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Re: st: Attempt to summarize how to avoid a forbidden regression with -IVREG2-, and some questions to ask


From   Austin Nichols <[email protected]>
To   [email protected]
Subject   Re: st: Attempt to summarize how to avoid a forbidden regression with -IVREG2-, and some questions to ask
Date   Wed, 27 Jan 2010 08:20:39 -0500

Kelvin Tan <[email protected]>:
There are two main issues: weak instruments and small violations of
the exclusion restriction.  If your instruments are weak, including
more nearly irrelevant instruments can result in even worse inference,
but method 1 introduces less of a problem in some sense--on the other
hand method 2 estimates the first-stage coefs on all those additional
excluded instruments, and you can do more overid tests; you can use
liml to get inference more robust to the many weak instruments
problem.  The exclusion restriction has to be satisfied very
strongly--that is, turn squared in your example should have no
correlation with the true error term.  Even a weak violation
(correlation close to zero but not exactly zero) can produce very bad
outcomes for inference.  Running a simulation with data like yours
(not the auto data) will clarify the importance of these tradeoffs for
your particular case.

On Wed, Jan 27, 2010 at 12:50 AM, Kelvin Tan
<[email protected]> wrote:
> 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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