#StackBounty: #nonparametric #stata Which one is the correct specification to estimate Nonparametric regressions with discrete and cont…

Bounty: 50

I was trying to implement manually the estimation of nonparametric regression using local-linear approximation with a mixture of discrete and continuous data.
consider a simple model:
$y=f(xc,xd)$
where xc is continuous and xd is discrete

Say that I want to estimate this model non parametrically. Which one of the two following regressions is the correct one (assuming local linear estimation.

1:
$$y=a0+a1*(xc-c)+e$$
2:
$$y=a0+a1*(xc-c)+a2*xd +e$$

Assume that both models are estimated using the correct kernel weights and that xd is a dummy.

I thought the correct model was (1), but npregress in Stata uses (2). Which one would be the correct one?

Thank you

EDIT:
Perhaps a different way to ask the same question.
Say that you have a 3 variables, y, xc (continuous) and xd (discrete), and that you want to estimate a nonparametric, using local linear kernel estimation, for:
$$y=f(xc,xd)$$
Empirically, how would you estimate this model using WLS? which one is the correct specification? equation 1 or equation 2 (assuming weights are appropriately obtained)


Get this bounty!!!

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