Opposite sign for 2SLS and rreg coefficient

[nonsi nkomo]

Hi

I ran a 2SLS regression with BMI as the dependent variable and exercise as the independent variable. The former is a continuous variable and the latter is measured in number of days. My results show a negative coefficient for exercise. My results from using rreg show that the coefficient for exercise is positive. Do these results sound "normal", or should I be concerned?

Kind Regards
Nonsi Nkomo

[Carlo Lazzaro]

Nonsi:
you don't share what you typed and what Stata gave you back. Hence: who knows what's the matter with your dataset?
At a very first glance you ran two very different models (by the way, -rreg- has been basically side-tracked in the last years), hence no wonder that you got different results and flipping signs of your coefficients.
Eventually, I fail to get the theoretical link between -ivregress- and -rreg-: if you have endogenous regressors, how can it be that they disappear if you switch to -rreg-?

[nonsi nkomo]

Hi Carlo

Here are the results and commands for the rreg and 2SLS respectively.

 

. rreg bodymass i.ex1 W2ExPEYP W6FriendNumYP sex1 eth1 W8EVERMAR wksearly W8DINCW inc2 W8W
> RKHRSA W8DDEGP W8GENA W1yschat W8SOCIALMED W1tvYP W8SLEEP2 W8AUDIT2 takeaway W8NOFCIGS W
> 1fameatYP W5agebd10mum educp W8LOIL

   Huber iteration 1:  maximum difference in weights = .75417667
   Huber iteration 2:  maximum difference in weights = .13798294
   Huber iteration 3:  maximum difference in weights = .04567642
Biweight iteration 4:  maximum difference in weights = .2953759
Biweight iteration 5:  maximum difference in weights = .03444413
Biweight iteration 6:  maximum difference in weights = .01333769
Biweight iteration 7:  maximum difference in weights = .00490729

Robust regression                               Number of obs     =      1,581
                                                F( 24,      1556) =      11.44
                                                Prob > F          =     0.0000

-------------------------------------------------------------------------------
     bodymass |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
          ex1 |
           2  |    .042047   .0126076     3.34   0.001     .0173173    .0667766
           3  |   .0474753   .0142525     3.33   0.001     .0195191    .0754314
              |
     W2ExPEYP |  -.0009637    .008418    -0.11   0.909    -.0174755    .0155482
W6FriendNumYP |  -.0076597   .0037825    -2.03   0.043    -.0150789   -.0002404
         sex1 |  -.0473381   .0088148    -5.37   0.000    -.0646282    -.030048
         eth1 |  -.0368955   .0133384    -2.77   0.006    -.0630586   -.0107324
    W8EVERMAR |   .0629756   .0132243     4.76   0.000     .0370363     .088915
     wksearly |  -.0052875   .0021844    -2.42   0.016    -.0095721   -.0010029
      W8DINCW |   .0011832   .0005497     2.15   0.032      .000105    .0022614
         inc2 |  -.0344596   .0150738    -2.29   0.022    -.0640267   -.0048926
    W8WRKHRSA |   -.034302   .0129911    -2.64   0.008    -.0597839     -.00882
      W8DDEGP |  -.0161561   .0087152    -1.85   0.064    -.0332508    .0009386
       W8GENA |   .0361508   .0049871     7.25   0.000     .0263688    .0459329
    W1yschat1 |   .0011352   .0006528     1.74   0.082    -.0001452    .0024156
  W8SOCIALMED |   .0028627   .0015897     1.80   0.072    -.0002555    .0059809
       W1tvYP |   .0082393   .0072707     1.13   0.257     -.006022    .0225006
     W8SLEEP2 |  -.0184265   .0038706    -4.76   0.000    -.0260186   -.0108344
     W8AUDIT2 |   .0142315   .0037959     3.75   0.000      .006786     .021677
     takeaway |     -.0201   .0082454    -2.44   0.015    -.0362733   -.0039268
    W8NOFCIGS |  -.0040771   .0011826    -3.45   0.001    -.0063969   -.0017574
   W1fameatYP |  -.0093275    .004269    -2.18   0.029    -.0177011   -.0009539
 W5agebd10mum |  -.0167242    .006939    -2.41   0.016    -.0303349   -.0031135
        educp |   .0257264   .0093114     2.76   0.006     .0074623    .0439905
       W8LOIL |  -.0087978   .0113105    -0.78   0.437    -.0309832    .0133876
        _cons |   4.146277   .3362552    12.33   0.000     3.486716    4.805838
-------------------------------------------------------------------------------

. 
end of do-file

. do "C:\Users\NONSIN~1\AppData\Local\Temp\STD1f88_000000.tmp"

. ivregress 2sls bodymass (ex1 = i.W2ExPEYP W6FriendNumYP) sex1 eth1 W8EVERMAR wksearly W8
> DINCW inc2 W8WRKHRSA W8DDEGP crime W8GENA W1yschat W8SOCIALMED W8SLEEP2 W8AUDIT2 takeawa
> y W8NOFCIGS W1fameatYP W5agebd10mum educp W4Hea1CMP, first

First-stage regressions
-----------------------

                                                Number of obs     =      1,496
                                                F(  22,   1473)   =       8.26
                                                Prob > F          =     0.0000
                                                R-squared         =     0.1098
                                                Adj R-squared     =     0.0965
                                                Root MSE          =     0.5762

-------------------------------------------------------------------------------
          ex1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
         sex1 |  -.1835183   .0334267    -5.49   0.000    -.2490872   -.1179494
         eth1 |  -.1183372   .0508423    -2.33   0.020    -.2180681   -.0186062
    W8EVERMAR |   .0145463   .0509227     0.29   0.775    -.0853425    .1144352
     wksearly |  -.0080275   .0083443    -0.96   0.336    -.0243955    .0083405
      W8DINCW |  -.0014621   .0021113    -0.69   0.489    -.0056036    .0026793
         inc2 |   .0152051       .058     0.26   0.793    -.0985663    .1289766
    W8WRKHRSA |   .0406568   .0499519     0.81   0.416    -.0573276    .1386412
      W8DDEGP |  -.0515102   .0330696    -1.56   0.120    -.1163788    .0133584
        crime |  -.0449501   .0373281    -1.20   0.229     -.118172    .0282718
       W8GENA |  -.1161386   .0176203    -6.59   0.000    -.1507022    -.081575
    W1yschat1 |   .0017466   .0024856     0.70   0.482    -.0031292    .0066224
  W8SOCIALMED |    .001861   .0060091     0.31   0.757    -.0099264    .0136484
     W8SLEEP2 |  -.0196757   .0148171    -1.33   0.184    -.0487406    .0093893
     W8AUDIT2 |   .0072065   .0144651     0.50   0.618     -.021168    .0355809
     takeaway |   .0987126   .0313586     3.15   0.002     .0372002     .160225
    W8NOFCIGS |  -.0027751   .0044742    -0.62   0.535    -.0115515    .0060014
   W1fameatYP |  -.0034978   .0162456    -0.22   0.830    -.0353646    .0283691
 W5agebd10mum |  -.0133767   .0264829    -0.51   0.614     -.065325    .0385716
        educp |   .0029759   .0355242     0.08   0.933    -.0667076    .0726593
    W4Hea1CMP |   .0177198   .0230165     0.77   0.441    -.0274289    .0628684
              |
     W2ExPEYP |
          No  |  -.1030739   .0319985    -3.22   0.001    -.1658414   -.0403063
W6FriendNumYP |   .0552231   .0143872     3.84   0.000     .0270015    .0834447
        _cons |   4.257115    2.46197     1.73   0.084    -.5722253    9.086455
-------------------------------------------------------------------------------


Instrumental variables (2SLS) regression          Number of obs   =      1,496
                                                  Wald chi2(21)   =     175.40
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =          .
                                                  Root MSE        =     .18311

------------------------------------------------------------------------------
    bodymass |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ex1 |  -.1227482   .0607943    -2.02   0.043    -.2419028   -.0035935
        sex1 |  -.0603355    .016776    -3.60   0.000    -.0932158   -.0274552
        eth1 |  -.0507507   .0176463    -2.88   0.004    -.0853368   -.0161647
   W8EVERMAR |   .0514247   .0162081     3.17   0.002     .0196574    .0831921
    wksearly |   -.008061   .0027281    -2.95   0.003    -.0134079    -.002714
     W8DINCW |   .0012493   .0006762     1.85   0.065    -.0000761    .0025746
        inc2 |  -.0385381   .0184437    -2.09   0.037    -.0746871   -.0023892
   W8WRKHRSA |  -.0204198   .0159202    -1.28   0.200    -.0516228    .0107832
     W8DDEGP |  -.0264327   .0110701    -2.39   0.017    -.0481298   -.0047356
       crime |   .0075083   .0120574     0.62   0.533    -.0161237    .0311404
      W8GENA |   .0233859   .0093928     2.49   0.013     .0049763    .0417955
   W1yschat1 |   .0022762   .0007936     2.87   0.004     .0007208    .0038317
 W8SOCIALMED |   .0043274   .0019092     2.27   0.023     .0005855    .0080693
    W8SLEEP2 |  -.0239701   .0048531    -4.94   0.000    -.0334819   -.0144583
    W8AUDIT2 |   .0154266   .0046634     3.31   0.001     .0062866    .0245666
    takeaway |  -.0083336   .0114321    -0.73   0.466    -.0307402    .0140729
   W8NOFCIGS |  -.0026457   .0014381    -1.84   0.066    -.0054645     .000173
  W1fameatYP |  -.0060647   .0051682    -1.17   0.241    -.0161943    .0040648
W5agebd10mum |  -.0142033   .0084834    -1.67   0.094    -.0308305     .002424
       educp |   .0246994   .0112523     2.20   0.028     .0026453    .0467535
   W4Hea1CMP |   .0023737   .0074278     0.32   0.749    -.0121846     .016932
       _cons |   4.763027   .8329812     5.72   0.000     3.130414     6.39564
------------------------------------------------------------------------------
Instrumented:  ex1
Instruments:   sex1 eth1 W8EVERMAR wksearly W8DINCW inc2 W8WRKHRSA W8DDEGP
               crime W8GENA W1yschat1 W8SOCIALMED W8SLEEP2 W8AUDIT2 takeaway
               W8NOFCIGS W1fameatYP W5agebd10mum educp W4Hea1CMP 2.W2ExPEYP
               W6FriendNumYP

. 
end of do-file

.

With regards to the use of 2SLS and rreg regressions, is it recommended that if I have an endogenous variable (which is exercise in my example), to use 2SLS only?

Kind Regards
Nonsi Nkomo

[Carlo Lazzaro]

Nonsi:
I would get rid of -rreg- and focus on -ivregress- only:
1) your first stage regression reports that both instruments of your endogenous regressor are statistical significant;
2) if I'm not mistaken, the coefficient for -ex1- in -2SLS- shows that, when adjusted for the remaining predictors, a one-day increase in exercise, reduces BMI of 0.123. The direction of the effect of -ex1- seems reasonable (I cannot say about its magnitude, though). Hence: what's the reason of your concern?

[nonsi nkomo]

Hi Carlo

My apologies, I should have mentioned that the dependent variable is the log of BMI. Therefore the results show that an extra day of exercise reduces BMI by 12.3%. I'm hoping this makes more "sense" in terms of the magnitude of the coefficient. I was worried about the results from rreg and 2sls reporting opposite signs for the coefficient of exercise. However, you have explained the issue of the endogenous variable, exercise, and how I should focus on ivregress. I think your explanation has pretty much addressed my previous concerns. Thank you so much for the help.

Kind Regards
Nonsi Nkomo

[Carlo Lazzaro]

Nonsi:
thanks for prividing further details about the metric of the dependent variable, that allows me to point out that, in log-linear regression models, the percentage approximation (-12.3% in BMI) works for small coefficient only (say 0.002).
In all the other cases, a more precise estimate comes from the following approach (let's consider again the effect of -ex1- on BMI as per 2SLS regression):

. di (exp( -.1227482)-1)*100
-11.551365

Hence, each day of physical exercise/training reduces the BMI by a smaller 11.55%.

[nonsi nkomo]

Thank you for that Carlo. I have also noticed that the correlation between exercise and BMI is positive. Should I be concerned?

Kind Regards
Nonsi Nkomo

[Carlo Lazzaro]

Nonsi:
no, you don't, as the results of 2SLS should be read as the effect of a 1-day increase in -ex1- on reducing BMI when adjusted for the remaining predictors.
Hence a head-to-head correlation (set aside the endogeneity issue, that correlation cannot take into account) does not seem that useful.

[nonsi nkomo]

Ah ok makes sense Carlos. Thanks again for the help.

Kind Regards
Nonsi Nkomo