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From |
"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: Which inverter? (was: RE: RE: ivreg2 weak-id statistic and quadratic terms) |

Date |
Tue, 21 Feb 2012 11:12:42 -0000 |

Hi all. Just a quick update to say that Miroslav wrote to me directly and confirmed that the source of the problem was scaling in his case as well. --Mark NB: With apologies for the thread-changing ... Miroslav wrote to me directly because for some reason he didn't receive my Statalist post, and only spotted it on the Statalist archive. I've had a similar experience recently - something was posted to Statalist and showed up in the Statalist archive, but I didn't receive it as an email even though I was getting plenty of other Statalist posts at the time. Has anybody else had this problem? > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > Schaffer, Mark E > Sent: 21 February 2012 00:11 > To: statalist@hsphsun2.harvard.edu > Subject: st: Which inverter? (was: RE: RE: ivreg2 weak-id > statistic and quadratic terms) > > Hi all. I have traced the problem to the choice of inverter. > At least, it's definitely the problem in the auto dataset > example below, and I'll bet it's the source of Miroslav's > problem as well. > > In most places, -ivreg2- and -ranktest- use Mata's general-purpose > invsym() inverter. In a few places they use Mata's QR > decomposition qrsolve(). It is where the latter is used that > things are going wrong. > In the simple example I constructed with the auto data, > qrsolve() has problems but invsym() does not. > > This is an interesting question. What's the best choice of > inverter when faced with scaling problems? > > Below is some simple Mata code and output corresponding to a > regression with the toy auto data set when the variables > create scaling problems. > Stata's built-in -regress- is the benchmark. > > In a nutshell: > > invsym() reproduces the -regress- results. > > lusolve() reproduces the -regress- results. > > svsolve() runs into problems - without rescaling it goes badly wrong. > > qrsolve() runs into problems - without rescaling it goes badly wrong. > > I've had a look at the discussions in the manual, and I > didn't spot anything there that would explain this. > > Would someone who knows more about numerical computing than > me care to comment? > > --Mark > > > Stata code: > ********************************************************************* > sysuse auto, clear > gen double weightsq=weight^2 > > * Rescaled to reduce scaling problems > gen double weight1=weight/1000 > gen double weight1sq=(weight/1000)^2 > > * -regress- benchmark > qui reg mpg turn weight weightsq > mat list e(b) > qui reg mpg turn weight1 weight1sq > mat list e(b) > > putmata y=mpg X=(turn weight weightsq 1) X1=(turn weight1 > weight1sq 1), replace > > mata: > > XX=quadcross(X,X) > Xy=quadcross(X,y) > XX1=quadcross(X1,X1) > Xy1=quadcross(X1,y) > > "Comparing beta hat for (1) unscaled and (2) scaled data" > > beta_inv=invsym(XX)*Xy > beta_inv1=invsym(XX1)*Xy1 > beta_inv, beta_inv1 > > beta_lu=lusolve(XX,Xy) > beta_lu1=lusolve(XX1,Xy1) > beta_lu, beta_lu1 > > beta_sv=svsolve(XX,Xy) > beta_sv1=svsolve(XX1,Xy1) > beta_sv, beta_sv1 > > beta_qr=qrsolve(XX,Xy) > beta_qr1=qrsolve(XX1,Xy1) > beta_qr, beta_qr1 > > end > ********************************************************************* > > > Output (using Stata 11.2) > ********************************************************************* > . sysuse auto, clear > (1978 Automobile Data) > > . gen double weightsq=weight^2 > > . > . * Rescaled to reduce scaling problems > . gen double weight1=weight/1000 > > . gen double weight1sq=(weight/1000)^2 > > . > . * -regress- benchmark > . qui reg mpg turn weight weightsq > > . mat list e(b) > > e(b)[1,4] > turn weight weightsq _cons > y1 -.148733 -.01356202 1.345e-06 55.081765 > > . qui reg mpg turn weight1 weight1sq > > . mat list e(b) > > e(b)[1,4] > turn weight1 weight1sq _cons > y1 -.148733 -13.562021 1.3448538 55.081765 > > . > . putmata y=mpg X=(turn weight weightsq 1) X1=(turn weight1 > weight1sq 1), replace > (1 vector, 2 matrices posted) > > . > . mata: > ------------------------------------------------- mata (type end to > exit) ---------------------------------- > : > : XX=quadcross(X,X) > > : Xy=quadcross(X,y) > > : XX1=quadcross(X1,X1) > > : Xy1=quadcross(X1,y) > > : > : "Comparing beta hat for (1) unscaled and (2) scaled data" > Comparing beta hat for (1) unscaled and (2) scaled data > > : > : beta_inv=invsym(XX)*Xy > > : beta_inv1=invsym(XX1)*Xy1 > > : beta_inv, beta_inv1 > 1 2 > +-------------------------------+ > 1 | -.1487330027 -.1487330027 | > 2 | -.0135620214 -13.5620214 | > 3 | 1.34485e-06 1.344853823 | > 4 | 55.08176484 55.08176484 | > +-------------------------------+ > > : > : beta_lu=lusolve(XX,Xy) > > : beta_lu1=lusolve(XX1,Xy1) > > : beta_lu, beta_lu1 > 1 2 > +-------------------------------+ > 1 | -.1487330027 -.1487330027 | > 2 | -.0135620214 -13.5620214 | > 3 | 1.34485e-06 1.344853823 | > 4 | 55.08176484 55.08176484 | > +-------------------------------+ > > : > : beta_sv=svsolve(XX,Xy) > > : beta_sv1=svsolve(XX1,Xy1) > > : beta_sv, beta_sv1 > 1 2 > +-------------------------------+ > 1 | .6585549729 -.1487330027 | > 2 | .0057662425 -13.5620214 | > 3 | -2.30511e-06 1.344853823 | > 4 | .0096556129 55.08176484 | > +-------------------------------+ > > : > : beta_qr=qrsolve(XX,Xy) > > : beta_qr1=qrsolve(XX1,Xy1) > > : beta_qr, beta_qr1 > 1 2 > +-------------------------------+ > 1 | .6586963952 -.1487330027 | > 2 | .0057696338 -13.5620214 | > 3 | -2.30575e-06 1.344853823 | > 4 | 0 55.08176484 | > +-------------------------------+ > > : > : end > ********************************************************************* > > > -----Original Message----- > > From: owner-statalist@hsphsun2.harvard.edu > > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of > Schaffer, > > Mark E > > Sent: 20 February 2012 22:36 > > To: statalist@hsphsun2.harvard.edu > > Subject: st: RE: ivreg2 weak-id statistic and quadratic terms > > > > Hi Miroslav, hi all. > > > > I've checked this with the toy auto dataset. I can replicate this > > behaviour. > > > > Miroslav - either before or after rescaling your covariates, do the > > estimated coefficients vary hugely in scale? > > > > In my toy auto dataset example, I am pretty sure that it is > driven by > > scaling problems. For example, after > > > > sysuse auto, clear > > gen double weight2=weight^2 > > ivreg2 price (mpg=turn) weight weight2 > > > > gives a large weak ID stat of 11.5. But there are big scaling > > problems in the first-stage and main estimations, with > coeffs that are > > something like a factor of 10^8 different in magnitude. > > > > If I estimate and just partial out the constant, > > > > ivreg2 price (mpg=turn) weight weight2, partial(_cons) > > > > the ill-conditioning is less pronounced and I get a weak ID stat of > > 0.73. > > > > If I partial out all the exogenous covariates, > > > > ivreg2 price (mpg=turn) weight weight2, partial(weight weight2) > > > > the ill-conditioning is gone and I again get a weak ID stat of 0.73. > > > > I will investigate further and will report back to the list > if I find > > anything more. It may be that -ivreg2- could handle these > cases more > > robustly. > > > > --Mark (ivreg2 coauthor) > > > > > -----Original Message----- > > > From: owner-statalist@hsphsun2.harvard.edu > > > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf > Of Miros Lav > > > Sent: 20 February 2012 21:25 > > > To: statalist@hsphsun2.harvard.edu > > > Subject: st: ivreg2 weak-id statistic and quadratic terms > > > > > > Dear all, > > > > > > I am using ivreg2 to estimate a model where a control > > variable enters > > > with a quadratic term. A simplified version of the command is as > > > follows > > > > > > ivreg2 y (a=instrument) x x^2, r cluster(id). > > > > > > Estimating this model results in a very large > > Kleinbergen-Paap weak-id > > > F statistic. > > > > > > However, generating z=x/1000 and z^2=z*z and estimating the model > > > > > > ivreg2 y (a=instrument) z z^2, r cluster(id) > > > > > > results in a very low Kleinbergen-Paap weak-id F statistic. > > > > > > (The z-statistics and significance levels in the first and second > > > stage regressions are the same as in the previous model.) > > > > > > Does anyone have an idea why these two equivalent models > result in > > > very different Kleinbergen-Paap weak-id F statistic? > > > > > > Thanks for your help! > > > > > > Miroslav > > > * > > > * 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/ > > > > > > > > > -- > > Heriot-Watt University is a Scottish charity registered > under charity > > number SC000278. > > > > Heriot-Watt University is the Sunday Times Scottish > University of the > > Year 2011-2012 > > > > > > > > * > > * 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/ > > > > > -- > Heriot-Watt University is a Scottish charity registered under > charity number SC000278. > > Heriot-Watt University is the Sunday Times Scottish > University of the Year 2011-2012 > > > > * > * 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/ > -- Heriot-Watt University is a Scottish charity registered under charity number SC000278. Heriot-Watt University is the Sunday Times Scottish University of the Year 2011-2012 * * 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/

**Follow-Ups**:**st: RE: RE: Which inverter? (was: RE: RE: ivreg2 weak-id statistic and quadratic terms)***From:*DE SOUZA Eric <eric.de_souza@coleurope.eu>

**References**:**st: Which inverter? (was: RE: RE: ivreg2 weak-id statistic and quadratic terms)***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

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