Quality Adjusted Cost Functions

We propose a simple method for estimating cost functions in the presence of endogenous and unobserved quality. The theory of production, the equilibrium conditions implied by optimizing behavior, and exogenous influences on product demand are used to identify the model. An important advantage of the method is that the data requirements, above those necessary for standard cost function estimation, are minimal and the data are usually readily available. Specifically, exogenous information that influences the demand for the firm's product is required. We apply this method to estimate quality-adjusted cost functions in the nursing home industry. Estimation of a translog cost function that ignores quality yields seriously misleading estimates of marginal cost and economies of scale. In particular, while estimation of a quality-exogenous cost function reports economies of scale, estimation of a quality adjusted cost function reveals diseconomies of scale for high quality homes, constant returns to scale for average quality homes, and economies of scale for low quality homes.