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I am trying to run an OLS regression, with log of per capita calorie as my dependent variable and age and years of education of household head, log per capita expenditure as my independent variables (other controls to be added eventually). When I run the regression with just age and education as control, they are significant and positive. However, as soon as I add log per capita expenditure, education becomes negative and significant. I am puzzled by this result- but the correlation coefficient (for education and log per capita expenditure) is not that large. I have posted my regression results below, as well as summary statistics. I was wondering if someone could help me understand what is going on here. I realize that this sort of problem might (or might not ) be overcome using other techniques than OLS, but I have just started learning OLS and would like to understand how to deal with this in OLS, or at least know why it cannot deal with this.

Thanks,

Monzur

.  regress log_pccal  age_hhhead eduy_hhhead [pw=hhweight], r


Linear regression                           Number of obs =    3355
                                                       F(  2,  3352) =  105.40
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.0692
                                                       Root MSE      =  .25583

------------------------------------------------------------------------------
             |               Robust
   log_pccal |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  age_hhhead |   .0049182   .0003602    13.65   0.000      .004212    .0056244
 eduy_hhhead |   .0075136   .0011997     6.26   0.000     .0051613    .0098659
       _cons |   7.537586   .0171067   440.62   0.000     7.504045    7.571126
------------------------------------------------------------------------------

.  regress log_pccal age_hhhead eduy_hhhead log_pcexp [pw=hhweight], r


Linear regression                                      Number of obs =    3355
                                                       F(  3,  3351) =  601.38
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.4123
                                                       Root MSE      =  .20332

------------------------------------------------------------------------------
             |               Robust
   log_pccal |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  age_hhhead |    .001919   .0002945     6.52   0.000     .0013415    .0024964
 eduy_hhhead |  -.0082508    .001044    -7.90   0.000    -.0102977   -.0062039
   log_pcexp |   .3777407   .0100402    37.62   0.000     .3580552    .3974262
       _cons |   4.795607   .0730719    65.63   0.000     4.652337    4.938877
------------------------------------------------------------------------------

.  estat vif

    Variable |       VIF       1/VIF  
-------------+----------------------
   log_pcexp |      1.20    0.832228
 eduy_hhhead |      1.16    0.863121
  age_hhhead |      1.07    0.930743
-------------+----------------------
    Mean VIF |      1.14


.  su log_pccal eduy_hhhead log_pcexp, d

                          log_pccal
-------------------------------------------------------------

Obs                3698
Mean           7.783589
Std. Dev.       .276406
Variance       .0764003
Skewness       .0350145
Kurtosis       3.511389

            years of education of household head
-------------------------------------------------------------

Obs                3698
Sum of Wgt.        3698
Mean           2.984857
Std. Dev.      3.776812

Variance       14.26431
Skewness       .9461994
Kurtosis       2.751041

              log of hh per capita expenditure
-------------------------------------------------------------

Obs                3698
Sum of Wgt.        3698

Mean           7.762185
Std. Dev.      .4636838

Variance       .2150027
Skewness       .4395734
Kurtosis       3.433132

. pwcorr log_pccal age_hhhead eduy_hhhead log_pcexp, sig

             | log~ccal age_hh~d eduy_h~d log_pc~p
-------------+------------------------------------
   log_pccal |   1.0000
             |
             |
  age_hhhead |   0.2282   1.0000
             |   0.0000
             |
 eduy_hhhead |   0.0855  -0.1133   1.0000
             |   0.0000   0.0000
             |
   log_pcexp |   0.6401   0.1796   0.3254   1.0000
             |   0.0000   0.0000   0.0000
         |
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marked as duplicate by gung regression Dec 19 '14 at 20:42

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ The answer is in the linked thread. Try reading that. If you still have a question afterwards, come back here & edit your question to state what you've learned & what you still don't understand. Then we can provide the information you need instead of just duplicating information elsewhere that already didn't help you. $\endgroup$ – gung Dec 19 '14 at 20:44
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Expenditures are highly correlated with both age and education. Check your data for multicollinearity.

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We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.

  • 2
    $\begingroup$ This is more of a comment than an answer. Would you mind expanding it a little? $\endgroup$ – gung Dec 19 '14 at 21:11
  • $\begingroup$ Those correlation coefficients are not "high" by any means! Did you notice the low VIFs? $\endgroup$ – whuber Dec 19 '14 at 23:51
  • 1
    $\begingroup$ Thanks whuber, I was about to point that out myself. I don't think there are issues of multicollinearity here $\endgroup$ – Monzur Dec 20 '14 at 0:15

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