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Re: st: Interpretation of margins in the presence of fixed effects


From   Jed Cohen <[email protected]>
To   [email protected]
Subject   Re: st: Interpretation of margins in the presence of fixed effects
Date   Fri, 6 Sep 2013 10:36:02 +0200

Hi Dana,

I would first off try both models without a constant term (noconstant
in stata). As you see in the first model your constant term is
actually just your ommitted age category. You can then add in all age
categories, and drop just one of the industry dummies. Then
interpretation is pretty straightforward and does not need the margins
command I believe. Your agedum coefficients become intercepts, and the
slope or any observation you want to predict will be the industry
number coefficient, which in this case is just a discrete change to
the intercept of the magnitude of the estimated industry coefficient.
Cheers!


On Fri, Sep 6, 2013 at 4:02 AM, Dana Shills <[email protected]> wrote:
> I have read the manual on the margins command in detail and it is still not clear to me what role do fixed effects (or say dummy variables) play in the computation of predictive margins.
>
> Suppose I want to look at the relation between firm size and age (specifically 9 age dummies) with and w/o industry dummies. The summary stats of these three variables are below
>
>     Variable |       Obs        Mean    Std. Dev.       Min        Max
> -------------+--------------------------------------------------------
>         size |        97    123.0103    166.3225          2        806
>       agedum |       100        3.78    2.213731          1          9
>         inum |       100        13.6    8.952174          1         31
>
> Case I: WITHOUT INDUSTRY DUMMIES
>
> . reg size i.agedum
>
>       Source |       SS       df       MS              Number of obs =      97
> -------------+------------------------------           F(  8,    88) =    4.04
>        Model |  713993.178     8  89249.1473           Prob> F      =  0.0004
>     Residual |  1941671.81    88  22064.4524           R-squared     =  0.2689
> -------------+------------------------------           Adj R-squared =  0.2024
>        Total |  2655664.99    96   27663.177           Root MSE      =  148.54
>
> ------------------------------------------------------------------------------
>         size |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>       agedum |
>           2  |      117.4   52.62008     2.23   0.028     12.82866    221.9713
>           3  |   30.73333    51.9304     0.59   0.555    -72.46742    133.9341
>           4  |   28.45263   51.30546     0.55   0.581    -73.50619    130.4115
>           5  |   108.5429   67.99285     1.60   0.114    -26.57865    243.6644
>           6  |   103.5429   67.99285     1.52   0.131    -31.57865    238.6644
>           7  |      -14.8   76.70628    -0.19   0.847    -167.2376    137.6376
>           8  |      323.4   76.70628     4.22   0.000     170.9624    475.8376
>           9  |     275.15   83.58873     3.29   0.001      109.035     441.265
>              |
>        _cons |       48.6   38.35314     1.27   0.208    -27.61881    124.8188
> ------------------------------------------------------------------------------
>
> . margins agedum
>
> Adjusted predictions                              Number of obs   =         97
> Model VCE    : OLS
>
> Expression   : Linear prediction, predict()
>
> ------------------------------------------------------------------------------
>              |            Delta-method
>              |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>       agedum |
>           1  |       48.6   38.35314     1.27   0.205    -26.57078    123.7708
>           2  |        166    36.0265     4.61   0.000     95.38935    236.6106
>           3  |   79.33333   35.01147     2.27   0.023     10.71212    147.9546
>           4  |   77.05263   34.07766     2.26   0.024     10.26164    143.8436
>           5  |   157.1429   56.14325     2.80   0.005     47.10411    267.1816
>           6  |   152.1429   56.14325     2.71   0.007     42.10411    262.1816
>           7  |       33.8   66.42959     0.51   0.611     -96.3996    163.9996
>           8  |        372   66.42959     5.60   0.000     241.8004    502.1996
>           9  |     323.75   74.27054     4.36   0.000     178.1824    469.3176
>
> I understand that the margins command is giving the predicted employment of each age bin. So the average employment of firms in the second age group (5-10 years) is 166 employees if all firms in the dataset were treated to be between 5-10 years old. And it is easy to see that the predicted margins are just the regression coefficients adjusted for the constant.
>
> Case II: WITH INDUSTRY DUMMIES
>
> . reg size i.agedum i.inum
>
>       Source |       SS       df       MS              Number of obs =      97
> -------------+------------------------------           F( 38,    58) =    1.67
>        Model |  1385935.82    38  36471.9953           Prob> F      =  0.0390
>     Residual |  1269729.17    58  21891.8822           R-squared     =  0.5219
> -------------+------------------------------           Adj R-squared =  0.2086
>        Total |  2655664.99    96   27663.177           Root MSE      =  147.96
>
> ------------------------------------------------------------------------------
>         size |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>       agedum |
>           2  |   185.1145   63.99243     2.89   0.005     57.01978    313.2093
>           3  |   105.8429   73.84605     1.43   0.157    -41.97599    253.6619
>           4  |    74.4776   66.75151     1.12   0.269    -59.14007    208.0953
>           5  |   171.1386   81.31018     2.10   0.040     8.378543    333.8986
>           6  |   219.9226   87.65383     2.51   0.015     44.46437    395.3808
>           7  |   23.76708   83.98693     0.28   0.778     -144.351    191.8852
>           8  |   477.1547   96.73068     4.93   0.000     283.5272    670.7822
>           9  |    595.833   129.2686     4.61   0.000     337.0737    854.5923
>              |
>         inum |
>           2  |  -234.5949   168.2358    -1.39   0.169    -571.3555    102.1657
>           3  |  -17.52719   160.0994    -0.11   0.913    -338.0009    302.9465
>           4  |  -55.42242   169.1826    -0.33   0.744    -394.0781    283.2333
>           5  |  -271.0341   187.8332    -1.44   0.154    -647.0231     104.955
>           6  |  -118.9656   166.5016    -0.71   0.478    -452.2547    214.3236
>           7  |  -95.84294   221.8941    -0.43   0.667    -540.0123    348.3264
>           8  |  -206.4776    219.635    -0.94   0.351    -646.1248    233.1696
>           9  |  -234.8429    195.681    -1.20   0.235    -626.5411    156.8552
>          10  |   -83.4776    219.635    -0.38   0.705    -523.1248    356.1696
>          11  |  -451.0993    188.756    -2.39   0.020    -828.9356   -73.26306
>          12  |  -271.1145   218.8122    -1.24   0.220    -709.1148    166.8857
>          13  |  -68.56328   168.2744    -0.41   0.685    -405.4011    268.2746
>          14  |  -55.88331   171.9721    -0.32   0.746    -400.1229    288.3562
>          15  |  -265.9787    191.091    -1.39   0.169     -648.489    116.5315
>          16  |  -125.1974   175.2724    -0.71   0.478    -476.0432    225.6484
>          17  |  -147.8429   221.8941    -0.67   0.508    -592.0123    296.3264
>          18  |  -148.5633   168.2744    -0.88   0.381    -485.4011    188.2746
>          19  |  -181.3566   181.0713    -1.00   0.321    -543.8101     181.097
>          20  |  -297.1145   218.8122    -1.36   0.180    -735.1148    140.8857
>          21  |  -13.84294   221.8941    -0.06   0.950    -458.0123    430.3264
>          22  |  -193.3253   167.3785    -1.16   0.253    -528.3697    141.7191
>          23  |  -160.5306   193.9322    -0.83   0.411    -548.7281    227.6669
>          24  |  -145.7978   165.7959    -0.88   0.383    -477.6744    186.0788
>          25  |     -109.5   181.2121    -0.60   0.548    -472.2354    253.2354
>          26  |  -290.1386   224.4886    -1.29   0.201    -739.5012    159.2241
>          27  |  -183.1603   191.4903    -0.96   0.343    -566.4698    200.1492
>          28  |   -77.4776    219.635    -0.35   0.726    -517.1248    362.1696
>          29  |  -120.0795   177.5111    -0.68   0.501    -475.4067    235.2476
>          30  |  -346.9226   226.8633    -1.53   0.132    -801.0388    107.1937
>          31  |  -204.4776    219.635    -0.93   0.356    -644.1248    235.1696
>              |
>        _cons |        134   147.9591     0.91   0.369    -162.1722    430.1722
> ------------------------------------------------------------------------------
>
> . margins agedum
>
> Predictive margins                                Number of obs   =         97
> Model VCE    : OLS
>
> Expression   : Linear prediction, predict()
>
> ------------------------------------------------------------------------------
>              |            Delta-method
>              |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>       agedum |
>           1  |  -22.27385   49.35852    -0.45   0.652    -119.0148    74.46706
>           2  |   162.8407   40.73507     4.00   0.000     83.00143      242.68
>           3  |   83.56909   47.28917     1.77   0.077    -9.115992    176.2542
>           4  |   52.20375   41.96549     1.24   0.214     -30.0471    134.4546
>           5  |   148.8647   66.87327     2.23   0.026      17.7955    279.9339
>           6  |   197.6487   71.66732     2.76   0.006     57.18337    338.1141
>           7  |   1.493234   70.09108     0.02   0.983    -135.8828    138.8692
>           8  |   454.8808   75.76749     6.00   0.000     306.3793    603.3824
>           9  |   573.5592   111.6518     5.14   0.000     354.7258    792.3926
>
> When we include the age dummies, it is not clear to me how we arrive at the number -22.27385 for the first age bin. Also how can size be negative?? What is the exact interpretation of this number?
>
> (Btw I just created a random sample of 100 observations from a larger dataset for purposes of illustration)
>
> Thank you for your help.
>
> Dana
> *
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-- 
----------------------------------------
Jed J. Cohen
Graduate Researcher
Virginia Tech
Dept. of Agricultural and Applied Economics
[email protected]

*
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