Hand Calculations of Marginal Effects: Adjusted Predictions at Representative values (APR)

[Jeff Thompson]

Hi All,

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// Stata-MP 14.2 - (user-written commands not possible)
// Large, "very short" (N>>T) longitudinal data of firm employment and payroll

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I'm well familiar with the -margins- command and the available resources, but still haven't been able to recreate the margins results based on adding up the coefficients. I've looked into the very helpful https://www3.nd.edu/~rwilliam/stats/Margins01.pdf, which provides example for the APM, MEM and AME but not for APR.
Similarly, the Stata videos by Chuck Huber https://www.youtube.com/watch?v=43uX4D_7uaI also show hand calculations but not for this type.

size: categorical variable
growth: discrete variable

xtreg payroll c.growth##i.size if growth>0
margins i.size, at(growth=(.1 .5 1))

To replicate growth of .1 at size 2 I tried to alter the examples given by the aforementioned resources

_b[growth]*.1+_b[2.size]+_b[2.size#growth]+_b[_cons]

but despite numerous variations, to no avail. Does someone know how APR margins are calculated?


Best,
Jeff

[Raffaele Grotti]

Hi Jeff,
I suspect that you do not get the same result as -marging- because you are not multiplying your interaction term _b[2.size#growth] by .1

Your code should thus be

_b[growth]*.1+_b[2.size]+_b[2.size#growth]*.1+_b[_cons] if e(sample)

I've also added -if e(sample)-, this is important if you have other control variables.

Here an example that mirrors you case:

webuse nlswork, clear
xtset idcode year

qui xtreg ln_wage i.race##c.hours if hours>20

margins race, at(hour=(40))

Adjusted predictions                            Number of obs     =     25,393
Model VCE    : Conventional

Expression   : Linear prediction, predict()
at           : hours           =          40

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        race |
      white  |   1.705663   .0072225   236.16   0.000     1.691508    1.719819
      black  |   1.562293   .0113957   137.09   0.000     1.539958    1.584628
      other  |   1.772997   .0575848    30.79   0.000     1.660133    1.885861
------------------------------------------------------------------------------

. 
. gen pw = _b[_cons]+_b[2.race]+_b[hours]*40+_b[2.race#hours]*40 if e(sample)
(3,141 missing values generated)

. sum pw

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
          pw |     25,393    1.562293           0   1.562293   1.562293

sum pw

Best,
Raffaele

[Jeff Thompson]

Spot on! Yeah this worked. However adding a second categorical variable messes things up:

age: values 1, 2, or 3

xtreg payroll c.growth##i.size i.age if growth>0, re vce(cluster id)
margins i.size, at(growth=(.1 .5 1))

Do you know how it would be calculated here? I thought the e(sample) would have sorted this out but not really sure what it's function plays.

*Note: added ,re vce(cluster id)

[Raffaele Grotti]

If you add a further variable you have to take it into account also in your by-hand-calculation.
Following on the previous example I add the var "collgrad"

xtreg ln_wage i.race##c.hours i.collgrad if hours>20, re vce(cluster idcode)

margins race, at(hour=(40))

gen pw = _b[_cons]+_b[2.race]+_b[hours]*40+_b[2.race#hours]*40+_b[1.collgrad]*collgrad if e(sample)
sum pw

Note that you were already estimating a -re-, which is the default.
Also, the -vce(cluster id)- only affects standard errors.

[Jeff Thompson]

Alright thanks! I tried this but didn't get them to add up. I may have to do with that _b[1.collgrad] is 0 because all other collgrad categories are in reference to it.


Sorry but I can't post the output due to copy/paste network restrictions all I have are the screenshots.

 xtreg payroll c.growth##i.size i.age if growth>0, re vce(cluster id)

margins i.size, at(growth=(.25 .5))

The red box is the number I'm trying to recalculate by hand. gen s is where I tried your code. gen s2 is where I tried finding the mean of all of the coefficients for age and this got the number closer. However, it's not the same and I'm still not sure if it's just a coincidence. Do you have any idea why this could be?