Panel data tobit and marginal effect

[Mika Shin]

About xttobit "re"
I have 3years panel data and try to estimate correlation between damage cost of disaster in 200 municipalities and some variables such as precipitation or land type dummy. Since the damage cost can be 0 when no rain in some municipalities, I think I need to use tobit model. Also, I studies that tobit could only take random effect.

However, I used to use panel data regression before and at that time, I had to test if random effect/ fixed effect model is better fitting. I am not sure if I could use "re" option in the "xttobit" command without test.

About Margins,
I need to estimate future damage cost if future precipitation would be certain amount, let's say in 2100, precipitation of A area will be 2000mm annually then what the damage cost will be.
I have data of current precipitation and damage cost.

Is this right to do?

xttobit y x1 x2 x3..., re

margins, dydx (x1,x2,x3...)

Even if i get result of margins, I am not sure how to interpret the value because it is panel data of 3 years.

Any suggestion will be welcome.
Thank you in advance.

[Mika Shin]

I need to add something. Because of non-linearity of Tobit model, estimated coefficients are not marginal effect. In this case , how could I get marginal effect of each variables?

[Phil Bromiley]

It is best to follow the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. Sometimes you can have errors in your code that you don't think are important and so don't include the errors in summaries like you provide.

I find predictive margins at specific values of the rhs variables easier to interpret than dydx sometimes. With re, your effects combine within and between effects which is a little tricky.

[Mika Shin]

Thank you for your reply, Phil Bromiley,

Here is my code and results table.

 xttobit ln_damage ln_aband ln_borrow ln_ov65y agrcop landD rain day y05, re

btaining starting values for full model:

Iteration 0:   log likelihood = -339.14294
Iteration 1:   log likelihood = -338.93638
Iteration 2:   log likelihood = -338.32976
Iteration 3:   log likelihood = -338.31535
Iteration 4:   log likelihood = -338.31533

Fitting full model:

Iteration 0:   log likelihood = -338.31533  
Iteration 1:   log likelihood = -338.31533  

Random-effects tobit regression                 Number of obs      =       165
Group variable: munici_code                     Number of groups   =       124

Random effects u_i ~ Gaussian                   Obs per group: min =         1
                                                               avg =       1.3
                                                               max =         3

Integration method: mvaghermite                 Integration points =        12

                                                Wald chi2(8)       =     46.28
Log likelihood  = -338.31533                    Prob > chi2        =    0.0000

------------------------------------------------------------------------------
   ln_damage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    ln_aband |    .489942    .108353     4.52   0.000      .277574      .70231
   ln_borrow |  -.0589191   .3115541    -0.19   0.850     -.669554    .5517158
    ln_ov65y |   .0317257   .4407089     0.07   0.943    -.8320477    .8954992
      agrcop |  -.0122168   .0063447    -1.93   0.054    -.0246521    .0002185
       landD |  -.3899634   .3999569    -0.98   0.330    -1.173865    .3939378
        rain |   .0009659   .0007808     1.24   0.216    -.0005644    .0024962
         day |  -.0231746   .0717746    -0.32   0.747    -.1638503    .1175011
         y05 |   .2103446   .2020655     1.04   0.298    -.1856965    .6063858
       _cons |   2.948357   .9619152     3.07   0.002     1.063038    4.833676
-------------+----------------------------------------------------------------
    /sigma_u |   1.002404   .2926813     3.42   0.001     .4287595    1.576049
    /sigma_e |   1.615141   .1752935     9.21   0.000     1.271572     1.95871
-------------+----------------------------------------------------------------
         rho |   .2780726   .1526802                       .069365    .6192013
------------------------------------------------------------------------------

  Observation summary:         0  left-censored observations
                             165     uncensored observations
                               0 right-censored observations

.

Also,since estimated coefficients are not marginal effect, I found code of marginal effect for Tobit as below. Now, how should I interpret the result of marginal effect in Tobit model?

.

margins, dydx( ln_aband )predict(    e(0,.))

Average marginal effects                          Number of obs   =        165
Model VCE    : OIM

Expression   : E(ln_damage|ln_damage>0), predict( e(0,.))
dy/dx w.r.t. : ln_aband

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
    ln_aband |   .3083194   .0689851     4.47   0.000     .1731111    .4435276
------------------------------------------------------------------------------
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