Since it is a university assignment the normal approach (as i have been taught, and is the recommendations in https://www.iuj.ac.jp/faculty/kucc62...blq5Qmk7KvdJLg) would be to start of with a simple model like a Pooled OLS, and then if that isn't sufficient, or the assumptions of the model don't seem to hold up, then you move on to fixed or random effects models. Gladly correct me if this approach isn't optimal.
My first issue when doing the Pooled OLS, is figuring out if it is actually done correctly (As i have seen different approaches from different sources). From what i can tell you do this by running clustered standard errors.
Code:
reg Covid19_cases x1 x2 x3 Country, vce(cluster Country)
Question 2. How do i test the assumptions of heteroskedasticity and autocorrelation when using clustered standard errors, as this seems to make it impossible to run a Breusch-Pagan test.
Code:
. hettest hettest not appropriate after robust cluster() r(498);
Furthermore, i know that -xtreg usually outperforms -reg (with clustered standard errors) when it comes to panel data regression.
So my Question 3 (See output from Pooled OLS and Random effects below) is how do i based on the stata output determine whether i should use Pooled OLS, fixed or random effects model. (As almost all my variables are static, i know that i'll probably end up with a -re effects model. I just simply haven't been able to statistically argue for this point of view, as i can't even test for things like heteroskedasticity and autocorrelation)
output from Pooled OLS:
Code:
Linear regression Number of obs = 4,592
F(19, 41) = 303.69
Prob > F = 0.0000
R-squared = 0.7294
Root MSE = 1242
(Std. Err. adjusted for 42 clusters in Country)
-----------------------------------------------------------------------------------------------
| Robust
Covid19_cases | Coef. Std. Err. t P>|t| [95% Conf. Interval]
------------------------------+----------------------------------------------------------------
Ages0_14Pct | 8123.495 11156.99 0.73 0.471 -14408.5 30655.49
Ages65_99Pct | 3038.334 11320.49 0.27 0.790 -19823.86 25900.53
Ages15_64Pct | 7851.408 11239.37 0.70 0.489 -14846.96 30549.78
Covid19_deaths | 9.630924 1.715408 5.61 0.000 6.166587 13.09526
CrimeIndex | -8.226521 5.282897 -1.56 0.127 -18.89555 2.442507
DAI_B_index | 1999.881 1276.736 1.57 0.125 -578.5393 4578.301
DAI_G_index | 290.8351 454.5301 0.64 0.526 -627.107 1208.777
DAI_P_index | 3.885746 690.839 0.01 0.996 -1391.292 1399.064
Gdp2018 | .1692471 .0260085 6.51 0.000 .1167219 .2217724
GdpAgriculturalPct | 1772.46 2558.133 0.69 0.492 -3393.794 6938.715
GdpIndustrialPct | -35.28193 2158.263 -0.02 0.987 -4393.983 4323.419
GdpServicePct | 150.5583 2216.818 0.07 0.946 -4326.396 4627.512
InternetUsage2014Pct | -283.9534 701.2951 -0.40 0.688 -1700.248 1132.341
popData2018 | -9.46e-07 4.60e-07 -2.06 0.046 -1.87e-06 -1.64e-08
pop_AnnualGrowthPct_2010_2018 | -15230.27 11371.27 -1.34 0.188 -38195.02 7734.475
pop_density18 | -.3554776 .4322918 -0.82 0.416 -1.228509 .5175533
SocialMobilityIndex | -9.681271 21.7794 -0.44 0.659 -53.66567 34.30313
StringencyIndex | 3.398476 1.255605 2.71 0.010 .8627302 5.934222
Country | .3061796 1.2523 0.24 0.808 -2.222892 2.835251
_cons | -7908.159 12120.52 -0.65 0.518 -32386.04 16569.72
-----------------------------------------------------------------------------------------------output from Random effects:
Code:
xtset Country Date
Code:
Random-effects GLS regression Number of obs = 4,592
Group variable: Country Number of groups = 42
R-sq: Obs per group:
within = 0.6600 min = 51
between = 0.9450 avg = 109.3
overall = 0.7293 max = 113
Wald chi2(18) = 9283.67
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
-----------------------------------------------------------------------------------------------
Covid19_cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------------------------------+----------------------------------------------------------------
Ages0_14Pct | 7719.581 17073.57 0.45 0.651 -25744 41183.17
Ages65_99Pct | 2600.686 16826.48 0.15 0.877 -30378.61 35579.98
Ages15_64Pct | 7477.483 17549.24 0.43 0.670 -26918.39 41873.36
Covid19_deaths | 9.728414 .1100511 88.40 0.000 9.512718 9.94411
CrimeIndex | -8.30544 6.737789 -1.23 0.218 -21.51126 4.900383
DAI_B_index | 1956.444 1257.037 1.56 0.120 -507.3033 4420.191
DAI_G_index | 308.9836 463.2871 0.67 0.505 -599.0424 1217.01
DAI_P_index | 64.28808 1023.292 0.06 0.950 -1941.327 2069.903
Gdp2018 | .1685496 .0209757 8.04 0.000 .127438 .2096611
GdpAgriculturalPct | 1816.435 4797.581 0.38 0.705 -7586.651 11219.52
GdpIndustrialPct | -124.5615 4119.166 -0.03 0.976 -8197.979 7948.856
GdpServicePct | 135.0255 4126.775 0.03 0.974 -7953.304 8223.356
InternetUsage2014Pct | -392.6615 1069.255 -0.37 0.713 -2488.362 1703.039
popData2018 | -9.59e-07 3.03e-07 -3.16 0.002 -1.55e-06 -3.64e-07
pop_AnnualGrowthPct_2010_2018 | -15717.27 16056.61 -0.98 0.328 -47187.65 15753.11
pop_density18 | -.3674106 .5401536 -0.68 0.496 -1.426092 .691271
SocialMobilityIndex | -8.118353 21.31227 -0.38 0.703 -49.88963 33.65293
StringencyIndex | 3.613653 .5180906 6.97 0.000 2.598214 4.629092
_cons | -7511.384 18162.4 -0.41 0.679 -43109.03 28086.26
------------------------------+----------------------------------------------------------------
sigma_u | 319.2514
sigma_e | 1214.6213
rho | .06462069 (fraction of variance due to u_i)
-----------------------------------------------------------------------------------------------Data description:
21 variables, and 4592 observations. (unbalanced dataset)
| Variable | Description | |
| Date | Time indicator (In days) | |
| StringencyIndex | Index measuring the goverment response to Covid19. 100 being the most severe response, and 0 being the loosest response. |
|
| Covid19_cases | Dependent variable Measuring the number of recorded covid19 cases |
|
| Covid19_deaths | Measuring the number of recording deaths caused by covid19 | |
| popData2018 | 2018 country population data | |
| DAI_index | Digital adoption index Measuring a countries digital adoption across three dimensions of the economy: people, government, and business |
|
| DAI_B_index | Measuring a countries digital adoption across business | |
| DAI_P_index | Measuring a countries digital adoption across people | |
| DAI_G_index | Measuring a countries digital adoption across government | |
| pop_AnnualGrowthPct_2010_2018 | Measuring a countries annual growth in population from 2010 to 2018 in pct. | |
| Ages0_14Pct | Measuring the pct. of a countries population who are between 0 and 14 years of age. | |
| Ages15_64Pct | Measuring the pct. of a countries population who are between 15 and 64 years of age. | |
| Ages65_99Pct | Measuring the pct. of a countries population who are between 65 and 99 years of age. | |
| Ages0_99Pct | Measuring the pct. of a countries population who are between 0 and 99 years of age. | |
| CrimeIndex | Index measuring crime rates by country. 100 being the highest crimes rates and 0 being the lowest |
|
| SocialMobilityIndex | Index measuring social mobility by country 100 being the highest social mobility and 0 being the lowest |
|
| Gdp2018 | Country GDP by 2018 numbers | |
| GdpAgriculturalPct | Pct. of a countries GDP that comes from the agriculture sector | |
| GdpIndustrialPct | Pct. of a countries GDP that comes from the industrial sector | |
| GdpServicePct | Pct. of a countries GDP that comes from the service sector | |
| InternetUsage2014Pct | % of a countries population that uses the internet, by 2014 numbers | |
| Country | Entity indicator | |
| Continent | Continent | |
| pop_density18 | Population density by country by 2018 numbers | |
Best regards, Walther Larsen
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