capturing unit and time specific coefficients

[Annette Popp]

Hello.
I am using Stata 16. I have an unbalanced panel data set with firm (gvkey) observations over time (fiscal_quarter). I'm running the following regression

reg DV x1 x2 x3 x4 c.x1#i.gvkey c.x1#i.fiscal_quarter c.x2#i.gvkey c.x2#i.fiscal_quarter c.x3#i.gvkey c.x3#i.fiscal_quarter c.x4#i.gvkey c.x4#i.fiscal_quarter, beta nocons

and would like to generate new variables (one assoicated with x1, x2, x3, x4) akin to

gen x1total = _b[x1] + _b[c.x1#gvkey] + _b[c.x1#fiscal_quarter]

for x1. In other words, I would like to capture the coefficient for x1, which can be done with

gen x1coeff = _b[x1]

and will be the same for each observation.

Next, I need to capture the coefficient for for the interaction of x1 with gvkey (my firm identifier), which will be the same for all observations within a firm but vary across firms, and capture the coefficient for the interaction of x1 with fiscal_quarter (my time variable), which will be the same for each time period across firms, but varies within firms.

I have searched extensively for a code on how to capture these coefficients to no prevail. I looked into using statsby, but it appears I would have to run the regression by groups (i.e., firms and then time periods), which is not what I want.

Any suggestions are greatly appreciated.
Best,
Annette

[Andrew Musau]

If I understand you correctly, you just want to loop.

Next, I need to capture the coefficient for for the interaction of x1 with gvkey (my firm identifier), which will be the same for all observations within a firm but vary across firms

levelsof gvkey, local(firms)
gen wanted= .
foreach num of numlist `firms'{
replace wanted= _b[c.x1#`num'.gvkey] if gvkey==`num'
}

Same logic for the other variables. Please note our preference for reproducible examples.

[Annette Popp]

Hi, Andrew,

Thank you so much. This works perfectly and was easily replicated for the remaining coefficients. I'm also interested in capturing standardized coefficients and ran the following model:

reg DV x1 x2 x3 x4 c.x1#i.gvkey c.x1#i.fiscal_quarter c.x2#i.gvkey c.x2#i.fiscal_quarter c.x3#i.gvkey c.x3#i.fiscal_quarter c.x4#i.gvkey c.x4#i.fiscal_quarter, beta

Next, I used

listcoef

and attempted to capture the standardized coefficient of x1 with

gen x1_stand_coeff = _bStdXY[x1]

which resulted in the error message: _bStdXY not found

I have not been able to find a command that accesses standardized coefficients similar to the way _b accesses "regular" coefficients. Do you have any suggestions?

Again, thank you very much!

Annette

[Andrew Musau]

One method that I use is to call esttab from SSC by Benn Jann that creates a matrix with the beta coefficients.

ssc install esttab
reg DV x1 x2 x3 x4...
esttab, beta
mat l e(beta)

You can now obtain the coefficients from this matrix. Let me know if you have any difficulties.

[Annette Popp]

Hi, Andrew,

Again, thank you for your support.

I followed your suggestion and wrote code to obtain the standardized coefficients from the matrix by recalling scalars based on their position as identified by row and column positions:

esttab, beta
mat l e(beta)

gen x1_time=.
levelsof fiscal_quarter, local(quarters)
foreach num of numlist `quarters' {
replace x1_time= beta[1,colnumb(beta,"`num'.fiscal_quarter#c.x1 if fiscal_quarter==`num'")]
}

Unfortunately, I receive

(0 real changes made)
(0 real changes made)
(0 real changes made)
(0 real changes made)
(0 real changes made)
(0 real changes made)
(0 real changes made)
...

I also noted that while

esttab, beta

returns all beta coefficients, once I write them to matrix "beta", all of the coefficients from the interaction terms (e.g., c.x1#i.fiscal_quarter) are listed as .z .

To evaluate whether the above listed code didn't result in any changes made because the interaction terms are missing in the matrix of standardized coefficients, I also ran the code and gathered "regular" coefficients. The matrix shows regular interaction coefficients, but I'm not able to capture them in my new variable and receive the same error message (0 real changes made).

Thank you very much for your time.

Annette

[Andrew Musau]

There is an issue with the -beta- option of esttab and factor variables which I had not noticed. Hopefully Ben Jann will view this thread and address it in a future update. esttab does not calculate the coefficients of factor variable interactions but instead assigns them missing values similar to the intercept.

webuse grunfeld,clear
regress invest mvalue i.company##c.kstock, beta
esttab, beta
mat list e(beta)

Results in:

. regress invest mvalue i.company##c.kstock, beta

      Source |       SS           df       MS      Number of obs   =       200
-------------+----------------------------------   F(20, 179)      =    225.72
       Model |  9002974.32        20  450148.716   Prob > F        =    0.0000
    Residual |  356969.596       179  1994.24355   R-squared       =    0.9619
-------------+----------------------------------   Adj R-squared   =    0.9576
       Total |  9359943.92       199  47034.8941   Root MSE        =    44.657

----------------------------------------------------------------------------------
          invest |      Coef.   Std. Err.      t    P>|t|                     Beta
-----------------+----------------------------------------------------------------
          mvalue |   .1057073   .0103627    10.20   0.000                 .6406865
                 |
         company |
              2  |   178.1454   33.57003     5.31   0.000                 .2470439
              3  |  -61.01103   32.20552    -1.89   0.060                -.0846073
              4  |   72.51596   39.98803     1.81   0.071                 .1005618
              5  |    123.015   50.88138     2.42   0.017                 .1705917
              6  |   90.24424   46.25708     1.95   0.053                 .1251466
              7  |   89.24089   49.96549     1.79   0.076                 .1237552
              8  |   72.46716   42.59822     1.70   0.091                 .1004942
              9  |   83.09874     53.648     1.55   0.123                 .1152376
             10  |   89.15305   47.73111     1.87   0.063                 .1236334
                 |
          kstock |   .3798827   .0174874    21.72   0.000                 .5274191
                 |
company#c.kstock |
              2  |    .028188   .0673826     0.42   0.676                 .0131362
              3  |  -.2436443   .0442144    -5.51   0.000                -.1607756
              4  |  -.0767067   .0934675    -0.82   0.413                -.0177305
              5  |  -.3578027   .0559295    -6.40   0.000                -.2605544
              6  |  -.2148316   .1549131    -1.39   0.167                -.0373009
              7  |  -.2562131   .0827691    -3.10   0.002                 -.121073
              8  |  -.4273763   .1666695    -2.56   0.011                 -.063353
              9  |  -.3129159   .1105414    -2.83   0.005                -.1358529
             10  |   .1019809   3.237561     0.03   0.975                 .0009578
                 |
           _cons |  -96.42841   43.24391    -2.23   0.027                        .
----------------------------------------------------------------------------------



. mat l e(beta)

e(beta)[1,23]
                          1b.           2.           3.           4.           5.           6.           7.           8.           9.          10.
         mvalue      company      company      company      company      company      company      company      company      company      company
y1    .64068651            0    .24704393   -.08460733    .10056184    .17059168    .12514662    .12375522    .10049417    .11523756     .1236334

                  1b.company#   2.company#   3.company#   4.company#   5.company#   6.company#   7.company#   8.company#   9.company#  10.company#
         kstock    co.kstock     c.kstock     c.kstock     c.kstock     c.kstock     c.kstock     c.kstock     c.kstock     c.kstock     c.kstock
y1    .52741909           .z           .z           .z           .z           .z           .z           .z           .z           .z           .z

                
          _cons
y1           .z

The workaround is to resort to the xi prefix to create the interactions. Make sure that you are obtaining the same coefficients as the original regression. Here is the code that estimates the regression in my example.

xi: reg invest mvalue i.company*kstock, beta
esttab, beta
mat list e(beta)

Res.:

. xi: reg invest mvalue i.company*kstock, beta
i.company         _Icompany_1-10      (naturally coded; _Icompany_1 omitted)
i.comp~y*kstock   _IcomXksto_#        (coded as above)

      Source |       SS           df       MS      Number of obs   =       200
-------------+----------------------------------   F(20, 179)      =    225.72
       Model |  9002974.32        20  450148.716   Prob > F        =    0.0000
    Residual |  356969.596       179  1994.24355   R-squared       =    0.9619
-------------+----------------------------------   Adj R-squared   =    0.9576
       Total |  9359943.92       199  47034.8941   Root MSE        =    44.657

-------------------------------------------------------------------------------
       invest |      Coef.   Std. Err.      t    P>|t|                     Beta
--------------+----------------------------------------------------------------
       mvalue |   .1057073   .0103627    10.20   0.000                 .6406865
  _Icompany_2 |   178.1454   33.57003     5.31   0.000                 .2470439
  _Icompany_3 |  -61.01103   32.20552    -1.89   0.060                -.0846073
  _Icompany_4 |   72.51596   39.98803     1.81   0.071                 .1005618
  _Icompany_5 |    123.015   50.88138     2.42   0.017                 .1705917
  _Icompany_6 |   90.24424   46.25708     1.95   0.053                 .1251466
  _Icompany_7 |   89.24089   49.96549     1.79   0.076                 .1237552
  _Icompany_8 |   72.46716   42.59822     1.70   0.091                 .1004942
  _Icompany_9 |   83.09874     53.648     1.55   0.123                 .1152376
 _Icompany_10 |   89.15305   47.73111     1.87   0.063                 .1236334
       kstock |   .3798827   .0174874    21.72   0.000                 .5274191
 _IcomXksto_2 |    .028188   .0673826     0.42   0.676                 .0131362
 _IcomXksto_3 |  -.2436443   .0442144    -5.51   0.000                -.1607756
 _IcomXksto_4 |  -.0767067   .0934675    -0.82   0.413                -.0177305
 _IcomXksto_5 |  -.3578027   .0559295    -6.40   0.000                -.2605544
 _IcomXksto_6 |  -.2148316   .1549131    -1.39   0.167                -.0373009
 _IcomXksto_7 |  -.2562131   .0827691    -3.10   0.002                 -.121073
 _IcomXksto_8 |  -.4273763   .1666695    -2.56   0.011                 -.063353
 _IcomXksto_9 |  -.3129159   .1105414    -2.83   0.005                -.1358529
_IcomXksto_10 |   .1019809   3.237561     0.03   0.975                 .0009578
        _cons |  -96.42841   43.24391    -2.23   0.027                        .
-------------------------------------------------------------------------------



. mat list e(beta)

e(beta)[1,21]
          mvalue   _Icompany_2   _Icompany_3   _Icompany_4   _Icompany_5   _Icompany_6   _Icompany_7   _Icompany_8   _Icompany_9  _Icompany_10
y1     .64068651     .24704393    -.08460733     .10056184     .17059168     .12514662     .12375522     .10049417     .11523756      .1236334

          kstock  _IcomXksto_2  _IcomXksto_3  _IcomXksto_4  _IcomXksto_5  _IcomXksto_6  _IcomXksto_7  _IcomXksto_8  _IcomXksto_9  _IcomXkst~10
y1     .52741909     .01313622    -.16077563    -.01773047    -.26055436     -.0373009    -.12107297    -.06335298    -.13585291     .00095784

           _cons
y1            .z

Now you have the coefficients - just named differently.

[Annette Popp]

Hi, Andrew,

One final THANK YOU for your assistance. Below is the code that allowed me to capture the standardized coefficients:

xi: reg DV i.gvkey|x1 i.fiscal_quarter|x1, nocons beta

esttab, beta
mat beta=e(beta) //create matrix "beta" which contains standardized coefficients
mat li beta

gen x1_firm=. 
levelsof gvkey, local(firms)
foreach num of numlist `firms' {
replace x1_firm= beta[1,colnumb(beta,"_IgvkXx1_`num'")] if gvkey==`num'
}

Best,
Annette