In line with the present level of technology and development, estimation methods for economic relationships are becoming complex and sophisticated. Nevertheless, without accurate and complete data such methods are of little use. Observations on variables have two important deficiencies, errors of measurement and lack of measurement. This study shall look for a generally applicable remedy to the latter of these problems.
In particular, it considers estimation of the Cobb-Douglas production function in the event of missing individual observations on one of the input variables. Due to the statistical form in which this function is estimated, such data deficiencies present a major problem. The Bayesian approach will be used in the estimation of the parameters.
Chapter 1 discusses the Bayesian Approach to inference and indicates the applicability of Bayes’ Theorem to the problem of inference. Bayesian and non-Bayesian methods are compared and contrasted.
The definition and derivation of the production function is looked at in Chapter 2. The discussion concentrates on the Cobb-Douglas function, particularly its algebraic interpretation, economic applications and problems.
The statistical model of the Cobb-Douglas function is derived in Chapter 3. To yield unbiased and consistent estimates, the model derived by Zellner, Kmenta and Dreze (1966) is the most acceptable. The development from the early deterministic models to the present sophisticated stochastic models is outlined. An extension to two dimensional models incorporating both time-series and cross-sectional data is also shown.
The two categories of missing observations are discussed in Chapter 4. That is, missing observations on the independent or dependent variables and grouped observations (with all individual observations missing). Various models that have been developed to facilitate estimation in the light of the problem are presented.
Chapter 5 involves the development of the remedy to the missing data problem. The concept used was not applied to any of the general models discussed in Chapter 4. The solution proposed for the estimation of the Cobb-Douglas production function in the event of missing data, is based upon prior knowledge of the distributional form of the input for which only aggregate observations are known. The statistical model of the function used, was developed in Chapter 3.
The application of this model was illustrated by a Bayesian analysis. This is contained in Chapter 7. A marginal posterior probability density function was derived for the coefficient related to the variable input with the data problem. This is the basis upon which inferences are drawn.
Although suitable 'live' data could not be obtained in the limited time available, data was generated using cross-sectional data, taken from a study by Bronfenbrenner and Douglas (1939) as a base. Chapter 6 shows the procedure involved. In Chapter 8, extensions to the technique are postulated, indicating the wide applicability of the model.
Finally, conclusions are drawn regarding the performance of the technique.