We replace var bi with var bi r d note that stata

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Var bi s N (0, 1) dβ we do not know Var bi . We replace Var bi with Var bi . β β r dβ β Note that Stata reports se bi = Var bi so we compute b β βi ri dβ Var bi Lecture 4 (econometrics and simple linear regression) = b βi βi se bi β EMET2007/6007 s tn 2 13 th March 2013 12 / 50 Under assumptions SLR 1 - SLR 6: b s N β , Var b βi βi i b βi βi β se bi s N (0, 1) The estimators are normally distributed around the true parameters with the variance that was derived earlier The standardized estimators follow a standard normal distribution Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 13 / 50 Testing hypotheses about a population parameter Under assumptions SLR 1 - SLR 6: (t-distribution for standardized estimators) b βi βi s tn 2 β se bi If the standardization is done using the estimated standard deviation (se bi = standard error), the normal distribution is replaced by a β t-distribution Note: The t-distribution is close to the standard normal distribution if n 2 is large. Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 14 / 50 Null hypothesis (for more general hypotheses, see below) H0 : β 1 = 0 The population parameter is equal to zero, i.e. after controlling for the other independent variables, there is no e¤ect of x on y t statistic (or t ratio) tb = β 1 b βi se bi β The t-statistic will be used to test the above null hypothesis. The farther the estimated coe¢ cient is away from zero, the less likely it is that the null hypothesis holds true. But what does “far” away from zero mean? Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 15 / 50 Distribution of the t-statistic if the null hypothesis is true tb = β 1 b βi β se bi s tn 2 Goal: De…ne a rejection rule so that, if it is true, H0 is rejected only with a small probability (= signi…cance level, e.g. 5%) Lecture 4 (econometrics and simple linear regression) EMET2007/6007 13 th March 2013 16 / 50 Testing against one-sided alternatives (H0 : β1 0, H1 : β1 > 0) Reject the null hypothesis in favour of the alternative hypothesis if...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online