Dummy variable interpretation

[Oliver Gatland]

     Source |       SS           df       MS      Number of obs   =     1,315
-------------+----------------------------------   F(28, 1286)     =    273.58
       Model |  946328.028        28  33797.4296   Prob > F        =    0.0000
    Residual |  158872.156     1,286  123.539779   R-squared       =    0.8563
-------------+----------------------------------   Adj R-squared   =    0.8531
       Total |  1105200.18     1,314  841.096031   Root MSE        =    11.115

------------------------------------------------------------------------------
       enrol |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         CPI |   .1847218   .0313612     5.89   0.000     .1231971    .2462465
 newmarriage |    -.32916   .0818746    -4.02   0.000    -.4897824   -.1685375
      depend |  -.2282612   .0387019    -5.90   0.000     -.304187   -.1523355
     edspend |   2.111124   .2682445     7.87   0.000     1.584879    2.637368
   mortality |  -.3557503   .0344384   -10.33   0.000     -.423312   -.2881887
 newfemteach |   .3355659   .0259151    12.95   0.000     .2847253    .3864065
       urban |   .1179031   .0243665     4.84   0.000     .0701007    .1657055
       lnGDP |   2.257544   .9004769     2.51   0.012     .4909787    4.024109
          UM |  -2.232604   1.267144    -1.76   0.078    -4.718501    .2532922
          LM |  -1.696402   1.918191    -0.88   0.377    -5.459528    2.066725
           L |  -2.078713   2.783371    -0.75   0.455    -7.539159    3.381733
             |
        year |
       2001  |   .2627674   1.840499     0.14   0.886    -3.347943    3.873477
       2002  |  -.1156184   1.834911    -0.06   0.950    -3.715366     3.48413
       2003  |   .1621663   1.842056     0.09   0.930    -3.451598     3.77593
       2004  |  -.7602889   1.842209    -0.41   0.680    -4.374354    2.853777
       2005  |  -.8418906    1.84367    -0.46   0.648    -4.458822    2.775041
       2006  |  -1.357138   1.844013    -0.74   0.462    -4.974742    2.260465
       2007  |  -1.241886   1.846762    -0.67   0.501    -4.864884    2.381112
       2008  |  -1.327063   1.850116    -0.72   0.473    -4.956639    2.302513
       2009  |  -1.505653   1.861639    -0.81   0.419    -5.157836    2.146531
       2010  |  -.7093271   1.864264    -0.38   0.704     -4.36666    2.948006
       2011  |  -.2339199   1.863438    -0.13   0.900    -3.889632    3.421792
       2012  |  -.5687192   1.864502    -0.31   0.760    -4.226518     3.08908
       2013  |     2.6685   1.867584     1.43   0.153    -.9953454    6.332345
       2014  |   3.751158    1.87445     2.00   0.046     .0738434    7.428473
       2015  |   4.425729   1.869453     2.37   0.018     .7582165    8.093242
       2016  |   5.518136   1.867712     2.95   0.003      1.85404    9.182233
       2017  |   5.279886   1.869216     2.82   0.005     1.612839    8.946933
             |
       _cons |    50.3543   9.066823     5.55   0.000     32.56691    68.14169
-----------------------------------------------------------------------------

[Oliver Gatland]

Hi,

above is my regression output. I am investigating the effect of corruption on education (specifically enrolment rates). I have added a dummy variable for country income classification. The variables above are L= Low income country, LM= low-middle income country, UM= upper-middle income country and I used High income country as my base. However since I have also included year dummies I am not sure how to interpret the constant. I think the constant represents a high income country in the year 2000. Is there any way I can find just the effect of a country being classified as high income across the years? Or can I only interpret it for each year separately?

Thanks for any help!

[Dick Campbell]

Your interpretation of the constant is correct. But what do you mean by "across the years." Your model assumes that the effect of income does not vary by year, that is, the model is additive and there is no year by income interaction. So, the effect of LM, for example, is -1.696 (rounded) regardless of year.

[Oliver Gatland]

Thanks for your response Dick,

What I meant was is there a way I can see the effect of a country being of High income regardless of year. (Similar to how the effect of LM regardless of year is -1.696)

[Dick Campbell]

A brute force approach would be to simply change the reference category. But the point to see here is that your equation already contains all of the possible information you can get about the effect of income. As it stands, you have chosen to see those effects in terms of contrasts to the high income category. You will notice that all of the dummy variables for income categories included in your model have negative coefficients, meaning that, given your model,, relative to high income countries, lower income reduces enrollment, regardless of year and regardless of the values of other variables. So, for example, low income countries (coded L) have estimated enrollments -2.078713 below high income countries in every year and regardless of the values of edspend, mortality, etc. Interpreting sets of dummy variables like year and income categories requires you to think hard about exactly what the model means, but it is effort well spent.

If you were to treat income as a factor variable you can use Stata's margins and then marginsplot to see this graphically. If you are not familiar with these techniques you might want to look at a Stata Journal paper by Rich Williams which explains in detail how to do it. (The Stata Journal (2012) 12, Number 2, pp. 308–331). This paper is accessible for free from the SJ website.