Modelling Exogenous Variables in Human Capital Formation through a Heteroscedastic Stochastic Frontier

The objective of this paper is to suggest the use of a stochastic frontier model in which the inefficiency component is heteroscedastic in the measurement of technical efficiency in Human Capital Formation in the Italian University System. The heteroscedastic frontier model enables one to consider the effect of students’ individual characteristics and the influences of the resources and organization of the specific faculty on efficiency. The suggested model is applied to the case of Florence University graduates. The results show that the model specification is strongly supported by the data. Moreover, the suggested specification explains variation in technical efficiency in terms of graduate-specific factors. The technical efficiency scores obtained are comparable across faculties.

带未知异方差广义空间模型的有效估计

空间单元大小以及其它的经济特征上的差异,常常会导致空间异方差问题。本文给出了广义空间模型异方差问题的三种不同估计方法。第一种方法是将异方差形式参数化,来克服自由度的不足,使用ML估计进行实现。而针对异方差形式未知时,分别采用了基于2SLS的迭代GMM估计和更加直接的MCMC抽样方法加以解决,特别是MCMC方法表现得更加优美。蒙特卡罗模拟表明,给定异方差形式条件下, ML估计通过异方差参数化的方法依然可以获得较好的估计效果。而异方差形式未知的情况下,另外两种方法随着样本数的增大时也可以与ML的估计结果趋于一致。     

非参数统计视角下的异方差检验设计及其应用

以数据生成过程为导向,探讨了异方差来源的基本类型;依据非参数统计的基本思想,设计了切实可行的Mood方差检验方法与平方秩检验方法,并针对异方差来源类型,分析了相应的检验思路。蒙特卡罗模拟表明,Mood方差检验方法在异方差检验方面具有很高的检验效力;平方秩检验方法在异常经济现象情形下检验效力较低,而在其他情形下检验效力很高。同时,进一步阐释了纠正异方差的基本逻辑。     

Estimating a class of triangular simultaneous equations models without exclusion restrictions

This paper provides a control function estimator to adjust for endogeneity in the triangular simultaneous equations model where there are no available exclusion restrictions to generate suitable instruments. Our approach is to exploit the dependence of the errors on exogenous variables (e.g. heteroscedasticity) to adjust the conventional control function estimator. The form of the error dependence on the exogenous variables is subject to restrictions, but is not parametrically specified. In addition to providing the estimator and deriving its large-sample properties, we present simulation evidence which indicates the estimator works well.     

The ZD-GARCH model: A new way to study heteroscedasticity

This paper proposes a first-order zero-drift GARCH (ZD-GARCH(1, 1)) model to study conditional heteroscedasticity and heteroscedasticity together. Unlike the classical GARCH model, the ZD-GARCH(1, 1) model is always non-stationary regardless of the sign of the Lyapunov exponent ${\gamma }_0$, but interestingly it is stable with its sample path oscillating randomly between zero and infinity over time when ${\gamma }_0=0$. Furthermore, this paper studies the generalized quasi-maximum likelihood estimator (GQMLE) of the ZD-GARCH(1, 1) model, and establishes its strong consistency and asymptotic normality. Based on the GQMLE, an estimator for ${\gamma }_0$, a $t$-test for stability, a unit root test for the absence of the drift term, and a portmanteau test for model checking are all constructed. Simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests. Applications demonstrate that a stable ZD-GARCH(1, 1) model is more appropriate than a non-stationary GARCH(1, 1) model in fitting the KV-A stock returns in Francq and Zakoïan (2012).     

异方差和多重共线性的影响——模拟蒙特卡洛

通过蒙特卡洛实验,在计量经济学软件R中实现数据生成过程,当古典线性回归模型基本假定中的同方差假定和无多重共线性假定被违背时,参数的显著性检验是否依然有效。     

Heteroscedasticity diagnostics for <Emphasis Type="Italic">t</Emphasis> linear regression models

The t regression models provide a useful extension of the normal regression models for datasets involving errors with longer-than-normal tails. Homogeneity of variances (if they exist) is a standard assumption in t regression models. However, this assumption is not necessarily appropriate. This paper is devoted to tests for heteroscedasticity in general t linear regression models. The asymptotic properties, including asymptotic Chi-square and approximate powers under local alternatives of the score tests, are studied. Based on the modified profile likelihood (Cox and Reid in J R Stat Soc Ser B 49(1):1–39, 1987), an adjusted score test for heteroscedasticity is developed. The properties of the score test and its adjustment are investigated through Monte Carlo simulations. The test methods are illustrated with land rent data (Weisberg in Applied linear regression. Wiley, New York, 1985). The project supported by NSFC 10671032, China, and a grant (HKBU2030/07P) from the Grant Council of Hong Kong, Hong Kong, China.