By Ruey S. Tsay
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Additional resources for Analysis of Financial Time Series (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section Series)
2), the truncated normal distribution with scaling properties (Sect. 3), and the 1 Estimation of Technical Inefﬁciency … 21 exponential distribution (Sect. 3 Readers are encouraged to read through the next section (on the half-normal distribution model) even if their interests lie in other models, because many of the discussions there are pertinent to the later sections but are not repeated. 5), a stochastic production frontier model with a normal distribution on vi and a half-normal distribution on ui can be written as ln yi ¼ ln yÃi À ui ; ð1:18Þ ln yÃi ¼ xi b þ vi ; ð1:19Þ ui $ N þ ð0; r2 Þ; ð1:20Þ vi $ Nð0; r2v Þ; ð1:21Þ where vi and ui are independently distributed to each other.
As explained in Wang and Schmidt (2002), if xi and zi are correlated, then the ﬁrst step of the two-step procedure is biased. Even when xi and zi are uncorrelated, ignoring the dependence of inefﬁciency on zi will cause the ﬁrst-step technical efﬁciency index to be underdispersed, so that the results of the second-step regression are likely to be biased downward. Wang and Schmidt provide Monte Carlo evidence of the bias. Given the undesirable statistical properties of the two-step procedure, the preferred approach to studying the exogenous influences on efﬁciency is the single-step procedure.
Mðui jei Þ ¼ 0). In contrast, none of the observations will be fully efﬁcient if one uses the conditional mean estimator ðEðui jei ÞÞ. Consequently, average inefﬁciency for a sample of ﬁrms will be lower if one uses the modal estimator. Since the conditional distribution of u is known, one can derive moments of any continuous function of uje. That is, we can use the same technique to obtain observation-speciﬁc estimates of the efﬁciency index ðexpðÀui ÞÞ. 27). Maximum likelihood estimates of the parameters are substituted into the equation to obtain the empirical values.
Analysis of Financial Time Series (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section Series) by Ruey S. Tsay