Results of Alternative Statistical Treatments of Sample Survey Data

A CAREFUL formulation of the probability and economic model which , underlies observations is indispensable for the choice of correct statistical procedures to be followed in drawing econometric inferences from samples. The sample design, the methods of collecting data, and underlying economic behavior will all contribute to the formulation of the model. The study of data collected in consumer surveys' has convinced us that one cannot proceed simply by the application of conventional statistical methods in the estimation of economic relationships because of the existence of some basic difficulties which we classify as follows: (1) weighting of observations, (2) heteroscedasticity, (3) nonlinearities, (4) the choice of alternative economic concepts, (5) errors of observation. In this paper, we shall describe some empirical calculations that deal with the first four difficulties. The fifth is reserved for future study. Observations may be weighted because of the use of differential sampling rates and because of differential response rates to survey questions in the different strata of the population. High rent (a correlate of high income) areas are deliberately over-sampled because they show more variability in respect to certain economic variables than other strata, and conversely low rent areas are under-sampled. The strata also have different response rates. The weights finally used are combinations of sampling and response rates which attempt to give each stratum the same relative importance in the sample that it has in the population; i.e., they are essentially inversely proportional to the net (effective) sampling rate. The heteroscedasticity which leads to the adoption of differential sampling rates must also be taken into account in the estimation of parameters in equations expressing economic behavior. In these equations, the variance of the so-called disturbances is a fundamental parameter to be estimated, and this variance is not uniform over some