Hi All,
Having read the following two posts:
http://www.stata.com/statalist/archive/2003-11/msg00795.html
http://www.stata.com/statalist/archive/2005-05/msg00158.html
I would like to attempt to summarize the methods that Wooldridge
(2000) suggested to avoid the forbidden regression, so
please feel free to correct me. At the end, I would also like to ask a
couple of questions about these methods, hopefully I can get some
feedback from Stata Users.
Wooldridge (2000), Econometric Analysis of Cross Section and Panel Data,
section 9.5, esp. pp. 236-7.
sysuse auto.dta, clear
gen weight2=weight^2
We are trying to estimate the following two equations:
weight = constant + price + turn + length + gear_ratio +mpg
price = constant + weight + weight^2 + turn + displacement
First method ----- Create an instrumental variable – weighthatsquared
– and use this as an additional instrument in ivreg2
* ------------------Begin code for First Method
-----------------------------------
regress weight turn length gear_ratio mpg turn displacement
predict weighthat, xb
gen weighthatsquared=weighthat^2
ivreg2 price (weight weight2=weighthatsquared length gear_ratio mpg)
turn displacement , endog(weight weight2) gmm2s robust
*-------------------- End code for First Method
-----------------------------------
Second method -- Create additional excluded instruments (cross-product
& and square of the excluded instruments) and use all these
instruments in ivreg2
*------------------- Begin code for Second Method
-----------------------------------
gen length2=length^2
gen gear_ratio2=gear_ratio^2
gen mpg2=mpg^2
gen lengthmpg=length*mpg
gen mpggear_ratio= mpg*gear_ratio
gen lengthgear_ratio=length*gear_ratio
ivreg2 price (weight weight2= length gear_ratio mpg length2
gear_ratio2 mpg2 lengthmpg mpggear_ratio lengthgear_ratio) turn
displacement , endog(weight weight2) gmm2s robust
*-------------------- End code for Second Method
-----------------------------------
Question 1:
Can we use the following instruments for the second method: turn^2,
displacement^2 , cross product of (turn, displacement) with (length,
gear_ratio, mpg)? If yes, how many of them and what sort of
combinations should we use? Product of any two instruments, or three
instruments?
Question 2:
Which is a preferred method (method 1 VS 2)? Any differences between
these two methods?
Question 3:
What if we have year dummies in the price equation, is following
estimation method right?
price = constant + weight + weight^2 + turn + displacement + year dummies
xi: ivreg2 price (weight weight2=weighthatsquared length gear_ratio
mpg) turn displacement , endog(weight weight2) i.year, gmm2s robust
Regards,
Kelvin Tan
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