Collinearity in Linear Structural Models of Market Power

The well-known structural model used to estimate market power suffers from a severe collinearity problem if both the marginal cost and demand equations are linear. If the equations hold exactly, the variables are perfectly collinear so the model cannot be estimated. If the true linear model equations hold with errors, one can estimate the equations, but the estimated coefficients are likely to be highly unstable and unreliable due to nearly perfect collinearity.