Hello Statalist,

In a scientific paper I would like to examine the effects of public debt on real economic growth and long-term real interest rates. In this context I set up a panel data set for 10 OECD countries with the corresponding data and programmed it in Stata as follows. The Hausman test shows that I should definitely go for random effects. Is that logical? A fixed effects model should actually make more sense.

Is there anything else to mind in the below mentioned output? Thank you!!





. egen countrynum = group (Country)

. list Country countrynum in 1/35, sepby (Country)

+--------------------+
| Country countr~m |
|--------------------|
1. | Germany 4 |
2. | Germany 4 |
3. | Germany 4 |
4. | Germany 4 |
5. | Germany 4 |
6. | Germany 4 |
7. | Germany 4 |
8. | Germany 4 |
9. | Germany 4 |
10. | Germany 4 |
11. | Germany 4 |
12. | Germany 4 |
13. | Germany 4 |
14. | Germany 4 |
15. | Germany 4 |
16. | Germany 4 |
17. | Germany 4 |
18. | Germany 4 |
19. | Germany 4 |
20. | Germany 4 |
21. | Germany 4 |
22. | Germany 4 |
23. | Germany 4 |
24. | Germany 4 |
25. | Germany 4 |
26. | Germany 4 |
27. | Germany 4 |
28. | Germany 4 |
29. | Germany 4 |
30. | Germany 4 |
31. | Germany 4 |
32. | Germany 4 |
33. | Germany 4 |
34. | Germany 4 |
35. | Germany 4 |
+--------------------+

. xtset countrynum
panel variable: countrynum (balanced)

. xtset countrynum Year, yearly
panel variable: countrynum (strongly balanced)
time variable: Year, 1981 to 2015
delta: 1 year

. xtline RatioofpublicdebttoGDPin

. xtline RatioofpublicdebttoGDPin, overlay

. xtsum RatioofpublicdebttoGDPin RealGDPgrowthin Longtermrealinterestratein

Variable | Mean Std. Dev. Min Max | Observations
-----------------+--------------------------------------------+----------------
Ratioo~n overall | 55.51457 23.20057 9.68 119.48 | N = 350
between | 16.03183 21.91 78.30571 | n = 10
within | 17.50102 10.80029 105.4703 | T = 35
| |
RealGD~n overall | 2.604 2.568419 -5.7 25.1 | N = 350
between | .8613813 1.711429 4.714286 | n = 10
within | 2.43456 -7.210286 22.98971 | T = 35
| |
Longte~n overall | 3.75036 2.493161 -6.609561 11.16918 | N = 350
between | .2979852 3.233443 4.133942 | n = 10
within | 2.477035 -6.559771 11.21897 | T = 35

. xtreg RatioofpublicdebttoGDPin RealGDPgrowthin Longtermrealinterestratein

Random-effects GLS regression Number of obs = 350
Group variable: countrynum Number of groups = 10

R-sq: Obs per group:
within = 0.0179 min = 35
between = 0.0006 avg = 35.0
overall = 0.0082 max = 35

Wald chi2(2) = 6.17
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0457

--------------------------------------------------------------------------------------------
RatioofpublicdebttoGDPin | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
RealGDPgrowthin | -.9239898 .3889364 -2.38 0.018 -1.686291 -.1616884
Longtermrealinterestratein | -.3891442 .3827909 -1.02 0.309 -1.1394 .3611121
_cons | 59.38007 5.966642 9.95 0.000 47.68567 71.07448
---------------------------+----------------------------------------------------------------
sigma_u | 17.728726
sigma_e | 17.623266
rho | .50298312 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------

. xtreg RatioofpublicdebttoGDPin RealGDPgrowthin Longtermrealinterestratein, fe

Fixed-effects (within) regression Number of obs = 350
Group variable: countrynum Number of groups = 10

R-sq: Obs per group:
within = 0.0179 min = 35
between = 0.0007 avg = 35.0
overall = 0.0082 max = 35

F(2,338) = 3.09
corr(u_i, Xb) = -0.0246 Prob > F = 0.0469

--------------------------------------------------------------------------------------------
RatioofpublicdebttoGDPin | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
RealGDPgrowthin | -.9293562 .3905765 -2.38 0.018 -1.697623 -.1610894
Longtermrealinterestratein | -.387602 .3838789 -1.01 0.313 -1.142695 .3674907
_cons | 59.38826 2.08861 28.43 0.000 55.27995 63.49657
---------------------------+----------------------------------------------------------------
sigma_u | 16.074485
sigma_e | 17.623266
rho | .45413592 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------
F test that all u_i=0: F(9, 338) = 29.09 Prob > F = 0.0000

. estimate store fe

. xtreg RatioofpublicdebttoGDPin RealGDPgrowthin Longtermrealinterestratein, re

Random-effects GLS regression Number of obs = 350
Group variable: countrynum Number of groups = 10

R-sq: Obs per group:
within = 0.0179 min = 35
between = 0.0006 avg = 35.0
overall = 0.0082 max = 35

Wald chi2(2) = 6.17
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0457

--------------------------------------------------------------------------------------------
RatioofpublicdebttoGDPin | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
RealGDPgrowthin | -.9239898 .3889364 -2.38 0.018 -1.686291 -.1616884
Longtermrealinterestratein | -.3891442 .3827909 -1.02 0.309 -1.1394 .3611121
_cons | 59.38007 5.966642 9.95 0.000 47.68567 71.07448
---------------------------+----------------------------------------------------------------
sigma_u | 17.728726
sigma_e | 17.623266
rho | .50298312 (fraction of variance due to u_i)
--------------------------------------------------------------------------------------------

. estimate store re

. hausman fe re

---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe re Difference S.E.
-------------+----------------------------------------------------------------
RealGDPgro~n | -.9293562 -.9239898 -.0053665 .0357555
Longtermre~n | -.387602 -.3891442 .0015422 .0288825
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test: Ho: difference in coefficients not systematic

chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 0.03
Prob>chi2 = 0.9854