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  • Can I do difference-in-difference analysis when my dependent variable is nominal?

    I am trying to estimate the effect of an economic shock on coordination among spouses in a household. However, I am confused if I am following the right approach as at the end of the output, I find "Note: 15 observations completely determined. Standard errors questionable." I have used the following command (both code and output are shown below):

    Code:
    mlogit household_coordination i.time_dummy##i.treat_dummy dependency_ratio sex_ratio age i.education_level i.religion i.social_group i.household_type household_cons_expenditure_month i.district [pweight=weight], r
    Here, household_coordination takes value
    1 if both spouses are working,
    2 if only husband is working,
    3 if only wife is working
    4 if neither is working

    time_dummy takes value 1 for post-shock time period and 0 for pre-shock time period
    treat_dummy takes value 1 if spouses are located in treated district and 0 otherwise

    dependency_ratio is the ratio of dependent population (aged <15 years and >70 years) to working age population in a household
    sex_ratio is the ratio of number of females to number of males in household
    social_group is the category of different caste hierarchy
    household_type is primary source of income for the household (regular, casual or self-employed)
    household_cons_expenditure_month is the monthly household expenditure (which reflects household wealth)

    The output that I got is:
    Code:
    note: 12.district omitted because of collinearity.
    Iteration 0:  Log pseudolikelihood = -1.339e+08  
    Iteration 1:  Log pseudolikelihood =  -98055617  
    Iteration 2:  Log pseudolikelihood =  -96952029  
    Iteration 3:  Log pseudolikelihood =  -96482460  
    Iteration 4:  Log pseudolikelihood =  -96475124  
    Iteration 5:  Log pseudolikelihood =  -96474536  
    Iteration 6:  Log pseudolikelihood =  -96474428  
    Iteration 7:  Log pseudolikelihood =  -96474404  
    Iteration 8:  Log pseudolikelihood =  -96474398  
    Iteration 9:  Log pseudolikelihood =  -96474397  
    Iteration 10: Log pseudolikelihood =  -96474397  
    Iteration 11: Log pseudolikelihood =  -96474397  
    Iteration 12: Log pseudolikelihood =  -96474397  
    Iteration 13: Log pseudolikelihood =  -96474397  
    Iteration 14: Log pseudolikelihood =  -96474397  
    Iteration 15: Log pseudolikelihood =  -96474397  
    Iteration 16: Log pseudolikelihood =  -96474397  
    
    Multinomial logistic regression                      Number of obs  =   16,678
                                                         Wald chi2(135) = 20652.55
                                                         Prob > chi2    =   0.0000
    Log pseudolikelihood = -96474397                     Pseudo R2      =   0.2795
    
    ------------------------------------------------------------------------------------------------------------------
                                                     |               Robust
                              household_coordination | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
    -------------------------------------------------+----------------------------------------------------------------
    Both_working                                     |
                                        1.time_dummy |  -.0158726    .073909    -0.21   0.830    -.1607316    .1289865
                                       1.treat_dummy |  -.7027549   .2072395    -3.39   0.001    -1.108937   -.2965729
                                                     |
                              time_dummy#treat_dummy |
                                                1 1  |   .1281244   .1071509     1.20   0.232    -.0818875    .3381362
                                                     |
                                    dependency_ratio |  -.1219124    .057091    -2.14   0.033    -.2338088    -.010016
                                           sex_ratio |  -.1188435   .0304601    -3.90   0.000    -.1785442   -.0591428
                                                 age |  -.0007664    .001335    -0.57   0.566     -.003383    .0018502
                                                     |
                                     education_level |
    Literate without formal schooling: EGS/NFEC/AEC  |   1.666589   .7360029     2.26   0.024     .2240496    3.109128
             Literate without formal schooling: TLC  |    2.69473   1.204716     2.24   0.025     .3335311     5.05593
          Literate without formal schooling: Others  |  -.0561974   .4548984    -0.12   0.902    -.9477818     .835387
                                      Below primary  |   .2598866     .11367     2.29   0.022     .0370974    .4826758
                                            Primary  |   .4768204   .1092037     4.37   0.000     .2627852    .6908557
                                             Middle  |   .3036858    .096105     3.16   0.002     .1153235     .492048
                                          Secondary  |   .1451055   .1070652     1.36   0.175    -.0647385    .3549495
                                   Higher Secondary  |   .2828705   .1199765     2.36   0.018     .0477209    .5180201
                         Diploma/Certificate Course  |    .568807   .1405261     4.05   0.000     .2933808    .8442331
                                           Graduate  |   .2132686    .125385     1.70   0.089    -.0324815    .4590186
                            Post graduate and above  |   .5067951   .1943475     2.61   0.009      .125881    .8877092
                                                     |
                                            religion |
                                              Islam  |  -1.355998   .0803341   -16.88   0.000     -1.51345   -1.198546
                                       Christianity  |  -.1689143   .0833294    -2.03   0.043    -.3322369   -.0055918
                                            Sikhism  |   25.05115   .5189643    48.27   0.000       24.034    26.06831
                                            Jainism  |  -23.75782   .3469834   -68.47   0.000     -24.4379   -23.07775
                                           Buddhism  |    25.7901   .6009491    42.92   0.000     24.61226    26.96794
                                     Zoroastiansism  |   24.92038    .369491    67.45   0.000     24.19619    25.64457
                                             Others  |   .2870845   .4157228     0.69   0.490    -.5277172    1.101886
                                                     |
                                        social_group |
                                    Scheduled Caste  |   .4039961   .2408501     1.68   0.093    -.0680614    .8760535
                               Other Backward Class  |   .0765286   .2317459     0.33   0.741    -.3776849    .5307422
                                             Others  |   .1848982   .2383234     0.78   0.438    -.2822071    .6520035
                                                     |
                                      household_type |
                                                  2  |   .2072669   .0674396     3.07   0.002     .0750877    .3394461
                                                  3  |   .3574103   .0728295     4.91   0.000     .2146671    .5001535
                                                  4  |   .4110147   .1255971     3.27   0.001      .164849    .6571804
                                                  5  |  -.0199414   .1033561    -0.19   0.847    -.2225156    .1826328
                                                  9  |   .1955746   .4441266     0.44   0.660    -.6748977    1.066047
                                                     |
                    household_cons_expenditure_month |   .0000501   4.75e-06    10.56   0.000     .0000408    .0000594
                                                     |
                                            district |
                                                  2  |  -.7354827   .1684331    -4.37   0.000    -1.065606   -.4053599
                                                  3  |   1.052953   .2027065     5.19   0.000     .6556558    1.450251
                                                  4  |   .3196974   .1401048     2.28   0.022      .045097    .5942978
                                                  5  |   .4145917   .1900838     2.18   0.029     .0420343    .7871492
                                                  6  |   .5879066   .1797885     3.27   0.001     .2355276    .9402856
                                                  7  |   .5823383   .1715462     3.39   0.001     .2461139    .9185627
                                                  8  |   .3241014    .170929     1.90   0.058    -.0109133    .6591162
                                                  9  |   1.273401   .1976022     6.44   0.000     .8861074    1.660694
                                                 10  |   .3069194   .1601108     1.92   0.055     -.006892    .6207308
                                                 11  |   .7176304   .1892114     3.79   0.000     .3467828    1.088478
                                                 12  |          0  (omitted)
                                                 13  |   .6179388   .1513468     4.08   0.000     .3213045     .914573
                                                 14  |   .0453671   .1563654     0.29   0.772    -.2611034    .3518377
                                                     |
                                               _cons |  -1.526854   .2685512    -5.69   0.000    -2.053205   -1.000504
    -------------------------------------------------+----------------------------------------------------------------
    Husband_working__wife_not                        |  (base outcome)
    -------------------------------------------------+----------------------------------------------------------------
    Wife_working__husband_not                        |
                                        1.time_dummy |  -.0255124   .1347011    -0.19   0.850    -.2895218     .238497
                                       1.treat_dummy |  -.0831364   .4087201    -0.20   0.839     -.884213    .7179402
                                                     |
                              time_dummy#treat_dummy |
                                                1 1  |   .5605286   .1939844     2.89   0.004     .1803263     .940731
                                                     |
                                    dependency_ratio |   .2090512   .1068879     1.96   0.050    -.0004452    .4185477
                                           sex_ratio |  -.4870676   .0827172    -5.89   0.000    -.6491904   -.3249449
                                                 age |   .0059034    .002428     2.43   0.015     .0011447    .0106622
                                                     |
                                     education_level |
    Literate without formal schooling: EGS/NFEC/AEC  |    3.34502   .9145126     3.66   0.000     1.552608    5.137431
             Literate without formal schooling: TLC  |  -21.55821    .942903   -22.86   0.000    -23.40627   -19.71016
          Literate without formal schooling: Others  |   1.061484   .5300408     2.00   0.045     .0226235    2.100345
                                      Below primary  |   .4720465   .1977124     2.39   0.017     .0845372    .8595557
                                            Primary  |   .4989601   .2066312     2.41   0.016     .0939704    .9039499
                                             Middle  |   .0873603   .1765532     0.49   0.621    -.2586776    .4333981
                                          Secondary  |   .2858166   .1979855     1.44   0.149     -.102228    .6738611
                                   Higher Secondary  |   .6099309   .2080757     2.93   0.003       .20211    1.017752
                         Diploma/Certificate Course  |   .6041262   .2346056     2.58   0.010     .1443076    1.063945
                                           Graduate  |   .5778673   .2207822     2.62   0.009     .1451421    1.010592
                            Post graduate and above  |   1.331876   .2988721     4.46   0.000      .746098    1.917655
                                                     |
                                            religion |
                                              Islam  |  -1.281868   .1553884    -8.25   0.000    -1.586424   -.9773124
                                       Christianity  |  -.2206113   .1529705    -1.44   0.149     -.520428    .0792055
                                            Sikhism  |    .538258   .2780025     1.94   0.053     -.006617    1.083133
                                            Jainism  |  -23.89828   .4425888   -54.00   0.000    -24.76573   -23.03082
                                           Buddhism  |   .9659883   .3684061     2.62   0.009     .2439256    1.688051
                                     Zoroastiansism  |  -.3787971   .2117749    -1.79   0.074    -.7938682     .036274
                                             Others  |  -1.902428   .6523045    -2.92   0.004    -3.180922   -.6239351
                                                     |
                                        social_group |
                                    Scheduled Caste  |   -1.91416   .3753603    -5.10   0.000    -2.649853   -1.178468
                               Other Backward Class  |   -1.65958   .3502335    -4.74   0.000    -2.346025   -.9731351
                                             Others  |  -1.374201   .3665997    -3.75   0.000    -2.092724   -.6556792
                                                     |
                                      household_type |
                                                  2  |   .3395539    .132186     2.57   0.010     .0804741    .5986337
                                                  3  |   .8102268   .1306138     6.20   0.000     .5542284    1.066225
                                                  4  |   .6770923   .2627861     2.58   0.010      .162041    1.192144
                                                  5  |   .0752352   .2303062     0.33   0.744    -.3761567    .5266271
                                                  9  |   3.079924   .3316687     9.29   0.000     2.429865    3.729983
                                                     |
                    household_cons_expenditure_month |  -.0000161   9.90e-06    -1.62   0.104    -.0000355    3.32e-06
                                                     |
                                            district |
                                                  2  |   1.133535   .3079185     3.68   0.000     .5300264    1.737045
                                                  3  |   -.743917   .4239013    -1.75   0.079    -1.574748    .0869144
                                                  4  |   1.056271   .3247245     3.25   0.001     .4198231     1.69272
                                                  5  |   .5961219    .348318     1.71   0.087    -.0865688    1.278813
                                                  6  |   .3265286   .3248551     1.01   0.315    -.3101756    .9632329
                                                  7  |   1.053702   .3016057     3.49   0.000     .4625657    1.644839
                                                  8  |   .5097657   .3119027     1.63   0.102    -.1015525    1.121084
                                                  9  |   -.095839   .3883903    -0.25   0.805      -.85707    .6653919
                                                 10  |   .1914888   .3744237     0.51   0.609    -.5423681    .9253457
                                                 11  |   .7565155   .3427428     2.21   0.027     .0847519    1.428279
                                                 12  |          0  (omitted)
                                                 13  |   .9412425   .3290607     2.86   0.004     .2962954     1.58619
                                                 14  |   1.665447   .3414197     4.88   0.000     .9962771    2.334618
                                                     |
                                               _cons |  -1.847752   .4199927    -4.40   0.000    -2.670923   -1.024582
    -------------------------------------------------+----------------------------------------------------------------
    Neither_working                                  |
                                        1.time_dummy |  -.1362492   .0984825    -1.38   0.167    -.3292713    .0567729
                                       1.treat_dummy |  -.1920688   .2965109    -0.65   0.517    -.7732195    .3890818
                                                     |
                              time_dummy#treat_dummy |
                                                1 1  |  -.1559826   .1500374    -1.04   0.299    -.4500504    .1380852
                                                     |
                                    dependency_ratio |  -.3220349    .094127    -3.42   0.001    -.5065204   -.1375493
                                           sex_ratio |  -.0424478   .0488557    -0.87   0.385    -.1382032    .0533075
                                                 age |    .010072   .0018666     5.40   0.000     .0064135    .0137304
                                                     |
                                     education_level |
    Literate without formal schooling: EGS/NFEC/AEC  |   .1984374   .6868283     0.29   0.773    -1.147721    1.544596
             Literate without formal schooling: TLC  |  -.9435335   1.019233    -0.93   0.355    -2.941194    1.054127
          Literate without formal schooling: Others  |  -2.167563   .5273915    -4.11   0.000    -3.201232   -1.133895
                                      Below primary  |  -.0195611   .1526759    -0.13   0.898    -.3188004    .2796781
                                            Primary  |   .1055706    .147593     0.72   0.474    -.1837065    .3948476
                                             Middle  |  -.1819045   .1298198    -1.40   0.161    -.4363468    .0725377
                                          Secondary  |    .095965    .144967     0.66   0.508    -.1881651    .3800952
                                   Higher Secondary  |    .361107   .1566339     2.31   0.021     .0541103    .6681037
                         Diploma/Certificate Course  |   .2877779   .1987094     1.45   0.148    -.1016854    .6772412
                                           Graduate  |   .6038103   .1684906     3.58   0.000     .2735748    .9340457
                            Post graduate and above  |   .6291799    .264365     2.38   0.017     .1110341    1.147326
                                                     |
                                            religion |
                                              Islam  |  -.3530826   .0970115    -3.64   0.000    -.5432217   -.1629435
                                       Christianity  |  -.2944134   .1168478    -2.52   0.012    -.5234309   -.0653959
                                            Sikhism  |   .3027214   .1992737     1.52   0.129     -.087848    .6932907
                                            Jainism  |  -3.538234   .4815603    -7.35   0.000    -4.482075   -2.594393
                                           Buddhism  |   .6449177   .2246501     2.87   0.004     .2046116    1.085224
                                     Zoroastiansism  |   1.491325   .2088949     7.14   0.000     1.081899    1.900752
                                             Others  |   .7508039   .6099618     1.23   0.218    -.4446992    1.946307
                                                     |
                                        social_group |
                                    Scheduled Caste  |  -.4276803   .3435522    -1.24   0.213     -1.10103    .2456695
                               Other Backward Class  |  -.2750426   .3272464    -0.84   0.401    -.9164338    .3663486
                                             Others  |   -.205541   .3298752    -0.62   0.533    -.8520845    .4410024
                                                     |
                                      household_type |
                                                  2  |   .5886372    .106114     5.55   0.000     .3806576    .7966167
                                                  3  |   .7196112    .106732     6.74   0.000     .5104204     .928802
                                                  4  |   .5472622   .1945804     2.81   0.005     .1658917    .9286327
                                                  5  |    .423022   .1340405     3.16   0.002     .1603075    .6857365
                                                  9  |   7.268856    .278214    26.13   0.000     6.723567    7.814146
                                                     |
                    household_cons_expenditure_month |  -.0000852   .0000104    -8.18   0.000    -.0001056   -.0000648
                                                     |
                                            district |
                                                  2  |  -.1673228   .1861948    -0.90   0.369    -.5322579    .1976124
                                                  3  |  -.1971598   .2986654    -0.66   0.509    -.7825331    .3882136
                                                  4  |   .0995576   .1784901     0.56   0.577    -.2502766    .4493917
                                                  5  |   .0626522   .2698674     0.23   0.816    -.4662781    .5915825
                                                  6  |   .2385216   .2703431     0.88   0.378    -.2913412    .7683843
                                                  7  |   .7957359   .2705633     2.94   0.003     .2654415     1.32603
                                                  8  |   .4868733   .2600771     1.87   0.061    -.0228684    .9966151
                                                  9  |   1.315812   .3054403     4.31   0.000     .7171601    1.914464
                                                 10  |   .3381227   .2086875     1.62   0.105    -.0708973    .7471427
                                                 11  |   .2636806   .2795222     0.94   0.346    -.2841728     .811534
                                                 12  |          0  (omitted)
                                                 13  |   .7078924    .202697     3.49   0.000     .3106136    1.105171
                                                 14  |   1.569477   .1991525     7.88   0.000     1.179145    1.959809
                                                     |
                                               _cons |  -1.485128   .3969955    -3.74   0.000    -2.263225    -.707031
    ------------------------------------------------------------------------------------------------------------------
    Note: 15 observations completely determined. Standard errors questionable.

  • #2
    Waiting on a better answer, beware of the interaction term (the DiD effect). In nonlinear models, the coefficient you obtain on an interaction term is very different from the interaction effect. See Ai and Norton (2003) for the seminal paper on this: https://www.sciencedirect.com/scienc...65176503000326.

    Comment


    • #3
      Thanks for sharing the paper! I am eager to get advice on how to improve this model.

      Comment


      • #4
        Further perhaps try to cluster standard errors at the e.g. household level. Observations completely determined, as far as I understand it, is the perfect prediction problem. When the outcome variable does not vary at all within the group of one regressor.

        Comment


        • #5
          Thanks! Clustering standard error at household level actually helped!

          Comment


          • #6
            Can it be that some of your explanatory variables do not vary on 'household coordination'? That is, for a category of your explanatory variable, all respondents reports e.g. 2 "only husband working". If this is the case, I think this will make the task very difficult to for the maximum likelihood estimator.

            Comment

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