Constraining panel data regression to deal with multicolinearity

[Ruben Jakobs]

Dear All,

I'm struggling with the following problem. I have a panel dataset with return and marketcap data on various securities. Besides I have dummies for industry and country. See sample below:

input int(date _j) double return long marketcap byte industry str14 country
14252 295 -.029411764705882495  207874 3 "Austria"
14259 319  -.03891233005157064  552000 2 "Austria"
14266 339 -.025473071324599684 4299390 7 "Portugal"
14273 301                    0  609427 8 "Portugal"
14280 327                    .  130248 3 "Germany"
14287 319  -.08069414316702818  552000 2 "Germany"
14294 307 -.004160887656033322  228750 8 "France"
14301 337                    0   46500 8 "France"

I want to run a regression with a dummy for all countries and industries without omitting dummies. I want to realize this by restricting my regression such that the sum of all industry dummy betas times their number of securities in that specific industry is zero, and the same for all country dummy betas. Mathematically this solves the problem of multicollinearity only I don't know how to realize this in stata.

I already tried the following code:

bysort _j: drop if industry==. 

levelsof country1, local(country1)
levelsof industry, local(industry)

local country1_constraint 0
local industry_constraint 0

foreach c of local country1 {
    count if country1 == `c'
    local country1_constraint `country1_constraint' + `r(N)'*cc`c'
    gen byte cc`c' = `c'.country1
}

foreach i of local industry {
    count if industry == `i'
    local industry_constraint `industry_constraint' + `r(N)'*ii`i'
    gen byte ii`i' = `i'.industry
}
display `"`industry_constraint'"'

constraint def 1 `country1_constraint' = 0
constraint def 2 `industry_constraint' = 0

cnsreg ret cc* ii*, noconstant constraints(1 2)

The problem with this code is that it does not work for panel data and that it still omits two dummies, one industry and one country.

Perhaps some of you can help me with this interesting case?

[Ruben Jakobs]

FYI this is the output of my code:

cnsreg ret cc* ii*, noconstant constraints(1 2)
note: cc12 omitted because of collinearity
note: ii9 omitted because of collinearity

Constrained linear regression                   Number of obs     =  1,318,853
                                                F(  18,1318835)   =      32.37
                                                Prob > F          =     0.0000
                                                Root MSE          =     0.0570

 ( 1)  46463*cc1 + 87208*cc2 + 47568*cc3 + 237840*cc4 + 236090*cc5 + 48559*cc6 +
       33694*cc7 + 145677*cc8 + 94145*cc9 + 44595*cc10 + 101082*cc11 +
       518293*o.cc12 = 0
 ( 2)  44581*ii0 + 98129*ii1 + 340901*ii2 + 193278*ii3 + 96144*ii4 + 208134*ii5 +
       27733*ii6 + 56496*ii7 + 472727*ii8 + 103091*o.ii9 = 0
------------------------------------------------------------------------------
      return |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         cc1 |   .0003957   .0002856     1.39   0.166    -.0001641    .0009556
         cc2 |   .0000548   .0002046     0.27   0.789    -.0003461    .0004557
         cc3 |   .0005556   .0002751     2.02   0.043     .0000163    .0010948
         cc4 |   .0009013   .0001129     7.98   0.000       .00068    .0011226
         cc5 |   .0009292   .0001164     7.98   0.000      .000701    .0011574
         cc6 |   .0003177   .0002664     1.19   0.233    -.0002046    .0008399
         cc7 |   .0009946   .0003508     2.84   0.005      .000307    .0016822
         cc8 |  -.0006696    .000161    -4.16   0.000    -.0009851   -.0003541
         cc9 |  -.0041605   .0001988   -20.92   0.000    -.0045502   -.0037707
        cc10 |   .0002611   .0002857     0.91   0.361    -.0002988    .0008211
        cc11 |  -.0005411   .0002012    -2.69   0.007    -.0009354   -.0001467
        cc12 |          0  (omitted)
         ii0 |   .0001002   .0002989     0.34   0.738    -.0004857    .0006861
         ii1 |   .0004428    .000195     2.27   0.023     .0000607    .0008249
         ii2 |   .0002788   .0000955     2.92   0.004     .0000917     .000466
         ii3 |   .0002778   .0001318     2.11   0.035     .0000195    .0005361
         ii4 |  -.0001704   .0002131    -0.80   0.424    -.0005881    .0002474
         ii5 |  -.0001667   .0001314    -1.27   0.205    -.0004243    .0000909
         ii6 |  -.0009099   .0003944    -2.31   0.021    -.0016829    -.000137
         ii7 |  -.0009552    .000261    -3.66   0.000    -.0014667   -.0004437
         ii8 |  -.0001405   .0000786    -1.79   0.074    -.0002944    .0000135
         ii9 |          0  (omitted)
------------------------------------------------------------------------------

[Nick Cox]

Cross-posted at https://stats.stackexchange.com/ques...lticolinearity

Please note our policy on cross-posting: You are asked to tell us about it.

[Ruben Jakobs]

Dear Nick Cox

my apologies for the inconvenience. Thank you for posting the link!

Is still hope the question gets answered.

Kind regards,

Ruben