[Abdul Sazali]

Hi Carlo Lazzaro, I have to deal with cross-sectional dependence and also endogeneity issue. I was trying to apply DK Standard Error with Instrumental Variable, but not successful yet. Could you please suggest me the method and stata command to handle these two issues?

Many thanks,
Abdul

[Carlo Lazzaro]

Abdul:
as per FAQ, please post what you typed and what Stata gave you back. Thanks.

[Abdul Sazali]

Hi Carlo Lazzaro, thank you very much for responding to my question and sorry for the delayed response as I didn't receive any notification.

I use Stata 18 to run a DID fixed effects regression model with panel data to estimate the effects of various variables on average fare variable "LnFare". To address the endogeneity issue, I use 2SLS using two instrumental variable (IV) "lnpop" and "lntrade" for the endogenous independent variable "LnPax". Here is the code that I use:

. xtivreg lnfare (lnpax = lnpop lntrade) asam totalcarriers desigcarriers fscper lngdp countryfuel atii i.year, fe vce(ro
> bust)

Fixed-effects (within) IV regression            Number of obs     =      5,032
Group variable: routeid                         Number of groups  =        629

R-squared:                                      Obs per group:
     Within  =      .                                         min =          8
     Between = 0.0121                                         avg =        8.0
     Overall = 0.0015                                         max =          8


                                                Wald chi2(15)     =   33619.84
corr(u_i, Xb) = -0.6653                         Prob > chi2       =     0.0000

                               (Std. err. adjusted for 629 clusters in routeid)
-------------------------------------------------------------------------------
              |               Robust
       lnfare | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
--------------+----------------------------------------------------------------
        lnpax |   .5087595    .322941     1.58   0.115    -.1241932    1.141712
         asam |  -.0898262   .0396187    -2.27   0.023    -.1674775   -.0121749
totalcarriers |  -.0583593    .031977    -1.83   0.068     -.121033    .0043143
desigcarriers |  -.0613801   .0325806    -1.88   0.060     -.125237    .0024767
       fscper |   .0023645   .0011204     2.11   0.035     .0001686    .0045604
        lngdp |  -.2661736   .1708156    -1.56   0.119    -.6009659    .0686188
  countryfuel |  -.1371823   .0428347    -3.20   0.001    -.2211367   -.0532279
         atii |  -.0119196   .0058801    -2.03   0.043    -.0234443   -.0003948
              |
         year |
        2013  |  -.1701968   .0547684    -3.11   0.002    -.2775408   -.0628527
        2014  |  -.2884796   .0704503    -4.09   0.000    -.4265597   -.1503994
        2015  |  -.5909791   .1349744    -4.38   0.000    -.8555241   -.3264342
        2016  |  -.6658244   .1440267    -4.62   0.000    -.9481116   -.3835373
        2017  |   -.631819   .1415059    -4.46   0.000    -.9091655   -.3544725
        2018  |  -.5676029   .1322243    -4.29   0.000    -.8267579    -.308448
        2019  |  -.6477493    .137719    -4.70   0.000    -.9176736    -.377825
              |
        _cons |   3.165659   2.092094     1.51   0.130    -.9347709    7.266089
--------------+----------------------------------------------------------------
      sigma_u |  .68559818
      sigma_e |  .24511511
          rho |  .88666584   (fraction of variance due to u_i)
-------------------------------------------------------------------------------
Endogenous: lnpax
Exogenous:  asam totalcarriers desigcarriers fscper lngdp countryfuel atii
            2013.year 2014.year 2015.year 2016.year 2017.year 2018.year
            2019.year lnpop lntrade

. 
end of do-file

Due to the presence of cross-sectional dependence, I am addressing this issue using Driscoll and Kraay standard errors. Therefore, I want to combine the instrumental variable with DK standard error.
I am using the following code to combine those two models:

. xtscc lnfare (lnpax = lnpop lntrade) asam totalcarriers desigcarriers fscper lngdp countryfuel atii i.year, fe lag(7)
parentheses unbalanced
r(132);

end of do-file

I assume that -xtscc- does not support 2SLS directly. I am trying to solve the problem by using the fitted value of the endogeneous variable "LnPax" using the following code:

. reg lnpax lnpop lntrade

      Source |       SS           df       MS      Number of obs   =     5,032
-------------+----------------------------------   F(2, 5029)      =    398.67
       Model |  1028.50044         2  514.250218   Prob > F        =    0.0000
    Residual |  6487.01765     5,029  1.28992198   R-squared       =    0.1369
-------------+----------------------------------   Adj R-squared   =    0.1365
       Total |  7515.51809     5,031   1.4938418   Root MSE        =    1.1357

------------------------------------------------------------------------------
       lnpax | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       lnpop |   .2790867    .027533    10.14   0.000       .22511    .3330634
     lntrade |   .1553236   .0083099    18.69   0.000     .1390326    .1716145
       _cons |   5.081224   .4201694    12.09   0.000     4.257509    5.904939
------------------------------------------------------------------------------

. 
. predict lnpax_hat, xb

. 
. xtscc lnfare lnpax_hat asam  totalcarriers desigcarriers fscper lngdp countryfuel atii ttci i.year, fe lag(7)

Regression with Driscoll-Kraay standard errors   Number of obs     =      5032
Method: Fixed-effects regression                 Number of groups  =       629
Group variable (i): routeid                      F( 16,     7)     =  11181.27
maximum lag: 7                                   Prob > F          =    0.0000
                                                 within R-squared  =    0.3708

-------------------------------------------------------------------------------
              |             Drisc/Kraay
       lnfare | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
--------------+----------------------------------------------------------------
    lnpax_hat |   .3538949   .0937294     3.78   0.007       .13226    .5755298
         asam |  -.0406039   .0062793    -6.47   0.000     -.055452   -.0257557
totalcarriers |  -.0115533   .0045423    -2.54   0.038    -.0222942   -.0008125
desigcarriers |  -.0203208    .002651    -7.67   0.000    -.0265895   -.0140521
       fscper |   .0006812   .0001883     3.62   0.009     .0002359    .0011266
        lngdp |   -.111765   .0497855    -2.24   0.060    -.2294891    .0059591
  countryfuel |  -.1129794   .0179368    -6.30   0.000    -.1553933   -.0705656
         atii |  -.0062816    .003112    -2.02   0.083    -.0136403    .0010771
         ttci |   .1281825   .0313967     4.08   0.005     .0539412    .2024238
              |
         year |
        2012  |          0  (empty)
        2013  |   -.085067   .0021041   -40.43   0.000    -.0900425   -.0800916
        2014  |  -.1569831   .0072683   -21.60   0.000    -.1741699   -.1397963
        2015  |  -.3878346    .029912   -12.97   0.000    -.4585653    -.317104
        2016  |  -.4711428   .0368914   -12.77   0.000    -.5583772   -.3839084
        2017  |  -.4301512    .031408   -13.70   0.000    -.5044193   -.3558831
        2018  |   -.379408   .0225107   -16.85   0.000    -.4326374   -.3261787
        2019  |  -.4560955   .0254834   -17.90   0.000    -.5163543   -.3958368
              |
        _cons |   2.484622   .9346575     2.66   0.033      .274508    4.694735
-------------------------------------------------------------------------------


. 
end of do-file

I am not confident at all with stages that I followed and I would like to ask your advice on:

1. Can Stata address endogeneity and cross-sectional dependence issues together in one model?
2. How to combine 2SLS IV with DK standard errors to handle the issues of endogeneity, cross-sectional dependence, heteroskedasticity, and autocorrelation?

Thank you very much.

Best,
Abdul

[Carlo Lazzaro]

Abdul:
see if JanDitzen 's -xtdcce2- module can help you out.

[JanDitzen]

I would be careful mixing the CCE estimator with IV regressions. See also my post here

[Carlo Lazzaro]

Jan:
I knew you posted on that, but was not able to recall the thread!
Thanks for chiming in.