And the coefficient on wealth is negative which is

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And the coefficient on wealth is negative, which is not consistent with economic theory. Wrong signs and insignificant coefficient estimates on a priori important variables are the classic symptoms of multicollinearity. As an indicator of the possible multicollinearity the squared correlation between t Y and t W is .9979, which suggests near extreme multicollinearity among the explanatory variables.
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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 15 The two variables are so highly correlated that it is impossible to isolate the individual effects. (1) If regress t W on t Y we get: ˆ t W = 7.54 + 10.19 t Y t (0.26) ( 62.04) R 2 = .99 There is almost perfect multicollinearity between t Y and t W (2) Regress ˆ t C on income only: ˆ t C = 24.45 + 0.51 t Y t (3.81) (14.24) R 2 = 0.96 Income variable is highly significant, whereas before it was insignificant. (3) Regress ˆ t C on wealth only: ˆ t C = 24.41 + 0.05 t W t (3.55) (13.29) R 2 = 0.96 Wealth variable is highly significant, whereas before it was insignificant. 4. Remedial Measures What can be done if multicollinearity is serious? We have two choices: (1) Do nothing (2) Follow some rules of thumb
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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 16 1. Do Nothing Multicollinearlity is essentially a data problem and some times we have no choice over the data that we have. 2. Some Rules of Thumb Some rules of thumb are as follows: 1. Use extraneous or prior information, For example, in the Cobb Douglas type production function, if one expects constant returns to sc ale to prevail, then (β2 + β3) = 1, in which case we could run the regression imposing this restriction, regressing the output-labor ratio on the capital-labor ratio. If there is collinearity between labor and capital, as generally is the case in most sample data, such a transformation may reduce or eliminate the collinearity problem. But a warning is in order here regarding imposing such a priori restrictions, “. . . since in general we will want to test economic theory’s a priori predictions rather than simply impose them on data for which they may not be true.” 2. Combine cross-sectional and time series data, This technique has been used in many applications and is worthy of consideration in situations where the cross-sectional estimates do not vary substantially from one cross section to another. 3. Omit a highly collinear variable, But in dropping a variable from the model we may be committing a specification bias or specification error.
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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 17 Thus, if economic theory says that income and wealth should both be included in the model explaining the consumption expenditure, dropping the wealth variable would constitute specification bias.
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