Elasticity and Marginal Effect of Tobit Regression

[Bryan Gensits]

Hi! I have been using stata14 for about a week and have been piecing together information online and feel as though I am getting a decent handle on it for my purposes. After running a Tobit regression on my data set, I need to find the marginal effects (dy/dx) and elasticities (ey/ex). This is where I have not been able to find clear answers.

For the marginal effect, I have told me simply running:

mfx

will work and others have told me running:

mfx, predict(e(0,.))

Likewise, post-Tobit elasticity, I have been seeing both:
mfx, eyex
and
mfx, predict(e(0,.)) eyex

If anyone has any insight on what the "predict(e(0,.))" function does, and if or why it may be necessary and wouldn't mind sharing their insights I would be greatly appreciative. In addition, if anyone knows has any recommendations or cautions with these results I would really appreciate it.

Thanks in advance,

Bryan Gensits
Royal University of Bhutan: College of Natural Resources

[Clyde Schechter]

-mfx- is an old command that has been superseded by -margins-. If you have run your -tobit- regression with factor notation used, then marginal effects are obtained with -margins, dydx()- and elasticities with -margins, eyex()-. Since you are new to Stata, it is best to form good habits from the start and learn to use Stata's up-to-date features.

You can learn all about factor-variable notation by running -help fvvarlist-; more information is available in the corresponding section of the on-line manuals. You can analogously learn about -margins- that way, but https://www3.nd.edu/~rwilliam/stats/Margins01.pdf provides a more focused, simpler introduction that covers most of what is needed.

[Marcos Almeida]

Hello Bryan,

Welcome to the Stata Forum/Statalist

To start, I recommend you take a look on:

. help margins

Also, please read the FAQ on how to share command and output under CODE delimiters or by instaling the SSC dataex.

That said, I believe you wish something like this:

. sysuse auto
(1978 Automobile Data)

.  generate wgt=weight/1000

. tobit mpg wgt i.foreign, ll(17)

Tobit regression                                Number of obs     =         74
                                                LR chi2(2)        =      76.31
                                                Prob > chi2       =     0.0000
Log likelihood = -162.52596                     Pseudo R2         =     0.1901

------------------------------------------------------------------------------
         mpg |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         wgt |  -7.797866   .8701668    -8.96   0.000    -9.532512    -6.06322
             |
     foreign |
    Foreign  |  -2.336203   1.259564    -1.85   0.068    -4.847097     .174691
       _cons |   44.93177   2.792179    16.09   0.000     39.36567    50.49788
-------------+----------------------------------------------------------------
      /sigma |   3.781249   .3593973                      3.064804    4.497694
------------------------------------------------------------------------------
            18  left-censored observations at mpg <= 17
            56     uncensored observations
             0 right-censored observations

. margins , eyex(wgt)

Average marginal effects                        Number of obs     =         74
Model VCE    : OIM

Expression   : Linear prediction, predict()
ey/ex w.r.t. : wgt

------------------------------------------------------------------------------
             |            Delta-method
             |      ey/ex   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         wgt |  -1.343588   .2084189    -6.45   0.000    -1.752082   -.9350948
------------------------------------------------------------------------------

. margins foreign, eyex(wgt)

Average marginal effects                        Number of obs     =         74
Model VCE    : OIM

Expression   : Linear prediction, predict()
ey/ex w.r.t. : wgt

------------------------------------------------------------------------------
             |            Delta-method
             |      ey/ex   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
wgt          |
     foreign |
   Domestic  |  -1.322087   .2002683    -6.60   0.000    -1.714605    -.929568
    Foreign  |  -1.565491   .3739453    -4.19   0.000     -2.29841   -.8325716
------------------------------------------------------------------------------

Hopefully that helps.

[Bryan Gensits]

Clyde and Marcos,

Thank you both very much for your responses. The PDF you provided, Clyde, goes over exactly what I am trying to do and I greatly appreciate you sharing that with me. The margins command is diverse enough solve exactly what I need it to at the moment elegantly.

Also, thank you, Marcos for explaining how to share code in STATALIST, I will definitely use that in the future.

Best,
Bryan Gensits
Royal University of Bhutan: College of Natural Resources

[Clyde Schechter]

The PDF you provided, Clyde, goes over exactly what I am trying to do and I greatly appreciate you sharing that with me.

You're welcome. But the thanks are really owed to Richard Williams for writing it!

[Marcos Almeida]

Bryan Gensits I recommend you take a look on the semielasticities in the Stata Manual as well. They may provide a handy output, depending on the way you wish to show the predictions;

Margins estimates and reports margins of responses and margins of derivatives of responses, also
known as marginal effects. A margin is a statistic based on a fitted model in which some of or all the
covariates are fixed. Marginal effects are changes in the response for change in a covariate, which
can be reported as a derivative, elasticity, or semielasticity.
[...]
dydx(varlist) estimate marginal effect of variables in varlist
eyex(varlist) estimate elasticities of variables in varlist
dyex(varlist) estimate semielasticity—d(y)=d(lnx)
eydx(varlist) estimate semielasticity—d(lny)=d(x)

[Bryan Gensits]

Marcos Almeida Great reference, thanks!

One more question for you: when I run

tobit LAND i.SOIL i.TO i.YIELD i.STRIGA i.DROUGHT AGE i.HEAD TEST VISIT WKSHOP, ll(0)
margins , eyex(SOIL)

I am given error

factor variables not allowed in option eyex()

However, if I do not input my variables as being factor variables and run

tobit LAND SOIL TO YIELD STRIGA DROUGHT AGE HEAD TEST VISIT WKSHOP, ll(0)
margins , eyex(SOIL)

Stata outputs identical results in the tobit table in terms of coefficiants, etc. and I do not get an error when I look of the elasticity of any given variable.

I do not know enough about the inner workings of stata at this point to know if this is mathamatically correct. Do you fundimentally see any problem with this approach?

Thanks again,
Bryan Gensits

[Marcos Almeida]

Hello Bryan,

You may wish to take a close look in #3.

There, on purpose, I shared two examples.

One them presents the average marginal effects (AME) in elasticities only for a continuous variable, whereas the other presents the AME of the very same continuous variable to different levels of the factor variable.

By the way, Richard William's lectures (hand-outs, presentations, whatever the name is) on margins, including the one shared in #2, are a "must read".

Really so. Definitely.

[Ariel Vazquez]

Where can I find an articles in magazines (jornal´s) that contain the syntax "do's" in stata? Thank You

[Marcos Almeida]

Ariel Vazquez This is a quite different theme, ideally, to be posted under a different thread. That said, the Stata Manual and the Stata Journal are the references you should always look for.

[Stephen Mailu]

I have ran a tobit spatial panel model and I would wish to estimate elasticities at specified levels of some independent variables. The code I have used is as follows;

sptobitsarxt $ylist $xlist , nc(42) wmfile(weights2) dist(weib) mfx(log) tests ll(0) tolog

Although marginal effects and elasticities are provided at the end, these are evaluated at the means of the RHS variables. If I however wish to calculate margins using for example the code;
margins, predict(ystar(0,.)), I get the response

margins not appropriate after mean
r(322);

Could someone give me a hint of how I should proceed?