The normalized CES production function: theory and empirics

The elasticity of substitution between capital and labor and, in turn, the direction of technical change are critical parameters in many fields of economics. Until recently, though, the application of production functions with non-unitary substitution elasticities (i.e., non Cobb Douglas) was hampered by empirical and theoretical uncertainties. As has recently been revealed, “normalization” of production functions and production-technology systems holds out the promise of resolving many of those uncertainties. We survey and critically assess the intrinsic links between production (as conceptualized in a macroeconomic production function), factor substitution (as made most explicit in Constant Elasticity of Substitution functions) and normalization (defined by the fixing of baseline values for relevant variables). First, we recall how the normalized CES function came into existence and what normalization implies for its formal properties. Then we deal with the key role of normalization in recent advances in the theory of business cycles and of economic growth. Next, we discuss the benefits normalization brings for empirical estimation and empirical growth research. Finally, we identify promising areas of future research on normalization and factor substitution.