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Re: st: indicator variable and interaction term different signs but both significant


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: indicator variable and interaction term different signs but both significant
Date   Sat, 06 Apr 2013 19:32:37 -0400

The significance of OC_D is not any big deal, or at least need not be. It is saying that, when MV = 0, the predicted difference between the two types of managers is statistically significant. At some other values of MV it may not be statistically significant. Since you say MV is continuous positive, 0 is, at best, the lowest possible value for MV, and in practice the lowest value may be much higher than 0.

To give another example, suppose that instead of MV the variable was weight. At 0 pounds the difference between two groups may be significant. But nobody weighs 0 pounds so it isn't a useful comparison. Center weight so that 0 = average weight, and the comparison becomes more useful, i.e. the coefficient for OC_D would be the expected different between the two types of managers who were both of average weight.

If you wanted to, you could compute the predicted difference between two managers who both weighed a negative millions pounds or a positive million pounds. The coefficients might be wildly significant but hardly helpful.

At 06:45 PM 4/6/2013, Nahla Betelmal wrote:
Thanks Anthony for the reply. Actually Overconfidence indicator
variable takes value of 1 for overconfident managers, and value of
zero for rational managers. The market value variable is a continuous
positive variable.

I am not sure that interpreting the indicator variable (OC_D) has
literal interpretation in the interaction model, I am confused due to
the significance ! otherwise I would only have focused on the
interaction term (i.e. overconfident managers manipulate earnings
upwardly when the market value of their firms is high) but I am not
sure if I got it right.

Many thanks, and I am looking for others responses as well

Nahla


On 6 April 2013 23:24, Anthony Fulginiti <fulginit@usc.edu> wrote:
> Hi Nahla,
>
> I would recommend waiting for others on Statalist to respond to provide confirmation of my interpretation. However, my thoughts are that this is suggesting that your main effect for overconfidence is suggesting that overconfident managers manipulate earnings less than other managers (if that is the reference group) at market value 0. The interaction would then suggest that the effect of the overconfidence variable on earnings manipulation is increasingly greater at higher market values. I look forward to hearing other replies.
>
>
> Anthony
>
>
> On Apr 6, 2013, at 2:45 PM, Nahla Betelmal wrote:
>
>> Dear Statalist,
>>
>> I am having difficulty interpreting the results from OSL regression. I
>> am trying to see whether Overconfident managers manipulate earnings in
>> a certain context.
>>
>> The dependent variable earnings_Mgt is continuous  The problem is that
>> the indicator variable for overconfidence (OC_D) is negative and
>> significant, while the interaction between the indicator variable and
>> market_value variable (OC_MV) is positive and significant. What does
>> that mean?
>> Does it mean that overconfident managers manipulate earnings less than
>> others (rational managers), but when the market value is high they
>> manipulate earnings more than rational managers do?
>>
>> Your help is highly appreciated,
>>
>> many thanks
>>
>> Nahla Betelmal
>>
>>
>> Linear regression              Number of obs  = 56
>> F( 8, 47)     = 3.60
>> Prob > F      = 0.0025
>> R-squared     = 0.3719
>> Root MSE      = .08355
>> Robust
>> earnings Mgt Coef. Std. Err. t P>t [95% Conf. Interval] >> size .0058268 .0092169 0.63 0.530 -.0127153 .0243689 >> leverage .0924198 .0724032 1.28 0.208 -.0532367 .2380763 >> MV .0046896 .0032752 1.43 0.159 -.0018993 .0112784 >> litigation .0310148 .0267527 1.16 0.252 -.0228048 .0848344 >> private_D -.0638102 .023056 -2.77 0.008 -.110193 -.0174275 >> same_D -.08197 .0273465 -3.00 0.004 -.136984 -.026956 >> OC_D -.0730767 .0288269 -2.54 0.015 -.131069 -.0150844 >> OC_MV .0105348 .0049493 2.13 0.039 .000578 .0204916 >> _cons .0381444 .0615391 0.62 0.538 -.0856564 .1619452
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Richard Williams, Notre Dame Dept of Sociology
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