Testing for Input Separability in the Canadian CATV Industry: An Application of Generalized Additive Mixed Models

Abstract

The nature of input relationships has important consequences for regulatory policies since the impact of rate-of-return regulation depends on the extent of substitution that is offered by production technologies which are adopted by regulated firms. The use of classical regression analysis had been criticized for various reasons, such as the linearity of regression functions in predictors, the fixed-variance premise of the response across sample observations, the i.i.d. postulation of the random error terms in addition to their normal distribution, and non-complying data in real cases. Instead, earlier research suggested the use of Generalized Additive Models (GAMs) that don’t have the aforementioned problems. Nevertheless, in the presence of complex covariate effects among data series, the use of Generalized Additive Mixed Models (GAMMs) is recommended. A GAMM is a non-ad hoc generalization of a Generalized Linear Mixed Model (GLMM) except that an additive unknown combination of nonparametric functions of covariates and random effects replace the predetermined linear predictor in the GLMM. We develop a nonparametric cost function using GAMMs. First, we estimate the model parameters using general spline smoothing techniques. Second, we apply residual deviance analysis to test the separability and complementarity between inputs. We use an unbalanced panel of operating data from the regulated Canadian cable television (CATV) firms from 1990 to 1996. This period is of particular interest to policymakers because the Canadian CATV was a rate- and entry-regulated industry prior to 1997.