with or without weight

[Paris Rira]

Dear Prof and colleagues,

I conducted two estimations, one with and one without weights. In the estimation without the weight, the coefficient is larger compared to the estimation with the weight. This difference raises questions about the appropriateness of the chosen weights. Shall I think that the weight is wrong? Which estimation I should consider as the reliable/ efficient one?
I discarded the entire output due to its length.

. reg lwage shr_immg i.year i.sk_rat_quartile i.Expgroup i.Expgroup#i.sk_rat_quartile i.Expgroup#i.year i.sk_rat_quartil
> e#i.year [aw= wieght],robust
(sum of wgt is 12,312,886)

Linear regression                               Number of obs     =        320
                                                F(131, 188)       =    4100.09
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9983
                                                Root MSE          =     .01257

------------------------------------------------------------------------------------------
                         |               Robust
                   lwage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                shr_immg |   .7652276   .4006971     1.91   0.058    -.0252125    1.555668
                         |
                    year |
                   2011  |  -.0247768   .0195741    -1.27   0.207    -.0633898    .0138363
                   2012  |   -.039046   .0174316    -2.24   0.026    -.0734328   -.0046593
                   2013  |  -.0569614   .0175539    -3.24   0.001    -.0915892   -.0223335
                   2014  |  -.0429618   .0191181    -2.25   0.026    -.0806753   -.0052482
                   2015  |  -.0377884   .0200167    -1.89   0.061    -.0772746    .0016977
                   2016  |  -.0172464   .0163993    -1.05   0.294    -.0495967    .0151039
                   2017  |   .0030977   .0195128     0.16   0.874    -.0353945    .0415898
                   2018  |    .055643   .0173336     3.21   0.002     .0214497    .0898364
                   2019  |   .0946934   .0193115     4.90   0.000     .0565983    .1327885
                         |
         sk_rat_quartile |
                      2  |   .0789576   .0084858     9.30   0.000      .062218    .0956972
                      3  |    .059397   .0150838     3.94   0.000     .0296418    .0891523
                      4  |   .4939467   .0197351    25.03   0.000      .455016    .5328775
                         |

Without weight:

  reg lwage shr_immg i.year i.sk_rat_quartile i.Expgroup i.Expgroup#i.sk_rat_quartile i.Expgroup#i.year i.sk_rat_quarti
> le#i.year ,robust

Linear regression                               Number of obs     =        320
                                                F(131, 188)       =    4013.33
                                                Prob > F          =     0.0000
                                                R-squared         =     0.9981
                                                Root MSE          =     .01405

------------------------------------------------------------------------------------------
                         |               Robust
                   lwage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------------------+----------------------------------------------------------------
                shr_immg |   1.353097   .4160027     3.25   0.001     .5324644     2.17373
                         |
                    year |
                   2011  |  -.0213799   .0190928    -1.12   0.264    -.0590435    .0162837
                   2012  |   -.029565   .0169838    -1.74   0.083    -.0630684    .0039384
                   2013  |  -.0462414   .0173351    -2.67   0.008    -.0804376   -.0120451
                   2014  |  -.0317497    .019167    -1.66   0.099    -.0695597    .0060603
                   2015  |  -.0277666   .0202777    -1.37   0.173    -.0677676    .0122344
                   2016  |  -.0088269   .0166888    -0.53   0.597    -.0417483    .0240945
                   2017  |   .0113036   .0191693     0.59   0.556     -.026511    .0491182
                   2018  |   .0542644   .0177676     3.05   0.003     .0192151    .0893138
                   2019  |   .0776262   .0211254     3.67   0.000      .035953    .1192994
                         |
         sk_rat_quartile |
                      2  |   .0686419   .0104295     6.58   0.000      .048068    .0892158
                      3  |   .0560242   .0160501     3.49   0.001     .0243629    .0876856
                      4  |   .5036946   .0187571    26.85   0.000     .4666933     .540696
                         |

Any ideas appreciated.

Cheers,
Paris

[Leonardo Guizzetti]

Weighted versus unweighted estimates are naturally going to be different. We don’t have enough information to guide you as to which is more appropriate.

What are the weights for? For example, are they cluster weights, something else? It’s likely not frequency weights or you would have used fweights instead.

What is the question you are trying to answer (in words, not syntax or math)? Some questions are more naturally answered by weighting.

[Paris Rira]

Dear Leonardo,

The regression is weighted by the sample size which is workers. The dep var is log wage of workers and indep is the share of immigrants. My question is the heterscadasticy issue can be solved solely by vce(robust)? if so, why do papers apply weight?

. hettest   shr_immg

Breusch–Pagan/Cook–Weisberg test for heteroskedasticity 
Assumption: Normal error terms
Variable: shr_immg

H0: Constant variance

    chi2(1) =   3.29
Prob > chi2 = 0.0699

So I use robust and weight to correct the heterscedasticity. While I realized that the unweighted one is larger, so I need to explain why it happens shall I drop the weight, or the correct cofficient is given by weight?

[Carlo Lazzaro]

Paris:
I would add what follows to Leonardo's helpful suggestions:
1) you have a sky-rocketing R_sq. Therefore, you are possibly overifitting your regression;
2) yes, heteoskedasticity can be dealt with -robust- standard errors (see the excellent teaching notes on this topic by Richard Williams at Heteroskedasticity (nd.edu)
3) once you have applied -robust- there's no need to re-run -hettest-, as the null of no heteroskedasticity would be rejected again, because -robust- changes standard errors, not residuals.

[Paris Rira]

Prof Carlo,

You are right, R is pretty high, though I should follow the literature which a lot of them use the same wage equation. If I drop any vars or change the specification, I must explain why, because of high R?! Is it an acceptable answer to referees?
Because the model has been organized through complex stratification i.e education -experience groups etc, it might need to use weight ...

[Maarten Buis]

In order for a sample to say something about a population, the sample needs be representative of a population. A "simple" way of achieving that is to draw the sample randomly. The problem is that a simple random sample is in practice everything but simple. So in practice, not everybody in the population gets the same chance of being included in the sample, and as a result the sample no longer represents the population. Weights are typically employed to correct that bias. But, as always, it is not that easy. You could also have weights to correct for intentional over-sampling of groups, or weights to correct for non-response. You need to decide what your unit of analysis is, e.g. is it households or individuals. This again influences what weight you want to use. For international comparisons: do you want to give each country the same weight or do you want to weight by population and if so, what population?

[Paris Rira]

Prof Buis,

The sample is the whole workers of firms in a country. I try to estimate the impact of immigrants on native wages. So the weight is native workers which are categorized into education-experience groups, 4 Education groups, 8 Experience groups, for 10 years. So its completely designed based on common attributes of workers. Workers in each of 4 groups, have the same characteristics. I believe that weight is a proper option as its customary in this field. The different results obtained through weighted and unweighted, made me think about it why it happened.

[Carlo Lazzaro]

Paris:
did you perform -linktest- after -regress-?

[Paris Rira]

Here it is:

. linktest

      Source |       SS           df       MS      Number of obs   =       320
-------------+----------------------------------   F(2, 317)       =  82235.76
       Model |  19.2571094         2   9.6285547   Prob > F        =    0.0000
    Residual |   .03711587       317  .000117085   R-squared       =    0.9981
-------------+----------------------------------   Adj R-squared   =    0.9981
       Total |  19.2942253       319  .060483465   Root MSE        =    .01082

------------------------------------------------------------------------------
       lwage | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        _hat |   .9788981   .1199436     8.16   0.000      .742912    1.214884
      _hatsq |   .0015595   .0088621     0.18   0.860    -.0158765    .0189954
       _cons |   .0712918   .4054803     0.18   0.861    -.7264809    .8690645
------------------------------------------------------------------------------

[Carlo Lazzaro]

Paris:
your model seems OK.
I do not see other issues, but the very high R_Sq.