Dear Statalist members,
First of all, I would like to thank Carlo Lazzaro for helping me resolve my initial query. Here is the related thread:
https://www.statalist.org/forums/for...ion-procedures
I have a new question, which involves a different aspect of my research, so I am starting a new thread here.
I am conducting a study using a balanced panel dataset of 77 government R&D programs observed over 11 years. The main research objective is to examine whether the evaluation results from year t-1 influence the government-proposed budget in year t.
This approach is based on previous studies, which have explored similar interaction effects between evaluation results and program characteristics.
My question:
I learned that when including interaction terms in a regression, the original variables (in this case, dum_Grade2, dum_Grade3, and dum_Type2) should also be included in the model. However, in my case, dum_Type2 is a time-invariant variable, and it would be dropped in a fixed effects (FE) model.
Therefore, I would like to clarify:
Thank you in advance for your time and insights.
First of all, I would like to thank Carlo Lazzaro for helping me resolve my initial query. Here is the related thread:
https://www.statalist.org/forums/for...ion-procedures
I have a new question, which involves a different aspect of my research, so I am starting a new thread here.
I am conducting a study using a balanced panel dataset of 77 government R&D programs observed over 11 years. The main research objective is to examine whether the evaluation results from year t-1 influence the government-proposed budget in year t.
- My independent variables are evaluation result dummies for year t-1, namely dum_Grade2 (indicating "Excellent") and dum_Grade3 (indicating "Insufficient").
- My dependent variable is the log-transformed government-proposed budget for year t, denoted as ln_GBUDGETt.
- interaction_Grade2_Type2 = dum_Grade2 * dum_Type2
- interaction_Grade3_Type2 = dum_Grade3 * dum_Type2
Code:
. egen center_Grade2 = mean(dum_Grade2) . egen center_Grade3 = mean(dum_Grade3) . egen center_Type2 = mean(dum_Type2) . gen interaction_Grade2_Type2 = (dum_Grade2 - center_Grade2) * (dum_Type2 - center_Type2) . gen interaction_Grade3_Type2 = (dum_Grade3 - center_Grade3) * (dum_Type2 - center_Type2)
Code:
. xtreg ln_GBUDGETt dum_Grade2 dum_Grade3 dum_Type2 interaction_Grade2_Type2 interaction_Grade3_Type2 ln_Period dum_Scale2 dum_NationalProject2 dum_Congress2 ln_GDPgrowth, fe vce(cluster ID
> )
note: dum_Type2 omitted because of collinearity.
Fixed-effects (within) regression Number of obs = 847
Group variable: ID Number of groups = 77
R-squared: Obs per group:
Within = 0.1885 min = 11
Between = 0.6430 avg = 11.0
Overall = 0.5360 max = 11
F(9, 76) = 5.54
corr(u_i, Xb) = 0.5650 Prob > F = 0.0000
(Std. err. adjusted for 77 clusters in ID)
------------------------------------------------------------------------------------------
| Robust
ln_GBUDGETt | Coefficient std. err. t P>|t| [95% conf. interval]
-------------------------+----------------------------------------------------------------
dum_Grade2 | -.0461032 .0574294 -0.80 0.425 -.1604837 .0682773
dum_Grade3 | -.1110424 .0923934 -1.20 0.233 -.2950598 .072975
dum_Type2 | 0 (omitted)
interaction_Grade2_Type2 | .1474514 .1252494 1.18 0.243 -.1020043 .3969072
interaction_Grade3_Type2 | -.2295972 .1842096 -1.25 0.216 -.5964824 .1372881
ln_Period | .1932306 .1130568 1.71 0.092 -.0319415 .4184028
dum_Scale2 | .9017088 .1966115 4.59 0.000 .510123 1.293295
dum_NationalProject2 | .0754921 .1083848 0.70 0.488 -.1403749 .2913591
dum_Congress2 | .0633894 .0490861 1.29 0.200 -.034374 .1611528
ln_GDPgrowth | -.0312415 .0135256 -2.31 0.024 -.0581801 -.004303
_cons | 9.735442 .3140126 31.00 0.000 9.110031 10.36085
-------------------------+----------------------------------------------------------------
sigma_u | .97561585
sigma_e | .44391609
rho | .82847629 (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
Code:
. xtreg ln_GBUDGETt dum_Grade2 dum_Grade3 dum_Type2 interaction_Grade2_Type2 interaction_Grade3_Type2 ln_Period dum_Scale2 dum_NationalProject2 dum_Congress2 ln_GDPgrowth, re vce(cluster ID
> )
Random-effects GLS regression Number of obs = 847
Group variable: ID Number of groups = 77
R-squared: Obs per group:
Within = 0.1879 min = 11
Between = 0.6039 avg = 11.0
Overall = 0.5395 max = 11
Wald chi2(10) = 109.13
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
(Std. err. adjusted for 77 clusters in ID)
------------------------------------------------------------------------------------------
| Robust
ln_GBUDGETt | Coefficient std. err. z P>|z| [95% conf. interval]
-------------------------+----------------------------------------------------------------
dum_Grade2 | -.0479763 .0564415 -0.85 0.395 -.1585996 .062647
dum_Grade3 | -.1145074 .0879319 -1.30 0.193 -.2868507 .057836
dum_Type2 | .7285303 .2021124 3.60 0.000 .3323972 1.124663
interaction_Grade2_Type2 | .133687 .1210221 1.10 0.269 -.103512 .3708861
interaction_Grade3_Type2 | -.239945 .1744614 -1.38 0.169 -.581883 .1019929
ln_Period | .2234043 .0977784 2.28 0.022 .0317622 .4150463
dum_Scale2 | 1.053447 .1844403 5.71 0.000 .6919507 1.414944
dum_NationalProject2 | .1090483 .1029717 1.06 0.290 -.0927725 .3108691
dum_Congress2 | .0807632 .0469217 1.72 0.085 -.0112017 .1727281
ln_GDPgrowth | -.0287817 .0142488 -2.02 0.043 -.0567089 -.0008546
_cons | 9.20711 .3015075 30.54 0.000 8.616166 9.798054
-------------------------+----------------------------------------------------------------
sigma_u | .67509119
sigma_e | .44391609
rho | .69813328 (fraction of variance due to u_i)
------------------------------------------------------------------------------------------
Code:
. xtoverid
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(ID)
Sargan-Hansen statistic 50.052 Chi-sq(9) P-value = 0.0000
This approach is based on previous studies, which have explored similar interaction effects between evaluation results and program characteristics.
My question:
I learned that when including interaction terms in a regression, the original variables (in this case, dum_Grade2, dum_Grade3, and dum_Type2) should also be included in the model. However, in my case, dum_Type2 is a time-invariant variable, and it would be dropped in a fixed effects (FE) model.
Therefore, I would like to clarify:
- Since my main interest lies in the interaction terms (interaction_Grade2_Type2 and interaction_Grade3_Type2), is it acceptable to interpret the interaction effects even if dum_Type2 is omitted from the fixed effects model?
- Alternatively, would it be more appropriate to use a random effects (RE) model or the Hausman-Taylor estimator to ensure that dum_Type2 remains in the model?
Thank you in advance for your time and insights.
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