# ch09 - Multiple Regression Analysis y = 0 1x1 2x2 kxk u 7...

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Economics 20 - Prof. Anderson 1 Multiple Regression Analysis y = β 0 + β 1 x 1 + β 2 x 2 + . . . β k x k + u 7. Specification and Data Problems

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Economics 20 - Prof. Anderson 2 Functional Form We’ve seen that a linear regression can really fit nonlinear relationships Can use logs on RHS, LHS or both Can use quadratic forms of x ’s Can use interactions of x ’s How do we know if we’ve gotten the right functional form for our model?
Economics 20 - Prof. Anderson 3 Functional Form (continued) First, use economic theory to guide you Think about the interpretation Does it make more sense for x to affect y in percentage (use logs) or absolute terms? Does it make more sense for the derivative of x 1 to vary with x 1 (quadratic) or with x 2 (interactions) or to be fixed?

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Economics 20 - Prof. Anderson 4 Functional Form (continued) We already know how to test joint exclusion restrictions to see if higher order terms or interactions belong in the model It can be tedious to add and test extra terms, plus may find a square term matters when really using logs would be even better A test of functional form is Ramsey’s regression specification error test (RESET)
Economics 20 - Prof. Anderson 5 Ramsey’s RESET RESET relies on a trick similar to the special form of the White test Instead of adding functions of the x ’s directly, we add and test functions of ŷ So, estimate y = β 0 + β 1 x 1 + … + β k x k + δ 1 ŷ 2 + δ 1 ŷ 3 +error and test H 0 : δ 1 = 0, δ 2 = 0 using F ~ F 2,n-k-3 or LM 2 2

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Economics 20 - Prof. Anderson 6 Nonnested Alternative Tests If the models have the same dependent variables, but nonnested x ’s could still just make a giant model with the x ’s from both and test joint exclusion restrictions that lead to one model or the other An alternative, the Davidson-MacKinnon test, uses ŷ from one model as regressor in the second model and tests for significance
Economics 20 - Prof. Anderson

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