Duality Theory And the Consistent Estimation Of Technological Parameters: Why Cost Function Estimation Can Be Wrong

In this article we show that technological parameter estimates obtained by estimating a cost function that is derivable as the dual of a production function can be biased and inconsistent if the stochastic structure of the model arises from certain types of behavioural assumptions made about rational agents. We consider a specific example in which firms are uncertain about prices. We show that when actual prices differ from expected prices and firms have to make decisions on the basis of their expectations, the inherited stochastic specification of the dual system is highly non-linear in the disturbance terms making consistent parameter estimation impossible by conventional methods. This is demonstrated by a Monte Carlo simulation study of two text-book examples using synthetic data. It is also shown that this type of result can arise when the researcher derives the error structure from the assumption that agents make optimization errors.