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# Re: st: Nonlinear regression command

 From Rick Kamphuis To statalist@hsphsun2.harvard.edu Subject Re: st: Nonlinear regression command Date Mon, 15 Jul 2013 10:45:27 +0200

```Thanks for the comments!
In the paper it is mentioned as a nonlinearity test, because of
dividing the sample in two groups with a saturation.
But indeed it is done with interactions. David,  I think you are
almost right with the model, but you can not remove dummy Ds because
than you get coefficients for the whole sample.
The aim of this regression is to get the coefficients for group 1 with
less than 20% and group 2 with more than 20% usage.
Therefore I think I have to made interactions with Ds for all
variables and with DL for all variables and then regress them all at
the same time.

Rick

On Fri, Jul 12, 2013 at 5:22 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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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```