Size of the effect of a variable obtained through margins, eydx(*)

[Bruno Hoepers]

Hi all. I’m writing a paper about the effect of govt’ advertising per county in an Argentine province for two elections. The dependent variable is “ps_gov_vote_share” (socialist party’s vote share for governor) and the main independent variable is “ln_total_r_ad_spend_cap” (total spending with ads per capita logged).

My main question relates to the size of the effect of “ln_total_r_ad_spend_cap”.

I need to know whether the effect is small, moderate or large when reporting the results. The output from the semi-elasticities follow below.

The value of .083 for "ln_total_r_ad_spend_cap" can be considered a small effect?

Thank you.

quietly: xi: ivregress 2sls ps_dep_vote_share ln_pop ln_pop_dens prop_pop_14_years_more perc_healthcare_cov perc_pop_seniors perc_analfabetos perc_pop_desocupados perc_nbi i.seccional i.year (ln_total_r_ad_spend_cap = rate_libraries_100t properties), robust cluster(localidad)

margins, eydx(*)

Average marginal effects                                   Number of obs = 720
Model VCE: Robust

Expression: Linear prediction, predict()
ey/dx wrt:  ln_total_r_ad_spend_cap ln_pop ln_pop_dens prop_pop_14_years_more perc_healthcare_cov perc_pop_seniors perc_analfabetos
            perc_pop_desocupados perc_nbi _Iseccional_2 _Iseccional_3 _Iseccional_4 _Iseccional_5 _Iseccional_6 _Iseccional_7
            _Iseccional_8 _Iseccional_9 _Iseccional_10 _Iseccional_11 _Iseccional_12 _Iseccional_13 _Iseccional_14 _Iseccional_15
            _Iseccional_16 _Iseccional_17 _Iseccional_18 _Iseccional_19 _Iyear_2015

-----------------------------------------------------------------------------------------
                        |            Delta-method
                        |      ey/dx   std. err.      z    P>|z|     [95% conf. interval]
------------------------+----------------------------------------------------------------
ln_total_r_ad_spend_cap |   .0830077   .0423331     1.96   0.050     .0000365     .165979
                 ln_pop |  -.1023227   .0347665    -2.94   0.003    -.1704638   -.0341816
            ln_pop_dens |   .0161023   .0184456     0.87   0.383    -.0200503    .0522549
 prop_pop_14_years_more |  -.4680305   .5370263    -0.87   0.383    -1.520583    .5845217
    perc_healthcare_cov |   .0058763    .139075     0.04   0.966    -.2667057    .2784583
       perc_pop_seniors |   .3367992    .589979     0.57   0.568    -.8195385    1.493137
       perc_analfabetos |  -1.270178   1.446377    -0.88   0.380    -4.105025    1.564669
   perc_pop_desocupados |  -1.445664   1.197676    -1.21   0.227    -3.793065    .9017375
               perc_nbi |  -.6554313    .355108    -1.85   0.065     -1.35143    .0405675
          _Iseccional_2 |  -.0059292   .0868682    -0.07   0.946    -.1761877    .1643293
          _Iseccional_3 |   .0146855   .0769567     0.19   0.849    -.1361469    .1655178
          _Iseccional_4 |   -.071583   .0777253    -0.92   0.357    -.2239219    .0807559
          _Iseccional_5 |   .2832511   .1121816     2.52   0.012     .0633792     .503123
          _Iseccional_6 |   .0505496   .0722534     0.70   0.484    -.0910646    .1921637
          _Iseccional_7 |   .3946172   .0874035     4.51   0.000     .2233095     .565925
          _Iseccional_8 |    .016916   .1014999     0.17   0.868    -.1820202    .2158522
          _Iseccional_9 |   .0502337   .0775807     0.65   0.517    -.1018216     .202289
         _Iseccional_10 |   .0922804   .0765663     1.21   0.228    -.0577869    .2423476
         _Iseccional_11 |   .2379143   .1010667     2.35   0.019     .0398272    .4360014
         _Iseccional_12 |   -.074107    .089389    -0.83   0.407    -.2493062    .1010922
         _Iseccional_13 |   .3139516   .0820587     3.83   0.000     .1531195    .4747837
         _Iseccional_14 |    .147159   .0952811     1.54   0.122    -.0395884    .3339065
         _Iseccional_15 |   .0419176   .0757153     0.55   0.580    -.1064818    .1903169
         _Iseccional_16 |   .1274646   .0890123     1.43   0.152    -.0469963    .3019256
         _Iseccional_17 |  -.0506149    .083844    -0.60   0.546    -.2149462    .1137164
         _Iseccional_18 |   .0766642   .0866556     0.88   0.376    -.0931776     .246506
         _Iseccional_19 |   .2563277   .1082632     2.37   0.018     .0441358    .4685196
            _Iyear_2015 |   .2720629   .0164858    16.50   0.000     .2397514    .3043745
————————————————————————————————————————————

[George Ford]

The elasticity is 0.083, so a 10% increase in ads increases outcome by 0.8%. It's inelastic, but when it comes to voting, small changes are important (only have to win by 1 vote).
I'd think dydx might be more informative (since the DV is a percentage).

Might look at:

margins, at(ln_total_r_ad_spend_cap = (min(step)max)) 
marginsplot

to see what the outcomes are at different levels of the X.

[Bruno Hoepers]

Thank you, George. I ran "margins" and got the results that follow:

 margins, at(ln_total_r_ad_spend_cap=(0(.5)6)) atmeans

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .3187315   .0146574    21.75   0.000     .2900035    .3474594
          2  |   .3447272   .0056419    61.10   0.000     .3336692    .3557851
          3  |   .3707229   .0097248    38.12   0.000     .3516626    .3897832
          4  |   .3967186   .0200764    19.76   0.000     .3573695    .4360677
          5  |   .4227143   .0309403    13.66   0.000     .3620725    .4833562
          6  |     .44871     .04192    10.70   0.000     .3665483    .5308718
          7  |   .4747058   .0529436     8.97   0.000     .3709382    .5784734
          8  |   .5007015   .0639884     7.82   0.000     .3752866    .6261164
          9  |   .5266972    .075045     7.02   0.000     .3796118    .6737827
         10  |   .5526929   .0861088     6.42   0.000     .3839227    .7214631
         11  |   .5786886   .0971775     5.95   0.000     .3882243     .769153
         12  |   .6046844   .1082495     5.59   0.000     .3925193    .8168494
         13  |   .6306801   .1193238     5.29   0.000     .3968097    .8645505
———————————————————————————————————————

[Bruno Hoepers]

The graph obtained with "marginsplot" follows below:

[George Ford]

looks like ad spending works