| Summary: | 碩士 === 國立臺灣大學 === 經濟學研究所 === 107 === In a typical stochastic frontier study, one of the important goals is to estimate the observation-specific technical inefficiency. A widely used predictor is the mean of the inefficiency term conditional on the composed error, E(ui|ϵi), proposed by Jondrow, et al. (1982). With the homoscedastic inefficiency, it is necessary to use the JLMS predictor since the mean of the inefficiency term is constant. However, when the stochastic frontier model expands to accommodate heteroscedasticity in the inefficiency term, the unconditional (E(ui)) is able to produce individual-specific predictor for inefficiency, and the computation of this predictor is much more easy. The choice of the predictors seems to be arbitrary in the literature. For instance, the unconditional mean predictor is preferred with the Bayesian method while the JLMS predictor is always adopted with the MLE estimation.
In this thesis, we aim at examining and comparing the statistical properties of the two predictors when the inefficiency term of the model is heteroscedastic. We start by advocating the proper notations for the predictors, which is an issue that has been neglected in the literature. We then discuss their statistical properties, including the consistency, unbiasedness, and the size of the mean square error (MSE). We find that, without the estimation effect, the JLMS predictor has a smaller MSE compared to the unconditional predictor. We provide a theoretical explanation of the result based on the signal-to-noise ratio of the predictors. If the estimation effect is taken into account, however, the relative size of the MSEs is difficult to tell analytically. We use simulations to show the numerical results.
We also discuss the predictors’ application in the context of out-of-sample prediction. We show that only the unconditional predictor is appropriate in this context. By the same token, we find that the marginal effect estimator proposed by Wang (2002) is more reasonable than that proposed by Kumbhakar and Sun (2013).
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