unbiased estimate is quite helpful when performing the Wald test, while application of Italianers correction factor works quite well when using the likelihood ratio test.

A dynamic specification of an AIDS import allocation model

In this paper we use the first-order autoregressive scheme in order to introduce dynamics into the AIDS model. We also consider the theoretical restrictions of additivity, homogeneity and symmetry, and use two different specifications of the covariance matrix. We estimate the models using import allocation data for the UK 1952–1979 of five EEC countries and test different specifications against each other.

Trade liberalization and the allocation over domestic and foreign supplies: a case study for Spanish manufacturing

The purpose of the paper is to investigate whether Spains accession to the European Union in 1986 caused a structural break in the allocation of total supplies of manufactures over domestic and foreign supplies. To that end the homogeneity-constrained Almost Ideal Demand System is used to specify the long-run equilibrium relationships between the shares in total supplies and total real demand and relative prices and a first-order error correction mechanism in order to describe the adjustment process to equilibrium. Using a formal statistical test, it turns out that a structural break actually occurred and led to a rather sharp decrease in the share of Spain and an increase in the shares of the other members of the European Union.

Bayesian limited-information analysis of nonlinear simultaneous equations systems☆

Abstract This paper presents a Bayesian limited-information estimation method that can be used to estimate a single nonlinear equation that forms part of a system of simultaneous equations. The method can be looked upon as the Bayesian counterpart of Amemiyas nonlinear limited-information maximum-likelihood estimator as well as a generalization of Drezes Bayesian limited-information estimator for linear simultaneous equations systems. The method is illustrated by applying it to the problem of estimating a CES-production function which forms part of a complete model of firm behavior.

A note on aggregation of CES-type production functions

In this note we shall be concerned with the aggregation of the constant elasticity of substitution (CES) type of production function. In particular we will derive the error made by using the arithmetic averages as they are usually published, rather than the theoretically required averages.

A new approach to maximum likelihood estimation of sum‐constrained linear models in case of undersized samples

Maximum likelihood procedures for estimating sum-constrained models like demand systems, brand choice models and so on, break down or produce very unstable estimates when the number of categories (n) is large as compared with the number of observations (T). In applied research, this problem is usually resolved by postulating the contemporaneous covariance matrix of the dependent variables to be known apart from a constant of proportionality. In this paper we develop a maximum likelihood procedure for sum-constrained models with large numbers of categories, which does not require too many observations, but nevertheless allows for n covariance parameters to be estimated freely.

Maximum likelihood estimation of market share models with large numbers of shares

Maximum likelihood procedures for estimating market share models break down or produce very unstable estimates when the number of brands is large as compared with the number of observations. The reason behind this phenomenon is that the estimate of the contemporaneous covariance matrix of the error terms of the model becomes singular or almost singular. This problem may be resolved by imposing restrictions on the contemporaneous covariance matrix. The resulting estimation procedure suggests that the model may contain a large number of shares, while the variance of each share may be estimated freely.

Estimation and testing of alternative production function models

Abstract The paper deals with four different decision models for a firm operating with a constant elasticity of substitution production function. The assumptions underlying the different models and their consequences for estimation are carefully specified. Maximum likelihood estimates of the parameters are obtained of the full four-equation models, using data pertaining to the Dutch manufacturing sector. Finally likelihood ratio test procedures are developed in order to determine whether one or more of the decision models can be rejected on the basis of this data.

On Bayesian and non-Bayesian estimation of a two-level CES production function for the Dutch manufacturing sector☆

In this paper maximum-likelihood estimates of the parameters of the two-level CES function, obtained by direct estimation of this function, are given. In addition the authors propose to show how a Bayesian analysis may help to find a solution to the difficulties related with, but not specific to, this particular estimation problem. It is shown that numerical integration of the posterior distribution may give an indication as to which parameter has to be pinpointed and at which value when multi-collinearity precludes unconditional maximization of the likelihood. It is suspected that this approach has a wider field of application.