I am trying to see earnings substitution between relative and accruals earnings management before and after a regime change for my thesis. The simultaneous equations that I use are consistent with prior literatures. Although this helps to see the substitution but I am quite not sure if the equation helps in see the difference in substitution before and after the regime change. My study revolves around regime change surrounding mandate of the proportion of independent directors
REM = b0 + b1x AEM + b3POST_REGIME + b4INDEPENDENT DIRECTORS + b5 POST_REGIME * INDEPENDENT DIRECTORS + Control variables
AEM = b0 + b1x REM + b3POST_REGIME + b4INDEPENDENT DIRECTORS + b5 POST_REGIME * INDEPENDENT DIRECTORS + Control variables
Although I used the interaction term to see the effect of the presence of independent directors on board post regime period but at this point I feel the interaction term seems a bit redundant cause dummy variable POST_REGIME should capture the effect of independent director since the regime change was particularly on independent directors on board.
Would be really helpful if you could give me some insights on this.
Consider the following:
Since POST captures regime change in independent directors, there is possibly no point interacting POST and independent directors because these are supposedly the same variables. Given you are interested in the impact of regime change on the substitution effect (REM vs AEM), you should consider interacting POST and AEM in eqn 1 and POST and REM in eqn 2. That should tell you the impact of POST on that relationship.
A simpler (but less tractable) way to think about this is to split the sample into PRE and POST and run the models without the interaction terms in the two subsamples, then observe and (statistically) compare the differences in coefficients. This will give you an initial idea whether the substitution effect is different across the two regimes.
Hope this helps.
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