tailieunhanh - SAS/ETS 9.22 User's Guide 147

SAS/Ets User's Guide 147. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 1452 F Chapter 21 The QLIM Procedure The Normal-Truncated Normal Model The normal-truncated normal model is a generalization of the normal-half normal model by allowing the mean of Ui to differ from zero. Under the normal-truncated normal model the error term component v is iid N C 0 a and u is iid N a . The joint density of v and u can be written as 1 f u v - --------------exp v 2jo or p ou u p 2 2o2 v2 I 2o21 The marginal density function of e for the production function is f e i f u e d 0 u 1 p --------- V2 o p oM ok ek I e p 2 exP----------2 o 2o2 L e- p p o o ok and the marginal density function for the cost function is f 1 e p p ek T p - ----- Hr o V o ok o L ouJ The log-likelihood function for the normal-truncated normal production model with N producers is ln L constant N lno N ln E p ei k ln ------ ok o i For more detail on normal-half normal normal-exponential and normal-truncated models see Kumbhakar and Knox Lovell 2000 and Coelli Prasada Rao and Battese 1998 . Heteroscedasticity and Box-Cox Transformation Heteroscedasticity If the variance of regression disturbance ez- is heteroscedastic the variance can be specified as a function of variables E e 2 a2 f zi y Heteroscedasticity and Box-Cox Transformation F 1453 The following table shows various functional forms of heteroscedasticity and the corresponding options to request each model. No. Model Options 1 y o 2 1 exp zi y 2 f z y o 2 exp zi y 3 f zi y o 2 1 pL 1 yi zn 4 f z y o2 1 Ef i yizn 2 5 f zi y o2 Ef i yi zu 6 f z y o2 Ef i yizn 2 LINK EXP default LINK EXP NOCONST LINK LINEAR LINK LINEAR SQUARE LINK LINEAR NOCONST LINK LINEAR SQUARE NOCONST For discrete choice models a2 is normalized a2 1 since this parameter is not identified. Note that in models 3 and 5 it may be possible that variances of some observations are negative. Although the QLIM procedure assigns a large penalty to move the optimization away from such region it is possible that the optimization cannot improve the objective .