ECON301_Handout_01_1213_02

O if this condition is not satisfied the ols

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o If this condition is not satisfied, the OLS regression coefficients will be inefficient . o In terms of our production example, this assumption implies that the variation in output is the same whether the quantity of labor is 20, 100, or any other number of units. Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 9
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ECON 301 (01) - Introduction to Econometrics I March , 2012 METU - Department of Economics Assumption 5 (A5) : No autocorrelation 7 or zero covariance between t u and s u [i.e., ts Cov(u ,u ) 0 = ]. This assumption can be made stronger by assuming that the values of u t are all statistically independent 8 . o This condition states that there should be no systematic association between the values of the disturbance term in any two observations. o If this condition is not satisfied, OLS will again give inefficient estimates. o This assumption implies that output is higher than expected today should not lead to higher (or lower) than expected output tomorrow. o Recall that correlation between X and Y is given by: 7 No autocorrelation means the correlation between any t u and s u ( ) is zero. 8 The value which the disturnbance term assumes in one period does not depend on the value which it assumed in any other period. Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 10
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ECON 301 (01) - Introduction to Econometrics I March , 2012 METU - Department of Economics XY Cov( X ,Y ) ρ σσ = where X σ and Y are standard deviations of X and Y, respectively. Therefore, if the correlation between X and Y is zero ( 0 = ), it implies that Cov( X ,Y ) 0 = . As a result, the no autocorrelation implies that ts Cov(u ,u ) 0 = where . 9 o Note that covariance between X and Y is given by [ ][ ] { } Cov( X ,Y ) E X E( X ) Y E(Y ) = −− Therefore, no autocorrelation implies zero covariance : [ ][ ] { } t t s s Cov(u ,u ) E u E(u ) u E(u ) 0 = −= From Assumption 3 , we know that t E(u ) 0 = and s = . Thus, no autocorrelation assumption implies that t t s s 00 0    =      ( ) E uu 0 = Assumption 6 (A6): The number of observations ( T ) must be greater than the number of parameters to be estimated 10 ( T>k+1 ) and that there are no exact linear relationship between the independent variables ( No perfect multicollinearity ). 9 Recall that a zero value of the covariance indicates no linear dependence between X and Y. 10 There are k independent variables and one intercept term, hence: k+1 . Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 11
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ECON 301 (01) - Introduction to Econometrics I March , 2012 METU - Department of Economics o Although this is stated as an assumption, it can easily be checked, so that it need not be assumed. o The problem of multicollinearity (two or more independent variables being approximately related in the sample data) is associated with this assumption. This issue will be discussed later.
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o If this condition is not satisfied the OLS regression...

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