Obtaining same coefficients on dummy variables from xtreg and reg

[Erdem Yilmaz]

Similar questions have popped up several times on the forum but I couldn't find an answer to what I am looking for...

I run simple regression with product code dummies and I get coeffcients on product code:

reg y x i.product_code, noconstant

But I have too many products and therefore too many product code dummies. Even I set mat size to be 11.000, it is not enough... Instead I want to use xtreg and obtain the same coeffcients. I know I could do:

xtset product_code
xtreg y x, fe
predict y_hat, u

But it does not give the same results. Is there a way of obtaining true coeffcients on product code dummies?

[Carlo Lazzaro]

Erdem:
have you tried using -areg- instead of -regress-?

. use "http://www.stata-press.com/data/r15/nlswork.dta"
. areg ln_wage i.idcode age if idcode<=5, abs(idcode) vce(cluster idcode)
note: 2.idcode omitted because of collinearity
note: 3.idcode omitted because of collinearity
note: 4.idcode omitted because of collinearity
note: 5.idcode omitted because of collinearity

Linear regression, absorbing indicators         Number of obs     =         61
Absorbed variable: idcode                       No. of categories =          5
                                                F(   1,      4)   =       0.64
                                                Prob > F          =     0.4676
                                                R-squared         =     0.3281
                                                Adj R-squared     =     0.2670
                                                Root MSE          =     0.3029

                                 (Std. Err. adjusted for 5 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      idcode |
          2  |          0  (omitted)
          3  |          0  (omitted)
          4  |          0  (omitted)
          5  |          0  (omitted)
             |
         age |   .0151366   .0188793     0.80   0.468    -.0372807    .0675539
       _cons |   1.374028   .5515226     2.49   0.067    -.1572444      2.9053
------------------------------------------------------------------------------

. xtreg ln_wage age if idcode<=5, fe

Fixed-effects (within) regression               Number of obs     =         61
Group variable: idcode                          Number of groups  =          5

R-sq:                                           Obs per group:
     within  = 0.0899                                         min =         11
     between = 0.0141                                         avg =       12.2
     overall = 0.0408                                         max =         15

                                                F(1,55)           =       5.43
corr(u_i, Xb)  = -0.1406                        Prob > F          =     0.0234

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0151366   .0064937     2.33   0.023     .0021228    .0281503
       _cons |   1.374028   .1936272     7.10   0.000     .9859904    1.762066
-------------+----------------------------------------------------------------
     sigma_u |  .20406388
     sigma_e |  .30293713
         rho |  .31212907   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4, 55) = 5.88                       Prob > F = 0.0005


.

[daniel klein]

I doubt that you will learn anything from looking at 11,000 coefficients, but you will have to judge how useful that approach really is. Anyway, when you type

reg y x i.product_code

Stata will omit one of the product_code indicator variables (typically the first) because it is collinear with the constant term. Hence, the coefficients from your first model represent the difference to the omitted product_code. To replicate these coefficients you want

xtreg y x i.product_code
predict u , u
sort product_code
replace u = u-u[1] if (_n < 1)

I do not know what you mean by "true" coefficients but when you are referring to coefficients that are not relative to the omitted reference, then you are already looking at what you want.

Following up on Carlo's suggestion, I believe that

areg ...
predict d , d

will give you the same results that you get after regress, when you include the indicators, manually.

Best
Daniel

[Erdem Yilmaz]

Actually my coefficients of interests are ones that are on the product code. Let me make it more explicit:

      Source |       SS           df       MS      Number of obs   =        78
-------------+----------------------------------   F(31, 47)       =     21.33
       Model |  95.8415874        31  3.09166411   Prob > F        =    0.0000
    Residual |  6.81388421        47   .14497626   R-squared       =    0.9336
-------------+----------------------------------   Adj R-squared   =    0.8898
       Total |  102.655472        78  1.31609579   Root MSE        =    .38076

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |   .0794534   .0582508     1.36   0.179    -.0377321    .1966389
             |
product_code |
   11000040  |   .7680966   .3064657     2.51   0.016     .1515671    1.384626
   11000098  |   .9083795   .2845688     3.19   0.003     .3359008    1.480858
   11000133  |   .8863397   .3341671     2.65   0.011     .2140823    1.558597
   11000138  |   .5385099   .3756782     1.43   0.158    -.2172571    1.294277
   11000171  |   .4858168   .4035712     1.20   0.235    -.3260637    1.297697
   11000174  |   1.037059   .3256593     3.18   0.003     .3819173    1.692201
   11000232  |   .5927253   .3491215     1.70   0.096    -.1096166    1.295067
   11000260  |   .5511151   .3692924     1.49   0.142    -.1918053    1.294036
   11000289  |   .6951976   .3458356     2.01   0.050    -.0005339    1.390929
   11000332  |   .8943599   .3709671     2.41   0.020     .1480703    1.640649
   11000357  |   .5956999   .3477373     1.71   0.093    -.1038572    1.295257
   11000424  |   .9345632    .351342     2.66   0.011     .2277543    1.641372
   11000474  |   1.016387   .3369966     3.02   0.004      .338437    1.694336
   11000514  |   .9097961   .2837978     3.21   0.002     .3388686    1.480724
   11000583  |   .8566272   .3905143     2.19   0.033     .0710138    1.642241
   11000640  |   .5362127   .3768546     1.42   0.161     -.221921    1.294346
   11000654  |   .9761923   .3862906     2.53   0.015     .1990758    1.753309
   11000786  |   .5888021   .3509596     1.68   0.100    -.1172377    1.294842
   11000850  |   .7574469   .3119561     2.43   0.019     .1298723    1.385022
   11000936  |   .9218053   .3025017     3.05   0.004     .3132505     1.53036
   11000944  |   .5815607   .3543886     1.64   0.107    -.1313772    1.294499
   11000952  |   .7414235   .3203981     2.31   0.025     .0968656    1.385981
   11000968  |   .5705761   .3596773     1.59   0.119    -.1530013    1.294154
   11000988  |   .8894636   .2950223     3.01   0.004     .2959554    1.482972
   11001038  |   .5914404    .349722     1.69   0.097    -.1121096     1.29499
   11001057  |   1.029517   .3297602     3.12   0.003      .366125    1.692909
   11001060  |   .4931866   .3995625     1.23   0.223    -.3106295    1.297003
   11001109  |   .7956432   .3232787     2.46   0.018     .1452903    1.445996
   11001124  |   .9478137    .345181     2.75   0.009     .2533992    1.642228
   11001179  |   .6126812   .3399947     1.80   0.078       -.0713    1.296662
------------------------------------------------------------------------------

I want to obtain same coefficients on the product codes from xtreg or another alternative

[Erdem Yilmaz]

I think I got it, thank you very much!

[Carlo Lazzaro]

Erdem:
elaborating on previous replies to your original post, you may probably try yourself and compare what -xtreg,fe- and -areg- give you back.
This is the only practical advice that springs to my mind, as no interested listers can challenge with this stuff without a -dataex- example/excerpt.

PS: Crossed with Erdem's reply, who refer he've made it. I would encourage Erdam to post his fix, as other listers may benefit from it.

[Erdem Yilmaz]

Dear Carlo,
Actually I was referring o coefficients that are not relative to the omitted reference, and based on Daniel's explanation,

 
 areg ... predict d , d

was what I wanted.

[Carlo Lazzaro]

Erdem:
sorry for mispelling your name in my previous reply and thanks for sharing what you did.