Working Paper: NBER ID: w3567
Authors: Paul J. Gertler; Donald M. Waidman
Abstract: 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.
Keywords: cost functions; endogenous quality; nursing homes; economies of scale
JEL Codes: I10; L15
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Ignoring quality in cost function estimation (C51) | Misleading estimates of marginal cost and economies of scale (D24) |
| Quality-exogenous translog cost function (D24) | Large economies of scale (F12) |
| Quality-adjusted cost function (D61) | Diseconomies of scale for high-quality homes (R31) |
| Quality-adjusted cost function (D61) | Constant returns to scale for average quality homes (R31) |
| Quality-adjusted cost function (D61) | Economies of scale for low-quality homes (R31) |
| Incorporating endogenous quality (L15) | More accurate representation of the structure of production (D20) |
| Conventional cost function estimates fail to account for quality (L15) | Inaccurate reflection of firm behavior and economic efficiency (D21) |
| Failure to account for quality (L15) | Biased estimates and invalid characterizations of production structure (C51) |