No abstract

No abstract

No abstract

OUR ORIGINAL PAPER ([1]) contained two examples aimed at making the simple point that different analysts, studying exactly the same companies, for exactly the same time period with exactly the same model could get completely different results simply as a result of changes in the way they identify the number of shares outstanding. Scott ([2]) missed the point of these examples entirely.In the first of our examples, we showed that it was possible to have the relation between a set of prices and a corresponding set of earnings dramatically distorted by some simple changes in the number of shares outstanding. He states that "What they have done is to impose a new theoretical structure on the data." Clearly, virtually any socioeconomic behavior can be explained by the assumption of an appropriate (or inappropriate) model. The point of the example is that there is no way to tell which theoretical structure to impose. Scott goes on to say "That a regression of price on earnings should become increasingly significant as DDW simulate more and more splits is the obvious and predictable result of such a procedure." This statement is simply incorrect. There is no reason why the regression should become increasingly more significant as Scott states. This may or may not happen. As we remarked in the original paper, the regression and/or correlation estimates may increase or decrease.Scott attempts to explain the change in the values of the estimated coefficients by appealing to "sampling variability." He states: "Since the estimated regression coefficients are random variables these differences are to be expected." This statement is misleading, because once the data are given, the estimated coefficients are no longer random variables but are fixed functions of the observations. Therefore, the changes observed in the estimated coefficients are functions (conditional upon the model and the specified fixed sample) of the particular splits which occur between different basis years.Scott proposes the use of generalized least squares (GLS) regression as a solution to potentially heteroscedastic error terms. Using Scott's theoretical model to specify the changes in variability in the regression error terms due to stock splits, GLS could be implemented by premultiplying each observation by the reciprocal of the standard deviation for that observation ([3]). Scott fails to realize that for his model his procedure leads to the use of the original data values at the time of the cross-sectional analysis. Therefore, in the case where both the independent and dependent variables are all per share variables, he is simply suggesting that cross-sectional analyses of per shlare data should be done on the basis of the time period for which they are collected. However, if the model contains variables which