I am trying to test the impact that margin trading status has on stock liquidity. I regress liquidity measure on a dummy variable (mt_csmar) which indicates whether a stock is margin eligiable or not, and some other control variables. I control firm fixed effect and time effect by regressing using reghdfe. This is fine.

But I would also like to see whether the coefficient of this mt_csmar dummy differs in bull or bear markets, compared with normal periods. I could run the same specifications for subsamples, such as during bull periods, bear periods or normal periods. However, it seems that, with reghdfe, I cannot test whether the coefficients on mt_csmar are statistically different in different subsamples. Hence I decided to use interaction terms, interacting bull and bear dummies with the mt_csmar.

I report the results for subsample analysis, and results for specifications using interaction terms below. From the subsample analysis, you can see that coefficients of mt_csmar is bear markets are positive, theose in bull and normal periods are both negative, but it is largeer in absoule terms during nromal periods. However, if I use interaction terms to do the analysis, the results are very different. coefficients on mt_csmar are more nagative during bull and bear markets than during normal periods.

My questions are :
1) which sets of results should I trust? Why the interaction terms analysis produce different conclusions than the subsample analysis?
2) if I should trust subsample results, then, how do I test the equality of coefficients after running the reghdfe?
3) bull and bear dummies are basically correlated with time effect, they were dropped in the reghdfe regressions when there are time fixed effects dummies, does this represent a problem? should i give up controlling time fixed effect and use xtreg instead?

Thank you very much for any comments you have, I have been go back and forth on this points for a while.





The following is bull market subsample:

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The following is bear market subsample
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The following is normal periods subsample
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The following is specifications with interaction terms

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