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  • Nonlinear Panel Data Models -- Finding the best fit

    Hello all,

    I am trying to navigate my way through nonlinear models using panel data. I am familiar with nonlinear models without panel data, but using these models with panel data is a new space for me. I am also familiar with xtreg and curvefit. My main goal right now is to find the model that best fits my data (e.g., quadratic, power, growth, etc.); i.e., to understand the relationship between my variables of interest. Here is my design and what I have done:

    My data: annual data over 10 years, 500 companies
    Dependent variable: Company financial performance
    Main independent (predictor) variable of interest: Company innovation

    Theoretically, I suspect an inverted U-shape relationship between performance and innovation; i.e., very little or very high innovation is associated with lower levels of company financial performance than moderate levels of innovation. Now I want to test this (or see if there is a different nonlinear relationship between financial performance and innovation).

    I have plotted the data on a twoway plot to observe the structure. It looks like an inverted U or an inverted growth (exponential) relationship, where increasing innovation at very low levels of innovation drastically increases financial performance but then this relationship tapers off (flattens out). So a few issues/question:

    1) I have used curvefit but I don't think it works with panel data. Maybe I am wrong? I also don't think the twoway scatter accounts for the panel structure of the data.

    2) I don't know if I can use nonlinear models with fixed effects. Does this make sense? So my code for a quadratic relationship (exploring an inverted U) looks like this:
    xtreg financial_performance c.innovation##c.innovation control_variables i.yr, fe

    I found the output is significant and plotted the output using marginsplot and all points towards an inverted U, but I want to make sure I'm not missing something in what I am doing.
    c.innovation = +ve and significant @ 1%
    c.innovation##c.innovation = -ve and significant @ 5%

    3) Should I be concerned with first-order autoregressive error terms to account for the repeated measurement of financial performance (my dependent variable) from the same firms. If so, how would I incorporate this into my models? I am wondering about GLS models (e.g., xtgls) but am not familiar with these.

    Thank you for any guidance and help you can provide!

    Sincerely,
    Roger



  • #2
    You didn't get a quick response. You'll increase your chances of a helpful response by following the FAQ on asking questions.

    There is no reason you can't just include c.innovation##c.innovation in the model. There is a routine for testing U shaped models - utest.ado. I'm not sure if it is right or works with panel data. The one thing to check is that your data really span the entire range of your U. It is quite possible to get a U when you only have curved data on the up or down side. I think utest tries to test something like this.

    If you have serial correlation, you can use robust clustered standard errors in the xtreg, or you can use xtregar. xtgls is normally recommended for samples with more within-panel observations and fewer panels. While xtreg is consistent for the parameters, xtregar corrects the parameters for the serial correlation so it might be more efficient. However, xtregar does not have heteroskedasticity correction - this may not be a problem if you're using roa or something as the dv.

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