Var var var se fall 2008 under econometrics prof

Info icon This preview shows pages 22–32. Sign up to view the full content.

View Full Document Right Arrow Icon
Var Var Var se - + = - - + = - - = -
Image of page 22

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 23 Testing a Linear Combo (cont) So, to use formula, need s 12 , which standard output does not have Many packages will have an option to get it, or will just perform the test for you In Stata, after reg y x1 x2 … xk you would type test x1 = x2 to get a p -value for the test More generally, you can always restate the problem to get the test you want
Image of page 23
Fall 2008 under Econometrics Prof. Keunkwan Ryu 24 Example: Suppose you are interested in the effect of campaign expenditures on outcomes Model is voteA = β 0 + β 1 log( expendA ) + β 2 log( expendB ) + β 3 prtystrA + u H 0 : β 1 = - β 2 , or H 0 : θ 1 = β 1 + β 2 = 0 β 1 = θ 1 β 2 , so substitute in and rearrange voteA = β 0 + θ 1 log( expendA ) + β 2 log( expendB - expendA ) + β 3 prtystrA + u
Image of page 24

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 25 Example (cont): This is the same model as originally, but now you get a standard error for β 1 β 2 = θ 1 directly from the basic regression Any linear combination of parameters could be tested in a similar manner Other examples of hypotheses about a single linear combination of parameters: β 1 = 1 + β 2 ; β 1 = 5 β 2 ; β 1 = -1/2 β 2 ; etc
Image of page 25
Fall 2008 under Econometrics Prof. Keunkwan Ryu 26 Multiple Linear Restrictions Everything we’ve done so far has involved testing a single linear restriction, (e.g. β 1 = 0 or β 1 = β 2 ) However, we may want to jointly test multiple hypotheses about our parameters A typical example is testing “exclusion restrictions” – we want to know if a group of parameters are all equal to zero
Image of page 26

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 27 Testing Exclusion Restrictions Now the null hypothesis might be something like H 0 : β k-q+1 = 0, ... , β k = 0 The alternative is just H 1 : H 0 is not true Can’t just check each t statistic separately, because we want to know if the q parameters are jointly significant at a given level – it is possible for none to be individually significant at that level
Image of page 27
Fall 2008 under Econometrics Prof. Keunkwan Ryu 28 Exclusion Restrictions (cont) To do the test we need to estimate the “restricted model” without x k-q+1 , , …, x k included, as well as the “unrestricted model” with all x ’s included Intuitively, we want to know if the change in SSR is big enough to warrant inclusion of x k-q+1 , , …, x k ( 29 ( 29 ed unrestrict is ur and restricted is r where , 1 - - - k n SSR q SSR SSR F ur ur r
Image of page 28

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 29 The F statistic The F statistic is always positive, since the SSR from the restricted model can’t be less than the SSR from the unrestricted Essentially the F statistic is measuring the relative increase in SSR when moving from the unrestricted to restricted model q = number of restrictions, or df r df ur n – k – 1 = df ur
Image of page 29
Fall 2008 under Econometrics Prof. Keunkwan Ryu 30 The F statistic (cont) To decide if the increase in SSR when we move to a restricted model is “big enough” to reject the exclusions, we need to know about the sampling distribution of our F stat Not surprisingly, F ~ F q,n-k-1 , where q is referred to as the numerator degrees of freedom and n – k – 1 as the denominator degrees of freedom
Image of page 30

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

View Full Document Right Arrow Icon
Fall 2008 under Econometrics Prof. Keunkwan Ryu 31 0
Image of page 31
Image of page 32
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