[George Ford]

The "nois" would go on line 15 of post #54.

[Jeff Wooldridge]

A few comments on this. First, our motivation for the test for the case when there are many higher-level fixed effects. (Leslie saw this issue come up in a seminar.) In our example, there are almost 500 school districts and about 1,700 schools. However, the mechanics of the test are the same even with a small number of groups, G, as in Paris' application.

With so few groups and many firms, it's not surprising to me the test rejects. The default is that heterogeneity at the individual (firm) level is correlated with the explanatory variables, but with lots of group FEs, maybe that won't be true. We found even with G=467, N=1,683 that we strong rejected the null that district level FEs is sufficient.

In Paris' case, I don't think one can justify clustering by sector because G = 8. Clustering at the firm level is what I would do. It's unlikely to change the outcome.

[Paris Rira]

You’d think immig matters more to certain sectors.

Yes, it is the case. In some sectors they are more than others.

or run the model sector by sector to see if the results differ much.

Since the question of the research is Firm-level, I would not do the estimation at the Sector level.

I believe that Prof Jeff is right, with a few sectors, it won't happen, while the firmFE already have been approved I won't be able even to explain to a referee why I would not go with FirmFE.

[George Ford]

immi_sh c.immi_sh#i.sector

[Paris Rira]

The results donot make a difference, also collinearity

Warning - endogenous variable(s) collinear with instruments
Vars now exogenous: immi_sh

foreach s in  3 6 7 9 10 11 12 13 {
    gen immi_sh_sector`s' = immi_sh * (sector == `s')
}

* Run the regression with all interaction terms
xtivreg2 ln_labor_productivity_w (immi_sh = IV_normalized) immi_sh_sector7 immi_sh_sector3 immi_sh_sector6 immi_sh_sector9 immi_sh_sector10 immi_sh_sector11 immi_sh_sector12 immi_sh_sector13  share_9 share_12 share_uni logsize lavg_firm_age lage yr_2 yr_3 yr_4 yr_5 yr_6 yr_7 yr_8 yr_9 yr_10, fe first robust

[Paris Rira]

I did also for each sector separately, 2 sectors are significant, the rest insignificant and small values.

[George Ford]

Firm fixed effects?

If so, you've got at least something.

[George Ford]

I'd run without instrumental variables too. cover the bases.

[Paris Rira]

Firm fixed effects?

If so, you've got at least something.

Yes, Prof. I have ran only with xtreg,fe since a couple of days ago which it has been proved.

[Paris Rira]

I'd run without instrumental variables too. cover the bases.

with IV or without IV does not make a difference. Apparently, I have to accept that immigration has no impact on productivity in Portugal!

[George Ford]

If you run with reghdfe including the firm and year FE, with different coefficients for each sector, and get some effects on a few of them, I think that's a useful result.

[Paris Rira]

for each sector the result of :

reghdfe ln_labor_productivity_w immi_sh  share_9 share_12 share_uni   logsize lavg_firm_age lage, a(year id) vce (robust)

is equal to this :

xtreg ln_labor_productivity_w immi_sh  share_9 share_12 share_uni  logsize lavg_firm_age lage i.year, fe

[George Ford]

 
 reghdfe ln_labor_productivity_w  c.immi_sh#i.sector logsize lavg_firm_age lage, absorb(id sector year) cluster(id)

[Paris Rira]

. reghdfe ln_labor_productivity_w c.immi_sh#i.sector share_9 share_12 share_uni logsize lavg_firm_age lage, a(sector year id) cl(i
> d)
(dropped 50256 singleton observations)
(MWFE estimator converged in 19 iterations)

HDFE Linear regression                            Number of obs   =  1,464,334
Absorbing 3 HDFE groups                           F(  14, 237899) =     157.65
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.7020
                                                  Adj R-squared   =     0.6441
                                                  Within R-sq.    =     0.0041
Number of clusters (id)      =    237,900         Root MSE        =     0.5279

                                   (Std. Err. adjusted for 237,900 clusters in id)
----------------------------------------------------------------------------------
                 |               Robust
ln_labor_produ~w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
sector#c.immi_sh |
              3  |   .0219473   .0352178     0.62   0.533    -.0470786    .0909732
              6  |  -.0654139    .025195    -2.60   0.009    -.1147954   -.0160325
              7  |   -.043856   .0217781    -2.01   0.044    -.0865406   -.0011714
              9  |   .0611481   .0204281     2.99   0.003     .0211095    .1011866
             10  |  -.0598753    .081568    -0.73   0.463    -.2197464    .0999959
             11  |   .0159053   .0532558     0.30   0.765    -.0884746    .1202853
             12  |  -.0376002   .0350577    -1.07   0.283    -.1063124     .031112
             13  |  -.0047025   .0400918    -0.12   0.907    -.0832813    .0738763
                 |
         share_9 |   .0720363   .0071816    10.03   0.000     .0579606     .086112
        share_12 |   .0764309   .0082528     9.26   0.000     .0602555    .0926062
       share_uni |   .0865986    .010264     8.44   0.000     .0664814    .1067158
         logsize |  -.0742474   .0023875   -31.10   0.000    -.0789269   -.0695679
   lavg_firm_age |   .0955467   .0026189    36.48   0.000     .0904137    .1006797
            lage |   .0101957   .0094043     1.08   0.278    -.0082365    .0286279
           _cons |   9.402414   .0381079   246.73   0.000     9.327724    9.477105
----------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
      sector |         8           1           7     |
        year |        10           1           9     |
          id |    237900      237900           0    *|
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

[George Ford]

what are share_9 share_12 share_uni? Aren't those interaction terms of immi_sh and sector? If so, leave them out.