Marginal effects with a heteroskedastic tobit

[Gaston Fernandez]

Dear all,

I am struggling to compute the average marginal effects using a Tobit allowing for heteroskedasticity. Any suggestions on this will be highly appreciated.

My dependent variable is a continuous variable that takes nonnegative values only when observations in my data violated some economic assumptions. Otherwise, it is zero (54% of the sample). This variable measures the amount of budget that can be extracted from an individual who violated those assumptions. Hence, I think a Tobit model would be suitable.

I conducted a Likelihood-ratio test, which rejected the null of homoskedasticity.

Therefore, I am running the following heteroskedastic Tobit:

capture program drop het_tob
program define het_tob
   qui {
    args lnf XB WA
    replace `lnf' = -0.5*(ln(2*_pi)+ln(exp(`WA')^2)+(($ML_y1-`XB')^2/exp(`WA')^2)) if $ML_y1>0 & $ML_y1!=.
    replace `lnf' = ln(1-normprob(`XB'/exp(`WA'))) if $ML_y1<=0
    }
    end

ml model lf het_tob (Tobit: MPImax = crtstd age_years age2) (Tobhet: crtstd age_years age2), title(Tobit with Heteroscedasticity)

ml maximize,  difficult nolog

Tobit with Heteroscedasticity                   Number of obs     =        205
                                                Wald chi2(3)      =      11.79
Log likelihood = -64.449366                     Prob > chi2       =     0.0081

------------------------------------------------------------------------------
      MPImax |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tobit        |
      crtstd |  -.0448083    .021168    -2.12   0.034    -.0862968   -.0033199
   age_years |  -.0160767   .0066348    -2.42   0.015    -.0290807   -.0030726
        age2 |   .0002018   .0000952     2.12   0.034     .0000153    .0003883
       _cons |   .2392886   .1001342     2.39   0.017     .0430292    .4355481
-------------+----------------------------------------------------------------
Tobhet       |
      crtstd |   .1956093   .0843663     2.32   0.020     .0302543    .3609642
   age_years |   .0084042    .025229     0.33   0.739    -.0410436    .0578521
        age2 |    .000042   .0003784     0.11   0.912    -.0006997    .0007838
       _cons |  -1.757924   .3580635    -4.91   0.000    -2.459716   -1.056133
------------------------------------------------------------------------------

I would like to compute the average marginal effects of the variable "crtstd" and its significance. I think I am missing some relevant option while using the margins command since once I ran it I obtained the estimated coefficient of "crtstd":

margins, dydx(crtstd)

Average marginal effects                        Number of obs     =        205
Model VCE    : OIM

Expression   : Linear prediction, predict()
dy/dx w.r.t. : crtstd

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      crtstd |  -.0448083    .021168    -2.12   0.034    -.0862968   -.0033199
------------------------------------------------------------------------------

I appreciate any advice on this.

Thanks!
Gastón

[FernandoRios]

Hi Gaston,
The problem that you are facing is that, by default, margins will only calculate marginal effects with respect to the linear combination of the first equation in your model.
That is why it only gives you the same results as the coefficient output.
In order to get the correct marginal effects, which will depend on what you are trying to analyze, you need to create a program that defines your outcome of interest.
see https://blog.stata.com/2016/03/17/pr...-predict-work/ for an example of how to program that subprogram.
Fernando

[Gaston Fernandez]

Thanks for your advice and information, FernandoRios. I'll give a try creating such a program.

Gastón

[Gaston Fernandez]

Eventually this could be useful for others.

I solved my inquiry using the intreg command as follows:

gen yup = MPImax
gen ylow = MPImax
replace ylow = . if MPImax <= 0

intreg ylow yup crtstd age_years age2, het(crtstd age_years age2) nolog

Interval regression                             Number of obs     =        205
                                                   Uncensored     =         95
                                                   Left-censored  =        110
                                                   Right-censored =          0
                                                   Interval-cens. =          0

                                                Wald chi2(3)      =      11.79
Log likelihood = -64.449367                     Prob > chi2       =     0.0081

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
model        |
      crtstd |  -.0448083    .021168    -2.12   0.034    -.0862968   -.0033199
   age_years |  -.0160767   .0066348    -2.42   0.015    -.0290807   -.0030726
        age2 |   .0002018   .0000952     2.12   0.034     .0000153    .0003883
       _cons |   .2392887   .1001342     2.39   0.017     .0430293    .4355481
-------------+----------------------------------------------------------------
lnsigma      |
      crtstd |   .1956093   .0843663     2.32   0.020     .0302544    .3609642
   age_years |   .0084043    .025229     0.33   0.739    -.0410436    .0578521
        age2 |    .000042   .0003784     0.11   0.912    -.0006997    .0007838
       _cons |  -1.757925   .3580634    -4.91   0.000    -2.459716   -1.056133
------------------------------------------------------------------------------

margins, dydx(crtstd) predict(pr(0,.)) over(age)

Average marginal effects                        Number of obs     =        205
Model VCE    : OIM

Expression   : Pr(y>0), predict(pr(0,.))
dy/dx w.r.t. : crtstd
over         : age

----------------------------------------------------------------------------------
                 |            Delta-method
                 |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-----------------+----------------------------------------------------------------
crtstd           |
             age |
 8-14 years old  |  -.1017403   .0327172    -3.11   0.002    -.1658648   -.0376158
15-21 years old  |  -.0842222   .0330351    -2.55   0.011    -.1489699   -.0194745
22-32 years old  |  -.0644649   .0338565    -1.90   0.057    -.1308225    .0018926
33-43 years old  |  -.0541335   .0348211    -1.55   0.120    -.1223816    .0141146
  44+ years old  |  -.0576073   .0337056    -1.71   0.087    -.1236691    .0084544
----------------------------------------------------------------------------------