Marginal effects in Cragg's double hurdle.

[Ashish Chouhan]

Dear Statalist members, I am trying to estimate the Cragg's double hurdle model using the Churdle command of STATA. While estimating the marginal effects, the marginal effects of one categorical variable (lease) is exceeding more than 1. Is there something wrong with my model? How shall i interpret the results?



churdle exp insuredarea opholding i.lease , select( opholding i.lease) ll(0) vce(robust)



Cragg hurdle regression Number of obs = 397
Wald chi2(2) = 202.45
Prob > chi2 = 0.0000
Log pseudolikelihood = -275.0199 Pseudo R2 = 0.3470

------------------------------------------------------------------------------
| Robust
insuredarea | Coefficient std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
insuredarea |
opholding | .288812 .0210412 13.73 0.000 .247572 .3300519
1.lease | -.7743153 .1416271 -5.47 0.000 -1.051899 -.4967313
_cons | -.0343409 .0551099 -0.62 0.533 -.1423543 .0736725
-------------+----------------------------------------------------------------
selection_ll |
opholding | .2690386 .0553767 4.86 0.000 .1605023 .3775749
1.lease | -.5977384 .2241819 -2.67 0.008 -1.037127 -.1583498
_cons | -.5226244 .1230515 -4.25 0.000 -.7638009 -.2814479
-------------+----------------------------------------------------------------
lnsigma |
_cons | -1.07543 .0755514 -14.23 0.000 -1.223508 -.9273522
-------------+----------------------------------------------------------------
/sigma | .3411509 .0257744 .2941962 .3955998
------------------------------------------------------------------------------

. margins, dydx(*)

Average marginal effects Number of obs = 397
Model VCE: Robust

Expression: Conditional mean estimates of dependent variable, predict()
dy/dx wrt: opholding 1.lease

------------------------------------------------------------------------------
| Delta-method
| dy/dx std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
opholding | .5662786 .0566524 10.00 0.000 .4552419 .6773153
1.lease | -1.023912 .140112 -7.31 0.000 -1.298526 -.7492975
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

.

[John Mullahy]

A marginal effect that (in absolute value) exceeds 1 would be problematic in a probability model but I see no reason why it is of concern in the Cragg model.

The marginal effects are estimating dE[y|x]/dx. If one applies a chain rule with E[y|x]=P(y>0|x)*E[y|y>0,x] then

dE[y|x]/dx = P(y>0|x)*dE[y|y>0,x]/dx + E[y|y>0,x]*dP(y>0|x)/dx

Both summands can exceed 1 in absolute value.

[Ashish Chouhan]

I truly appreciate your guidance, Professor Mullahy. Your explanation was incredibly helpful.

[Ashish Chouhan]

Professor Mullahy, i would like to ask you an extended question on interpretation of the marginal effects in Cragg's model. If the marginal effects exceed one, how should i interpret it in context of a dummy variable (lease in my case) and a continuous variable (for example Income).

[John Mullahy]

With

E[y|x,dummy] = P(y>0|x,dummy)*E[y|y>0,x,dummy]

the marginal effect of the dummy is

E[y|x,dummy=1]-E[y|x,dummy=0] = P(y>0|x,dummy=1)*E[y|y>0,x,dummy=1] - P(y>0|x,dummy=0)*E[y|y>0,x,dummy=0]

where x is the vector of covariates other than the dummy variable of interest.

[Ashish Chouhan]

Thank you so much professor Mullahy for the clarification.