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Unformatted text preview: Applied Econometrics William Greene Department of Economics Stern School of Business Applied Econometrics 3. Linear Least Squares Vocabulary Some terms to be used in the discussion. Population characteristics and entities vs. sample quantities and analogs Residuals and disturbances Population regression line and sample regression Objective : Learn about the conditional mean function. Estimate β and σ 2 First step: Mechanics of fitting a line (hyperplane) to a set of data Fitting Criteria The set of points in the sample Fitting criteria  what are they: LAD Least squares and so on Why least squares ? (We do not call it ‘ordinary’ at this point.) A fundamental result: Sample moments are “good” estimators of their population counterparts We will spend the next few weeks using this principle and applying it to least squares computation. An Analogy Principle In the population E[ y  X ] = X β so E[ y  X β  X ] = Continuing E [x i ε i ] = 0 Summing, Σ i E [x i ε i ] = Σ i 0 = 0 Exchange Σ i and E E [ Σ i x i ε i ] = E[ X ′ ε ] = E[ X ′ ( y  X β ) ] = Choose b , the estimator of β to mimic this population result: i.e., mimic the population mean with the sample mean...
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This note was uploaded on 09/27/2008 for the course FM 101 taught by Professor Greece during the Spring '08 term at New York College of Podiatric Medicine.
 Spring '08
 Greece

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