st: RE: RE: xtivreg2: orthog option

["Fitzgerald, James" <J.Fitzgerald2@ucc.ie>]

Mark,

________________________________________
From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] on behalf of Schaffer, Mark E [M.E.Schaffer@hw.ac.uk]
Sent: 05 July 2012 13:48
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: RE: RE: RE: RE: RE: RE: RE: RE: RE: xtivreg2: orthog option

James,


> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> Fitzgerald, James
> Sent: 05 July 2012 11:15
> To: statalist@hsphsun2.harvard.edu
> Subject: st: RE: RE: RE: RE: RE: RE: RE: RE: RE: xtivreg2:
> orthog option
>
> Mark,
>
> I followed your suggestion as far as I understood it. As
> such, I undertook the following steps:
>
> 1. I estimated the model with suspect instruments treated as
> endogenous. As I have no reason to suspect any one regressor
> is endogenous and others are not, I ran the model with all
> regressors assumed to be endogenous and used 3 lags as
> exluded instruments.
>
> xtivreg2 ltdbv yr* (lnsale tang itang itangdum tax prof mtb
> capexsa liq ndts=l.lnsale l2.lnsale l3.lnsale l.tang l2.tang
> l3.tang l.itang l2.itang l3.itang l.itangdum l2.itangdum
> l3.itangdum l.tax l2.tax l3.tax l.prof l2.prof l3.prof l.mtb
> l2.mtb l3.mtb l.capexsa l2.capexsa l3.capexsa l.liq l2.liq
> l3.liq l.ndts l2.ndts l3.ndts), fe cluster(firm) gmm2s
>
> The p-value on the Hansen J-Stat turned out to be 0.01.
>
> 2. I then tested the orthogonality of the different lags
>      orthog(l.lnsale l.tang . . . l.ndts) gave a C stat
> p-value of 0.5196
>      orthog(l2.lnsale l2.tang . . . l2.ndts) gave a C stat
> p-value of 0.3318
>      orthog(l3.lnsale l3.tang . . . l3.ndts) gave a C stat
> p-value of 0.0022
>
> 3. I dropped the l3 lags and the Hansen J Stat p-value was 0.5588.
>     I then used the endog option on each of the endogenous
> variables i.e.
>
> xtivreg2 ltdbv yr* (lnsale tang itang itangdum tax prof mtb
> capexsa liq ndts=l.lnsale l2.lnsale l3.lnsale l.tang l2.tang
> l.itang l2.itang l.itangdum l2.itangdum l.tax l2.tax l.prof
> l2.prof l.mtb l2.mtb l.capexsa l2.capexsa l.liq l2.liq l.ndts
> l2.ndts), fe cluster(firm) gmm2s endog(lnsale)
>
> And replaced lnsale with tang, itang etc.
>
> 4. All the endog tests indicated the regressors are not
> endogenous, so I conclude there is no need to use xtivreg2,
> fe and instead I can use xtreg, fe
>
> How does this sound??
>
> James
> ________________________________________

<snip>

This looks reasonable.  Just a few thoughts:

In steps 1-2, it looks like you are getting a large C stat for L3
because L1 and L2 are identifying one beta_hat, and L3 is identifying a
different beta_hat.  At least one of these two beta_hats must be
inconsistent.  You're concluding that the 2nd one is inconsistent, and
so you're dropping the L3s as IVs.

This could be defensible, but it looks a bit odd.  The more usual case
is that older lags are more likely to be valid IVs than recent lags.

An alternative interpretation of your results is that the 1st beta_hat
is inconsistent, and so you should drop the L1s and L2s and use just the
L3s as IVs.  You might want to try that and see what happens.  (There's
no point doing a C test for the L1s and L2s, by the way, because using
just the L3s gives you an exactly identified equation, and the C stat
will the same large J stat you got when you used all the IVs.) 

I just tried this and I found that all my estimates become completely insignificant when I use L3s as IVs, but are aprroximately what would be expected when i use L1s and L2s. Also, the underidentification statistic is completely insignificant with the L3s, but marginally significant when I use the L1s and L2s (I think it is only marginally significant as for some of the regressors the lags may not be good instruments).
Does this suggest that beta_hat based on L1 and L2 is consistent?

Also, in step 3, you can test for the endogeneity of all your regressors
lnsale-ndts all at once - the endog option takes varlists.

When I test them one at a time (employing L1 and L2 as lags) I get the following endogeneity test p-values:
lnsale = 0.6859
tang = 0.2336
itang = 0.7719
itangdum = 0.001
tax = 0.0068
prof = 0.7691
mtb = 0.7357
capexsa = 0.2933
liq = 0.2511
ndts = 0.5358

I conclude that itangdum and tax need to be instrumented.
Please ignore my earlier comment that all regressors are exogenous!

When i test for the endogeneity of all my regressors at once I get a p-value of 0.0002.
This tells me that one or more of my regressors are indeed endogenous

Given the p-values from the individual endog tests I now specify itangdum and tax as endogenous, and the other variables as exogenous.
To confirm the other variables are exogenous, I specify orthog(varlist) and I get a C Stat p-value of 0.4742.

Does this seem right?

Now I am left with the issue of assessing the "strength" of the instruments. 

I get the following statistics (I have kept all of the excluded instruments i.e. L1s and L2s of all 10 explanatory variables)

Summary results for first-stage regressions

                             (Underid)                                             (Weak id)
Variable      F( 20,  1049)  P-val  AP Chi-sq( 19) P-val  AP F( 19,  1049)
itangdum          111.58    0.0000      2194.99   0.0000       114.94
tax                      3.66    0.0000          72.32   0.0000         3.79
NB: first-stage test statistics cluster-robust
Stock-Yogo weak ID test critical values for single endogenous regressor:
5% maximal IV relative bias    21.38
10% maximal IV relative bias    11.46
20% maximal IV relative bias     6.31
30% maximal IV relative bias     4.51
10% maximal IV size             59.92
15% maximal IV size             31.58
20% maximal IV size             21.90
25% maximal IV size             16.99
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
Underidentification test
Ho: matrix of reduced form coefficients has rank=K1-1 (underidentified)
Ha: matrix has rank=K1 (identified)
Kleibergen-Paap rk LM statistic          Chi-sq(19)=59.63   P-val=0.0000
Weak identification test
Ho: equation is weakly identified
Cragg-Donald Wald F statistic                                       5.56
Kleibergen-Paap Wald rk F statistic                                 3.60
Stock-Yogo weak ID test critical values for K1=2 and L1=20:
5% maximal IV relative bias    20.48
10% maximal IV relative bias    11.03
20% maximal IV relative bias     6.11
30% maximal IV relative bias     4.39
10% maximal IV size             46.62
15% maximal IV size             24.96
20% maximal IV size             17.61
25% maximal IV size             13.84
Source: Stock-Yogo (2005).  Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
Weak-instrument-robust inference
Tests of joint significance of endogenous regressors B1 in main equation
Ho: B1=0 and orthogonality conditions are valid
Anderson-Rubin Wald test           F(20,1049)=     2.82     P-val=0.0000
Anderson-Rubin Wald test           Chi-sq(20)=    56.61     P-val=0.0000
Stock-Wright LM S statistic        Chi-sq(20)=    47.94     P-val=0.0004
NB: Underidentification, weak identification and weak-identification-robust
test statistics cluster-robust


My intuition is that the stats relating to itangdum are strong, but the stats relating to tax are weak.

I specify the first option and STATA generates the first stage regressions of tax and itangdum. The results suggest that many of the instruments do not explain variation in either variable.
Can I remove these instruments and, as long as my Hansen J stat indicates the remaining excluded instruments are still valid, still conclude that the variables specified as exogenous can still be considered exogenous? The reason I want to do this is that I find that the weak i.d stats often improve dramatically when these instruments are removed.

Also, if I find an instrument to be weak, as I believe tax is, should I; drop tax from the model, leave the instrument in and just conclude that it is uninterpretable, or specify tax as exogenous but that it is uninterpretable?

Thanks again

James





Cheers,
Mark


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