Lecture+9+Multiple+Regression+Analysis+-+Estimation

Lecture+9+Multiple+Regression+Analysis+-+Estimation -...

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Lecture 9, ECON 123A, Fall 2011 Dale J. Poirier 9-1 Lecture 9 Multiple Regression Analysis: Estimation 3.1 Regression The Model with Two Independent Variables Example: Augment the wage regression example in Chapter 2 to where exper is years of labor market experience. Suppose we are primarily interested in the effect of educ on wage, holding fixed all other factors affecting wage; that is, we are interested in the parameter $ 1 . (3.1)
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Lecture 9, ECON 123A, Fall 2011 Dale J. Poirier 9-2 C Compared with a simple regression analysis relating wage to educ, effectively takes exper out of the error term and puts it explicitly in the equation. C Because exper appears in the equation, its coefficient, $ 2 measures the ceteris paribus effect of exper on wage , which is also of some interest. (3.1)
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Lecture 9, ECON 123A, Fall 2011 Dale J. Poirier 9-3 C Not surprisingly, just as with simple regression, we will have to make assumptions about how u in (3.1) is related to the independent variables, educ and exper . B Because (3.1) contains experience explicitly, we will be able to measure the effect of education on wage, holding experience fixed. B In a simple regression analysis, which puts exper in the error term, we would have to assume that experience is uncorrelated with education, a tenuous assumption.
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Lecture 9, ECON 123A, Fall 2011 Dale J. Poirier 9-4 Example: Consider the problem of explaining the effect of per student spending ( expend ) on the average standardized test score ( avgscore ) at the high school level. Suppose that the average test score depends on funding, average family income ( avginc ), and other unobservables: The coefficient of interest for policy purposes is $ 1 , the ceteris paribus effect of expend on avgscore . (3.2)
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Lecture 9, ECON 123A, Fall 2011 Dale J. Poirier 9-5 C By including avginc explicitly in the model, we are able to control for its effect on avgscore . B This is likely to be important because average family income tends to be correlated with per student spending: spending levels are often determined by both property and local income taxes. B In simple regression analysis, avginc would be included in the error term, which would likely be correlated with expend, causing the OLS estimator of $ 1 in the two-variable model to be biased.
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Dale J. Poirier 9-6 Generally, we can write a model with two independent variables as where $ 0 is the intercept, $ 1 measures the change in y with respect to x 1 , holding other factors fixed, and $ 2 measures the change in y with respect to x 2 , holding other factors fixed. C Multiple regression analysis is also useful for generalizing functional relationships between variables. As an example, suppose family consumption ( cons ) is a quadratic function of family income ( inc ): where u contains other factors affecting consumption. (3.3)
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This note was uploaded on 12/13/2011 for the course ECON 123a taught by Professor Staff during the Fall '08 term at UC Irvine.

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Lecture+9+Multiple+Regression+Analysis+-+Estimation -...

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