Analysis of Productivity at the Firm Level: An Application to Life Insurers

Abstract

Analysis of at the Firm Level: An Application to Life Insurers: Comment The non-parametric measurement of total factor productivity (TFP) has become widely accepted and applied to many industries [2], and more recently to life insurers. A limitation of this approach is that differences in TFP may arise due to factors other than production efficiency. Denny, Fuss and Waverman [5], for example, identify two additional attributes to differences in TFP across time: exploitation of economies of scale, and changes in deviation from marginal cost pricing. To help overcome these limitations, various researchers employed the parametric technique of neoclassical cost estimation [10]. The parametric approach is a more general and detailed specification of the production structure of an industry or a company than the TFP approach. Further, in most recent studies of this type, researchers have utilized flexible functional forms in order to avoid imposing unnecessary restrictions on the production technology (see for example Berndt and Khaled [1] among many others). This approach is appealing but is often expensive to undertake and requires substantial time series observations. For practitioners, however, TFP analysis has various advantages. TFP is a relative measure showing how the ratio of total output to total input changes from one period to the other. It is relatively inexpensive to perform and since the data are displayed in an index number form, it is easy to identify anomalies in the data. In addition, TFP and the variables used in its construction may reveal valuable information on trends and changes in an industry. Moreover, Diewert and Morrison [7] have added another factor, the terms of trade effect, in explaining productivity. This Comment extends the study of Weiss [13] in which new techniques for measuring output of life insurers are developed and used in computing divisia and exact indexes of TFP for one stock and one mutual insurer over a five-year interval. Weiss [13] maintains that because the rate of technological change calculated using the Tornqvist approximation (TFP) equals the exact measure of the shift of the variable cost function due to technological change ( t) (see Diewert [6]), the nature of returns to scale is constant. In her words, Productivity theory suggests that superlative indexes such as the exact index and the Tornqvist-Theil approximation to the divisia index yield similar results if the production function reflects constant returns to scale, regardless of whether the insurer is acting competitively... [13, p. 74]. Given the result obtained by Weiss, which indicates that the divisia and exact indexes vary directly with each other, it was concluded that ...the sample insurers' production functions exhibited constant returns to scale over the sample periods [13, p. 74]. While this is true if all inputs are variable, if some of the inputs are fixed (e.g. number of square feet of home office building and constant dollar capital input in Weiss), the statement is in error, primarily because the shift in the variable cost function due to technological change ( t) is greater than the negative value of the overall production relationship's rate of technological change ( t). that is, t at t where at is the mean share of variable relative to total costs (at The latter can be proven with the aid of two equations: t = 1/2 (at + at - 1) t + R ( ) where t is the shift in total cost function due to technological change and R ( ) is a remainder term of first differences which are at least of second order. t = - t + R* ( ) where t is the rate of technological change corresponding to the joint production function (of all inputs), and R* ( ) is a remainder term of finite differences which are at least of second order.(1) Now suppose there is a constant mark-up, over marginal cost pricing structure. …