Model diagnostics for three-dimensional panel data with reghdfe

Andrea Gimeno Solaz

Join Date: Oct 2024
Posts: 3

Model diagnostics for three-dimensional panel data with reghdfe

07 Oct 2024, 08:49

Hello! I am having some trouble running the necessary model diagnostics for a fixed effects regression undertaken with reghdfe for a three-dimensional panel dataset (index variables are reporting_econ_id, partner_econ_id and year). I first set up the panel structure of my dataset like this:

Code:

encode reportingecon, gen(reporting_econ_id)
encode partnerecon, gen(partner_econ_id)

egen panel_id = group(reporting_econ_id partner_econ_id)

xtset panel_id year

The resulting dataset looks like this:

Code:

 Observations:        12,200                  
    Variables:            65                  7 Oct 2024 08:40
-----------------------------------------------------------------------------------------
Variable      Storage   Display    Value
    name         type    format    label      Variable label
-----------------------------------------------------------------------------------------
partnerecon     str14   %14s                  PartnerEcon
reportingecon   str37   %37s                  ReportingEcon
agree           float   %9.0g                
year            int     %8.0g                 Year
idealpointdis~e float   %9.0g                 IdealPointDistance
region          str27   %27s                  
buildingprodu~x float   %9.0g                 Building Productive Capacity.x
economicinfra~x float   %9.0g                 Economic Infrastructure.x
tradepolicyre~x float   %9.0g                 Trade Policy & Regulations.x
traderelateda~x float   %8.0g                 Trade-related Adjustment.x
total_aftx      float   %9.0g                 Total_AfT.x
col_fr          byte    %8.0g                 COL_FR
col_uk          byte    %8.0g                 COL_UK
col_us          byte    %8.0g                 COL_US
col_jp          byte    %8.0g                 COL_JP
dist            float   %8.0g                
distcap         float   %8.0g                
distw           float   %8.0g                
distwces        float   %8.0g                
inflowsofasyl~s double  %10.0g                Inflows of asylum seekers
inflowsoffore~n long    %8.0g                 Inflows of foreign population
incomegroup     int     %8.0g                 IncomeGroup
hdi             double  %10.0g                
le              float   %9.0g                
mys             float   %8.0g                
gni_capita      double  %10.0g                
lldcs           byte    %8.0g                 LLDCs
count_interna~d int     %8.0g                
count_intrast~e int     %8.0g                
count_interst~e int     %8.0g                
share_world_m~h float   %8.0g                 Share_World_Merch
civ_liberties   byte    %8.0g                
pol_freedom     byte    %8.0g                
balanced_exp    float   %8.0g                 Balanced_EXP
balanced_imp    float   %8.0g                 Balanced_IMP
final_exp       float   %8.0g                 Final_EXP
final_imp       float   %8.0g                 Final_IMP
goodsexports    float   %8.0g                 GoodsExports
goodsimports    float   %8.0g                 GoodsImports
net_fdi         double  %8.0g                 Net_FDI
sum_total_aft   float   %8.0g                
other_aft       float   %8.0g                
net_oda         float   %8.0g                 Net_ODA
gdp             float   %8.0g                 GDP
natural_resou~s float   %8.0g                
reporting_eco~d long    %37.0g     reporting_econ_id
                                              ReportingEcon
partner_econ_id long    %14.0g     partner_econ_id
                                              PartnerEcon
panel_id        float   %9.0g                 group(reporting_econ_id partner_econ_id)
mean_totalaft   float   %9.0g                
ln_aft          float   %9.0g                
ln_gnicap       float   %9.0g                
ln_servicesexp  float   %9.0g                
ln_servicesimp  float   %9.0g                
ln_goodsexp     float   %9.0g                
ln_goodsimp     float   %9.0g                
ln_fdi          float   %9.0g                
ln_gdp          float   %9.0g                
ln_otheraft     float   %9.0g                
ln_oda          float   %9.0g                
ln_dist         float   %9.0g                
partner_us      float   %9.0g                
partner_jp      float   %9.0g                
partner_fr      float   %9.0g                
partner_uk      float   %9.0g                
partner_ge      float   %9.0g                
-----------------------------------------------------------------------------------------
Sorted by: panel_id  year

I run several nested models, all of which present a good (<0.001) F-statistic. I am presenting below the last model I run and its output:

Code:

reghdfe ln_aft ///
    c.hdi#i.partner_econ_id ///
    c.ln_gnicap#i.partner_econ_id ///
    c.pol_freedom#i.partner_econ_id ///
    lldcs#i.partner_econ_id ///
    c.share_world_merch#i.partner_econ_id ///
    c.count_internationalised#i.partner_econ_id ///
    c.count_intrastate#i.partner_econ_id ///
    c.agree#i.partner_econ_id ///
    c.ln_dist#i.partner_econ_id ///
    c.inflowsofforeignpopulation#i.partner_econ_id ///
    c.col_fr#i.partner_fr ///
    c.col_uk#i.partner_uk ///
    c.col_us#i.partner_us ///
    c.ln_servicesexp#i.partner_econ_id ///
    c.ln_servicesimp#i.partner_econ_id ///
    c.ln_goodsexp#i.partner_econ_id ///
    c.ln_goodsimp#i.partner_econ_id ///
    c.ln_fdi#i.partner_econ_id ///
    c.ln_gdp#i.partner_econ_id ///
    c.ln_otheraft#i.partner_econ_id ///
    c.ln_oda#i.partner_econ_id ///
    c.natural_resources#i.partner_econ_id, ///
    absorb(reporting_econ_id year) ///
    vce(cluster reporting_econ_id)

Code:

HDFE Linear regression                            Number of obs   =      3,394
Absorbing 2 HDFE groups                           F( 101,    105) =   21660.24
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.6215
                                                  Adj R-squared   =     0.5958
                                                  Within R-sq.    =     0.3635
Number of clusters (reporting_econ_id) =        106Root MSE       =     1.5892

                            (Std. err. adjusted for 106 clusters in reporting_econ_id)
--------------------------------------------------------------------------------------
                     |               Robust
              ln_aft | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------------+----------------------------------------------------------------
     partner_econ_id#|
               c.hdi |
             France  |  -8.365468   4.863386    -1.72   0.088    -18.00866    1.277727
            Germany  |   3.294893   4.579765     0.72   0.473    -5.785934    12.37572
              Japan  |  -.2702511   5.346708    -0.05   0.960    -10.87179    10.33128
     United Kingdom  |  -21.16168   8.192214    -2.58   0.011    -37.40532    -4.91803
      United States  |   3.296014   4.816464     0.68   0.495    -6.254144    12.84617
                     |
     partner_econ_id#|
         c.ln_gnicap |
             France  |   1.654401   .3692053     4.48   0.000     .9223349    2.386467
            Germany  |  -.2690675   .3143735    -0.86   0.394     -.892412     .354277
              Japan  |   .1885545   .4065309     0.46   0.644    -.6175211    .9946301
     United Kingdom  |   1.550292    .751632     2.06   0.042     .0599441    3.040639
      United States  |  -.1473826   .3312212    -0.44   0.657    -.8041331    .5093679
                     |
     partner_econ_id#|
       c.pol_freedom |
             France  |   -.020727   .1377542    -0.15   0.881    -.2938681    .2524141
            Germany  |  -.2221254    .093777    -2.37   0.020    -.4080678    -.036183
              Japan  |  -.1019459     .09783    -1.04   0.300    -.2959248     .092033
     United Kingdom  |  -.0557523   .2033243    -0.27   0.784    -.4589068    .3474023
      United States  |  -.0473356   .1130292    -0.42   0.676    -.2714517    .1767804
                     |
               lldcs#|
     partner_econ_id |
          0#Germany  |     19.686   8.013725     2.46   0.016     3.796268    35.57574
            0#Japan  |   33.09791   7.802076     4.24   0.000     17.62784    48.56799
   0#United Kingdom  |   14.82509   14.15851     1.05   0.297    -13.24861    42.89879
    0#United States  |   1.247056    8.29337     0.15   0.881    -15.19716    17.69128
           1#France  |  -2.582377   8.305405    -0.31   0.756    -19.05046    13.88571
          1#Germany  |    17.4672   7.124526     2.45   0.016      3.34058    31.59382
            1#Japan  |   30.54564    7.63674     4.00   0.000      15.4034    45.68789
   1#United Kingdom  |   15.82774   14.82191     1.07   0.288    -13.56137    45.21685
    1#United States  |          0  (omitted)
                     |
     partner_econ_id#|
 c.share_world_merch |
             France  |   5.06e-09   1.56e-09     3.25   0.002     1.97e-09    8.15e-09
            Germany  |   7.84e-09   1.87e-09     4.20   0.000     4.14e-09    1.15e-08
              Japan  |   1.33e-09   1.75e-09     0.76   0.450    -2.14e-09    4.80e-09
     United Kingdom  |   4.03e-09   2.98e-09     1.35   0.180    -1.89e-09    9.94e-09
      United States  |  -5.86e-10   1.88e-09    -0.31   0.756    -4.32e-09    3.15e-09
                     |
     partner_econ_id#|
                  c. |
count_internationa~d |
             France  |  -.1853612   .3224705    -0.57   0.567    -.8247606    .4540381
            Germany  |   .3177221   .2043412     1.55   0.123    -.0874488     .722893
              Japan  |  -1.002047   .3420969    -2.93   0.004    -1.680362   -.3237322
     United Kingdom  |   1.223445   .3890161     3.14   0.002     .4520983    1.994792
      United States  |   .3365063   .2292649     1.47   0.145    -.1180837    .7910963
                     |
     partner_econ_id#|
  c.count_intrastate |
             France  |  -.1750101   .2163461    -0.81   0.420    -.6039844    .2539642
            Germany  |  -.0597992   .1261983    -0.47   0.637    -.3100271    .1904287
              Japan  |   .1070002   .1399799     0.76   0.446     -.170554    .3845544
     United Kingdom  |   .0940048   .2631432     0.36   0.722    -.4277596    .6157693
      United States  |  -.0741203   .2729971    -0.27   0.787    -.6154232    .4671826
                     |
     partner_econ_id#|
             c.agree |
             France  |  -.3751798   2.000095    -0.19   0.852       -4.341     3.59064
            Germany  |  -.8791131   1.258728    -0.70   0.486    -3.374939    1.616713
              Japan  |  -3.347968   1.446109    -2.32   0.023    -6.215335   -.4806007
     United Kingdom  |  -7.730057   4.073688    -1.90   0.061    -15.80743    .3473138
      United States  |   1.982738    1.11721     1.77   0.079    -.2324823    4.197958
                     |
     partner_econ_id#|
           c.ln_dist |
             France  |    1.06597   .4135629     2.58   0.011     .2459514    1.885989
            Germany  |  -.2094744   .2356301    -0.89   0.376    -.6766853    .2577365
              Japan  |  -1.430836   .3959467    -3.61   0.000    -2.215925   -.6457466
     United Kingdom  |   3.303015    1.02918     3.21   0.002      1.26234    5.343689
      United States  |  -.3303684   .4735732    -0.70   0.487    -1.269377    .6086397
                     |
     partner_econ_id#|
                  c. |
inflowsofforeignpo~n |
             France  |   .0000397   .0000323     1.23   0.221    -.0000242    .0001037
            Germany  |  -4.63e-06   9.71e-06    -0.48   0.635    -.0000239    .0000146
              Japan  |   .0000239   .0000188     1.27   0.208    -.0000135    .0000612
     United Kingdom  |   .0000103    .000019     0.54   0.588    -.0000273    .0000479
      United States  |   1.34e-06   7.16e-06     0.19   0.852    -.0000129    .0000155
                     |
 partner_fr#c.col_fr |
                  0  |  -.0216491   .0117221    -1.85   0.068    -.0448919    .0015937
                  1  |          0  (omitted)
                     |
 partner_uk#c.col_uk |
                  0  |   .0311397   .0112371     2.77   0.007     .0088585    .0534208
                  1  |          0  (omitted)
                     |
 partner_us#c.col_us |
                  0  |  -.0453175   .0155515    -2.91   0.004    -.0761532   -.0144818
                  1  |          0  (omitted)
                     |
     partner_econ_id#|
    c.ln_servicesexp |
             France  |  -.1009793   .2092745    -0.48   0.630    -.5159319    .3139733
            Germany  |   -.207759   .1561096    -1.33   0.186    -.5172955    .1017776
              Japan  |  -.2755614   .1402912    -1.96   0.052    -.5537329    .0026101
     United Kingdom  |   .8352024    .433984     1.92   0.057    -.0253078    1.695713
      United States  |  -.1605652    .185467    -0.87   0.389     -.528312    .2071815
                     |
     partner_econ_id#|
    c.ln_servicesimp |
             France  |   .6009642   .3221383     1.87   0.065    -.0377766    1.239705
            Germany  |   .2302156   .1748801     1.32   0.191    -.1165393    .5769705
              Japan  |   .2120279   .1970995     1.08   0.285    -.1787841    .6028398
     United Kingdom  |  -1.694077   .4940615    -3.43   0.001     -2.67371   -.7144445
      United States  |  -.0054276   .1892335    -0.03   0.977    -.3806427    .3697875
                     |
     partner_econ_id#|
       c.ln_goodsexp |
             France  |   .1951882    .097819     2.00   0.049     .0012312    .3891453
            Germany  |   .0984622   .0580864     1.70   0.093    -.0167125    .2136368
              Japan  |   .0798342   .0472478     1.69   0.094    -.0138493    .1735178
     United Kingdom  |  -.1348263   .2461635    -0.55   0.585    -.6229231    .3532705
      United States  |   .0000854   .0625908     0.00   0.999    -.1240207    .1241915
                     |
     partner_econ_id#|
       c.ln_goodsimp |
             France  |   .1697972   .1846939     0.92   0.360    -.1964168    .5360111
            Germany  |   .3880155   .1473953     2.63   0.010     .0957578    .6802732
              Japan  |   .2614983   .1054035     2.48   0.015     .0525025     .470494
     United Kingdom  |   2.576976   .6400928     4.03   0.000     1.307791    3.846162
      United States  |   .1719541   .1727773     1.00   0.322    -.1706314    .5145395
                     |
     partner_econ_id#|
            c.ln_fdi |
             France  |  -.0145596   .1069726    -0.14   0.892    -.2266665    .1975473
            Germany  |   .1115391   .0939308     1.19   0.238    -.0747083    .2977864
              Japan  |   .0547202   .0833109     0.66   0.513      -.11047    .2199104
     United Kingdom  |  -.2255714   .2416279    -0.93   0.353    -.7046748    .2535321
      United States  |   .2981682   .0998416     2.99   0.004     .1002007    .4961356
                     |
     partner_econ_id#|
            c.ln_gdp |
             France  |   .2970983   .7400153     0.40   0.689    -1.170215    1.764412
            Germany  |   .3629671   .6773162     0.54   0.593    -.9800258     1.70596
              Japan  |   .6390817   .6335713     1.01   0.315    -.6171731    1.895337
     United Kingdom  |  -.2613469   .9532113    -0.27   0.784    -2.151389    1.628695
      United States  |   .7210528   .7093308     1.02   0.312    -.6854192    2.127525
                     |
     partner_econ_id#|
       c.ln_otheraft |
             France  |  -.3257992   .1550674    -2.10   0.038    -.6332691   -.0183292
            Germany  |  -.4180295   .1444829    -2.89   0.005    -.7045124   -.1315466
              Japan  |  -.3335356   .1180767    -2.82   0.006    -.5676599   -.0994112
     United Kingdom  |   .0687922   .3324009     0.21   0.836    -.5902974    .7278818
      United States  |  -.7653098    .162958    -4.70   0.000    -1.088425   -.4421941
                     |
     partner_econ_id#|
            c.ln_oda |
             France  |   .5525117   .1661286     3.33   0.001     .2231093    .8819141
            Germany  |   .4890086   .1321145     3.70   0.000     .2270501    .7509672
              Japan  |    .183862   .1384814     1.33   0.187    -.0907211    .4584451
     United Kingdom  |   .0938438   .2027709     0.46   0.644    -.3082134     .495901
      United States  |   .8958777   .2354309     3.81   0.000     .4290618    1.362694
                     |
     partner_econ_id#|
 c.natural_resources |
             France  |   .0266695   .0220096     1.21   0.228    -.0169715    .0703105
            Germany  |   .0160756   .0178215     0.90   0.369    -.0192611    .0514123
              Japan  |   .0079434   .0157231     0.51   0.614    -.0232325    .0391194
     United Kingdom  |   -.039139   .1104802    -0.35   0.724    -.2582009    .1799229
      United States  |   .0093805   .0170574     0.55   0.584    -.0244412    .0432021
                     |
               _cons |  -36.39202   14.46701    -2.52   0.013    -65.07744   -7.706611
--------------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------------+
       Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------------+---------------------------------------|
 reporting_econ_id |       106         106           0    *|
              year |        11           1          10     |
-----------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

However, I am now running into issues trying to run model diagnostics, such as B-P/LM test using xttest2 or Pasaran CD test using xtcsd. For xttest2, I receive the following error: "Error: too few common observations across panel to compute full rank VCE"; while for xtcsd I receive the following "Error: The panel is highly unbalanced. Not enough common observations across panel to perform Pesaran's test. Insufficient observations". I believe these erros might be due to the fact that my panel dataset has panel_id as the cross-section identifier. How can I fix these issues and still run my model diagnostics? Thank you in advance!

Last edited by Andrea Gimeno Solaz; 07 Oct 2024, 09:42.

Tags: None

Carlo Lazzaro

Join Date: Apr 2014
Posts: 17606

07 Oct 2024, 11:11

Andrea:
welcome to this forum.
Some comments about your query:
1) your model is very complicated;
2) in case of small T and large N, the Breusch-Pagan test is not valid;
3) the error message after -xtcsd- is due to your dataset. In addition, I am not clear with the way you created your -panelid-;
4) I would be more interested in ruing out misspecifications of the functional form of the regressand, replicating by hand the -linktest- approach, as you can see in the following toy-example:

Code:

. use "https://www.stata-press.com/data/r18/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. reghdfe ln_wage c.age##c.age, abs(idcode year) vce(cluster idcode)
(dropped 551 singleton observations)
(MWFE estimator converged in 8 iterations)

HDFE Linear regression                            Number of obs   =     27,959
Absorbing 2 HDFE groups                           F(   2,   4158) =      44.91
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.6593
                                                  Adj R-squared   =     0.5995
                                                  Within R-sq.    =     0.0115
Number of clusters (idcode)  =      4,159         Root MSE        =     0.3013

                             (Std. err. adjusted for 4,159 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0728746   .0136873     5.32   0.000     .0460402    .0997089
             |
 c.age#c.age |  -.0010113   .0001076    -9.39   0.000    -.0012224   -.0008003
             |
       _cons |   .4586164   .3651743     1.26   0.209    -.2573205    1.174553
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
      idcode |      4159        4159           0    *|
        year |        15           0          15     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

. predict fitted, xb
(24 missing values generated)

. gen sq_fitted=fitted^2
(24 missing values generated)

. reghdfe ln_wage fitted sq_fitted , abs(idcode year) vce(cluster idcode)
(dropped 551 singleton observations)
(MWFE estimator converged in 8 iterations)

HDFE Linear regression                            Number of obs   =     27,959
Absorbing 2 HDFE groups                           F(   2,   4158) =      55.72
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.6598
                                                  Adj R-squared   =     0.6001
                                                  Within R-sq.    =     0.0129
Number of clusters (idcode)  =      4,159         Root MSE        =     0.3011

                             (Std. err. adjusted for 4,159 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   6.536005   1.294478     5.05   0.000     3.998137    9.073873
   sq_fitted |  -1.730508    .404729    -4.28   0.000    -2.523993   -.9370228
       _cons |  -4.401739   1.037021    -4.24   0.000    -6.434853   -2.368624
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
      idcode |      4159        4159           0    *|
        year |        15           0          15     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

.

As expected, this toy-example shows misspecificaction as the -sq_fitted- term of the the auxiliary regression is highly significant.

Kind regards,
Carlo
(StataNow 18.5)

Comment

Andrea Gimeno Solaz

Join Date: Oct 2024

Posts: 3
#3

08 Oct 2024, 08:42

Dear Mr. Lazzaro, thank you very much for your response and your help. I understand the issue you describe about misspecifications of the functional form of the regression - I was then wondering what your suggestion would be for the best approach to deal with my dataset and the analysis I want to run. The dataset is three-dimensional as it compiles data from aid flows to several recipient countries (reporting_econ_id), by five different partner countries (partner_econ_id), and each combination of reporting-partner country contains time-series data (year) between 2005 and 2021.

My goal with this analysis is to explore whether the driving factors behind aid flows to reporting economies vary across the selected partner economies (hence, the interaction terms between all of my independent variables and the partner_econ_id variable).

Because of this three-dimensional structure, I was not able to set up the panel structure of the dataset as xtest reporting_econ_id year (because then I get an error saying there are repeated time observations). That is why I tried to go around this by creating the identifying variable panel_id, which groups reporting_econ_id and partner_econ_id together to create one unique identifier, and then I used this panel_id together with year to establish the panel data structure of the dataset.

Thank you very much again for your help.

All the best,

Andrea
Comment
Carlo Lazzaro

Join Date: Apr 2014

Posts: 17606
#4

08 Oct 2024, 10:07

Andrea:
thanks for clarifying,
You do not need to -xtset- your panel dataset with -timevar- (-panelid- only is mandatory), unless you're planning to use time-series commands (such as lags and leads) to analyse your data.
That said, you can still your -timevar- as a predcitor.

Kind regards,
Carlo
(StataNow 18.5)
Comment

Andrea Gimeno Solaz

Join Date: Oct 2024
Posts: 3

08 Oct 2024, 11:31

Dear Mr. Lazzaro,

Thank you very much for the clarification. So I replicated your example for manually reproducing the -linktest- approach, as you can see below:

Code:

 reghdfe ln_aft ///
>         c.hdi#i.partner_econ_id ///
>         c.ln_gnicap#i.partner_econ_id ///
>         c.pol_freedom#i.partner_econ_id ///
>         c.share_world_merch#i.partner_econ_id ///
>         c.count_internationalised#i.partner_econ_id ///
>         c.count_intrastate#i.partner_econ_id ///
>         c.agree#i.partner_econ_id ///
>         c.ln_dist#i.partner_econ_id ///
>         c.inflowsofforeignpopulation#i.partner_econ_id ///
>         c.col_fr#1.partner_econ_id ///
>         c.col_uk#4.partner_econ_id ///
>         c.col_us#5.partner_econ_id ///
>     c.ln_servicesexp#i.partner_econ_id ///
>         c.ln_servicesimp#i.partner_econ_id ///
>         c.ln_goodsexp#i.partner_econ_id ///
>         c.ln_goodsimp#i.partner_econ_id ///
>         c.ln_fdi#i.partner_econ_id ///
>         c.ln_gdp#i.partner_econ_id ///
>         c.ln_otheraft#i.partner_econ_id ///
>         c.ln_oda#i.partner_econ_id ///
>         c.natural_resources#i.partner_econ_id, ///
>     absorb(reporting_econ_id year) ///
>     vce(cluster reporting_econ_id)
(MWFE estimator converged in 5 iterations)

HDFE Linear regression                            Number of obs   =      3,394
Absorbing 2 HDFE groups                           F(  93,    105) =   26877.17
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.6043
                                                  Adj R-squared   =     0.5784
                                                  Within R-sq.    =     0.3344
Number of clusters (reporting_econ_id) =        106Root MSE       =     1.6231

                              (Std. err. adjusted for 106 clusters in reporting_econ_id)
----------------------------------------------------------------------------------------
                       |               Robust
                ln_aft | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-----------------------+----------------------------------------------------------------
 partner_econ_id#c.hdi |
               France  |  -9.774424    4.86841    -2.01   0.047    -19.42758   -.1212671
              Germany  |   1.754164   4.649332     0.38   0.707    -7.464603    10.97293
                Japan  |  -1.351766   5.303489    -0.25   0.799    -11.86761    9.164074
       United Kingdom  |   -20.2625   8.642618    -2.34   0.021    -37.39922    -3.12579
        United States  |   4.447394   4.937665     0.90   0.370    -5.343084    14.23787
                       |
       partner_econ_id#|
           c.ln_gnicap |
               France  |   1.629878   .3645321     4.47   0.000     .9070784    2.352678
              Germany  |  -.0697332   .3210155    -0.22   0.828    -.7062477    .5667813
                Japan  |     .49134   .3927402     1.25   0.214    -.2873913    1.270071
       United Kingdom  |   1.755348   .7696412     2.28   0.025     .2292913    3.281404
        United States  |  -.4558249   .3520782    -1.29   0.198    -1.153931    .2422811
                       |
       partner_econ_id#|
         c.pol_freedom |
               France  |  -.0932653    .138572    -0.67   0.502    -.3680279    .1814972
              Germany  |  -.2096648   .0941688    -2.23   0.028     -.396384   -.0229455
                Japan  |  -.0776171   .1020882    -0.76   0.449    -.2800392    .1248051
       United Kingdom  |  -.0738517   .1888351    -0.39   0.697    -.4482769    .3005734
        United States  |  -.0157842   .1156214    -0.14   0.892    -.2450401    .2134718
                       |
       partner_econ_id#|
   c.share_world_merch |
               France  |   5.55e-09   1.74e-09     3.19   0.002     2.10e-09    9.00e-09
              Germany  |   6.99e-09   1.89e-09     3.70   0.000     3.25e-09    1.07e-08
                Japan  |   4.91e-10   1.71e-09     0.29   0.775    -2.90e-09    3.88e-09
       United Kingdom  |   6.37e-09   2.87e-09     2.22   0.028     6.84e-10    1.21e-08
        United States  |   4.25e-10   1.78e-09     0.24   0.812    -3.11e-09    3.95e-09
                       |
       partner_econ_id#|
                    c. |
count_internationali~d |
               France  |  -.2066316   .3224321    -0.64   0.523    -.8459549    .4326917
              Germany  |   .2801063   .2106067     1.33   0.186    -.1374878    .6977004
                Japan  |  -1.099743   .3584609    -3.07   0.003    -1.810505   -.3889816
       United Kingdom  |   .9411661   .4569142     2.06   0.042     .0351897    1.847143
        United States  |   .6019295   .2314808     2.60   0.011     .1429459    1.060913
                       |
       partner_econ_id#|
    c.count_intrastate |
               France  |  -.1697378   .2274151    -0.75   0.457    -.6206601    .2811844
              Germany  |  -.1121022   .1292339    -0.87   0.388    -.3683492    .1441447
                Japan  |   .1842267   .1752289     1.05   0.296    -.1632198    .5316732
       United Kingdom  |   .0510352   .2834562     0.18   0.857    -.5110062    .6130765
        United States  |  -.0151646   .2884437    -0.05   0.958    -.5870952     .556766
                       |
       partner_econ_id#|
               c.agree |
               France  |   -2.41855   2.092758    -1.16   0.250    -6.568102    1.731002
              Germany  |   .1471977   1.307049     0.11   0.911    -2.444438    2.738834
                Japan  |  -1.390888   1.656588    -0.84   0.403    -4.675595     1.89382
       United Kingdom  |  -4.832314    3.96525    -1.22   0.226    -12.69467    3.030045
        United States  |   2.480542   1.247521     1.99   0.049     .0069379    4.954147
                       |
       partner_econ_id#|
             c.ln_dist |
               France  |   .5646493   .3782154     1.49   0.138    -.1852819     1.31458
              Germany  |  -.2937255   .2219439    -1.32   0.189    -.7337993    .1463482
                Japan  |  -.6858377   .4129811    -1.66   0.100    -1.504703    .1330275
       United Kingdom  |   2.223294   1.038035     2.14   0.035     .1650627    4.281525
        United States  |  -.7813526   .4535387    -1.72   0.088    -1.680636    .1179309
                       |
       partner_econ_id#|
                    c. |
inflowsofforeignpopu~n |
               France  |   .0000306   .0000324     0.94   0.347    -.0000336    .0000948
              Germany  |  -5.96e-06   9.93e-06    -0.60   0.550    -.0000257    .0000137
                Japan  |   .0000454   .0000293     1.55   0.124    -.0000127    .0001035
       United Kingdom  |    .000022   .0000214     1.03   0.307    -.0000205    .0000644
        United States  |  -2.44e-06   6.75e-06    -0.36   0.719    -.0000158     .000011
                       |
       partner_econ_id#|
              c.col_fr |
               France  |   .0130181   .0087437     1.49   0.140    -.0043191    .0303553
                       |
       partner_econ_id#|
              c.col_uk |
       United Kingdom  |  -.0237955   .0125387    -1.90   0.060    -.0486575    .0010664
                       |
       partner_econ_id#|
              c.col_us |
        United States  |   .0444401   .0152937     2.91   0.004     .0141155    .0747646
                       |
       partner_econ_id#|
      c.ln_servicesexp |
               France  |  -.1295067   .2169798    -0.60   0.552    -.5597375    .3007241
              Germany  |  -.1768757   .1513394    -1.17   0.245    -.4769538    .1232023
                Japan  |  -.2530778    .146205    -1.73   0.086    -.5429753    .0368197
       United Kingdom  |   .7495948   .4542527     1.65   0.102    -.1511043    1.650294
        United States  |  -.2579884   .2010137    -1.28   0.202    -.6565614    .1405846
                       |
       partner_econ_id#|
      c.ln_servicesimp |
               France  |   .6254141   .3171176     1.97   0.051    -.0033716      1.2542
              Germany  |   .1737926   .1753416     0.99   0.324    -.1738773    .5214626
                Japan  |   .0971037   .2054254     0.47   0.637    -.3102169    .5044243
       United Kingdom  |  -1.346223   .5504452    -2.45   0.016    -2.437655   -.2547921
        United States  |   .1794095   .2190367     0.82   0.415    -.2548998    .6137188
                       |
       partner_econ_id#|
         c.ln_goodsexp |
               France  |   .2435825   .0916151     2.66   0.009     .0619267    .4252383
              Germany  |   .0589114   .0589896     1.00   0.320    -.0580542     .175877
                Japan  |    .049922   .0495375     1.01   0.316    -.0483016    .1481457
       United Kingdom  |  -.3051458   .2553684    -1.19   0.235    -.8114941    .2012025
        United States  |  -.0198432   .0650736    -0.30   0.761    -.1488722    .1091857
                       |
       partner_econ_id#|
         c.ln_goodsimp |
               France  |    .268227    .188086     1.43   0.157    -.1047127    .6411667
              Germany  |   .3279165   .1393334     2.35   0.020     .0516441    .6041888
                Japan  |   .1859517   .1078043     1.72   0.087    -.0278044    .3997078
       United Kingdom  |   1.448157   .4357101     3.32   0.001     .5842249     2.31209
        United States  |   .1219501   .1744274     0.70   0.486    -.2239073    .4678074
                       |
       partner_econ_id#|
              c.ln_fdi |
               France  |   .0328726   .1092139     0.30   0.764    -.1836783    .2494235
              Germany  |   .1313913   .0889613     1.48   0.143    -.0450025     .307785
                Japan  |   .0797486   .0869451     0.92   0.361    -.0926475    .2521447
       United Kingdom  |  -.4663534   .2563915    -1.82   0.072    -.9747305    .0420237
        United States  |   .2350082   .1098859     2.14   0.035     .0171247    .4528917
                       |
       partner_econ_id#|
              c.ln_gdp |
               France  |   .1692535   .6951185     0.24   0.808    -1.209038    1.547545
              Germany  |   .5913072   .6749127     0.88   0.383    -.7469201    1.929534
                Japan  |   .9110806   .6366517     1.43   0.155    -.3512821    2.173443
       United Kingdom  |   .4966505   .9158035     0.54   0.589    -1.319219     2.31252
        United States  |   .7073532   .7093183     1.00   0.321     -.699094      2.1138
                       |
       partner_econ_id#|
         c.ln_otheraft |
               France  |  -.3035774   .1521357    -2.00   0.049    -.6052343   -.0019205
              Germany  |  -.4945058   .1474889    -3.35   0.001     -.786949   -.2020625
                Japan  |  -.4801013   .1113553    -4.31   0.000    -.7008984   -.2593043
       United Kingdom  |  -.0677292   .3317936    -0.20   0.839    -.7256147    .5901562
        United States  |  -.6690468   .1501203    -4.46   0.000    -.9667075    -.371386
                       |
       partner_econ_id#|
              c.ln_oda |
               France  |   .3812168   .1459949     2.61   0.010      .091736    .6706977
              Germany  |   .6039819   .1399394     4.32   0.000     .3265079     .881456
                Japan  |    .457013   .1416147     3.23   0.002     .1762172    .7378088
       United Kingdom  |    .163035   .2023019     0.81   0.422    -.2380922    .5641623
        United States  |   .7048839   .1891274     3.73   0.000     .3298792    1.079889
                       |
       partner_econ_id#|
   c.natural_resources |
               France  |   .0165229   .0228758     0.72   0.472    -.0288356    .0618814
              Germany  |   .0167739   .0184246     0.91   0.365    -.0197586    .0533065
                Japan  |   .0162419   .0160979     1.01   0.315    -.0156772     .048161
       United Kingdom  |   .0734116   .0815908     0.90   0.370    -.0883679     .235191
        United States  |   .0078063   .0180705     0.43   0.667    -.0280241    .0436368
                       |
                 _cons |  -24.94542   13.56641    -1.84   0.069    -51.84511    1.954272
----------------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------------+
       Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------------+---------------------------------------|
 reporting_econ_id |       106         106           0    *|
              year |        11           1          10     |
-----------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

predict fitted, xb
(8,251 missing values generated)

gen sq_fitted=fitted^2
(8,251 missing values generated)

 reghdfe ln_aft fitted sq_fitted , abs(reporting_econ_id year) vce(cluster reporting_eco
> n_id)
(MWFE estimator converged in 5 iterations)

HDFE Linear regression                            Number of obs   =      3,394
Absorbing 2 HDFE groups                           F(   2,    105) =     270.35
Statistics robust to heteroskedasticity           Prob > F        =     0.0000
                                                  R-squared       =     0.6045
                                                  Adj R-squared   =     0.5903
                                                  Within R-sq.    =     0.3348
Number of clusters (reporting_econ_id) =        106Root MSE       =     1.5999

                    (Std. err. adjusted for 106 clusters in reporting_econ_id)
------------------------------------------------------------------------------
             |               Robust
      ln_aft | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      fitted |   1.014911   .0514039    19.74   0.000     .9129864    1.116835
   sq_fitted |   -.006426   .0074768    -0.86   0.392    -.0212511    .0083991
       _cons |   .0247937   .0582262     0.43   0.671    -.0906581    .1402454
------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------------+
       Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------------+---------------------------------------|
 reporting_econ_id |       106         106           0    *|
              year |        11           1          10     |
-----------------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

My sq_fitted term is not statistically significant, therefore should I understand that the model is working properly? Would I need to run additional model diagnostics?

Thank you very much again for your help.

Comment

Carlo Lazzaro

Join Date: Apr 2014

Posts: 17606
#6

09 Oct 2024, 02:09

Andrea (please, Carlo is enough. Thanks):
with so many predictors this was expected.
Stick with your current model, then.

Kind regards,
Carlo
(StataNow 18.5)
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