Asymmetric Complementarity and Dynamic Optimization in Pharmaceuticals

Abstract

Manohar Rao had varied interests in applied and theoretical econometrics, including chaos theory, optimization, complementarities between freight and passenger traffic to name a few. This paper which also deals with complementarity is in honor of his memory. In popular press as well as academic literature, costly prescriptions are often blamed on monopolistic mergers and diversion of funds from R&D to advertising. We evaluate these allegations by estimating a variable elasticity of substitution (EoS) production function for pharmaceuticals. Our S = f(K,L,A,R) relates sales (S) to four inputs: capital (K), labor (L), promotion and advertising (A), and R&D expenditures (R). We discuss solutions to data problems due to distinct time lags for A and R and due to missing price and physical quantity data. Our estimates of the scale elasticity (ScE) suggest economies of scale (ScE >1) and perhaps help justify some recent pharmaceutical mergers and acquisitions. We study alleged diversion of funds away from R&D by formulating it as a test of complementarity between two inputs A and R, extending Vinod and Rao’s (2000) model by incorporating f(.) explicitly. If pharmaceuticals can substitute R by A, but not vice versa, we show that definitionally symmetric EoS is not suitable. Hence, we propose a new nonsymmetric measure based on correlations between input levels of one input and marginal productivity of another input. Thus, we argue that symmetry can and should be tested rather than assumed.