2 1 18566 ln ln44 sic 18566 3 1 pc for aic 148 158

Info icon This preview shows pages 13–14. Sign up to view the full content.

View Full Document Right Arrow Icon
(2 1) 185.66 ln ln(44) 1.70 44 44 SIC 185.66 3 1 4.84 41 44 PC For AIC, 1.48 < 1.58, for SC, 1.64 < 1.70, and for PC, 4.38<4.84. So they provide evidence that model (1) is preferable to model (2). 4. Testing for Normality of the Disturbances The normality of disturbances is necessary if the t test, F test, chi- square test etc., are to be valid in small samples 2 . It is therefore a vital part of the specification of the classical model, and should always be tested (Thomas, 1997, p.343). The Jarque-Berra (1980) statistic to test for normality of the disturbances is defined as: 2 Recall that for large samples, the tests will be asymptotically valid even if the disturbances are not normally distributed. How large does the sample size have to be for estimators to display their asymptotic properties? We generally accept that at least it must be larger than 30 but it may not suffice. Goldfeld and Quandt (1972, p.277) report an example in which a sample size of 30 is sufficiently large and an example in which a sample of 200 is required. They also note that large sample sizes are needed if interest focuses on estimation of estimator variances rather than on estimation of coefficients (Kennedy, 2001, p.29).
Image of page 13

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 14 2 2 3 4 2 3 2 ( / 3) 6 24 JB T where 2 1 2 ˆ T t t u T , 3 1 3 ˆ T t t u T and 4 1 4 ˆ T t t u T (second, third and fourth moments of the residuals about their zero mean). It is possible to show that, under the null hypothesis of normally distributed disturbances, the JB test statistic has a chi-square distribution with 2 degrees of freedom: 2 2 ( ) df JB We therefore reject the null hypothesis of normality if JB exceeds the relevant critical chi-square value: 2 2 ( ) df JB The Jarque-Bera test for normality is also sometimes regarded as a test of misspecification. It is useful for detecting what are known as “outliers” among the data observations. An outli er refers to an observation with a very large residual, that is, a case where the fitted value of the dependent variable is very different from the actual one (Thomas, 1997, p.346)
Image of page 14
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern