Thus in practical work 10 i vif serious

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Thus in practical work: 10 i VIF serious multicollinearity (due to that exp. variable). Note that VIF>10 implies 2 0.90 i P Example Consider the model 0 1 1 2 2 3 3 t t t t t Y a a X a X a X u . 1 0 1 2 2 3 t t t t X b b X b X v , 2 1 0.95 P 2 0 1 1 2 3 t t t t X c c X c X w , 2 2 0.80 P 3 0 1 1 2 2 t t t t X d d X d X z , 2 3 0.75 P
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 12 1 1 20 10 1 0.95 VIF serious MC 1 1 5 10 1 0.80 VIF no serious MC 1 1 4 10 1 0.75 VIF no serious MC 5. Condition number The characteristic roots or eigenvalues of * * X X say λ 1 , λ 2 , λ k , can be used to measure the extent of the multicollinearity in the data. If there are one or more near-linear dependences in the data, then one or more characteristic roots will be small. One or more small eigenvalues imply that there are near-linear dependences among the columns of X. Some analysts prefer to examine the condition number of, defined as: max min (13) Generally: If the condition number is less than 100, there is no serious problem with multicollinearity.
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 13 Condition number between 100 and 1000 imply moderate to strong multicollinearity, If it exceeds 1000, severe multicollinearity is indicated. Suppose that for a model with 4 explanatory variables, the eigenvalues are as follows: λ 1 =4.2048, λ 2 =2.1626, λ 3 =1.1384, λ 4 =0.0001.The condition number, max min , equals 4.2048/0.0001=42048 which exceeds 1000. This indicates presence of severe multicollinearity. Example As an illustration of the problems introduced by multicollinearity, consider the consumption equation: t C = a 0 + a 1 t Y + a 2 t W +u t where t C is consumption expenditures at time t , t Y is income at time t and t W is wealth at time t . Economic theory suggests that the coefficient on income should be slightly less than one and the coefficient on wealth should be positive. The time-series data for this relationship are given in the following table:
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 14 t C t Y t W 70 80 810 65 100 1009 90 120 1273 95 140 1425 110 160 1633 115 180 1876 120 200 2052 140 220 2201 155 240 2435 150 260 2686 Table 2 Consumption Data Applying least squares to this equation and data yields ˆ t C = 24.775 + 0.942 t Y - 0.042 t W t (3.67) (1.14) (-0.53) R 2 =0.9635, SSR = 324.446, F = 92.40 High R 2 shows that income and wealth together explain about 96% of the variation in consumption. The coefficient estimate for the marginal propensity to consume seems to be a reasonable value however it is not significantly different from either zero or one.
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