The Linear Approximation of the CES Function with n Input Variables

The Taylor approximation to the n-input constant elasticity of substitution (CES) function is presented and compared to Kmenta's well-known approximation for n = 2. The n-input approximation is, as for n = 2, a translog function, but with more complex restrictions on the translog parameters. Bias and consistency of the Taylor approximation to the n-input CES function are discussed, and it is argued that the approximation will only give reliable results for a limited regime of CES parameters and input values. A test of CES structure of the n-input translog function is performed for the fleet of Danish trawlers operating in the North Sea from 1987-99.