Standard error of the difference of coefficients

[Felix Chappuis]

Dear Statalist Members

I run a regression where I compare the the evolution of a coefficient over a time period relative to the evolution of the coefficient of an other time period. What are the coefficients of these differences?

Linear regression Number of obs = 1,456
F(15, 181) = 46.18
Prob > F = 0.0000
R-squared = 0.4522
Root MSE = .12453

(Std. err. adjusted for 182 clusters in code)
----------------------------------------------------------------------------------
| Robust
ln_employment_~e | Coefficient std. err. t P>|t| [95% conf. interval]
-----------------+----------------------------------------------------------------

year#c.avg_GAP_c |
2014 | -.1807587 .5320225 -0.34 0.734 -1.230523 .8690053
2015 | .0920542 .410935 0.22 0.823 -.7187851 .9028935
2016 | .7385884 .5160883 1.43 0.154 -.2797349 1.756912
2017 | .5241659 .5402929 0.97 0.333 -.5419169 1.590249
2018 | 1.125851 .6353221 1.77 0.078 -.1277395 2.379441
2019 | .8788087 .61297 1.43 0.153 -.3306774 2.088295
2020 | .8352193 .5538894 1.51 0.133 -.2576914 1.92813
|
avg_GAP_c | -6.701872 .6575281 -10.19 0.000 -7.999278 -5.404465
_cons | -.2272959 .0148515 -15.30 0.000 -.2566003 -.1979915

In this case the coefficient of 2019 vs. 2018 relative to 2014 vs. 2013 (base year in this regression) would be (0.8788087-1.125851-(-0.1807587))=-0.0662836. What would here be the standard error? Would be very thankful for your help.

Have a great day.

Félix

[Carlo Lazzaro]

Félix:
do you mean something along the lines of the following toy-example?

use "https://www.stata-press.com/data/r16/auto.dta"
. reg price i.foreign i.rep78

      Source |       SS           df       MS      Number of obs   =        69
-------------+----------------------------------   F(5, 63)        =      0.19
       Model |  8372481.37         5  1674496.27   Prob > F        =    0.9670
    Residual |   568424478        63  9022610.75   R-squared       =    0.0145
-------------+----------------------------------   Adj R-squared   =   -0.0637
       Total |   576796959        68  8482308.22   Root MSE        =    3003.8

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     foreign |
    Foreign  |    36.7572   1010.484     0.04   0.971    -1982.533    2056.048
             |
       rep78 |
          2  |   1403.125   2374.686     0.59   0.557    -3342.306    6148.556
          3  |   1861.058   2195.967     0.85   0.400    -2527.232    6249.347
          4  |   1488.621   2295.176     0.65   0.519    -3097.921    6075.164
          5  |   1318.426   2452.565     0.54   0.593    -3582.634    6219.485
             |
       _cons |     4564.5   2123.983     2.15   0.035     320.0579    8808.942
------------------------------------------------------------------------------

. lincom i2.rep78-i3.rep78

 ( 1)  2.rep78 - 3.rep78 = 0

------------------------------------------------------------------------------
       price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |  -457.9326   1199.496    -0.38   0.704    -2854.934    1939.069
------------------------------------------------------------------------------

.

[Felix Chappuis]

Carlo:

Thank you so much, that is exactly, what I was looking for.

Have a great Sunday.

Félix