Navigating Interpretational Complexity

Multiplicative Forms The R' of the regression was about 0.93 and yielded the following coefficient estimates: Variable Number 0) Coefficien Estimate (B,) † statistic 1 0.950 74.8 2 0.390 15.9 3 0.047 1.7 4 0.140 4.1 5 0.074 5.9 6 0.058 5.3 7 0.018 1.7 8 - 0.005 0.4 9 1.020 110.3 10 - 0.063 2.5 11 0.430 9.2 12 0.011 0.4 These data indicate that size (variables 1 and 9) is highly significant in explaining bank operating costs. The coefficients near unity for these two variables indicate that a 1% increase in the number of accounts per office or the number of offices per bank causes about a 1% increase in the total operating cost of a bank. The negative coefficient of variable 10 shows that if a regular account is substituted for a special account, costs will decrease. The coefficient of 0.43 for variable 11 indicates that increasing wage rates by 10% leads to a 4.3% increase in total costs. When a cost function is estimated in multiplicative form, the traditional dichotomy between fixed and variable costs is no longer clear. A relevant consideration is still incremental costs associated with a change in activity levels, but these incremental costs are now a function of the current or proposed activity levels. Analysis and interpretation are therefore more difficult with the multiplicative model. Comparing the Explanatory Power of Multiplicative and Linear Models Earlier in this chapter, we described the use of R° as a measure of the goodness-of-fit criterion. It would be natural, but incorrect, to estimate both the linear and the multiplicative form of the model and choose the one whose regression had the higher R'. Even seemingly experienced analysts fall into this trap occasionally. Such a comparison is invalid. The R° of the linear model represents the percentage of variation of the dependent variable, Y, explained by the linear model, whereas the R° of the multiplicative regression equals the percentage of variation of log Y ex-plained.