lect11_2010

# lect11_2010 - 1 22 Introduction to Econometrics Econ 322...

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Unformatted text preview: 1 / 22 Introduction to Econometrics Econ 322 Fall, 2010 Lecture 10: Simple Linear Regression III October 11, 2010 Topics Covered triangleright Topics Covered Some Additional Assumptions Homoscedasticity Assumption An estimator for the variance of ˆ β 1 An Alternative Assumption An Alternative Assumption (cont) Heteroscedasticity and OLS A Heteroscedastic-Consistent Estimator for σ 2 ˆ β 1 Summary Making Inferences with OLS Estimates The Test Statistic The distribution of the test statistic Confidence Intervals Case 1: Homoscedastic errors Case 2: Heteroscedastic errors Summary 2 / 22 1. Homoscedasticity and Heteroscedasticity 2. Hypothesis testing 3. Confidence Intervals Some Additional Assumptions Topics Covered triangleright Some Additional Assumptions Homoscedasticity Assumption An estimator for the variance of ˆ β 1 An Alternative Assumption An Alternative Assumption (cont) Heteroscedasticity and OLS A Heteroscedastic-Consistent Estimator for σ 2 ˆ β 1 Summary Making Inferences with OLS Estimates The Test Statistic The distribution of the test statistic Confidence Intervals Case 1: Homoscedastic errors Case 2: Heteroscedastic errors Summary 3 / 22 square So far we have made very few assumptions. Our assumptions so far are: 1. E ( epsilon1 i | X ) = 0 for each i 2. the sample is random 3. X and epsilon1 have finite fourth moments square Lets now think about the regression error, epsilon1 i . square In almost every econometrics text book you will see the following assumption about the distribution of the regression error. It is commonly referred to as an assumption of homoscedasticity . Homoscedasticity Assumption Topics Covered Some Additional Assumptions triangleright Homoscedasticity Assumption An estimator for the variance of ˆ β 1 An Alternative Assumption An Alternative Assumption (cont) Heteroscedasticity and OLS A Heteroscedastic-Consistent Estimator for σ 2 ˆ β 1 Summary Making Inferences with OLS Estimates The Test Statistic The distribution of the test statistic Confidence Intervals Case 1: Homoscedastic errors Case 2: Heteroscedastic errors Summary 4 / 22 square We assume that epsilon1 i ∼ (0 , σ 2 epsilon1 ) for all i . This assumption states that the regression error for each observation is identically distributed with the same variance. square Implications of this assumption – If we assume that the regression error is homoscedastic then we can simplify the analysis of the variance of the OLS slope estimator ˆ β 1 . – In particular, square Since we assume that the observations are drawn randomly (i.i.d) then Homoscedasticity Assumption (cont) Topics Covered Some Additional Assumptions triangleright Homoscedasticity Assumption An estimator for the variance of ˆ β 1 An Alternative Assumption An Alternative Assumption (cont) Heteroscedasticity and OLS A Heteroscedastic-Consistent Estimator for σ 2 ˆ β 1 Summary Making Inferences with OLS Estimates The Test Statistic The distribution of the test statistic Confidence Intervals...
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## This document was uploaded on 10/26/2011 for the course ECON 327 at Rutgers.

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lect11_2010 - 1 22 Introduction to Econometrics Econ 322...

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