large Coefficient and its solution

[Paris Rira]

Dear profs and colleagues,

I am running this model. As you can see the Coefficient and std. err are super large. Do you know what is the reason and what can be done about that?

input float ln_mig_firm double firm_age float(foreign_aff region) byte per float(sector immi_sh S_emplo_sh impu_sh_origin S_emplo_iv)
 .6931472   3 1 3 0  9 .06990359 0 .024657136 0
2.0794415 151 0 1 0  3 .01748677 0 .019646525 0
1.0986123  85 1 3 0  7 .06990359 0 .024657136 0
1.0986123  38 1 3 0  7 .06990359 0 .024657136 0
1.0986123  37 1 3 0  6 .06990359 0 .024657136 0
1.3862944  81 1 2 0  3 .03521399 0 .018607123 0
 .6931472  40 1 1 0  7 .01748677 0 .019646525 0
 .6931472  53 1 5 0  3 .05653952 0 .005587324 0
  1.94591  54 1 2 0  3 .03521399 0 .018607123 0
 .6931472  52 1 3 0 13 .06990359 0 .024657136 0
 .6931472  53 0 1 0  7 .01748677 0 .019646525 0
2.0794415  69 1 1 0  3 .01748677 0 .019646525 0
1.7917595  40 1 1 0  3 .01748677 0 .019646525 0
 2.944439  39 1 3 0  9 .06990359 0 .024657136 0
1.3862944  51 1 1 0  3 .01748677 0 .019646525 0
 3.367296  69 1 3 0  6 .06990359 0 .024657136 0
2.1972246  52 1 1 0  6 .01748677 0 .019646525 0
 3.178054  37 1 3 0  6 .06990359 0 .024657136 0
 .6931472  39 1 3 0  3 .06990359 0 .024657136 0
 1.609438  22 1 3 0  9 .06990359 0 .024657136 0
 .6931472  47 0 1 0  7 .01748677 0 .019646525 0
1.0986123  90 1 2 0  7 .03521399 0 .018607123 0
 1.609438  43 1 4 0 13 .15849853 0 .010140276 0
1.0986123  51 1 2 0 11 .03521399 0 .018607123 0
 .6931472  61 1 1 0  7 .01748677 0 .019646525 0
1.0986123  39 1 3 0  3 .06990359 0 .024657136 0
2.6390574  37 1 2 0  3 .03521399 0 .018607123 0
  1.94591  36 1 2 0  3 .03521399 0 .018607123 0
 2.397895  81 1 2 0  3 .03521399 0 .018607123 0
1.0986123  56 1 1 0  7 .01748677 0 .019646525 0
 1.609438  40 1 1 0  3 .01748677 0 .019646525 0
3.4011974  71 1 3 0  9 .06990359 0 .024657136 0
2.0794415  38 1 3 0  7 .06990359 0 .024657136 0
 .6931472  44 1 1 0  3 .01748677 0 .019646525 0
 .6931472  36 1 2 0  3 .03521399 0 .018607123 0
 1.609438  40 1 1 0  3 .01748677 0 .019646525 0
 1.609438  44 0 3 0  3 .06990359 0 .024657136 0
 2.397895  45 1 3 0  3 .06990359 0 .024657136 0
2.6390574  45 1 2 0  3 .03521399 0 .018607123 0
1.0986123  46 1 3 0  9 .06990359 0 .024657136 0
 2.484907  46 0 1 0  3 .01748677 0 .019646525 0
xtivreg ln_mig_firm firm_age foreign_aff   i.region#i.per i.sector#i.per (immi_sh S_emplo_sh= impu_sh_origin S_emplo_iv ) , fe first vce(robust)


Fixed-effects (within) IV regression            Number of obs     =     15,213
Group variable: NPC_FIC                         Number of groups  =      3,998

R-squared:                                      Obs per group:
     Within  = 0.0810                                         min =          1
     Between = 0.0011                                         avg =        3.8
     Overall = 0.0001                                         max =         10


                                                Wald chi2(71)     =   55406.90
corr(u_i, Xb) = -0.5211                         Prob > chi2       =     0.0000

                            (Std. err. adjusted for 3,998 clusters in NPC_FIC)
------------------------------------------------------------------------------
             |               Robust
 ln_mig_firm | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
     immi_sh |   66.08293   5.802629    11.39   0.000     54.70999    77.45587
  S_emplo_sh |  -12.28756   9.261594    -1.33   0.185    -30.43995    5.864832
    firm_age |  -.0292598   .0076699    -3.81   0.000    -.0442925    -.014227
 foreign_aff |  -.1434471   .0831989    -1.72   0.085    -.3065139    .0196198
             |
  region#per |
        1 1  |  -.2850273    .253099    -1.13   0.260    -.7810923    .2110377

Cheers,
Paris

[George Ford]

In a linear model, the size of the coef depends on the scale of the variable. SE isn't large relative to coefficient.

[Paris Rira]

Dear Ford,

whats your suggestion to reduce the scales?

[George Ford]

rescaling of the Xs. multiply immi_sh by 100. and the coef will by 0.66.

Or, use margins to get the effect. It will account for the scale.

[Paris Rira]

what about STANDARDIZing VARIABLES ?

egen S_ln_mig_firm = std(ln_mig_firm)
egen S_firm_age = std(firm_age)
egen S_foreign_aff = std(foreign_aff)
egen S_immi_sh = std(immi_sh)

                                             F(23,3997)        =          .
corr(u_i, Xb) = -0.3411                         Prob > F          =          .

                             (Std. err. adjusted for 3,998 clusters in NPC_FIC)
-------------------------------------------------------------------------------
              |               Robust
S_ln_mig_firm | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
    S_immi_sh |  -.0867684   .0904104    -0.96   0.337    -.2640232    .0904863
   S_firm_age |  -.1856058   .1545148    -1.20   0.230     -.488541    .1173294
S_foreign_aff |  -.0547414    .030351    -1.80   0.071    -.1142463    .0047635
              |
       sector |
           6  |  -.3900656   .2201712    -1.77   0.077     -.821724    .0415927

am I allowed to do so?

[Maarten Buis]

No one will put you in jail for standardizing coefficients, but can you meaningfully interpret them. Standardizing is useful when your variable has no meaningful scale (e.g. some index), otherwise you should stay away from that as you will loose more than you will gain.

[George Ford]

Have you run it without the iv? Could be a problem with a bad IV. If the size is a lot different, then I'd start there.

[Paris Rira]

No one will put you in jail for standardizing coefficients, but can you meaningfully interpret them.

Dear Maarten, Thank you for getting back to me and good news about jail
The point is that independent variables do not have the same scales, one is between 0 and 1 others are between 1 to 10. By standardizing through the centering method I reach reasonable results kinda.

The second question arises, "How should I interpret the standardized coefficient"? Does the interpretation differ from the unstandardized one?

[Paris Rira]

Have you run it without the iv? Could be a problem with a bad IV.

Dear Ford,
The situation is mixed. First of all, your assumption of different scales is totally correct. Secondly, once I regress --xtreg ln_mig_firm immi_sh firm_age foreign_aff i.sector i.region i.year , fe robust--without IV the coefficients make sense.
So I dont know where is the problem exactly, Different scales or Bad IV or Both!

[Maarten Buis]

The point is that independent variables do not have the same scales, one is between 0 and 1 others are between 1 to 10.

Why would that be a problem? You just need to know what the scales mean, and interpret your coefficients correctly. It does not matter whether one number is bigger than the other, because you interpret coefficients at their own merrit not one compared to another.

[Paris Rira]

Actually it affects the coefficient. Please have a look at #1.
immi_sh | 66.08293 such a large number

[George Ford]

I think you got an IV problem if that big coef is absent in xtreg.

[Paris Rira]

Finding a proper IV is not easy indeed. This IV has already worked in another dependent variable with this new dependent variable does not .

[George Ford]

Might have a scale problem there too. You could study the first stage prediction. Probably a couple of outliers or something else strange.

[Maarten Buis]

Actually it affects the coefficient. Please have a look at #1.
immi_sh | 66.08293 such a large number

Ofcourse, and it should. But it does not matter, as long as you interpret it correctly. Assuming that the variable immi_sh is the share of immigrants, theoretically ranging from 0 (no immigrants) to 1 (everybody is an immigrant). In that case your interpretation is that your expected outcome changes by 66 (whatever the unit is) if you go from a no immigrant society to an all immigrant society. You consider the effect large, but that makes sense: the change in x is also pretty extreme...

As George Ford already mentioned in #4 it is probably easier to interpret if you first multiply immi_sh by 100 so you are talking about a percentage point change in immigrant share rather than going from no immigrants to all immigrants. That way your interpretation will be that your outcome changes 0.66 for a percentage point change in immigrant share. Notice that this is just a different way of saying the same thing, so the underlying model does not change even though the numbers change.

Standardizing has a couple of problems: now your interpretation is your outcome changes by b standard deviations for a standard deviation change in immigrant share. What does that mean? On top of that you are dealing with panel data: what standard deviation do you want to use? I strongly recommend you stay away from that can of worms.