Fairlie decomposition

[Anthon Balthon]

Hello,

I am using the fairlie STATA module for decomposition (https://ideas.repec.org/c/boc/bocode/s456727.html) to analyze the following model:

Independent variables: aa001, aa004, ba016, ea104, eb001, eb002, ec003
Dependent variable: eh041 (binary: 0, 1)
Group variable: groupvar (binary: 0, 1)

However, I am unable to locate any information, either on STATAList.org or elsewhere, that helps me to interpret these results correctly. Also the publications by Fairlie didn't help me forward.

Question: Can anyone please help me to get into the right direction to interpret the results below?

Your response is highly appreciated!


The fairlie module is run using the following command:

fairlie eh041 aa001 aa004 ba016 ea104 eb001 eb002 ec023, by(groupvar)

This produces the following output:

Iteration 0:   log likelihood = -877.38553
Iteration 1:   log likelihood = -862.66744
Iteration 2:   log likelihood = -862.24213
Iteration 3:   log likelihood = -862.24169

Logistic regression                               Number of obs   =       2976
                                                  LR chi2(7)      =      30.29
                                                  Prob > chi2     =     0.0001
Log likelihood = -862.24169                       Pseudo R2       =     0.0173

------------------------------------------------------------------------------
eh041        |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       aa001 |   .4093181   .1622917     2.52   0.012     .0912323     .727404
       aa004 |   .0152344   .0065036     2.34   0.019     .0024875    .0279812
       ba016 |    -.16377   .0795174    -2.06   0.039    -.3196213   -.0079188
       ea104 |  -.0061618   .0080322    -0.77   0.443    -.0219046     .009581
       eb001 |   .2024671   .1832657     1.10   0.269    -.1567272    .5616613
       eb002 |  -.2667996   .1977646    -1.35   0.177    -.6544111    .1208119
       ec023 |   .1391324   .0841333     1.65   0.098    -.0257658    .3040306
       _cons |   1.896858   .6315424     3.00   0.003     .6590576    3.134658
------------------------------------------------------------------------------

Decomposition replications (100)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5
..................................................    50
..................................................   100

Non-linear decomposition by groupvar (G)

                                                Number of obs     =      6,312
                                                  N of obs G=0    =       2976
                                                  N of obs G=0    =       3336
                                                  Pr(Y!=0|G=0)    =  .91330645
                                                  Pr(Y!=0|G=1)    =  .89868106
                                                  Difference      =   .0146254
                                                  Total explained =  .00011247
------------------------------------------------------------------------------
eh041        |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       aa001 |   .0004943   .0005906     0.84   0.403    -.0006633    .0016518
       aa004 |  -.0010569   .0006778    -1.56   0.119    -.0023854    .0002716
       ba016 |  -.0001179   .0005283    -0.22   0.823    -.0011533    .0009176
       ea104 |  -.0002608   .0004181    -0.62   0.533    -.0010804    .0005587
       eb001 |  -.0001183    .000191    -0.62   0.536    -.0004927    .0002561
       eb002 |   .0006998   .0005598     1.25   0.211    -.0003974     .001797
       ec023 |   .0004668   .0003892     1.20   0.230    -.0002961    .0012296
------------------------------------------------------------------------------

[Justin Niakamal]

I've never heard the Fairlie decomposition, but for what it's worth, here's my interpretation.

The difference between white and black computer ownership rates is 0.3030. As expected, the largest factor explaining this large racial disparity in home computer ownership is income. Lower levels of income among blacks account for 0.0775 to 0.1031 (or 25.6 to 34.0 percent) of the white/black gap in the probability of having a home computer. In all specifications these contributions are statistically significant. Lower levels of education among blacks also contribute to the racial gap in computer ownership.

This passage is from "An Extension of the Blinder-Oaxaca Decomposition Technique to Logit and Probit Models" (referenced below). You can see the coefficients referenced in Table 1.

You can produce similar results using

use http://fmwww.bc.edu/RePEc/bocode/h/homecomp.dta, clear
fairlie homecomp female age (educ:hsgrad somecol college)(marstat:married prevmar) if white==1|black==1 [pw=wgt],by(black)

So with all this in mind, I would interpret your results as follows:

The difference between eh041 amongst groupvar is 0.0146254. The largest positive factor contributing to the differential is eb002, which accounts for .0006998 of the gap in probability for eh041 (or 4.8% (.0006998/.0146254)). However, given the results you've shown above, none of these factors appear to be statistically significant.

Lastly,

Another potentially important issue regarding use of the technique is the effect of ordering of variables in the decomposition. As noted above, because of the nonlinearity of the decomposition equation the results may be sensitive to the ordering of variables. To investigate this issue, Specification 4 of Table 2 reports estimates in which the order of switching distributions of variables is reversed.

It looks like the fairlie command has a randomized ordering option. This might be something worth exploring.

Hope this helps.


Fairlie, Robert W., An Extension of the Blinder-Oaxaca Decomposition Technique to Logit and Probit Models (January 2006). Yale University Economic Growth Center Discussion Paper No. 873; IZA Discussion Paper No. 1917. Available at SSRN: https://ssrn.com/abstract=497302

[Anthon Balthon]

Thank you Justin. I appreciate your comment!

May I ask about your opinion regarding the relevance of the logistic regression results that the Fairlie decomposition produces?

How would these results fit into the results of the decomposition? For example, the model appears to be significant (Prob > chi2 = 0.0001), but then the decomposition results show that no factors are significant.

[Justin Niakamal]

I think you should look into the ordering of the variables in the decomposition and see how that changes things. The model appears to be significant, but only for a few factors. One might expect "more significant" results (higher z-scores) given the number of observations. It also could be the case that the difference (0.0146254) is too low for the decomposition to produce statistically significant results (I'm not sure if that's the case, however). I would also pay attention to the signs of the coefficients. Are they what you'd expect? etc.