Returns to Scale in the U. S. Life Insurance Industry. Comment
评论Peter Praetz关于美国寿险公司规模报酬的研究，指出其错误使用保费作为产出代理变量，导致对规模效应的夸大，并建议使用成本加权产出度量。
The recent study of 90 U.S. life insurance companies presented by Peter Praetz in the September, 1980 issue of the Journal does shed some light on the industry. It does not, however, demonstrate the existence of increasing returns to scale among these insurers as it claims. Moreover, it exhibits two common misuses of regression analysis. The scale problem is not new. Geehan [3; quotes from page 503] points out that premiums are a biased proxy for output because premium receipts per unit of output (properly defined) are positively correlated with firm size. This, he suggests, from larger firms producing a slightly different product, with a higher level of premiums per policy. He notes that larger firms have greater average policy sizes and a higher percentage of permanent insurance than do smaller firms. Geehan convincingly argues that a cost-weighted aggregate is a superior measure of output. He shows with Canadian data that a log-linear model incorrectly using premiums as the measure of output (with the log of the ratio of each firm's total cost to its level of premiums as the dependent variable) overweights the significance of scale effects even after some crude adjustment for product mix has been made. (Apparently, the negative correlation between firm size and price that Belth observes [1] is more than compensated by the tendency of larger firms to sell policies with higher premiums.) The newer study by Professor Praetz is based on more observations than that of Geehan. It also makes more adjustments for product mix (Geehan's adjustments are the same as Houston and Simon's [4]). Nevertheless, the findings using a log-linear model incorrectly employing premiums as the measure of output are similar to Geehan's. Specifically Praetz reports an R2 (R2 adjusted for degrees-of-freedom) value of .56 as opposed to (by my calculation) .65 in Geehan. Professor Praetz refers to the low R2 values Geehan receives for models employing his cost-weighted measure of output (log [cost/output] is the dependent variable) as a weakness in those models. The low R2's, however, are merely reflections of Geehan's main point. He demonstrates with the Canadian data that if output is measured correctly, the deviations of firm's cost/output ratios around their mean cannot be significantly explained by scale effects when other potential effects (a firm's corporate organization, age, and recent change in output) are considered concurrently. Accordingly, one should expect low R2 values in the findings. Moreover, there is no reason to anticipate any different results if this structure were applied to Praetz's data. Professor Praetz compounds his confusion over the meaning and use of R2 values with his strongest results. He constructs two models where total firm