Multiple regression analysis y=Bo B Bx+ Bx +.Bkk+u 27. Specification and Data Problems Economics 20- Prof anderson
Economics 20 - Prof. Anderson 1 Multiple Regression Analysis y = b0 + b1 x1 + b2 x2 + . . . bk xk + u 7. Specification and Data Problems
Functional form o We've seen that a linear regression can really fit nonlinear relationships Can use logs on rhs, lhs or both o Can use quadratic forms ofx's Can use interactions ofx's o How do we know if we' ve gotten the right functional form for our model? Economics 20- Prof anderson
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?
Functional Form(continued) o First, use economic theory to guide you Think about the interpretation e Does it make more sense for x to affect y percentage(use logs)or absolute terms Does it make more sense for the derivative of x, to vary with x,(quadratic) or with x2 (interactions)or to be fixed? Economics 20- Prof anderson
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 x1 to vary with x1 (quadratic) or with x2 (interactions) or to be fixed?
Functional Form(continued) e 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 lus 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 4
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)
Ramsey's reset RESET relies on a trick similar to the special form of the White test o Instead of adding functions of the x's directly, we add and test functions of y ◆So, estimate y=β0+βx1+….+B1x+ 8,y2+8y +error and test o Ho: 8=0,82=0 using F-F2 or LM-X2 Economics 20- Prof anderson 5
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 = b0 + b1 x1 + … + bk xk + d1 ŷ 2 + d1 ŷ 3 +error and test H0 : d1 = 0, d2 = 0 using F~F2,n-k-3 or LM~χ2 2