ivregress vs. ivreg2: discrepant estimates

[John Bullock]

I'm using Stata 13.1 and ivreg2 3.1.08. When I estimate a simple 2SLS model with ivregress (or ivreg) and ivreg2, I get discrepant estimates. Here is an example:

webuse set "https://s3.amazonaws.com/miscFileSharing/"
webuse "example.dta", clear
ivregress 2sls eqwlth yearYoung (educ = CA10)
ivreg2         eqwlth yearYoung (educ = CA10)

In this example, the differences between the two sets of estimates are minimal. But they are very large in more complex examples.

The discrepancies vanish when I use the noconstant option.

How can I make sense of these differences? I've looked to the documentation and to previous Statalist postings, but I haven't found any answers.

[Cross-posted to http://stackoverflow.com/q/24896510/697473.]

[Martin Bresslein]

Hi John,

not sure what you did but using your code, I do NOT obtain different estimates. The only thing that differs between ivregress and ivreg2 in the results is the test statistic against the null model.

clear all

webuse set "https://s3.amazonaws.com/miscFileSharing/"
webuse "example.dta", clear

ivregress 2sls eqwlth yearYoung (educ = CA10)
estimates store ivregress

ivregress 2sls eqwlth yearYoung (educ = CA10), noconstant
estimates store ivregressnoc

ivreg2 eqwlth yearYoung (educ = CA10)
estimates store ivreg2

ivreg2 eqwlth yearYoung (educ = CA10), noconstant
estimates store ivreg2noc

estimates table iv*, b se stats(r2 F chi2)

estout iv* using "ivreg_compare.xls", replace cells(b se) stats(r2 F chi2)

	ivregress	ivregressnoc	ivreg2	ivreg2noc
	b/se	b/se	b/se	b/se
educ	0.0091198	-0.1287089	0.0091198	-0.1287089
	0.3992889	0.0486875	0.3992889	0.0486875
yearYoung	-0.0033483	0.0027588	-0.0033483	0.0027588
	0.0160922	0.0003219	0.0160922	0.0003219
_cons	10.19741		10.19741
	26.40686		26.40686
r2	0.00581		0.00581	0.761853
F			10.53602	40927.95
chi2	21.07459

I also used different data but have not encountered any problems.

Cheers,
Martin

[John Bullock]

Hi, Martin,

Thank you. This is curious: I re-ran my code and found the same discrepancies. A Stack Overflow poster also found them when using ivreg2 3.1.08. When he used ivreg2 2.2.08, they disappeared. (See http://stackoverflow.com/q/24896510/697473.)

A little more detail: I am using Stata/SE 13.1 for Windows (64-bit x86-64, revision 03 July 2014). Here are the specific discrepancies that I observe:

webuse set "https://s3.amazonaws.com/miscFileSharing/"
webuse "example.dta", clear
ivregress 2sls eqwlth yearYoung (educ = CA10)
estimates store ivregress
ivreg2         eqwlth yearYoung (educ = CA10)
estimates store ivreg2
estimate table iv*, b se stats(r2 F chi2)
estout iv* using "ivreg_compare.xls", replace cells(b se) stats(r2 F chi2)

	ivregress	ivreg2
	b/se	b/se
educ	0.00912	0.009119
	0.399289	0.399287
yearYoung	-0.00335	-0.00335
	0.016092	0.016092
_cons	10.19741	10.19736
	26.40686	26.40675
r2	0.00581	0.00581
F		10.53602
chi2	21.07459

The most notable discrepancy lies with the constant. It's small here, but I observe larger differences in more complex examples that involve other variables.

Can you think of anything that might explain these differences in the estimates and the standard errors?

Thank you again. ivreg2 is a great package.

John

[Richard Williams]

Rounding may be throwing the comparisons off. Here is what I get. This is hardly anything I would worry about. Maybe John could post his code and output from the runs that concern him

. estimates table iv*, b se stats(r2 F chi2)

------------------------------------------------------------------
    Variable | ivregress    ivregres~c     ivreg2     ivreg2noc   
-------------+----------------------------------------------------
        educ |  .00911975   -.12870886    .00911902   -.12870886  
             |  .39928893    .04868749    .39928736    .04868749  
   yearYoung | -.00334826    .00275884   -.00334823    .00275884  
             |  .01609221    .00032186    .01609215    .00032186  
       _cons |  10.197412                 10.197363               
             |  26.406859                 26.406755               
-------------+----------------------------------------------------
          r2 |  .00581002                 .00580961    .76185299  
           F |                            10.536019    40927.953  
        chi2 |  21.074592                                         
------------------------------------------------------------------
                                                      legend: b/se

[John Bullock]

Thank you, Richard. It does look as though rounding error may be the culprit in my previous example—although it still seems noteworthy that you and I and the Stack Overflow poster get estimates that differ from Martin's. (And if rounding error is at issue, how might it be fixed?)

Here is an example in which I observe much bigger differences between ivregress and ivreg2:

webuse set "https://s3.amazonaws.com/miscFileSharing/"
webuse "example2.dta", clear
ivregress 2sls eqwlth female i.yearInt_fac yearYoung age (educ = CA10)
estimates store ivregress
xi:ivreg2      eqwlth female i.yearInt_fac yearYoung age (educ = CA10)
estimates store ivreg2
estimate table iv*, keep(educ _cons) b se stats(r2 F chi2)

----------------------------------------
    Variable | ivregress      ivreg2    
-------------+--------------------------
        educ |  .14855169    .00194942  
             |  .33970699     .3450602  
       _cons |  240.08429    183.16973  
             |  79.546067    80.627928  
-------------+--------------------------
          r2 |  .05051654    .05087311  
           F |               19.107363  
        chi2 |  438.94529               
----------------------------------------
                            legend: b/se

These differences seem too big to be due to rounding error in any simple way. In this example, too, the differences vanish when I add the noconstant option.

Thanks again,
John

[Richard Williams]

There is an older version called ivreg29 that you can download from SSC. Download and try this:

webuse set "https://s3.amazonaws.com/miscFileSharing/"
webuse "example2.dta", clear
xi:ivregress 2sls eqwlth female i.yearInt_fac yearYoung age (educ = CA10)
estimates store ivregress
xi:ivreg29      eqwlth female i.yearInt_fac yearYoung age (educ = CA10)
estimates store ivreg29
estimate table iv*, keep(educ _cons) b se stats(r2 F chi2)

Output:

. estimate table iv*, keep(educ _cons) b se stats(r2 F chi2)

----------------------------------------
    Variable | ivregress     ivreg29    
-------------+--------------------------
        educ |  .14855169    .14774287  
             |  .33970699    .33969388  
       _cons |  240.08429    239.77831  
             |  79.546067    79.542996  
-------------+--------------------------
          r2 |  .05051654    .05058984  
           F |               19.934099  
        chi2 |  438.94529               
----------------------------------------
                            legend: b/se

Not a perfect match, but very close.

I suggest you write to the authors, perhaps including a link to this thread.

[Richard Williams]

Complete comparison of ivregress, ivreg29, and ivreg2:

clear all
webuse set "https://s3.amazonaws.com/miscFileSharing/"
webuse "example2.dta", clear
xi:ivregress 2sls eqwlth female i.yearInt_fac yearYoung age (educ = CA10)
estimates store ivregress
xi:ivreg29      eqwlth female i.yearInt_fac yearYoung age (educ = CA10)
estimates store ivreg29
xi:ivreg2      eqwlth female i.yearInt_fac yearYoung age (educ = CA10)
estimates store ivreg2
estimate table iv*, keep(educ _cons) b se stats(r2 F chi2)

. estimate table iv*, keep(educ _cons) b se stats(r2 F chi2)

-----------------------------------------------------
    Variable | ivregress     ivreg29       ivreg2    
-------------+---------------------------------------
        educ |  .14855169    .14774287    .00194942  
             |  .33970699    .33969388     .3450602  
       _cons |  240.08429    239.77831    183.16973  
             |  79.546067    79.542996    80.627928  
-------------+---------------------------------------
          r2 |  .05051654    .05058984    .05087311  
           F |               19.934099    19.107363  
        chi2 |  438.94529                            
-----------------------------------------------------
                                         legend: b/se

EDIT: If you add the noconst option, all three programs give exactly identical results:

. estimate table iv*, keep(educ ) b se stats(r2 F chi2)

-----------------------------------------------------
    Variable | ivregress     ivreg29       ivreg2    
-------------+---------------------------------------
        educ |  .12397097    .12397097    .12397097  
             |  .33479445    .33479445    .33479445  
-------------+---------------------------------------
          r2 |               .79596685    .79596685  
           F |               4360.0473    4360.0473  
        chi2 |                                       
-----------------------------------------------------
                                         legend: b/se

[John Bullock]

Thank you again, Richard. I wrote to the authors of ivreg2 to let them know about your results. I heard back from one of them, Mark Schaffer. If you let the instruments in the example that I provided be Z, it turns out that Z'Z is computationally difficult to work with. (It has a high condition number.) Mark adds this:

If you partial out the constant with the partial option, ivreg2 agrees with the others - the condition number is only 27 million in that case - so this is the short run solution. But we should definitely revisit these numerical issues.

[Martin Bresslein]

Dear John and Richard,
sorry for getting back late. This is indeed curious, I have now updated to what apparently is version 3.1.09 and still find no discrepancies (maybe the authors already updated something?) I have the same Stata version as John installed. Unfortunately, i could not webuse your example dataset anymore (has somebody removed it?). Instead, I used the same dataset for comparison as before, which is from Cameron/Trivedi on returns to schooling, mus06kling.dta, since I use it for teaching purposes.

. ivregress 2sls lwage76 black smsa76 south76 exp76 exp762 ///
>         (ed76 = momed daded nearc4)

. ivreg2 lwage76 black smsa76 south76 exp76 exp762 ///
>         (ed76 = momed daded nearc4)   


. estimates table ivregress ivreg2 ///
>         , b se stats(r2 F chi2)

----------------------------------------
    Variable | ivregress      ivreg2    
-------------+--------------------------
        ed76 |  .09384369    .09384369  
             |  .01208606    .01208606  
       black | -.16960972   -.16960972  
             |   .0212013     .0212013  
      smsa76 |   .1511791     .1511791  
             |  .01673919    .01673919  
     south76 | -.11806809   -.11806809  
             |  .01568892    .01568892  
       exp76 |  .09173059    .09173059  
             |  .00818818    .00818818  
      exp762 | -.00225558   -.00225558  
             |  .00031927    .00031927  
       _cons |   4.399835     4.399835  
             |  .20609734    .20609734  
-------------+--------------------------
          r2 |  .28294129    .28294129  
           F |               139.28791  
        chi2 |  837.67554               
----------------------------------------
                            legend: b/se

Thanks anyway for pointing this out, so at least I will be more careful in the future when working with these commands. At least, the authors of ivreg2 seem to have an explanation.

Martin

[Gabriel Aboyadana]

In case anyone else is confused about the results from ivreg2 and ivregress, I use stata 15 and I get the same results for both.

[Johanna Krenz]

Hi,

I wonder what the corresponding ivreg2 command is for

ivregress 2sls dependentvar explanatories (endogvar=instrument) , vce(hac nwest)

From the description I thought it should be

ivreg2 dependentvar explanatories (endogvar=instrument) , bw(auto)

However, the latter gives me much larger SE.

Thanks in advance.