Using least squares and tobit in second stage DEA efficiency analyses
The paper examines second stage DEA efficiency analyses, within the context of a censoring data generating process (DGP) and a fractional data DGP, when efficiency scores are treated as descriptive measures of the relative performance of units in the sample. It is argued that the efficiency scores are not generated by a censoring process but are fractional data. Tobit estimation in this situation is inappropriate. In contrast, ordinary least squares is a consistent estimator, and, if White's [White, H., 1980. A heteroskedastic-consistent covariance matrix and a direct test for heteroskedasticity. Econometrica 48, 817-838] heteroskedastic-consistent standard errors are calculated, large sample tests can be performed which are robust to heteroskedasticity and the distribution of the disturbances. For a more refined analysis Papke and Wooldridge's [Papke, L.E., Wooldridge, J.M., 1996. Econometric methods for fractional response variables with an application to 401(k) plan participation rates. Journal of Applied Econometrics 11 (6), 619-632] method has some advantages, but is more complex and requires special programming.
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