Cross-sectional dependence in non-linear panel model

[alessio lombini]

Hello everyone,

I have an unbalanced panel data I am trying to perform panel regression analysis and these are the diagnostic tests I performed to correctly specify my model:

1. Bresuch-pagan Lagrange multiplier (LM) (xttest0): Prob > chibar2 = 0.0000 (proving a panel-wise effect)
2. Mundlak test: Prob > chi2 = 0.9015 (leading to a RE model)
3. Wooldridge (2002) test for serial correlation (xtserial): Prob > chibar2 = 0.0000 (proving the presence of serial correlation and the need for cluster standard errors)
4. Pesaran's and Friedman's test of cross sectional independence: Prob > chibar2 = 0.0000 (proving the presence of cross-sectional independence)
5. Test for a U-shaped relationship between the dependent and several independent variables, which proved the need for a non-linear model.

Now, here the question. Do you know how to solve the issue of cross-sectional independence in a non-linear model with the above-mentioned features? Unfortunately, I could find clues neither in the previous post nor in the literature. For instance, in "Robust standard errors for panel regressions with cross-sectional dependence" (on page 5) there is a nice discussion of the issue but it concerns only linear panel models.

I thank you in advance to whoever is willing to shed some light on this problem. Also, I attach here a sample of my dataset.
Best regards

* Example generated by -dataex-. For more info, type help dataex
clear
input str8 country float(date new_cases_per_million new_tests_per_thousand) double population float(population_density median_age hospital_beds_per_thousand human_development_index) double gdp_per_capita
"AFG" 721 .0008965518          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 722   .14425807          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 723   1.6715333          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 724    10.83958          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 725     13.9565          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 726   4.2741613          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 727    1.238097          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 728    .9496334          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 729   1.7874516          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 730   4.1520667          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 731    4.352097          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 732   2.8978064          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 733    .6338928          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 734    .6131936          . 38928341  54.42 18.6   .5 .51  2018
"AFG" 735       2.818          . 38928341  54.42 18.6   .5 .51  2018
"AGO" 721           0          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 722  .006806451          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 723  .020233333          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 724   .05783871          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 725   .20076667          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 726    .8480322          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 727   1.4781935          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 728   2.3509667          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 729    5.725064          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 730    4.395633          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 731   2.3693225          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 732   2.2015162          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 733   1.0985714          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 734    1.476129          . 32866268  23.89 16.8   .8 .58  6459
"AGO" 735   4.4027333          . 32866268  23.89 16.8   .8 .58  6459
"ALB" 721           0      .0018  2877800 104.87   38 2.89  .8 13851
"ALB" 722    2.723774 .018275863  2877800 104.87   38 2.89  .8 13851
"ALB" 723      6.1389  .07623333  2877800 104.87   38 2.89  .8 13851
"ALB" 724   4.0800967  .07248387  2877800 104.87   38 2.89  .8 13851
"ALB" 725     16.1929  .10343333  2877800 104.87   38 2.89  .8 13851
"ALB" 726    30.72468  .15003225  2877800 104.87   38 2.89  .8 13851
"ALB" 727    47.49374   .2404516  2877800 104.87   38 2.89  .8 13851
"ALB" 728      47.907  .29183334  2877800 104.87   38 2.89  .8 13851
"ALB" 729    80.99822   .4167742  2877800 104.87   38 2.89  .8 13851
"ALB" 730   200.46564      .6532  2877800 104.87   38 2.89  .8 13851
"ALB" 731    225.6877       .789  2877800 104.87   38 2.89  .8 13851
"ALB" 732     222.067  1.0714194  2877800 104.87   38 2.89  .8 13851
"ALB" 733    360.3943  1.3543847  2877800 104.87   38 2.89  .8 13851
"ALB" 734    201.6549  1.0328387  2877800 104.87   38 2.89  .8 13851
"ALB" 735    68.66357      .9171  2877800 104.87   38 2.89  .8 13851
"ARE" 721   .05924138   .2100909  9890400 112.44   34  1.2 .89 66306
"ARE" 722   2.0971613     .99635  9890400 112.44   34  1.2 .89 66306
"ARE" 723     39.8266     3.1187  9890400 112.44   34  1.2 .89 66306
"ARE" 724    72.00197    3.55471  9890400 112.44   34  1.2 .89 66306
"ARE" 725     47.5545     4.5754  9890400 112.44   34  1.2 .89 66306
end
format %tm date

[alessio lombini]

Put in simpler words, is there anyone who knows how I should specify my panel regression model in order to deal with both cross-sectional dependence and non-linearity?