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From |
Kelvin Tan <kelvin.tan.statalist@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Sat, 6 Feb 2010 08:17:15 +1000 |

Hi All, Sorry for posting this message again as I am not sure if this mesage has been properly posted. Thanks for Austin's advice. I would like to ask another question in regard to Weak identification test (Kleibergen-Paap rk Wald F statistic). I tried Method 1 as follows, *----Begin Code--------------- regress y2 on all excluded Instruments, included instruments from y1 equation, time dummies ( but excluding y1 endogeneous dependent variable). predict y2hat, xb gen y2hatsquared=y2hat^2 *xlist is a list of predictors for y1 xi:ivreg2 y1 (y2 y2^2 = excluded instruments y2hatsquared) xlist, cluster(id) gmm2s endog(y2 y2^2) *------End Code ------------------------ Is Kleibergen-Paap rk Wald F statistic valid to test for weak instruments as there are two endogenous variables in the equation (y2 and y2^2)? Can anyone advise me what to do next if Kleibergen-Paap rk Wald F statistic=6.298 (see Results 1) is smaller than 5% maximal IV relative bias of 11.04? Should I repeat this analysis with LIML or CUE estimator (see Results 2) as they are more robust to weak instruments. Results 1: ------------------------------------------------------------------------------ Underidentification test (Kleibergen-Paap rk LM statistic): 13.633 Chi-sq(3) P-val = 0.0035 ------------------------------------------------------------------------------ Weak identification test (Kleibergen-Paap rk Wald F statistic): 6.298 Stock-Yogo weak ID test critical values: 5% maximal IV relative bias 11.04 10% maximal IV relative bias 7.56 20% maximal IV relative bias 5.57 30% maximal IV relative bias 4.73 10% maximal IV size 16.87 15% maximal IV size 9.93 20% maximal IV size 7.54 25% maximal IV size 6.28 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ Hansen J statistic (overidentification test of all instruments): 0.968 Chi-sq(2) P-val = 0.6163 -endog- option: Endogeneity test of endogenous regressors: 9.223 Chi-sq(2) P-val = 0.0099 Regressors tested: y2 y2^2 ----------------------------------------------------------------- Results 2: based on LIML or CUE: ------------------------------------------------------------------------------ Weak identification test (Kleibergen-Paap rk Wald F statistic): 6.298 Stock-Yogo weak ID test critical values: 10% maximal LIML size 4.72 15% maximal LIML size 3.39 20% maximal LIML size 2.99 25% maximal LIML size 2.79 Source: Stock-Yogo (2005). Reproduced by permission. NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors. ------------------------------------------------------------------------------ I look forward to hearing from you all. Regards, Kelvin On Wed, Jan 27, 2010 at 11:20 PM, Austin Nichols <austinnichols@gmail.com> wrote: > Kelvin Tan <kelvin.tan.statalist@gmail.com>: > 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 > <kelvin.tan.statalist@gmail.com> 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 > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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