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Short summary: I want to examine of a multinational has a higher or lower effective tax rate ( ETR=dependent veriable) compared to small companies and large domestic companies. ( categorical variable 1=SME ; 2= large domestic and 3=MNE) However, I do not Know if I can tell in the end this is true, because main effects and interactions have other signs. What if I include (according to theory) another interaction term, how can I interpret the dummy variable MNE...

Can I conclude from this regression that being a MNE increases the ETR by 5,6% ( holding the other variables constant)? I red that the main effect of the variables in the interaction term have to be interpreted as the effect of that variable for the reference group ( SMEs in my case). But what can I conclude now if I interpret both main effect and interactions: that being a multinational on average increases the ETR by 5,6% or and that multinationals with a higher equity ratio decrease the ETR by -6,7% compared to SMEs ( so that multinationals with a higher equity ratio have on average actually a lower ETR compared to SMEs (5,6% -6,7%= -1,1).... Help

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Pieter Buyl
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  • you seem to nix up small, large and MNE. compare small with MNe –  Apr 25 '16 at 11:35
  • Large domestic is good enough to compare with MNe. State your objecitive more clearly. –  Apr 25 '16 at 11:46
  • Thanks for the comment. I just want to now in the end ( so also considering the interactions) which type of firm has the highest ( or lowest ) ETR(=dependent variable)...And i'm a bit confused because the single effect of MNE1 and the interaction effect of MNE1x EQRATIO have opposing signs... – Pieter Buyl Apr 25 '16 at 13:17
  • how did you equity ratio? Higher equity ratio results in higher amount of dividends and hence greater ETR and a lower equity permits deduction of interest on debentures/bonds etc. that finally reduces the profits. Hiher chargeable expendture should reduce profits. It is difficult to explain. Also think of a proper interaction term for MNe × eq ratio.Take for example capital emploed divided by sales or ... –  Apr 25 '16 at 14:02
  • I didn't use dividends in my model, it's also not appropriate to do so... I just want to deduct from THIS model if MNE face lower ETRs or higher ETRs ( the interpretation of the main effects and interaction effects)...in the model ( to explain) you can accept the model is correctly specified... – Pieter Buyl Apr 25 '16 at 14:19
  • the question is like this: Can I interpret from this model that being categorized as a MNE result in lower ETR ( dependent var) compared to SMEs: ETR1i= β_0+ 0.027MNE+0.033LARGEDO- 0.004〖CAP INT〗_i+0.024〖INTANG〗_i-0.108〖FINAR〗_i-0.030〖EQRATIO〗_i-0.064〖EQRATIO〗_i xMNE+0.001〖EQRATIO〗_i xLARGEDOM-0.062〖FINAR〗_i xMNE-0.04FINARxLARGEDOM+0.020〖LEV〗_i-.171 〖LOSS〗_i-0.001〖SIZE〗_i+ .156〖ROA〗_i+ β_(14-28) 〖INDUSTRY〗_i+ε_i – Pieter Buyl Apr 25 '16 at 14:39
  • If the model iz assuned to be valid, you can not interpret it the way you are perceiving. The category is not a singular basis. ETR is concurrently under influece exerted by several other factors (you have already included a few of those –  Apr 25 '16 at 15:54
  • OK thank you for your comment. Is it possible to say that the equity ratio of MNE has a 6.4 % more negative effect compared to SMEs , holding the other continuous variables in the at a certain level? Thanks – Pieter Buyl Apr 25 '16 at 19:04
  • run two regression for Mne. and sme. Ignore interaction. –  Apr 26 '16 at 00:41
  • it seems you are interested in checking whether being an Mne reduces tax burden i.e. reduces ETR. If so revise your body text for question. –  Apr 26 '16 at 00:47
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    OK. What do you exactly mean with run two regressions for MNE and SME...make a subsample? ( I heard it's not possible top compare magnitudes of the slopes when doin that?) I indeed want to verify if being classified as an sme reduces the ETR or the opposite ( zo the hypothesis is a question mark)... – Pieter Buyl Apr 26 '16 at 06:30
  • subsample - separate datasets and run regression. To me, profit/loss variable is one and same. If you get higher significant regression coefficient, for sme, the case is built for sme otherwise it goes to favour MNE. –  Apr 26 '16 at 07:24
  • See [interaction of categorical and continuous variables](http://stats.stackexchange.com/q/101216/17230). All you need do to examine the relationships predicted by your model is plot ETR vs EqRATIO for each of SME, MNE, & LARGE DOM, holding the rest fixed. $\mathrm{ETR}_\mathrm{SME} = 0.135 - 0.030 \times \mathrm{EqRATIO} + \mathrm{constant}$, $\mathrm{ETR}_\mathrm{MNE} = (0.135 + 0.056) + (- 0.030 + 0.001) \times \mathrm{EqRATIO} + \mathrm{constant}$ & so on. Vary EqRATIO over values of interest, & it may aid interpretation to set other variables equal to their means, or typical values. – Scortchi - Reinstate Monica Apr 26 '16 at 08:57
  • Thank you. And what if I also include an interaction with these dummies and FINAR? ( than I can not hold the other variables constant or am I wrong? – Pieter Buyl Apr 26 '16 at 12:10
  • the post you added there " interaction of categorical and continuous variables" I understand completely. It is however when more interactions with the same categorical variables are included that I lose the understanding of it... – Pieter Buyl Apr 26 '16 at 12:17
  • Repeat the plot specified above for a few different values of FINAR. Or use some type of 3-dimensional plot - a contour or a wireframe plot. – Scortchi - Reinstate Monica Apr 26 '16 at 12:35
  • which regression model did you use for ouput- ordinary multiple rgression multinomial regression ? Further you need to postulate a clearcut hypothesis or set a focussed objective of your study. is it for master or doctoral degree? –  May 04 '16 at 13:13
  • Doctoral. Iets old regression With robuust standard errors... Question is whether small ANC medium Enterprises Bear a higher tax burden compared to multinationals or not... – Pieter Buyl May 09 '16 at 07:03

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