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Re: st: Nonlinear regression command

 From David Hoaglin To statalist@hsphsun2.harvard.edu Subject Re: st: Nonlinear regression command Date Fri, 12 Jul 2013 11:22:08 -0400

```Dear Rick,

Like Maarten, I see interactions, but no nonlinearity.

The indicator variables Ds and DL seem to be mutually exclusive (once
you clarify which of Ds and DL is one when the extent of derivative
use is exactly 20%) and exhaustive.  Thus, you can remove Dsi and the
corresponding square brackets and define interaction predictors for
each of the variables in the square brackets following DL: DLExtentit
= DLi*Extentit, DLLevit = DLi*Levit, ..., DLExeopit = DLi*Exeopit.
Then the model would be
Total Riskit = a0 + a1 Extentit + ... + a9 Exeopit + a10 DLi + a11
DLExtentit + ... + a19 DLExeopit + sigmait
(I'm not sure what you mean by sigmait.  I would have expected
something like epsilonit.)
Thus, a1 is the slope of Total Risk against Extent when DL = 0 (i.e.,
when Ds = 1), and a11 is the additional slope of Total Risk against
Extent when DL = 1.  These slopes (and the other coefficients in the
model) summarize the contribution of the corresponding predictor after
adjusting for simultaneous linear change in the other predictors in
the model.

I hope this helps.

David Hoaglin

On Fri, Jul 12, 2013 at 8:11 AM, Rick Kamphuis
<r.kamphuis@tilburguniversity.edu> wrote:
> Dear Statalist,
>
> I have a formula, but I don't know how to replicate it in Stata, because of
> problems with the command.
>
> The formula I want to put in is from the Nguyen and faff 2010 paper: Are
> firms hedging or speculating? The relationship between financial
> derivatives and firm risk.
>
> The formula looks like this:
>
> Total Riskit = Dsi [a0 + a1 Extentit + a2 Levit +a3 Sizeit + a4 DYit + a5
> MTBVit + a6 Liqit + a7 CRit + a8 Exeshit + a9 Exeopit] + DLi [a10 + a11
> Extentit + a12 Levit +a13 Sizeit + a14 DYit + a15 MTBVit + a16 Liqit + a17
> CRit + a18 Exeshit + a19 Exeopit] +sigmait
>
> Where a is alpha and Ds and DL are dummies. Extent is the most important
> independent variable and all other variables are control variables. Behind
> every variable it is paste behind it because of the paneldata format.
>
> This formula is to test for a nonlinear relationship between total risk and
> the Extent (derivatives outstanding divided by size). The first dummy
> variable (Ds) is set equal to unity if the extent of derivative is 20% or
> less and zero otherwise. Similarly, DL is set equal to unity if the extent
> of derivative usage is 20% or more and zero otherwise. The threshold level
> of 20% is chosen as it represent the average extent of derivative usage
> demonstrated by firms in portfolio 6 (where maximum risk reduction is
> achieved).
>
> So the coefficients of primary interest in this equation are a1 and a11.
> Consistent with the results obtained from the section 'portfolio analysis'
> it is expected that moderate users (with an extent of derivative usage of
> less than 20%) will experience a reduction in risk and hence a negative
> sign is predicted for a1. For a11 it is the other way around.
> My question is: what is the command in stata to run this regression from
> above.
>
> I have thought about to cut the groups and do this regression two times
> with the moderate users and excessive users. However, I think this is not
> the meaning of this test.
>
> Hopefully someone can help me.
>
> Thanks,
>
> Rick Kamphuis
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```