econ 140 9 - ECONOMICS 140 Professor Enrico Moretti 4/05/10...

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ECONOMICS 140 Professor Enrico Moretti 4/05/10 Lecture 9 ASUC Lecture Notes Online is the only authorized note-taking service at UC Berkeley. Do not share, copy or illegally distribute (electronically or otherwise) these notes. Our student-run program depends on your individual subscription for its continued existence. These notes are copyrighted by the University of California and are for your personal use only. D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. LECTURE I'm starting off today’s lecture where we left last week. The broad theme of last week's and today's lecture is problems with the regression model. As we saw last week, there are six problems with the regression model. First problem is when we include irrelevant variables. The second more serious problem is when we exclude relevant variables. The third problem is multicollinearity, the fourth problem is measurement error, the fifth problem is heteroscedacity and the sixth problem is data scatter. Today, we will cover problems number three, four, and possibly number five. Examples of Excluding Relevant Variables Last week, I proved to you that when we exclude a relevant variable, we will have a bias. E[ = β 1 + Bias Bias= β 2 * Σx 2 (x 1 - ) Σ (x 1 - ) 2 = β 2 * b 12 If β 2 = 0, then the variable omitted is not relevant to the outcome. If b 12 = 0, then there is no correlation between x 2 and x 1 . This means that we are excluding a variable that is not correlated with the variable of interest. Remember that the true model is: The estimated model is: When we leave out the second beta variable, x 1 is picking up two effects, the effect of x 2 and the true effect of x 1 . Student: What about the fit even if x 1 and x 2 are uncorrelated? Would the true equation have a better fit than the estimated equation? Even if x 1 and x 2 are uncorrelated, the goodness of fit can only go up when we have more variables. I have to stress that goodness of fit is a 2 nd or 3 rd order concern, one that we do not need to think too much about. Now I will pick up from where we left off last week with some examples. Imagine if I wanted to explain the relationship between your grade in this class and IQ. Example 1: The true model is: The estimated model is: How does the estimated β, , relate to the β you get from estimating the true model? My guess is that your estimated beta will be too large compared to the true β. There will be a positive bias. To what extend is this true? It is true under two conditions: 1. γ > 0 2. b 12 > 0
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Economics 140 ASUC Lecture Notes Online: Approved by the UC Board of Regents 4/05/10 D O N O T C O P Y Sharing or copying these notes is illegal and could end note taking for this course. 2
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econ 140 9 - ECONOMICS 140 Professor Enrico Moretti 4/05/10...

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