An Examination of the distributions underlying business survey responses in New Zealand

Abstract

The aim of this thesis is to examine the nature of the distributions underlying business survey responses in New Zealand. These distributions are widely used in the analysis of survey data. Their most common application is in procedures which derive quantitative statistics from qualitative survey data. They are also used in econometric procedures recently developed by the French economist Marc Ivaldi which use survey data to test structural economic models. Both of these applications often assume that the distributions are normal. The purpose of this study is to examine the empirical validity of this assumption. It is demonstrated initially how techniques which are used to estimate the mean of a variable often assume, for simplicity, that it has a univariate normal distribution. Similarly, Ivaldi's procedure assumes that combinations of variables have a normal joint distribution to derive the correlation between them. The validity of these assumptions has been challenged by empirical evidence. In the univariate case, the actual distributions have usually been found to be skewed or excessively peaked. This makes it unlikely that the New Zealand bivariate distributions are normal. However, the extension to a bivariate framework can still provide useful information about the characteristics of the distributions, including the nature of the non-normality present. To test the bivariate normality hypothesis, the polychoric correlation coefficient procedure is used. This maximum likelihood technique estimates the degree of correlation between the quantitative variables underlying the qualitative responses to survey questions. The data used is from the New Zealand Institute of Economic Research's Quarterly Survey of Business Opinion over the period September 1975-June 1993. It is found that 50% of the models reject the bivariate normality hypothesis. However, the usefulness of the normal distribution varies considerably between individual models and across surveys. The rejection of normality is attributed to excessive peakedness caused by too many respondents answering 'no change' to survey questions relative to the number expected with the bivariate normal distribution. In addition, the acceptance or rejection of normality for each question pair is generally found to be independent of the conclusion reached for other distinct pairs in each survey.