多元回归分析模型识别和数据问题.ppt

多元回归分析模型识别和数据问题
第1页，共29页，编辑于2022年，星期六
contents
Functional form misspecification
Using proxy variables
Measuree add and test functions of ŷ
So, estimate y = b0 + b1x1 + … + bkxk + d1ŷ2 + d1ŷ3 +error and test
H0: d1 = 0, d2 = 0 using F~F2,n-k-3 or LM~χ22
第6页，共29页，编辑于2022年，星期六
RESET test, example
Housing price equation ()
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, ŷ and SSRr=, n=88 R2=
Calculate ŷ2, ŷ3, and plug them to the original equation, and estimate it. That is, reg price on lotsize, sqrft, bdrms, ŷ2, ŷ3, and SSRur= n=88 R2=
So the F value = [(-)/2]/() = , the p-value=, therefore, we will reject the null hypothesis that there is no misspecification.
In the same way, we can calculate the second model
F= [(-)/2]/()=, p-value=. So we can’t reject the null hypothesis at the 5% significance.
第7页，共29页，编辑于2022年，星期六
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. For example, we have to choose model between
y = b0 + b1x1 + b2x2 +u (m1)
y = b0 + b1log(x1) + b2log(x2)+u (m2)
Which model to choose?
Method 1: estimate a comprehensive model
y = d0 + d1x1 + d2x2+ d3log(x1) + d4log(x2)+u
H0: d3 =0, d4=0 for the second model and H0: d1 =0, d1=0 for the first one.
Method 2: the Davidson-Mackinnon test
If (m1) is true, then the fitted values from (m2) should be insignificant in (m1). Thus, to test (m1), we first estimate (m2) by OLS to obtain the fitted values, ŷ. Then plug it in to (m1), that’s y = b0 + b1x1 + b2x2 +q ŷ+ u
A significant t statistic is a rejection o