多元回归分析模型识别和数据问题.ppt

第八章　多元回归分析 模型识别和数据问题 contents Functional form misspecification Using proxy variables Measurement error in variables Missing data and Outlying observations Functional from misspecification 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) First, use economic theory to guide you Y=AKaLbeu or lnY = lnA + alnK + blnL + u Think about the interpretation log(wage)=b0 + b1 educ + u, or log(educ) as independent variable 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) We already know how to test joint exclusion restrictions to see if higher order terms or interactions belong in the model log(wage) = b0 + b1 educ + b2 exper +b3 tenure +u log(wage) = b0 + b1 educ + b2 exper +b3 tenure + b4 educ2 + b5 exper2 + b6 tenure2 +b7 educ?tenure+ u 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) First estimate log(wage) = b0 + b1 educ + b2 exper +b3 tenure +u Get fitted value ? (log(wage) of above equation) Then, consider the expanded equation log(wage) = b0 + b1 educ + b2 exper +b3 tenure + d4 ?2 + d5 ?3 + u RESET is the F statistic for tesing H0: d4=0, d5=0 In Stata, the RESET test command: ovtest RESET test, example Housing price equation (hprice.raw) price = b0 +b1 lotsize +b2 sqrft +b3 bdrms +u log(price) = b0 +b1 log(lotsize) +b2 log(sqrft) +b3 bdrms +u RESET test procedure Estimate the models: reg price on lotsize, sqrft, bdrms, and get fitted value of price, ? and SSRr=300723.806, n=88 R2=0.6724 Calculate