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  • Random effects Tobit vs. Pooled Tobit

    Dear Statalisters,

    I run a D-I-D analysis using a balanced household-month panel data. ~170,000 obs. overall.

    My independent variables vary either "between" households (e.g. demographic dummies) or "within" households (policy change dummy, control for monthly advertising expenditures, etc.).
    There are no explanatory variables that vary across both households and months (e.g Xit).
    If I understand correctly, since there is no "between" variation in the panel,
    I get the same results for fixed-effects, random-effects, and Pooled OLS models (except for different standard errors).

    The "reduced form" results are:

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    So far so good...

    Also, my dependent variable is the monthly meat purchase amount per household, which is censored at 0. This means that I should probably use Tobit.
    To take advantage of the panel structure of my data, I ran a random-effects Tobit (using the -metobit- command) and compared the results to a Pooled Tobit model.
    I was surprised to find that unlike the RE/Pooled OLS case the results are different.
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    Click image for larger version

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    So, my questions are:

    1. why are the RE-Tobit results different from the Pooled-Tobit, unlike the linear models?
    2. Can I rely on the Pooled Tobit results?
    I see that the LR test in the metobit results rejects the H of equal models, but I thought that maybe the test is misspecified in the absence of "between" variation.

    Any help would be greatly appreciated,

    Thanks,
    Adam
    Attached Files

  • #2
    Dear Adam Dvir,

    Your data is not censored, it is just non-negative. I would consider using a Poisson regression (with robust/clustered standard errors) to start with; this is valid even if your dependent variable is not a count.

    Best wishes,

    Joao

    Comment


    • #3
      Dear Joao Santos Silva,

      Thank you very much for the reply,

      I tend to agree that the data is not really censored, although the applied literature has many examples of using Tobit with similar data, such as purchases or time-diary data, because of the large number of zeros.

      In addition, if the data is not censored, isn't OLS the best approach?
      When I aggregate the data to 2 periods (before and after) and run an OLS DID regression I get the same results as before (though standard errors are much larger), but with much fewer zero values.

      I am less familiar with the Poisson regression, so I have to look deeper into it.

      Thanks,
      Adam

      Comment


      • #4
        Dear Adam Dvir,

        Tobit used to be the standard estimator for this kind of data, but that is really difficult to justify. Poisson regression (PPML) is now the standard approach to deal with trade data that also has a lot of zeros, and is gaining popularity in other areas where we have corner-solutions data like yours. OLS is not suitable because it ignores that the conditional expectation cannot be negative, and can be very misleading.

        Best wishes,

        Joao

        Comment


        • #5
          Thank you so much Joao Santos Silva,

          It sure helps.
          Adam

          Comment


          • #6
            Dear Joao Santos Silva,

            Thank you again for the inputs and directions.
            I have explored a bit in the literature on the use of PPML in empirical research.
            As you said, I found a lot of work, especially in the trade literature, but couldn't find an example of using PPML when the dependent variable is not "count".
            Do you happen to have some references for using PPML with data like mine?

            Many thanks,
            Adam

            Comment


            • #7
              Dear Adam Dvir,

              There are early papers in the health economics literature using Poisson regression for variables just like yours, see this pioneering work by Manning and Mullahy. Also, trade data are not counts, so all the literature on trade using PPML are good examples of that; the key paper in that literature is this one which, as you can see, has many citations. The approach is now being used in many other contexts.

              Best wishes,

              Joao

              Comment


              • #8
                Dear Joao Santos Silva,

                Thanks a lot for the response and references. I carefully read your 2006 paper and found it very insightful.
                Also, following your advice, I ran an -xtpoisson- RE regression and got results that make a lot of sense and are very close to the OLS FE results I got earlier (see below in comparison to #1).

                If possible, I'd be grateful if I could ask a few more questions to make sure I understood correctly:
                1. I could not understand The meaning of the estimated coefficients of the -xtpoisson- regression below. Although the coefficient of interest (iprod_class#after) is negative and significant as expected, the coefficient is on a completely different scale of the dependent variable (150 grams and more in most non zero obs.). Should it be interpreted as the change in the probability to purchase?
                2. Stata produces a note (marked in yellow) for using non-count data. I guess that's ok since that's exactly what we were doing.
                3. To predict the change in weight of the treatment (Pastrami & Sausages) and control (Snacks) categories after the reform I used the -margins- command (see below). I used predict(nuo), which is, as stated in the Stata's manual: "predicted number of events; assumes fixed or random effect is zero". I wanted to make sure that this is the value that needed to be predicted, since the data is not "count". Therefore, in this case, it is predicting the conditional expectations of the dependent variable. If so, the results make a lot of sense.
                Many many thanks,
                Adam


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                Comment


                • #9
                  Dear Adam Dvir,

                  Please note that you should be using FE, not RE.

                  1 - The interpretation is as in a log-log model (the coefficients are either elasticities or semi-elasticities).
                  2 - You can ignore the warning.
                  3 - I do not think you can use margins in this context because the fixed effects are not estimated.

                  Best wishes,

                  Joao

                  Comment


                  • #10
                    Dear Joao Santos Silva ,

                    Thank you so much for all the good advice.

                    I ran the model with FE instead of RE and the results are identical.
                    This is probably due to the non-between variation in my panel.

                    Do you still think that the use of -margins- could be problematic?

                    Thanks,
                    Adam




                    Comment


                    • #11
                      Dear Adam Dvir,

                      Since you have 74 observations per group, just run a Poisson regression including one dummy per group. Then you can use margins and do whatever you like.

                      Best wishes,

                      Joao

                      Comment


                      • #12
                        Dear Joao Santos Silva,

                        Thank you so much for all the helpful tips and advice.
                        It definitely helped me a lot.

                        Best,
                        Adam

                        Comment

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