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Unformatted text preview: Lecture 9 : Specification Choosing the Independent Variables and Choosing a Functional Form Econ 444, Winter 2010 Feb 15, 2010 1. Omitted Variables Omitted Variable : an important explanatory (or independent) variable that has been left out of the regression equation. Suppose that the true regression model is Y i = + 1 X 1 i + 2 X 2 i + i (1) where, Y i is quantity demanded of coffee. X 1 i is price of coffee. X 2 i is price of tea. But by mistake you omit (or forget) to include X 2 i and instead estimate the following equation, Y i = + 1 X 1 i + * i (2) What is the effect of this omission? 1 The unknown error term changes to * i where, * i = i + 2 X 2 i (3) 2 As long as X 1 i and X 2 i are correlated , X 1 i will be correlated with * i . Violates Classical Assumption 3 3 This would mean that now OLS is biased : E ( 1 ) , 1 (4) The bias caused by leaving a variable out of a equation is called omitted variable bias . Can we determine the true magnitude of the bias? No Can we at least guess the direction of the bias? Yes Expected Bias = omit f(correlation between included variable and omitted variable) So two things determine the sign or direction of the expected bias : 1 Expected sign of the coefficient ( omit ) of the omitted variable. 2 Sign of the correlation between the included variable and the omitted variable. Example 1 Consider a production function that states that output ( Y ) depends on the amount of labor ( X 1 ) and capital ( X 2 ) used....
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This note was uploaded on 04/13/2010 for the course ECON 444 taught by Professor Ogaki during the Winter '07 term at Ohio State.
 Winter '07
 OGAKI
 Econometrics

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