Heteroskedasticity

Summary

异方差的概念、类型、图示
异方差的来源
异方差的后果：影响有效性（t、F检验失效，OLS不再是BLUE）

*A Heteroskedasticity-Robust LM Statistic:
reg y x1 x2 x3
predict uh, r
reg x4 x1 x2 x3
predict r1, r
reg x5 x1 x2 x3
predict r2, r
gen r1u = r1*uh
gen r2u = r2*uh
reg 1 r1u r2u, noc
dis "LM统计量为：" _N-e(rss)

异方差的检验：BP 检验（局限性）、White检验

*The Breusch-Pagan Test for Heteroskedasticity:
reg y x1 x2 x3
predict uhat, r
gen uhsq = uhat^2
reg uhsq x1 x2 x3
test x1 x2 x3 //F检验
dis "LM统计量为：" _N*e(r2) //LM检验

*A Special Case of the White Test for Heteroskedasticity:
reg y x1 x2 x3
predict yhat
predict uhat, r
gen yhsq = yhat^2
gen uhsq = uhat^2
reg uhsq yhat yhsq
test yhat yhsq
dis "LM统计量为：" _N*e(r2)

异方差的处理：

1. 异方差稳健标准误：robust
2. WLS/GLS（已知异方差）
3. FWLS（未知异方差）

*A Feasible GLS Procedure to Correct for Heteroskedasticity:
reg y x1 x2 x3
predict uh, r
gen lusq = ln( uh^2 )
reg lusq x1 x2 x3
predict gh
gen hh = exp(gh)
reg y x1 x2 x3 [aw=1/hh]
reg y x1 x2 x3 [aw=1/hh], r

*Estimating the Linear Probability Model by Weighted Least Squares:
reg y x1 x2 x3
predict yh
replace yh = 0.01 if yh < 0.01
replace yh = 0.99 if yh > 0.99
gen hh = yh*(1-yh)
reg y x1 x2 x3 [aw=1/hh]