Econometrics-I-8 - Econometrics I Professor William Greene...

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Part 8: Hypothesis Testing Econometrics I Professor William Greene Stern School of Business Department of Economics
Image of page 1

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

View Full Document Right Arrow Icon
Part 8: Hypothesis Testing Econometrics I Part 8 – Interval Estimation  and Hypothesis Testing ™    1/50
Image of page 2
Part 8: Hypothesis Testing Interval Estimation p b = point estimator of p We acknowledge the sampling variability. n Estimated sampling variance n b = + sampling variability induced by  ™    2/50
Image of page 3

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

View Full Document Right Arrow Icon
Part 8: Hypothesis Testing p Point estimate is only the best single guess p Form an interval, or range of plausible values p Plausible  likely values with acceptable degree of probability. p To assign probabilities, we require a distribution for the variation of the estimator. p The role of the normality assumption for  ™    3/50
Image of page 4
Part 8: Hypothesis Testing Confidence Interval bk = the point estimate Std.Err[bk] = sqr{[σ2( XX )-1]kk} = vk Assume normality of ε for now: n bk ~ N[βk,vk2] for the true βk. n (bk-βk)/vk ~ N[0,1] Consider a range of plausible values of βk given the point estimate bk. bk sampling error. n Measured in standard error units, n |(bk – βk)/ vk| < z* n Larger z*  greater probability (“confidence”) n Given normality, e.g., z* = 1.96  95%, z*=1.64590% n Plausible range for βk then is bk ± z* vk ™    4/50
Image of page 5

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

View Full Document Right Arrow Icon
Part 8: Hypothesis Testing Computing the Confidence Interval Assume normality of ε for now: n bk ~ N[βk,vk2] for the true βk. n (bk-βk)/vk ~ N[0,1] vk = [σ2( X’X )-1]kk is not known because σ2 must be estimated. Using s2 instead of σ2, (bk-βk)/Est.(vk) ~ t[n-K]. (Proof: ratio of normal to sqr(chi-squared)/df is pursued in your text.) Use critical values from t distribution instead of standard normal. Will be the same as normal if n > 100. ™    5/50
Image of page 6
Part 8: Hypothesis Testing Confidence Interval Critical t[.975,29]  =  2.045 Confidence interval based on t:           1.27365 –  2.045 * .1501 Confidence interval based on normal: 1.27365 –  1.960 * .1501 ™    6/50
Image of page 7

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

View Full Document Right Arrow Icon
Part 8: Hypothesis Testing Testing a Hypothesis Using a Confidence Interval Given the range of plausible values Testing the hypothesis that a coefficient equals zero or some other particular value: Is the hypothesized value in the confidence interval? Is the hypothesized value within the range of plausible values? If not, reject the hypothesis. ™    7/50
Image of page 8
Part 8: Hypothesis Testing Test a Hypothesis About a Coefficient ™    8/50
Image of page 9

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

View Full Document Right Arrow Icon
Part 8: Hypothesis Testing Classical Hypothesis Testing We are interested in using the linear regression to support or cast doubt on the validity of a theory about the real world counterpart to our statistical model. The model is used to test hypotheses about the underlying data generating process. ™    9/50
Image of page 10
Part 8: Hypothesis Testing Types of Tests p Nested Models: Restriction on the parameters of a particular model y = 1 + 2x + 3z + , 3 = 0 p Nonnested models: E.g., different RHS variables yt = 1 + 2xt + 3xt-1 + t yt = 1 + 2xt + 3yt-1 + wt p Specification tests:  ~ N[0,2] vs. some other distribution ™    10/50
Image of page 11

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

View Full Document Right Arrow Icon
Image of page 12
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