ivregress 2sls and ivreg2 with interaction term problems

[Jae Li]

Dear Statalist,

I want to run a two-stage least squares regression as follow: X2 is the endogenous variable and Z is the instrument variable for X2

Y = a + b1*(X1*X2) + b2*X2 + b3*X3 + b4*X4 + e

Here is my trial code for your review:

gen XX = X1 * X2
gen XZ = X1 * Z
ivregress 2sls Y X3 X4 (X2 XX = Z XZ ) i.ind i.year, vce(cluster gvkey) first small

May I ask that is the above codes correct? This is cos that I found some variables' t-statistics are very large and not reasonable in comparing to its coefficient size.

Moreover, if I use -ivreg2-:

ivreg2 Y X3 X4 (X2 XX = Z XZ) i.ind i.year, first savefirst savefprefix(st1)

It shows the error message of not enough space to run the command. As -ivreg2- should generate the same result as -ivregress-, so do you possibly know how to fix it?

Many thanks for your help in advance!

[Jeff Wooldridge]

Jae: A few things occur to me. First, the -ivregress- command is correct, but it appears that you have panel data. Is that true? If so, it would be better to use -xtivreg- with the fe option.

Second, it's very unusual to have an interaction term without both variables appearing in level form. Is X1 a time-invariant variable, and that's why you've dropped it? If so, that's fine. Id X1 is time-varying, it should be included on its own unless you have a very compelling reason not to include it.

Third, depending on the the distribution of X1, the coefficient on X2 may not make sense. Is X1 = 0 a possible value? Is it the most interesting? If I were you, unless X1 or X2 is binary, I would center X1 and X2 around their means before constructing the interaction. Then I would include the new interaction in the command in place of XX. Everything else can be the same, provided you include X1 if it doesn't drop out.

I hope this helps.
JW

[Jae Li]

@Jeff Wooldridge Hi Jeff, thank you for your reply! Yes, I have the firm-year panel dataset. X1 is a time-variant variable and the reason why I didn't include it early is that it showed the error message as follow:

. ivregress 2sls Y X2 X3 X4 (X2 XX = Z XZ) i.ind i.year, vce(cluster gvkey) first small
X2 included in both exogenous and endogenous variable lists
r(498);

X1 and X2 are not binary and what do you mean by

I would center X1 and X2 around their means before constructing the interaction.

Here is my data for your convenience:

----------------------- copy starting from the next line -----------------------

* Example generated by -dataex-. To install: ssc install dataex
clear
input double(gvkey fyear Y) float(X2 X1 XX X3) double(X4 Z) float XZ
1004 1996     .3893348821168493 .15005416            .            .            .                     .   .022895710519446624              .
1004 1997     .4653784058408889  .3055648 -.0006213948 .00004086949    .05828597    .05828596722772893    .03691815797727448  -.00002294075
1004 1998    .36124128480407774  .4205541    .04202772   .015053927    .03912865    .03912864467845512   .004097908973594291    .0001722258
1004 1999    -.3642299485125939  .3317953  .0046245945    .00164823  .0013802256  .0013802256745596734   -.04680481118435945  -.00021645328
1004 2000    .01726735722579929 .25740355    .01033187    .00256886  -.004753422  -.004753421909888002    .00743340594404824   .00007680098
1004 2001   -.07551470396289003 .23492795 -.0007141203  -.000203201    -.3030406   -.30304056849768934  -.009418574587445428   6.725995e-06
1004 2002   -.10861777278297745 .14362174   -.02260957  -.003125648   -.09470968   -.09470968122164215  -.012611051791004711   .00028513043
1004 2003    -.2304267863797853 .10416707     .1180897   .012860627   -.07692934   -.07692933965673936  -.003422089262890286   -.0004041135
1004 2004   -.05547208969887356 .15939006   -.05151777   -.00808914   .024295164     .0242951643303968  -.013124727064817456    .0006761567
1004 2005   .024978409822681624 .29272246    -.1044033   -.02732049    .03580018    .03580018013922705 -.0014850137120063184   .00015504032
1004 2006    -.0954024032036714 .25169766    .08546003    .02648179   -.07645996   -.07645996225376923 -.0012574489988757508  -.00010746163
1004 2007    -.0845068810490816  .2058052  -.016820569  -.003605663   -.06510061   -.06510060653090477   .027250866160150503  -.00045837506
1004 2008   -.16531429339648235 .13576216   .017732024   .002408864   -.05342312   -.05342311901040375    -.0545471906728272   -.0009672321
1004 2009    1.4695022503098516 .10695989   -.18312024  -.018946454     .5976559     .5793575905263424    .03219268955988557    -.005895133
1004 2010    .28322566203410976 .12824324 -.0008314206  .0003887125   .068939514    .06893951093984975    .02382430727100004  -.00001980802
1004 2011    .19216067243208845  .3634054    -.0435303  -.014890214   .015978998   .015978996895930984   .006037552504908899  -.00026281647
1004 2012   -.12275635882888472 .27930394   .023933755   .006298324    .09675346    .09675345502328128  -.015422316937569291    -.000369114
1004 2013    .13613445657762357 .20084077   .026585015   .005524121   -.04027607  -.040276065858961374  .0052172415310371995   .00013870044
1004 2014     .0152078589373028 .26178357  .0008313548   .000437346    .03030743    .03030742979275861  -.004564879773790989  -3.795035e-06
1004 2015   -.32298545052145455 .14836548   -.02634652 -.0039041904    -.2782805    -.2782804925615589  -.025049533726396706     .000659968
1004 2016  -.023376372342905728 .16238867  -.009403908 -.0008310482    .19967043    .19967043474316598  -.005200339147208584   .00004890351
1004 2017    .06091394802607564  .1891309   .013109388   .002410516  -.014076783  -.014076783042401075  .0004984304896323391   6.534119e-06
1013 1996  -.003657296062134194   .781308            .            .            .                     .  -.010938884583745232              .
1013 1997   -.10445437797323934  .6266558    .03904557   .024430415    .02112072   .021120719441373746  -.002286911852704349  -.00008929378
1013 1998    .12183120858460537  .5596372  .0008470226 .00045849686  -.016843753   -.01684375351536137  -.012483406756380308 -.000010573728
1013 1999     1.603367180672709 .50525403   .071760476     .0362853   .026461944   .026461944418630243  -.007190199637636879  -.00051597215
1013 2000    .41896046282326493  .7356958    .10808422    .07660134    -.0483946   -.04839460047563916   .011911386056815394     .001287433
1013 2001    -.3227632234663735 .54299486  -.069439165   -.03781945  -.018599449   -.01859944927040489  -.022346401376802463    .0015517154
1013 2002    -.3524057753766528 .27411425  -.072309695  -.019858664    .27832627    .27832628763936657   -.01583849984525968     .001145277
1013 2003    1.2276581860082205  .2362358   -.03794617  -.008939632     .4423902    .44239024033886365  -.008545635127135758    .0003242741
1013 2004    -.1893792983299024  .2986672    .02635451   .007838542    .04338088    .04338087669636408  -.010401668040611633  -.00027413087
1013 2005  -.019790204258939518  .3338488  -.011970015  -.003861428   .027617754     .0276177542929707     .0039892211186773  -.00004775104
1013 2006   -.04950536672542776  .3678787   .005238182  .0018870813    .05796504    .05796504437942833   .005608873684063378  .000029380304
1013 2007   -.04296424580304587  .4008714 -.0016377056 -.0008069192  -.004782456  -.004782455479516267  -.005197630664214816   8.512189e-06
1013 2008    -.1703564469336915  .3344481   -.04447687  -.014901514  -.033361256    -.0333612558796354  .0038831359837411226  -.00017270973
1013 2009     .4392944811163212  .2496523   -.01600357  -.004084575     .2000825     .2000824990785784  -.007204770566765326   .00011530205
1013 2010   .050816432185755676  .3148358    .01889436   .006505953     .2216326     .2216326168809946  -.008906396372106275  -.00016828063
1021 1998    -.3270400904256069         .   -.18312024            .   -.19594727                     .                     .              .
1034 1996    .37921367476642076  .5429029            .            .            .                     . -.0013570361902374146              .
1034 1997    .08724184735285609 .56652945    .05166875    .02998645   .018507125   .018507125590426426   .007605911575473676   .00039298795
1034 1998    .02605450408937856 2.1260178   .006716339    .05144883    .03668794    .03668794166654921   .013953675927821377   .00009371762
1034 1999    1.1030896110808759  .3945288   .017115256   .006737141   .028644087   .028644086549651216    .02637582612505911     .000451429
1034 2000     .5983367778696518  .5905251    .04266314    .02292502   -.02276361  -.022763610426336525  .0007273917945693834  .000031032818
1034 2001     .5472473026017204  .6312767    .03137543   .019112866  -.008722925   -.00872292502311871  -.012183357488769518   -.0003822581
1034 2002   -.14501429844544425  .4632155  -.014266137   -.00662908  -.005839717  -.005839717159742305  -.020999837071571516    .0002995866
1034 2003     .4509973227932287 .50581324    .19684157    .10021486    .06520628    .06520628262200931  -.025855698931705463    -.005089476
1034 2004   -.11260232634839872  .3893614   .008921117    .00349514  -.008493598  -.008493597531924024  -.021546574215769734   -.0001922195
1034 2005   -.16858099052734532  .3554265   .004304598  .0019824472  -.009005173  -.009005172766352954  -.012237103973170904  -.00005267582
1034 2006   .020444513927999397 2.1260178   .022221206    .11254533  -.005544019  -.005544018714040842  -.007223672270701582   -.0001605187
1034 2007   -.11344096509420024  .4708317   .013069052   .005969115   .007017793   .007017793054665371   -.01035529517271331  -.00013533389
1036 1999    .13754778755620975 .25994956    .01486309   .003459714   .017888715   .017888714838773013   -.01744845359985129  -.00025933795
1038 1996    -.1262567236179785 .19397832            .            .            .                     .   -.00793019559660867              .
1038 1997   -.14214787874692647  .4503616    .10902151    .04517711  -.036551677   -.03655167748885496  -.006966234443517922   -.0007594694
1038 1998    .13230616269940607  .3878911   -.02519987  -.009146205   -.19163844   -.19163844013302067    .01199034365447813   -.0003021551
1038 1999    -.4427742146089716  .3942453   -.08859255  -.032382213    -.0421459   -.04214589785884267  -.037383146641648046     .003311868
1038 2000   -.34275192223606765 .30870315  -.009011244 -.0017737413   -.03658284  -.036582838876971176  -.016305241485048805    .0001469305
1038 2001    .16099054481370043  .4393761  .0031157956  .0012885277   .002313474  .0023134740379949417  -.019132256688804125   -.0000596122
1038 2002    .13631935412533483 .37123665    .01015722   .006662805  -.015051125  -.015051124151796103   -.02476878726572278  -.00025158204
1038 2003    -.2625819356021558 .29480794    .01455587   .004756961   -.05697068   -.05697067802644928   -.02199043434607633   -.0003200899
1043 1996    -.5282960061048376         .            .            .            .                     .                     .              .
1045 1996   -.26233574435461565 .53097475            .            .            .                     .   .001831815104425741              .
1045 1997    .20753158970198085  .4003251    .05555619   .021677023    .06048309    .06048309362959117   .012838396907865415    .0007132525
1045 1998    .12429384709892746  .4026795      .039642   .015155034     .1174204    .11742039451375606   .005662490934663424   .00022447246
1045 1999    -.2713629734076202  .3634226   .019415336   .007224598    .05637984    .05637983693496178  -.028141966990723882   -.0005463857
1045 2000   -.10187830550899322  .3121225    .05297467   .016506383   -.08761643   -.08761643151575257   .002296956041432729   .00012168048
1045 2001   -.17725669702063993  .3755867     .1334846    .05237895    -.3111337    -.3111337572062279  -.009108345613024184    -.001215824
1045 2002   -.11150894629451319 .22537266     .1292169      .029197     .0838859    .08388589814615746  -.011087331897436057   -.0014326706
1045 2003     .5320570439993246 .21849217    .28171661    .12513778     .5622083     .5622082658422489  -.009898349451330923   -.0027885295
1045 2004   -.37891788879161276 .20971584    -.0467941  -.008923312    -.2291292   -.22912919521331787   -.03563995035292436    .0016677396
1045 2005    .08162696828694532  .2030386    .15601628   .033245172    .03076349    .03076348809356039   .010325597457178898    .0016109613
1045 2006 -.0005064232654928211 .47005895    .01261492   .007105999    .13721085     .1372108452099686  -.006381133532265116  -.00008049748
1045 2007   -.17290051880288412  .1721502   -.05125244  -.007751074   .018083353   .018083352750788134  -.008265225780987274   .00042361295
1045 2008  -.004533983933742126  .1598372    -.1643146  -.027522266   -.07844698   -.07844697404652833   -.02481447606951653      .00407738
1045 2009    1.0366518190453782   .091823   -.02543141 -.0010968033     .5976559     .5793575905263424   .014900286028171679   -.0003789353
1045 2010    .05088679919770433 .13966556  -.029200356  -.003488859  -.062935024   -.06293502458304699  -.005191144386283938   .00015158327
1045 2011   -.19695212280142324    .26251   -.04944227  -.013087386   -.12696376   -.12696376743798074   -.00569420151342016   .00028153422
1045 2013     .2326263024375866 .24084175   -.03969125  -.010346804  -.005690183  -.005690182597997288  -.002086472993234796   .00008281472
1045 2014     .5407933824578168  .3241753  -.007085282  -.002803429   .023862926     .0238629266332282   .007078081687423047   -.0000501502
1045 2015   -.10269043685684362 .24784432  -.004787728 -.0012640887    .07277559    .07277558748144657 -.0029494412805628613  .000014121122
1045 2016    .06920310054400657 .23503803  -.017666504 -.0045105577   -.04058373   -.04058372445235198   .003978663982660938  -.00007028908
1045 2017   -.09501677634623894 .23849922   .012000147  .0027908266    .02472686   .024726860594290138  -.013565934621432274   -.0001627932
1050 1996   -.11722887062529111  .0984922            .            .            .                     .   .017749262432855704              .
1050 1997     .2805263801571533  .1948423  -.008525417 -.0021489954    .05881343    .05881342925131321   .022179641031851473   -.0001890907
1050 1998    -.5019196109604399 .08836136   -.06691301   -.00684381   -.03854464   -.03854464428150095  -.023477731490348597    .0015709656
1050 1999    .03738012378640371  .1524473    .03877497   .006945475    .02363031   .023630309384316206  -.028359934681300967   -.0010996555
1050 2000    -.4503664169243338 .13132577   .025812676   .003971329  -.020072155   -.02007215532163779 -.0036388109734902447  -.00009392745
1050 2002    .21730624515178198         .    .01980436            . -.0008556675                     .                     .              .
1050 2003  -.028729522326037538         .    .04244003            .   .005806206                     .                     .              .
1050 2004    -.3069607955051685         .   .027760306            .  -.010396745                     .                     .              .
1050 2005    .19322146592358758         .   -.02975475            .   .027675813                     .                     .              .
1050 2006     .3443873337015737 .27306992   .003107568  .0005453273    .02964698    .02964697778224945  -.003400386166311827 -.000010566931
1050 2007     .1616944042247621  .2073829   .018709054  .0039616707   -.01985489  -.019854889623820784   -.03060573705698887   -.0005726044
1050 2008     .1147684237722493  .3210443   -.02123126   -.00656431   -.03119811  -.031198111662108986  .0018687898835746054  -.00003967676
1050 2009   -.16697050565822746  .1506991    .05507761    .00860272    -.3760616    -.3470109477639198   -.04060886250944088   -.0022366391
1050 2010    .15886950803181704  .1624078    .06192502   .010939204  .0001812693 .00018126927316188812  -.023050548109873687   -.0014274057
1050 2011   -.06497377034150886  .1714605  -.005709718  .0006107414    -.0192518  -.019251801073551178   .003979091139936641  -.00002271949
1050 2012   -.17860298214016504  .1803095  -.007337215 -.0020146205   .022101223    .02210122416727245  -.010263882651230415   .00007530831
1050 2013    -.3853516359805036         .  -.014730498            .  -.013049152                     .                     .              .
1050 2015    -.2159404860303201  .1898694  -.008858779  -.001931331   -.10557035   -.10557034588418901 -.0025538233171780674  .000022623757
1050 2016    .04785648882681855 .12960367   .025108453   .003705581    .10281926    .10281926227940455   .008753730939704652   .00021979264
end

------------------ copy up to and includin

Many thanks for your help! Looking forward to hearing from you soon!

[Jeff Wooldridge]

You should drop the first occurrence of X2.

If X1 = 0 is not an interesting value then the coefficient on X2 in the model with the interaction won't be meaningful. So use the term

(X1 - m1)*X2

instead, where m1 is the sample average of X1.

[Jae Li]

@Jeff Wooldridge Hi Jeff, thank you for your reply! I tried your suggestion to replace XX with (X1 - m1)*X2. However, the unmatched cases between estimated coefficients and t-statistics still exist in -ivregress- regressions.

Do you possibly have any other advice? I will be more appreciated that!

[Phil Bromiley]

To expand a little on Jeff's comment, when you have b1 x1 + b2 x2 + b3 x1*x2 b2 is the coefficient on x2 when x1=0. It is quite possible that x1 never equals zero which makes b2 (the coefficient on x2) by itself not interesting and even misleading (since readers may focus on it). One solution is to change the mean of x1 so the mean of x1 equals zero and thus is a value that is reasonably common in the sample (Jeff's solution). Note this doesn't change the estimates substantively. Alternatively, you can explain the issue, and then discuss dy/dx2 at different values of x1.

In any case, when you have such interactions, you' may want to use margins to examine the influence of dy/x2 (which is b2 + b3*x1) at different values of x1. While this is not difficult in linear models without margins, margins makes it much easier to do, provides standard errors, and handles non-linear models (e.g., logit) easily.

[Jae Li]

@Phil Bromiley Hi Phil, thank you for explaining it in more details! I tried that suggestion to run the -ivregress-. However, the coefficient size and t-statistic value still can't be matched.

I am thinking about whether I should use the linear instrumental variable estimation for such non-linear instrument regression as the x2 is correlated to (x1*x2). The literature uses two-stage least square analysis so that's why I would like to follow. I may try to use margins as a robustness check but still hope to get the result for 2sls. Many thanks for any feedback you may have!

[Badiah Eljahimi]

@Jeff Wooldridge Hi Jeff, I have four models ( dynamic panel models ) :

1- linear model
GDP = β1 FDX + β2 INF + β4 GOV + β5 GFCF + β6 TRD + β7 LBOR

2- model with an interactive term
GDP = β1 FDX + β2 INF + β3 FDX * INF + β4 GOV + β5 GFCF + β6 TRD + β7 LBOR

3- non-linear model :
GDP = β1 FDX + β2 FDX²+ β3 INF + β4 GOV + β5 GFCF + β6 TRD + β7 LBOR

4- non-linear with interactive term
GDP = β1 FDX + β2 FDX²+ β3 INF + β4 FDX * INF + β5 FDX² * INF + β6 GOV + β7 GFCF + β8 TRD + β9 LBOR

Where GDP is the dependent variable, FDX is the endogenous variable and INF, GOV, GFCF, TRD and LBOR are the exogenous variables and lagged variables are used as the instrumental variables.


What is the Tow Stage Least Square (2SLS) estimation command for each model, please?



Can I use -xtivreg- with the fe option for the first model? xtivreg GDP GDP_lag1 GDP_lag2 INF GOV GFCF TRD LBOR (FDX= FDX_lag1 GOV _lag1 GFCF_lag1 TRD_lag1 LBOR_lag1), fe

if yes, what about the rest of the models ( 2, 3 and 4)


I would be very grateful for any help


Many Thanks

Badiah