RE: st: interaction dummy or separate regression

["Khieu, Hinh" <Hdkhieu@usi.edu>]

Austin,
Thanks again for your prompt help. Chg in Y is capital expenditures. I may need to run the model again on something else. That is why I put Y for generalization. I have several definitions of abnormal investment: 1/as in my original email, abnormal are those values that exceed 200% of industry averages for the past 3 years, 2/abnormal = residuals from a regression of a normal investment equation. As you can see, both measures are like Y = A minus B. And Y could be positive and negative. Only positive Y's are abnormal and the negative Y's are irrelevant for me. If stata code should be:
Xtreg Y debt equity if small firm==0, fe robust
The only way for me to get Y to be abnormal is either to drop the negative Y or to add the second condition in the If statement "& Y>0".
If I use the residual values from definition 2 of the measure, I don't know how appropriate it is for the following reason: residuals are forecast error and if something else in the second stage can explain the forecast error, it should be in the first stage too.  This logic leads me to use just Investment (which includes both normal and abnormal values) as dependent variable. Using it that way and including the dummy or separating the sample into two, according to you, would be problematic.
I wonder if you have any suggestions. I would appreciate them.
Thank you so much.
Hinh


________________________________________
From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols [austinnichols@gmail.com]
Sent: Wednesday, September 28, 2011 12:34 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: interaction dummy or separate regression

Khieu, Hinh <Hdkhieu@usi.edu>L
I already ruled out option 2, as selection on the dependent variable
is not allowed. Option 1 is okay, but I would suggest you explore an
alternative link, as the explanatory variables likely have a very
nonlinear relationship with Y. Imagine the cube root of y is a linear
function of x, and you regress y on x, in which case extreme values of
y will seem to have a very different relationship with x. See the help
file for -glm- for starters.  You can also select on X, as I
mentioned, which may illuminate the appropriate link, if you can
construct a reasonable piecewise linear approximation. Better advice
may follow if you are more explicit about what you are modeling.  I.e.
what is Y, what is the data, etc.

On Wed, Sep 28, 2011 at 1:19 PM, Khieu, Hinh <Hdkhieu@usi.edu> wrote:
> Austin,
> Thank you very much for your note. I have a feeling it is not right, but not what is not right and you answered it. So, to test whether debt or equity is used to finance abnormal Y, there are only two ways:
> 1. put abnormal Y as dependent variable and drop all dummy and interaction terms
> 2. still keep Chg in Y as dependent variable but run one regression based on Abnormal Y observations alone and another regression based on Other Y.
> I wonder if you can do me a favor by commenting my two solutions above.
> Thank you very much.
> Regards,
> Hinh
>
>
> ________________________________________
> From: owner-statalist@hsphsun2.harvard.edu [owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols [austinnichols@gmail.com]
> Sent: Wednesday, September 28, 2011 12:11 PM
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: interaction dummy or separate regression
>
> Khieu, Hinh <Hdkhieu@usi.edu> :
> You are not going to get unbiased estimates of any of those coefs, if
> that's what you mean.  You are not allowed to select on Y, nor include
> a transformation of it as a regressor, and I strongly recommend you
> explore what you are estimating using a simulation on generated data
> where you know the true effects (a1, a2, etc.).  You are allowed to
> select on an exogenous X variable, but not on "abnormal" Y.
>
> On Wed, Sep 28, 2011 at 1:00 PM, Khieu, Hinh <Hdkhieu@usi.edu> wrote:
>> Dear statalist members,
>>
>>
>>
>> I have the following model and I am not sure if there is an econometric issue with it. I would appreciate any amount of help. Change in Y = a1*growth opportunities + a2*profit + a3*debt + a4*equity +  a5*dummy (=1 if change in Y is abnormally high, zero otherwise) + a6 * debt * dummy + a7 * equity * dummy, where abnormally high is defined to be whenever change in Y is greater than 2 times the industry average of Y over the last 3 years (t, t-1, and t-2).
>>
>>
>>
>> I run fixed effects regression with firm and year dummies on the above model for 2 groups of firms: large firms versus small firms. My question is: is there any mechanical or econometric problem with using the dummy for abnormal Y and its interaction with debt and equity? I know I  can split the sample into abnormal Y and normal Y and run two separate regressions. But I want to know specifically if the model above is problematic from an econometric perspective. What if I drop the dummy and keep only the interactions?

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