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# ch10 - Random Regressors and Moment Based Click to edit...

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Click to edit Master subtitle style Principles of Econometrics, 3rd Edition Chapter 10 Random Regressors and Moment Based Estimation Prepared by Vera Tabakova, East Carolina University

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Principles of Econometrics, 3rd Edition Chapter 10: Random Regressors and Moment Based Estimation 10.1 Linear Regression with Random x ’s 10.2 Cases in Which x and e are Correlated 10.3 Estimators Based on the Method of Moments 10.4 Specification Tests 2Slide 10-2 Principles of Econometrics, 3rd Edition
Principles of Econometrics, 3rd Edition Chapter 10: Random Regressors and Moment Based Estimation The assumptions of the simple linear regression are: SR1. SR2. SR3. SR4. SR5. The variable xi is not random, and it must take at least two different values. SR6. (optional) 3Slide 10-3 Principles of Econometrics, 3rd Edition 1 2 1, , i i i y x e i N = β +β + = K ( ) 0 i E e = 2 var( ) i e = σ cov( , ) 0 i j e e = 2 ~ (0, ) i e N σ

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Principles of Econometrics, 3rd Edition Chapter 10: Random Regressors and Moment Based Estimation The purpose of this chapter is to discuss regression models in which xi is random and correlated with the error term ei . We will: Discuss the conditions under which having a random x is not a problem, and how to test whether our data satisfies these conditions. Present cases in which the randomness of x causes the least squares estimator to fail. Provide estimators that have good properties even when xi is random and correlated with the error ei . 4Slide 10-4 Principles of Econometrics, 3rd Edition
Principles of Econometrics, 3rd Edition 10.1 Linear Regression With Random X’s A10.1 correctly describes the relationship between yi and xi in the population, where β1 and β2 are unknown (fixed) parameters and ei is an unobservable random error term. A10.2 The data pairs , are obtained by random sampling . That is, the data pairs are collected from the same population, by a process in which each pair is independent of every other pair. Such data are said to be independent and identically distributed. 5Slide 10-5 Principles of Econometrics, 3rd Edition 1 2 i i i y x e = β +β + ( 29 , 1, , i i x y i N = K

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10.1 Linear Regression With Random X’s A10.3 The expected value of the error term ei , conditional on the value of xi , is zero. This assumption implies that we have (i) omitted no important variables, (ii) used the correct functional form, and (iii) there exist no factors that cause the error term ei to be correlated with xi . If , then we can show that it is also true that xi and ei are uncorrelated, and that . Conversely, if xi and ei are correlated, then and we can show that . 6Slide 10-6
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ch10 - Random Regressors and Moment Based Click to edit...

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