Tobit marginal effects

[maria ago]

Dear Stata users,
I estimate a Tobit model (by Stata 14), and then compute marginal effects (dE(y|x)/dx, using either margins or mfx), obtaining the outcome reported in the attachment tobit output.txt .
As you can see, coefficients (that should represent the effects on the latent variable) and marginal effects are the same. Am I using the wrong commands?
Thank you very much for your attention
Maria

[Clyde Schechter]

If you read the FAQ, as all are requested to do before posting, you will see that attaching files is discouraged. I am among those who will not open an attachment from somebody I don't know, so I haven't looked at it. So I don't actually know what you've done.

But I have a good guess as to what went wrong here. If you used -margins, dydx()- (or eydx or eyex or dyex) and no other options, the default prediction in -margins- after -tobit- is xb. So you are only getting the marginal effect on the linear predictor which, of course, is just the coefficient. Run -help tobit postestimation- and then click on the -margins- link to see the other things you can specify for -margins- to predict. I don't know exactly what your goals are, but I think most often people want to use the -predict(ystar(a, b))- option (with suitable values of a and b, of course). Then you will get marginal effects (or semi- or full-elasticities) on something more like the outcome variable.

[maria ago]

Thank you very much for your kind reply, I apologize for the attachment.
My goal is obtaining dE(y|x)/dx : the impact of my covariates on the expected value of y (not conditional on y>0). I have read the help you mention, and tried several options but I obtain always the same coefficients.

The only way I obtain different figures is when I compute dE(y|y>0 x)/dx, but it is not what I need

Hope you can visualize my output in what follows:

tobit deban south lnage llncapinv, ll(0)

Tobit regression Number of obs = 3,836
LR chi2(3) = 2148.62
Prob > chi2 = 0.0000
Log likelihood = -22440.609 Pseudo R2 = 0.0457

------------------------------------------------------------------------------
deban | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
south | -566.879 266.9171 -2.12 0.034 -1090.192 -43.56589
lnage | -64.47111 138.8334 -0.46 0.642 -336.6655 207.7232
llncapinv | 4441.337 91.39977 48.59 0.000 4262.14 4620.534
_cons | -36714.28 795.0454 -46.18 0.000 -38273.04 -35155.53
-------------+----------------------------------------------------------------
/sigma | 5072.311 76.40259 4922.518 5222.105
------------------------------------------------------------------------------
1,654 left-censored observations at deban <= 0
2,182 uncensored observations
0 right-censored observations



margins, dydx(*) predict (ystar(.,.)) atmeans

Conditional marginal effects Number of obs = 3,836
Model VCE : OIM

Expression : E(deban), predict(ystar(.,.))
dy/dx w.r.t. : south lnage llncapinv
at : south = .141293 (mean)
lnage = 2.921056 (mean)
llncapinv = 8.128421 (mean)

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
south | -566.879 266.9171 -2.12 0.034 -1090.027 -43.73114
lnage | -64.47111 138.8334 -0.46 0.642 -336.5795 207.6373
llncapinv | 4441.337 91.39977 48.59 0.000 4262.197 4620.477
------------------------------------------------------------------------------


margins, dydx(*) predict (e(.,.)) atmeans

Conditional marginal effects Number of obs = 3,836
Model VCE : OIM

Expression : E(deban), predict(e(.,.))
dy/dx w.r.t. : south lnage llncapinv
at : south = .141293 (mean)
lnage = 2.921056 (mean)
llncapinv = 8.128421 (mean)

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
south | -566.879 266.9171 -2.12 0.034 -1090.027 -43.73114
lnage | -64.47111 138.8334 -0.46 0.642 -336.5795 207.6373
llncapinv | 4441.337 91.39977 48.59 0.000 4262.197 4620.477
------------------------------------------------------------------------------




margins, dydx(*) predict (e(0,.)) atmeans

Conditional marginal effects Number of obs = 3,836
Model VCE : OIM

Expression : E(deban|deban>0), predict(e(0,.))
dy/dx w.r.t. : south lnage llncapinv
at : south = .141293 (mean)
lnage = 2.921056 (mean)
llncapinv = 8.128421 (mean)

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
south | -185.4931 87.39765 -2.12 0.034 -356.7893 -14.19684
lnage | -21.09612 45.43383 -0.46 0.642 -110.1448 67.95256
llncapinv | 1453.286 30.66317 47.40 0.000 1393.187 1513.385
------------------------------------------------------------------------------

[Jeff Wooldridge]

Maria: The correct option is

predict (ystar(0,.))

Your current option tells Stata to act as if there's no censoring even though you estimated the model allowing it. Also, I would not use "atmeans." Usually it makes more sense to average the partial effects rather than evaluate the partial effects at the mean -- especially when you have dummy or other discrete explanatory variables. If south is a dummy variable, you should use i.south in the Stata command.

[maria ago]

Thank you very much, I do appreciate your precious help!
The outcome I obtain:

margins, dydx(*) predict (ystar(0,.))

Average marginal effects Number of obs = 3,836
Model VCE : OIM

Expression : E(deban*|deban>0), predict(ystar(0,.))
dy/dx w.r.t. : 1.south lnage llncapinv

------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.south | -236.2525 108.2937 -2.18 0.029 -448.5042 -24.00085
lnage | -27.59021 59.41536 -0.46 0.642 -144.0422 88.86176
llncapinv | 1900.656 40.00744 47.51 0.000 1822.243 1979.07
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.


The star in the Expression shown by Stata - E(deban*|deban>0), predict(ystar(0,.)) - makes me doubt: am I estimating the marginal impact on the latent variable (y*)?

I wish you a happy week end

Best Regards
Maria

[Jeff Wooldridge]

Maria: Good observation. I've been meaning to alert the Stata people to this mislabeling. First, for some strange reason, Stata chose to use y* for the observed variable and y for the latent variable -- exactly backwards in my opinion. In fact, I don't know where they got that notation. Maybe we can start a movement for Stata to change this because, in my experience, it's a source of confusion.

Second, the label that shows conditioning on "deban > 0" is wrong. I've checked the calculations by hand in other examples, and the above margins command is computing the APE of E(y|x), where y is the observed outcome. It is not conditioning on positive outcomes.That would be an easier fix on their part.

[maria ago]

Thank you so much, you are solving a puzzle that was driving me (and my students) crazy! I agree Stata should amend this notation, how can I signal this point?

Thank you again for your kindness and your luminous explanation!
All the best
Maria

[Jeff Wooldridge]

Hi Maria: I'm not sure whom to contact at Stata. I'll try to find out and then suggest they change the notation and correct the conditioning statement.

[River Huang]

Dear Jeff, I use the same notations as yours. And, I think Stata uses the uncommon notations as (from help tobit)

[Preeti Jaiswal]

Maria: Good observation. I've been meaning to alert the Stata people to this mislabeling. First, for some strange reason, Stata chose to use y* for the observed variable and y for the latent variable -- exactly backwards in my opinion. In fact, I don't know where they got that notation. Maybe we can start a movement for Stata to change this because, in my experience, it's a source of confusion.

Second, the label that shows conditioning on "deban > 0" is wrong. I've checked the calculations by hand in other examples, and the above margins command is computing the APE of E(y|x), where y is the observed outcome. It is not conditioning on positive outcomes.That would be an easier fix on their part.

Has this mislabeling been corrected or does STATA still use the same notation?