I am wondering if any routine has been written for price elasticity in mixlogit in stata. It seems that simulation is still needed to obtain proper price elasticity.
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There is no dedicated routine, but the procedure described here http://www.stata.com/statalist/archi.../msg00283.html can (with some minor modifications) be used to calculate elasticities instead of marginal effects. -
Would the modification be to increase the relevant vbl by 1% instead of 1 unit?Comment
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Yes, that's right. Also in step 4) you should calculate the percentage change in the probabilities, instead of the difference.Would the modification be to increase the relevant vbl by 1% instead of 1 unit?Last edited by Arne Risa Hole; 10 Dec 2015, 09:28.Comment
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Is what I post below the correct way of computing the elasticity (toward the end of the post, in blue font)? If so, how can I specify which outcome to predict in mixlpred, for example for cross-elasticities? As I understand it, because there is no IIA restriction for mixed logit, the elasticities are allowed to vary by alternative. I have also attached the dataset I used in this toy example:
where:Code:. use mixed_fishing,clear . sort id fishmode . list id fishmode d q p income dbeach dprivate ybeach yprivate in 1/6,sepby(id) noobs +------------------------------------------------------------------------------------------+ | id fishmode d q p income dbeach dprivate ybeach yprivate | |------------------------------------------------------------------------------------------| | 3 beach 0 .5333 161.874 3.75 1 0 3.75 0 | | 3 pier 0 .4522 161.874 3.75 0 0 0 0 | | 3 private 1 .2413 24.334 3.75 0 1 0 3.75 | |------------------------------------------------------------------------------------------| | 4 beach 0 .0678 15.134 2.083333 1 0 2.083333 0 | | 4 pier 1 .0789 15.134 2.083333 0 0 0 0 | | 4 private 0 .1643 55.93 2.083333 0 1 0 2.083333 | +------------------------------------------------------------------------------------------+
Code:storage display value variable name type format label variable label ----------------------------------------------------------------------------------------------------------------------- id float %9.0g person id number fishmode str7 %9s available alternatives d float %9.0g =1 if chosen alternative q float %9.0g catch rate for available alternatives p float %9.0g price for available alternatives income float %9.0g monthly income in thousands $ dbeach float %9.0g =1 if beach is chosen alternative dprivate float %9.0g =1 if private is chosen alternative ybeach float %9.0g =dbeach*income yprivate float %9.0g =dprivate*income
First, fit the model:
Code:. ** Set macros . * Outcome . global ylist d . . * Model covariate . global xlist q dbeach dprivate ybeach yprivate . global rand p . global id id . global group id . . * Mixed logit or random-parameters logit model . mixlogit $ylist $xlist, group ($group) id($id) rand($rand) nrep(200) Iteration 0: log likelihood = -602.08535 (not concave) Iteration 1: log likelihood = -447.20449 Iteration 2: log likelihood = -434.71017 Iteration 3: log likelihood = -433.83131 Iteration 4: log likelihood = -433.79169 Iteration 5: log likelihood = -433.79161 Iteration 6: log likelihood = -433.79161 Mixed logit model Number of obs = 2190 LR chi2(1) = 66.04 Log likelihood = -433.79161 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ d | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- Mean | q | .8526843 .9235166 0.92 0.356 -.957375 2.662743 dbeach | -.7796412 .2245532 -3.47 0.001 -1.219757 -.339525 dprivate | -.2189507 .3033658 -0.72 0.470 -.8135368 .3756353 ybeach | .1203407 .0492813 2.44 0.015 .0237512 .2169302 yprivate | .1735461 .0709019 2.45 0.014 .0345809 .3125114 p | -.1072691 .0258052 -4.16 0.000 -.1578464 -.0566917 -------------+---------------------------------------------------------------- SD | p | .0592371 .017146 3.45 0.001 .0256316 .0928427 ------------------------------------------------------------------------------ . preserve
Then manually compute elasticities:
Finally, get average elasticity by using -summarize-Code:. * Manually compute elasticities (http://www.stata.com/statalist/archive/2012-02/msg00283.html) . * see also Cameron and Trivedi p. 353 . * 1) Use -mixlpred- to calculate predicted probabilities in the original scenario . . mixlpred pred0,nrep(200) . . . * 2) Increase the relevant variable by 1 unit for all individuals in the sample . . replace p=p*1.01 (2190 real changes made) . . . . * 3) Use -mixlpred- to calculate predicted probabilities in the alternative scenario . . mixlpred pred1,nrep(200) . . . . *4) Calculate the difference between the predicted probabilities in 1) . *and 3) and average this difference over individuals. This gives you an . *estimate of the marginal effect. . . * in step 4) you should calculate the percentage change in the probabilities, instead of the difference. . generate elast=((pred1-pred0)/pred0)/(.01)
Code:. . summ elast Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- elast | 2190 -.1833987 .3490297 -1.115784 .3557601Last edited by Hawa Harahap; 10 Dec 2015, 15:33.Comment
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That's not quite right, as you typically want to increase e.g. the price of one specific alternative, not all of the alternatives. Note also that you should not include indicators of an alternative being chosen as explanatory variables in the model, but you can include alternative-specific constants and their interactions with individual-level characteristics. See the example below which uses the same data set as in your example:
Code:use http://www.stata-press.com/data/mus/mus15data.dta * Set up data and estimate model generate id = _n reshape long d p q, i(id) j(fishmode beach pier private charter) string gen charter = fishmode=="charter" gen pier = fishmode=="pier" gen private = fishmode=="private" gen charter_inc = charter*income gen pier_inc = pier*income gen private_inc = private*income global xlist q charter pier private charter_inc pier_inc private_inc mixlogit d $xlist, group(id) rand(p) nrep(200) *Calculate direct and cross price elasticities w.r.t. the private mode preserve mixlpred pred0, nrep(200) replace p = p*1.01 if fishmode=="private" mixlpred pred1, nrep(200) generate elast = 100*(pred1-pred0)/pred0 *Cross elasticity, beach mode sum elast if fishmode=="beach" *Cross elasticity, charter mode sum elast if fishmode=="charter" *Cross elasticity, pier mode sum elast if fishmode=="pier" *Direct elasticity, private mode sum elast if fishmode=="private" restore
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OK, thank you, Arne. I thought I was missing something (and I was). I appreciate your help!
HHComment
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I have a follow-up question about standard errors when pweights and clusters are used in estimating mixlogit. Using the same dataset:
Add weights and clustering to estimationCode:*make bogus cluster and pweight variables egen cluster=cut(id),group(197) gen pweight=abs(rnormal()) svyset cluster [pweight=pweight] reshape long d p q, i(id) j(fishmode beach pier private charter) string gen charter = fishmode=="charter" gen pier = fishmode=="pier" gen private = fishmode=="private" gen charter_inc = charter*income gen pier_inc = pier*income gen private_inc = private*income global xlist q charter pier private charter_inc pier_inc private_inc
Now when we calculate and cross elasticities, should we weight and cluster to get the robust SE? In other words, would svy: mean have to be used instead of -summarize-, or can -summarize- be used as-is, because the weighting and clustering has already been applied to get the parameter estimates?Code:mixlogit d $xlist [pw=pweight], group(id) rand(p) nrep(200) robust cluster(cluster)
For example:
Code:*Calculate direct and cross price elasticities w.r.t. the private mode preserve mixlpred pred0, nrep(200) replace p = p*1.01 if fishmode=="private" mixlpred pred1, nrep(200) generate elast = 100*(pred1-pred0)/pred0 *Cross elasticity, beach mode *sum elast if fishmode=="beach" svy: mean elast if fishmode=="beach" *Cross elasticity, charter mode *sum elast if fishmode=="charter" svy: mean elast if fishmode=="charter" *Cross elasticity, pier mode *sum elast if fishmode=="pier" svy: mean elast if fishmode=="pier" *Direct elasticity, private mode *sum elast if fishmode=="private" svy: mean elast if fishmode=="private" restore
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You don't get SEs at all using this approach unfortunately (cluster-adjusted or otherwise). You could use bootstrapping but that's likely to be impractical in most applications given the time it typically takes to estimate mixed logit models.Comment
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Noted. Thanks again for your help!Comment
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Following the above post I have a specific question.
What if I have in the model an interacted variable with the variable price, p.
And I want again to calculate the elasticity. Should I increase the interacted variable 2 besides the variable p?
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Thank you Arne so much for the code. I tried running and have some questions.Originally posted by Arne Risa Hole View Post
1. If individual-specific variables are binary or categorical, I can let it interact like price and income in this example?
2. Interpretation
In the output, as "private" is chosen for direct elasticity, I got the following:
Can I interpret that for 10% price increase in private mode, there will be 108% less demand for private mode itself?Code:sum elast if fishmode=="private" Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- elast | 1,182 -1.089557 1.058432 -8.242974 1.38986
3. Is it essential to test the significance of the elasticity in this case, as mixlogit results show that private mode is statistically insignificant and it may impact the direct elasticity?
Thank you so much.Comment
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