non-parametric estimation of a global relationship with fixed effects

[David Kunst]

My benchmark model is quadratic of the form

Yct=a+b1Xct+b2X-squaredct+Dc+ect

, where D_ct is a full set of country dummies. My key findings are (1) that there is a non-linear relationship between Y and X (controlling for country fixed effects), and (2) that this relationship differs across two sub-samples. I would like to assess the robustness of (2) to relaxing the assumption of a quadratic relationship visually by plotting fitted values from some less restrictive, non- or semi-parametric regression method against X for both samples.

However, I am struggling to find a suitable command that can deal with the country fixed effects. Does anyone have a suggestion? Unfortunately, my University is still on Stata 14 (hence not sure if the new command "npregress" in Stata 15 would help).

[FernandoRios]

Hi David
I think there is a small misunderstanding about semi/non-parametric methods. They usually attempt to capture relationships using local relationships rather than global ones.
That being said, even if you had access to Stata14, npregress may not have been the best alternative for you, as it does not handle well mutliple Fixed effects. (because it uses local adjustments).
Since you provide no more information on your problem, im assuming you are indeed trying to capture some nonlinear relationships between two variables , with fixed effects having a linear effect. In that scenario, your best alternative may be fractional polynomial regressions. Look into -help fp-.
HTH
Fernando

[David Kunst]

Hi Fernando,
you're right, the title is confusing- of course, it's about a local relationship between Y and X. The "global" was lingering in my mind because for linear models, including country fixed effects would amount to achieving identification solely based on deviations from country-specific averages. However, this intuition does not carry over to non-linear fixed effects models, where the country means do enter the identification- i.e., the point of my quadratic benchmark model is to identify a global non-linear relationship between Y and X, in spite of adding the country fixed effects. However, these thoughts are quite peripheral to my question about performing a robustness check that imposes less structure, thus allows for more "local" relationships- hence I should have removed "global" from the title indeed, thanks for pointing this out.
I'll check out "fp", thanks for the suggestion!
Best,
David