Sorry, I did not realize that there was more pages, so couldnt find my post. Look at #18 for my question
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Sorry, I did not realize that there was more pages, so couldnt find my post. Look at #18 for my questionLast edited by Gustav Egede Hansen; 16 Nov 2021, 07:16.Comment
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@Fei Wang I have a question if you dont mind. For the time being, I am using a poisson regression to estimate the effect of my treatment variable on salary.
I am looking to use the margins-command to calculate the percentage change in salary before the treatment (time = 99) and after (time = 101). - dydx - seems to yield sensible results:Code:xtpoisson salary i.treatment##i.time..., vce(robust) fe
In the contrary, the results from running the eydx seem wrong. The sentence you wrote "an advantage of using -poisson- is that the reported coefficient has already been the semi-elasticity (if you don't have interactions)" has gotten me a bit confussed because if the reported coefficients are semi-elastic wouldn't be possible to just use dydx to interpret them across the treatment-variable (rather than using eydx)?Code:margins, dydx(treatment) at(time = 99 101)) lincom _b[1.treatment:2._at]-_b[1.treatment:1bn._at] di (exp(r(estimate))-1)*100
Best,
GustavComment
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I don't understand your calculation in #18. If you'd like to derive "the percentage change in salary before the treatment (time = 99) and after (time = 101)", I would show a simple way as below, with a poisson regression based on you example data in #1. After setting time 99 as the base, the original coefficient of "time#c.treatment" at 101 is exactly what you need (that's what I meant by "reported coefficient has already been the semi-elasticity"). I also show how you could equivalently derive this number with -margins-.
Code:. poisson salary c.treatment##ib(99).time, vce(cluster id) Iteration 0: log pseudolikelihood = -36592.386 Iteration 1: log pseudolikelihood = -36592.386 Poisson regression Number of obs = 100 Wald chi2(7) = . Prob > chi2 = . Log pseudolikelihood = -36592.386 Pseudo R2 = 0.1445 (Std. Err. adjusted for 16 clusters in id) ---------------------------------------------------------------------------------- | Robust salary | Coef. Std. Err. z P>|z| [95% Conf. Interval] -----------------+---------------------------------------------------------------- treatment | .0263173 .076578 0.34 0.731 -.1237728 .1764074 | time | 97 | -.0202027 .0205503 -0.98 0.326 -.0604805 .020075 98 | 8.97e-16 1.19e-08 0.00 1.000 -2.33e-08 2.33e-08 100 | -.0202027 .0205503 -0.98 0.326 -.0604805 .020075 101 | 1.06e-15 .033385 0.00 1.000 -.0654334 .0654334 102 | .0263173 .0263149 1.00 0.317 -.0252589 .0778935 103 | 1.04e-15 . . . . . | time#c.treatment | 97 | -.0263173 .0382658 -0.69 0.492 -.1013169 .0486823 98 | -.04652 .0322794 -1.44 0.150 -.1097865 .0167464 100 | -.0061146 .0333884 -0.18 0.855 -.0715547 .0593255 101 | -.1771402 .0446678 -3.97 0.000 -.2646875 -.0895929 102 | -.2034575 .0396627 -5.13 0.000 -.281195 -.12572 103 | -.1771402 .0509788 -3.47 0.001 -.2770568 -.0772236 | _cons | 10.48331 .0540899 193.81 0.000 10.37729 10.58932 ---------------------------------------------------------------------------------- . margins, eydx(treatment) at(time = (99 101)) Average marginal effects Number of obs = 100 Model VCE : Robust Expression : Predicted number of events, predict() ey/dx w.r.t. : treatment 1._at : time = 99 2._at : time = 101 ------------------------------------------------------------------------------ | Delta-method | ey/dx Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- treatment | _at | 1 | .0263173 .076578 0.34 0.731 -.1237728 .1764074 2 | -.1508229 .0829549 -1.82 0.069 -.3134116 .0117658 ------------------------------------------------------------------------------ . di r(table)[1,2]-r(table)[1,1] -.1771402Comment
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Thanks for the reply. I need the fixed effects, so I need to use the xtpoisson. Curiously, when I run - possion -, then eydx provides the elasticity, but when I run - xtpoisson - then dydx seems to provide the elasticity. Can you explain this? To me, it seems like xtpoisson has already calculated the coefficients in semi-elastic form, which is why the dydx following xtpoisson is similar to eydx following poisson. But this is just from experimenting.Last edited by Gustav Egede Hansen; 16 Nov 2021, 10:12.Comment
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-margins- after -xtlogit, fe- or -xtpoisson, fe- won't give meaningful results because they are both conditional MLE where heterogeneity distributions are not specified. The original coefficients from -xtpoisson, fe- have already been semi-elasticities and you won't need -margins- anyway.
Another solution where FE can be accounted for and -margins- can be used is to go with -poisson- + Mundlak device to which Jeff gave an example in here (replacing oprobit with poisson). With unbalanced data, some adjustment is needed, and you may refer to Jeff's paper in here. BTW, If your poisson regression only controls for treatment, time and their interactions, then my estimation in #19 has already been an application of this approach with balanced panel data (-xtpoisson, fe- with the same model specification should give similar coefficients).Last edited by Fei Wang; 16 Nov 2021, 11:19.Comment
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To further explain the Mundlak device in #21, I only keep balanced panel from the example data in #1. With the same model specification, results are consistent, too. With unbalanced panel (as in #19) or adding time-varying covariates, the first model specification needs adjustment. One advantage of the first method is that time-invariant variables, like gender, can be controlled for, while it's dropped from the second model.
Code:. bys id (time): keep if _N == 7 (23 observations deleted) . . poisson salary c.treatment##ib(99).time gender Iteration 0: log likelihood = -540.67223 Iteration 1: log likelihood = -540.66877 Iteration 2: log likelihood = -540.66877 Poisson regression Number of obs = 77 LR chi2(14) = 49279.35 Prob > chi2 = 0.0000 Log likelihood = -540.66877 Pseudo R2 = 0.9785 ---------------------------------------------------------------------------------- salary | Coef. Std. Err. z P>|z| [95% Conf. Interval] -----------------+---------------------------------------------------------------- treatment | -.0007677 .0031363 -0.24 0.807 -.0069147 .0053794 | time | 97 | -5.07e-17 .0030151 -0.00 1.000 -.0059095 .0059095 98 | -5.63e-17 .0030151 -0.00 1.000 -.0059095 .0059095 100 | -2.28e-17 .0030151 -0.00 1.000 -.0059095 .0059095 101 | 2.86e-16 .0030151 0.00 1.000 -.0059095 .0059095 102 | 3.06e-16 .0030151 0.00 1.000 -.0059095 .0059095 103 | 3.20e-16 .0030151 0.00 1.000 -.0059095 .0059095 | time#c.treatment | 97 | 4.36e-16 .0044291 0.00 1.000 -.0086809 .0086809 98 | 4.44e-16 .0044291 0.00 1.000 -.0086809 .0086809 100 | 8.90e-17 .0044291 0.00 1.000 -.0086809 .0086809 101 | -.1410786 .0045183 -31.22 0.000 -.1499342 -.132223 102 | -.1410786 .0045183 -31.22 0.000 -.1499342 -.132223 103 | -.1410786 .0045183 -31.22 0.000 -.1499342 -.132223 | gender | -.29438 .0014577 -201.95 0.000 -.2972369 -.291523 _cons | 10.59846 .0021684 4887.68 0.000 10.59421 10.60271 ---------------------------------------------------------------------------------- . . xtset id panel variable: id (balanced) . xtpoisson salary c.treatment##ib(99).time gender, fe note: treatment dropped because it is constant within group note: gender dropped because it is constant within group Iteration 0: log likelihood = -3453.2366 Iteration 1: log likelihood = -443.11526 Iteration 2: log likelihood = -442.71387 Iteration 3: log likelihood = -442.71387 Conditional fixed-effects Poisson regression Number of obs = 77 Group variable: id Number of groups = 11 Obs per group: min = 7 avg = 7.0 max = 7 Wald chi2(12) = 5966.20 Log likelihood = -442.71387 Prob > chi2 = 0.0000 ---------------------------------------------------------------------------------- salary | Coef. Std. Err. z P>|z| [95% Conf. Interval] -----------------+---------------------------------------------------------------- time | 97 | -1.41e-17 .0030151 -0.00 1.000 -.0059095 .0059095 98 | -1.37e-17 .0030151 -0.00 1.000 -.0059095 .0059095 100 | -1.45e-17 .0030151 -0.00 1.000 -.0059095 .0059095 101 | -4.13e-17 .0030151 -0.00 1.000 -.0059095 .0059095 102 | -4.09e-17 .0030151 -0.00 1.000 -.0059095 .0059095 103 | 5.96e-23 .0030151 0.00 1.000 -.0059095 .0059095 | time#c.treatment | 97 | 1.18e-15 .0044291 0.00 1.000 -.0086809 .0086809 98 | 1.18e-15 .0044291 0.00 1.000 -.0086809 .0086809 99 | 0 (omitted) 100 | 9.21e-16 .0044291 0.00 1.000 -.0086809 .0086809 101 | -.1410786 .0045183 -31.22 0.000 -.1499343 -.132223 102 | -.1410786 .0045183 -31.22 0.000 -.1499343 -.132223 103 | -.1410786 .0045183 -31.22 0.000 -.1499343 -.132223 ----------------------------------------------------------------------------------Comment
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Thanks for this elaborate explanation of the Mundlak device! I still have a question for xtpoisson. If the "the original coefficients from -xtpoisson, fe- have already been semi-elasticities" wouldnt it been wise to subsequently use - dydx - to interpret them, especially given the use of interaction between time and treatment? And of couse still using - di (exp(r(estimate))-1)*100 - to have the precentage change.Last edited by Gustav Egede Hansen; 17 Nov 2021, 00:12.Comment
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In the estimation below, the interaction of treatment and time101 has already been what you need: The intervention decreases salary by 14.88%. If you need accurate percentage, then the last line tells that the intervention decreases salary by 13.82%.
Using -margins, dydx- after -xtpoisson, fe- reports the original coefficients which are actually "eyex". So I wouldn't trust any result derived from -margins- in this case, regardless whether it happens to give correct answers.
Code:. xtset id panel variable: id (unbalanced) . xtpoisson salary c.treatment##ib(99).time, fe note: treatment dropped because it is constant within group Iteration 0: log likelihood = -5157.3203 Iteration 1: log likelihood = -609.10207 Iteration 2: log likelihood = -608.27842 Iteration 3: log likelihood = -608.27842 Conditional fixed-effects Poisson regression Number of obs = 100 Group variable: id Number of groups = 16 Obs per group: min = 3 avg = 6.2 max = 7 Wald chi2(12) = 9002.57 Log likelihood = -608.27842 Prob > chi2 = 0.0000 ---------------------------------------------------------------------------------- salary | Coef. Std. Err. z P>|z| [95% Conf. Interval] -----------------+---------------------------------------------------------------- time | 97 | 1.43e-17 .0027776 0.00 1.000 -.005444 .005444 98 | 2.73e-17 .0028284 0.00 1.000 -.0055436 .0055436 100 | 6.94e-17 .0027776 0.00 1.000 -.005444 .005444 101 | 2.82e-17 .0028761 0.00 1.000 -.0056371 .0056371 102 | 9.81e-17 .0029418 0.00 1.000 -.0057659 .0057659 103 | -2.17e-19 .0028284 -0.00 1.000 -.0055436 .0055436 | time#c.treatment | 97 | .0033096 .004007 0.83 0.409 -.0045439 .0111631 98 | .0033096 .0040424 0.82 0.413 -.0046132 .0112325 99 | 0 (omitted) 100 | .0016513 .0040466 0.41 0.683 -.0062798 .0095824 101 | -.14877 .0041968 -35.45 0.000 -.1569955 -.1405445 102 | -.1491716 .0042385 -35.19 0.000 -.1574789 -.1408643 103 | -.1484763 .0041901 -35.43 0.000 -.1566888 -.1402638 ---------------------------------------------------------------------------------- . di (exp(_b[101.time#c.treatment])-1)*100 -13.823273Comment
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This makes a lot of sense. Thank you so much Fei Wang for your explanations and patience! You have helped me out tremendously!Comment
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