this is my first post so please let me know if anything can be improved upon!
I am conducting an analysis in which I explain the logged levelized-cost of electrity of onshore wind energy (log_lcoe_on) by cumulative capacity (log_cc_on) and a knowledge stock (log_ks_rd_aug), which consists of accumulated past expenditures in R&D. Additionally, I use feed-in tariffs measured in USD per kilowatt hour (this is not my full specification but the issue also occurs in this more parsimonious specification). The data consists of annual country-level observations (6 countries with 20 years each).
To this I added country-level FE. While conducting postestimation analyses I noticed that "sigma_u" after running random effects is 0. Previous Statalist entries suggested that this implies an absence of panel-wise effects and that pooled OLS should be used (which in this case yields the same coefficients as RE) (https://www.statalist.org/forums/for...plier-equals-1). However, including FE did change results by quite a bit and also the repoted "rho" and "F-values" suggest the FE model to be suitable. I could identify that this issue only occurs when feed-in tariffs are included, but I don't know why it is like that - it may be because of the zero values. Another issue is that, even without feed-in tarifs, the Hausman test returns a negative chi2 which I understood is critical, too.
Since I don't understand why these issues occur I also don't know how to solve them. Any help on this would be highly appreciated!
Please find my outputs and a plot of the feed-in tariff below.
Code:
. ********* POLS *********
. reg log_lcoe_on log_cc_on log_ks_rd_aug fd_in_trff, vce(robust)
Linear regression Number of obs = 120
F(3, 116) = 27.37
Prob > F = 0.0000
R-squared = 0.3781
Root MSE = .24315
-------------------------------------------------------------------------------
| Robust
log_lcoe_on | Coefficient std. err. t P>|t| [95% conf. interval]
--------------+----------------------------------------------------------------
log_cc_on | -.0460654 .0085744 -5.37 0.000 -.0630481 -.0290827
log_ks_rd_aug | -.0631807 .0138594 -4.56 0.000 -.0906309 -.0357305
fd_in_trff | 1.499136 .4131649 3.63 0.000 .6808104 2.317461
_cons | -1.437684 .1321524 -10.88 0.000 -1.699428 -1.175939
-------------------------------------------------------------------------------
.
.
. ********* FE *********
. xtreg log_lcoe_on log_cc_on log_ks_rd_aug fd_in_trff, fe
Fixed-effects (within) regression Number of obs = 120
Group variable: cntry Number of groups = 6
R-squared: Obs per group:
Within = 0.7476 min = 20
Between = 0.1010 avg = 20.0
Overall = 0.3001 max = 20
F(3,111) = 109.60
corr(u_i, Xb) = -0.7116 Prob > F = 0.0000
-------------------------------------------------------------------------------
log_lcoe_on | Coefficient Std. err. t P>|t| [95% conf. interval]
--------------+----------------------------------------------------------------
log_cc_on | -.0031357 .0130257 -0.24 0.810 -.0289471 .0226757
log_ks_rd_aug | -.2184333 .0176014 -12.41 0.000 -.2533116 -.1835551
fd_in_trff | .7140114 .3078071 2.32 0.022 .104071 1.323952
_cons | -.1522363 .1348406 -1.13 0.261 -.419432 .1149595
--------------+----------------------------------------------------------------
sigma_u | .31892833
sigma_e | .15586972
rho | .80719591 (fraction of variance due to u_i)
-------------------------------------------------------------------------------
F test that all u_i=0: F(5, 111) = 34.26 Prob > F = 0.0000
.
.
. ********* RE *********
. xtreg log_lcoe_on log_cc_on log_ks_rd_aug fd_in_trff, re
Random-effects GLS regression Number of obs = 120
Group variable: cntry Number of groups = 6
R-squared: Obs per group:
Within = 0.5856 min = 20
Between = 0.0398 avg = 20.0
Overall = 0.3781 max = 20
Wald chi2(3) = 70.53
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
log_lcoe_on | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
log_cc_on | -.0460654 .014093 -3.27 0.001 -.0736872 -.0184436
log_ks_rd_aug | -.0631807 .0160545 -3.94 0.000 -.0946469 -.0317144
fd_in_trff | 1.499136 .3981048 3.77 0.000 .7188644 2.279407
_cons | -1.437684 .1434132 -10.02 0.000 -1.718769 -1.156599
--------------+----------------------------------------------------------------
sigma_u | 0
sigma_e | .15586972
rho | 0 (fraction of variance due to u_i)
-------------------------------------------------------------------------------
.
.
. ********* RE without fd_in_trff *********
. xtreg log_lcoe_on log_cc_on log_ks_rd_aug, re
Random-effects GLS regression Number of obs = 120
Group variable: cntry Number of groups = 6
R-squared: Obs per group:
Within = 0.7179 min = 20
Between = 0.2219 avg = 20.0
Overall = 0.2984 max = 20
Wald chi2(2) = 116.87
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
-------------------------------------------------------------------------------
log_lcoe_on | Coefficient Std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
log_cc_on | -.0292927 .0146369 -2.00 0.045 -.0579806 -.0006048
log_ks_rd_aug | -.1317308 .0183369 -7.18 0.000 -.1676705 -.0957911
_cons | -.7754473 .1523597 -5.09 0.000 -1.074067 -.4768278
--------------+----------------------------------------------------------------
sigma_u | .04758568
sigma_e | .15888889
rho | .08231155 (fraction of variance due to u_i)
-------------------------------------------------------------------------------
. ********* Hasuman test *********
. qui: xtreg log_lcoe_on log_cc_on log_ks_rd_aug, fe
. est sto fixed
. qui: xtreg log_lcoe_on log_cc_on log_ks_rd_aug, re
. est sto random
. hausman fixed random
---- Coefficients ----
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fixed random Difference Std. err.
-------------+----------------------------------------------------------------
log_cc_on | -.0046799 -.0292927 .0246128 .
log_ks_rd_~g | -.2204806 -.1317308 -.0887498 .
------------------------------------------------------------------------------
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.
Test of H0: Difference in coefficients not systematic
chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -566.18
Warning: chi2 < 0 ==> model fitted on these data
fails to meet the asymptotic assumptions
of the Hausman test; see suest for a
generalized test.Thank you in advance!
Fabian
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