Announcement

Collapse
No announcement yet.
X
  • Filter
  • Time
  • Show
Clear All
new posts

  • Panel Data – Proportion dependent variable in fixed effects regression

    Dear Community,

    I'm currently working on my master's thesis where we aim to study the effect that certain rules have on the number of leveraged buyouts that take place in a given country.

    The panel is structured as follows (numbers are made up in this example):
    Country Year No. of leveraged Transactions Total Transactions (leveraged+non-leveraged) Leveraged / Total Rule (dummy) GDP ($trn) Population US 10Y Yield ...
    A 2000 3 10 .3 0 1 200 7
    A 2001 2 8 .25 1 1.2 344 6
    A 2002 0 3 0 1 1.7 355 5
    B 2000 6 6 1 0 .4 73 7
    B 2001 5 20 .25 0 .7 75 6
    B 2002 3 9 .33 1 1 76 5
    I originally intended to use the absolute `no. of leveraged transactions` as the dependent variable (count data). 'Rule dummy' is the main independent variable of interest and I've also included some time-varying controls like GDP and population.


    Running the regression with country and year fixed effects I get:


    DV: No. of Leveraged Transactions

    Estimate Std. Error t-value Pr(>|t|)

    rule -4.17157 0.96766 -4.311 1.807e-05 *** (No controls)


    When adding e.g. GDP and the 10Y yield as controls I instead get:

    Estimate Std. Error t value Pr(>|t|)
    (Intercept) 8.3480 3.6333 2.298 0.02186 *
    rule 1.2833 1.1805 1.087 0.27736
    gdp_trn 2.9497 0.2662 11.080 < 2e-16 ***
    US10y 0.2163 1.4732 0.147 0.88331

    The rule becomes insignificant, which is not surprising as more transactions take place as GDP increases, i.e, GDP is highly correlated with the number of leveraged transactions.


    I was wondering if there's a way to improve the model to avoid the aforementioned issue.


    Here are some ideas I've come up with:

    1) Use 5th column as the dependent variable (leveraged / total transactions).
    2) Use gdp growth instead of the absolute GDP figures.

    Here's what I'd like to know:

    -The DV would now be proportions (from 0 to 1) instead of count data. Would this be a problem in my fixed effects set up? I assume that beyond the change in the interpretation of the coefficient, the regression output would also change as the proportions incorporate the total number of transactions vs. the original DV?

    - Alternatively, is it also sensible to keep the original DV (count data) but replace GDP with GDP_growth?

    - If I use GDP_growth, should I also use population_growth (otherwise absolute population would explain the number of leveraged buyouts)?

    I'd really appreciate any comments or feedback! Please let me know if something is not clear.

    Best regards,
    Diego



  • #2
    use leveraged/total? that will avoid the scale effect on GDP.

    Comment


    • #3
      Uhhhh.... you might also wanna look at beta regression or (I think it's called) fractional regression. There are specific estimators you can use for outcomes betwixt 0 and 1, and you can happily use fixed effects in them, too.

      Comment


      • #4
        HTML Code:
        https://www3.nd.edu/~rwilliam/stats3/FractionalResponseModels.pdf

        Comment


        • #5
          Originally posted by George Ford View Post
          use leveraged/total? that will avoid the scale effect on GDP.
          Hello George,

          Thank you for your suggestion! I'll most likely use leveraged/total as the DV in the regression model.

          Comment


          • #6
            Originally posted by Jared Greathouse View Post
            Uhhhh.... you might also wanna look at beta regression or (I think it's called) fractional regression. There are specific estimators you can use for outcomes betwixt 0 and 1, and you can happily use fixed effects in them, too.
            Hello Jared,

            Thank you for your feedback! I'm a layman when it comes to beta regression, but it seems to suit my model quite well.

            I've come across this really useful paper by Papke and Woolridge that looks at fractional response variables bounded between 0 and 1:

            https://www.sciencedirect.com/scienc...0440760800050X

            Comment


            • #7
              Originally posted by George Ford View Post
              HTML Code:
              https://www3.nd.edu/~rwilliam/stats3/FractionalResponseModels.pdf
              This has proven to be quite helpful! Many thanks to you George!

              Comment

              Working...
              X