Hi,
I have estimated the following specification including a triple interaction of 3 dummies:
where worker_female takes value 1 for female workers; after_rq_change takes value 1 after a policy intervention in the platform under analysis and payment_proposal takes value 1 if the employer reveals the budget in that specific job. The dependent variable is the log value of a proposal made by a given worker in the platform to a specific project.
The fixed effects included in the absorb option capture the main effects of the 3 dummies. Hence, the output looks like this:
How should I interpret the coefficient of the triple interaction in this case, if the main effects and the double interaction after_rq_change#payment_proposal are dropped due to collinearity with the fixed effects? Is the final effect the sum of the constant plus the triple interaction coefficient plus the remaining double interaction coefficients? I.e, is the final effect equal to 4.997 - 0.017639 + 0.00118 -0.0000105 (the constant plus all non-dropped coefficients)?
And, regardless of the magnitude, is it right to say that females make lower proposals after the policy change when the budget is revealed as compared to males?
To better understand the calculation of the magnitude, I have used the margins command. I have added the option noestimcheck because otherwise everthing appears as not estimable due to collinearity with the fixed effects (I followed this post: https://www.statalist.org/forums/for...-fixed-effects). This is the code I use:
and this is the output:
As I understand it, the corresponding marginal effect for the triple interaction is 4.98093, but I don't know how to interpret this. Does it mean that the average proposal of a female after the change when the budget is revealed is 4.981 on average? Given that this margin is lower than all the other marginal effects combining the 3 dummies, does it means that the average proposal of a female after the change when the budget is revealed is lower than in the other 7 possibilities?
In the context of the analysis, I want to stress that females make lower proposals as compared to males after the change if the budget is revealed. Is this a correct statement? If I want to show this in a report, should I include the entire marginal coefficients table?
Thank you in advance for your help!
Estrella
I have estimated the following specification including a triple interaction of 3 dummies:
Code:
reghdfe lamount_converted i.worker_female##i.after_rq_change##i.payment_proposal, absorb(i.posted i.cno i.ono i.cat i.wno i.eno i.pno) vce(cluster pno)
The fixed effects included in the absorb option capture the main effects of the 3 dummies. Hence, the output looks like this:
Code:
. reghdfe lamount_converted i.worker_female##i.after_rq_change##i.payment_proposal, absorb(i.posted i.cno i.ono i.cat i.wno i.eno i.pno) vce(cluster pno)
(dropped 64511 singleton observations)
note: 1bn.worker_female is probably collinear with the fixed effects (all partialled-out values are close to zero; tol = 1.0e-09)
note: 1bn.after_rq_change is probably collinear with the fixed effects (all partialled-out values are close to zero; tol = 1.0e-09)
note: 1bn.payment_proposal is probably collinear with the fixed effects (all partialled-out values are close to zero; tol = 1.0e-09)
note: 1bn.after_rq_change#1bn.payment_proposal is probably collinear with the fixed effects (all partialled-out values are close to zero; tol = 1.0e-09)
(MWFE estimator converged in 21 iterations)
note: 1.worker_female omitted because of collinearity
note: 1.after_rq_change omitted because of collinearity
note: 1.payment_proposal omitted because of collinearity
note: 1.after_rq_change#1.payment_proposal omitted because of collinearity
HDFE Linear regression Number of obs = 2,600,850
Absorbing 7 HDFE groups F( 3, 202376) = 13.99
Statistics robust to heteroskedasticity Prob > F = 0.0000
R-squared = 0.7636
Adj R-squared = 0.7264
Within R-sq. = 0.0000
Number of clusters (pno) = 202,377 Root MSE = 0.6357
(Std. err. adjusted for 202,377 clusters in pno)
----------------------------------------------------------------------------------------------------------------
| Robust
lamount_converted | Coefficient std. err. t P>|t| [95% conf. interval]
-----------------------------------------------+----------------------------------------------------------------
worker_female |
0 | 0 (base)
1 | 0 (omitted)
|
after_rq_change |
0 | 0 (base)
1 | 0 (omitted)
|
worker_female#after_rq_change |
1 1 | -.0000105 .0043705 -0.00 0.998 -.0085766 .0085556
|
payment_proposal |
0 | 0 (base)
1 | 0 (omitted)
|
worker_female#payment_proposal |
1 1 | .00118 .0044597 0.26 0.791 -.0075608 .0099209
|
after_rq_change#payment_proposal |
1 1 | 0 (omitted)
|
worker_female#after_rq_change#payment_proposal |
1 1 1 | -.0176395 .0051821 -3.40 0.001 -.0277963 -.0074827
|
_cons | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
----------------------------------------------------------------------------------------------------------------
Absorbed degrees of freedom:
-----------------------------------------------------+
Absorbed FE | Categories - Redundant = Num. Coefs |
-------------+---------------------------------------|
posted_date | 731 1 730 |
cno | 185 1 184 |
ono | 168 1 167 ?|
cat | 17 1 16 ?|
wno | 54622 168 54454 ?|
eno | 96358 178 96180 ?|
pno | 202377 202377 0 *|
-----------------------------------------------------+
? = number of redundant parameters may be higher
* = FE nested within cluster; treated as redundant for DoF computation
How should I interpret the coefficient of the triple interaction in this case, if the main effects and the double interaction after_rq_change#payment_proposal are dropped due to collinearity with the fixed effects? Is the final effect the sum of the constant plus the triple interaction coefficient plus the remaining double interaction coefficients? I.e, is the final effect equal to 4.997 - 0.017639 + 0.00118 -0.0000105 (the constant plus all non-dropped coefficients)?
And, regardless of the magnitude, is it right to say that females make lower proposals after the policy change when the budget is revealed as compared to males?
To better understand the calculation of the magnitude, I have used the margins command. I have added the option noestimcheck because otherwise everthing appears as not estimable due to collinearity with the fixed effects (I followed this post: https://www.statalist.org/forums/for...-fixed-effects). This is the code I use:
Code:
margins i.worker_female##i.after_rq_change##i.payment_proposal, atmeans noestimcheck
Code:
. margins i.worker_female##i.after_rq_change##i.payment_proposal, atmeans noestimcheck
Adjusted predictions Number of obs = 2,600,850
Model VCE: Robust
Expression: Linear prediction, predict()
At: 0.worker_female = .8021051 (mean)
1.worker_female = .1978949 (mean)
0.after_rq_change = .302415 (mean)
1.after_rq_change = .697585 (mean)
0.payment_proposal = .593281 (mean)
1.payment_proposal = .406719 (mean)
----------------------------------------------------------------------------------------------------------------
| Delta-method
| Margin std. err. z P>|z| [95% conf. interval]
-----------------------------------------------+----------------------------------------------------------------
worker_female |
0 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
1 | 4.99284 .0026521 1882.58 0.000 4.987642 4.998038
|
after_rq_change |
0 | 4.997467 .0004977 1.0e+04 0.000 4.996492 4.998443
1 | 4.996046 .0001896 2.6e+04 0.000 4.995674 4.996417
|
worker_female#after_rq_change |
0 0 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
0 1 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
1 0 | 4.997852 .0013815 3617.79 0.000 4.995145 5.00056
1 1 | 4.990668 .0035825 1393.08 0.000 4.983646 4.997689
|
payment_proposal |
0 | 4.997371 .0001939 2.6e+04 0.000 4.996991 4.997751
1 | 4.995169 .000273 1.8e+04 0.000 4.994634 4.995704
|
worker_female#payment_proposal |
0 0 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
0 1 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
1 0 | 4.997365 .0023799 2099.84 0.000 4.992701 5.00203
1 1 | 4.98624 .0034923 1427.79 0.000 4.979395 4.993085
|
after_rq_change#payment_proposal |
0 0 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
0 1 | 4.997606 .0005981 8355.63 0.000 4.996434 4.998778
1 0 | 4.99737 .000261 1.9e+04 0.000 4.996859 4.997882
1 1 | 4.994113 .0003937 1.3e+04 0.000 4.993342 4.994885
|
worker_female#after_rq_change#payment_proposal |
0 0 0 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
0 0 1 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
0 1 0 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
0 1 1 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
1 0 0 | 4.997372 .0006993 7146.52 0.000 4.996002 4.998743
1 0 1 | 4.998552 .0039722 1258.37 0.000 4.990767 5.006338
1 1 0 | 4.997362 .0036992 1350.95 0.000 4.990112 5.004612
1 1 1 | 4.980903 .003979 1251.78 0.000 4.973104 4.988701
----------------------------------------------------------------------------------------------------------------
In the context of the analysis, I want to stress that females make lower proposals as compared to males after the change if the budget is revealed. Is this a correct statement? If I want to show this in a report, should I include the entire marginal coefficients table?
Thank you in advance for your help!
Estrella
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