Can anyone help me interpreting my result?

[kolpo kotha]

Hello, In my analysis. I want to see the effect of different types of taxation (Personal income tax (PIT), Corporate income tax(CIT), General taxes on goods and services (GTGS)) on economic growth (measured by GDP per capita growth). I set two regression: one for South Asian sample (consists of 6 countries), another one for World sample (a total of 85 countries). In world sample, I interacted the dummy variable for South Asia with PIT, CIT, GTGS. Also I interacted these with size of the shadow economy and globalisation index (to see what happens in the presence of globalisation/openness).

However, someone told me the interpretation for interaction term with the presence of globalisation (that I used In the regression in world sample) does not convey the same meaning as like as the one found in the regression of only South Asian countries.

I have uploaded the regression result of both South Asian Sample and World Sample. Can you please help me how to interpret the final output of these two regression. Thank you.

[Clyde Schechter]

Well, that is correct. But first you have a more important problem. Your World model is mis-specified. Because you have the CIT*GLOB*SA interaction, you must also have all of the sub-interactions and "main" effects it contains. You missed GLOB*SA. Without that, your model is not valid. I suggest you rerun it.

I'm also guessing that this happened, in part, because you did not use factor variable notation and, instead, you generated your own interaction variables. That's particularly unfortunate here because three way interaction models are very difficult to understand, and the -margins- command (which can only be used when the regression uses factor variable notation) makes it so much easier. So, read -help fvvarlist- first to learn how to write your regression using factor variable notation. Use the ## operator for your interaction terms: that way you don't have to worry about forgetting one of the subinteractions--Stata will take care of that automatically for you. Next introduce yourself to the -margins- command by reading the excellent Richard Williams' https://www3.nd.edu/~rwilliam/stats/Margins01.pdf. This will give you a feel for how -margins- can help you understand interaction models. While I don't recall any three-way interaction examples in that particular document, the principles are the same as for two-way interactions.

When all is said and done it is extremely difficult to explain three-way interaction models to non-professional audiences, and very difficult to explain them to professional ones! Graphs are, in my opinion, the only way to make them understandable. So the -marginsplot- command will be your best friend in this project.

[kolpo kotha]

Hi Clyde Schechter: Thank you for your response.

"CIT*GLOB*SA* implies how the Corporate Income Tax (CIT) affect economic growth in the presence of globalisation in south Asia? Am I right?
What would it mean when I will include "GLOB*SA" ?

[kolpo kotha]

Well, that is correct. But first you have a more important problem. Your World model is mis-specified. Because you have the CIT*GLOB*SA interaction, you must also have all of the sub-interactions and "main" effects it contains. You missed GLOB*SA. Without that, your model is not valid. I suggest you rerun it.

I'm also guessing that this happened, in part, because you did not use factor variable notation and, instead, you generated your own interaction variables. That's particularly unfortunate here because three way interaction models are very difficult to understand, and the -margins- command (which can only be used when the regression uses factor variable notation) makes it so much easier. So, read -help fvvarlist- first to learn how to write your regression using factor variable notation. Use the ## operator for your interaction terms: that way you don't have to worry about forgetting one of the subinteractions--Stata will take care of that automatically for you. Next introduce yourself to the -margins- command by reading the excellent Richard Williams' https://www3.nd.edu/~rwilliam/stats/Margins01.pdf. This will give you a feel for how -margins- can help you understand interaction models. While I don't recall any three-way interaction examples in that particular document, the principles are the same as for two-way interactions.

When all is said and done it is extremely difficult to explain three-way interaction models to non-professional audiences, and very difficult to explain them to professional ones! Graphs are, in my opinion, the only way to make them understandable. So the -marginsplot- command will be your best friend in this project.

Hi Clyde Schechter: Thank you for your response.

"CIT*GLOB*SA* implies how the Corporate Income Tax (CIT) affect economic growth in the presence of globalisation in south Asia? Am I right?
What would it mean when I will include "GLOB*SA" ?

[Clyde Schechter]

Wrong question. The question is, what would it mean if you don't include GLOB*SA and the answer to that question is that it invalidates the model. CIT*GLOB*SA doesn't mean anything at all useful unless all of the sub-interactions and constituent effects are also in the model.

Added:

"CIT*GLOB*SA* implies how the Corporate Income Tax (CIT) affect economic growth in the presence of globalisation in south Asia? Am I right?

Even if your model were complete and correctly specified, this would not be the correct interpretation of CIT*GLOB*SA. In fact, the interpretation of that term by itself is extremely complicated and probably close to incomprehensible. I can't think of any situation where this term, by itself, would be of interest to anyone. It is one of several terms that have to be added up in order to get the predicted values of the income growth for when CIT is present in the presence of globalization in south Asia.

[kolpo kotha]

Wrong question. The question is, what would it mean if you don't include GLOB*SA and the answer to that question is that it invalidates the model. CIT*GLOB*SA doesn't mean anything at all useful unless all of the sub-interactions and constituent effects are also in the model.

Added:

Even if your model were complete and correctly specified, this would not be the correct interpretation of CIT*GLOB*SA. In fact, the interpretation of that term by itself is extremely complicated and probably close to incomprehensible. I can't think of any situation where this term, by itself, would be of interest to anyone. It is one of several terms that have to be added up in order to get the predicted values of the income growth for when CIT is present in the presence of globalization in south Asia.

Thank you very much. Can you please suggest any other modification to improve the model?

Can I interpret CIT*GLOB in south asian sample in the usual manner? The results are not significant. How to justify them? Please suggest.

[Clyde Schechter]

Well, since I don't know what you mean by "the usual fashion" I can neither agree nor disagree. Based on your original post, I have a hunch that what you call the usual fashion is something I would disagree with.

On the assumption that these are linear regressions and that CIT and GLOB are both dichotomous variables, the coefficient of CIT#GLOB in the south asian sample estimates the difference between the effect of CIT when GLOB = 1 and the effect of CIT when GLOB = 0. Or, if you prefer, it is also the difference between the effect of GLOB when CIT = 1 and the effect of GLOB when CIT = 0.

As for why it is not "significant", the reasons are the usual ones. A non-significant result, in any context, simply means that the data were not able to identify this difference with sufficient precision to determine whether it is positive or negative. This may be because of insufficient sample size (overall, or perhaps in one of the CIT # GLOB groups), or noisiness of the data that exceeds the strength of the difference you are trying to detect. This, in turn, may indicate that the data are very noisy, or the effect is very small, or both to some extent. The only way to justify any finding, whether "significant" or not, is that the data were properly collected and managed, the model a reasonable approximation to the real world data generating process, and the calculations performed correctly. At that point the data have spoken.

I am not an economist and I have no ideas about how to improve your model. There are several economists who are active on the Forum, and one of them may join in. Or you could ask one of your colleagues in your discipline. My remark about the importance of including GLOB*SA was based purely on statistics: any model that omitted that, in any context, would be invalid (or, at least, would not be subject to interpretation as an interaction model). But there are no other statistical violations that I can see in your model, so any further improvements would be based on content, where I have no expertise.

[kolpo kotha]

Well, since I don't know what you mean by "the usual fashion" I can neither agree nor disagree. Based on your original post, I have a hunch that what you call the usual fashion is something I would disagree with.

On the assumption that these are linear regressions and that CIT and GLOB are both dichotomous variables, the coefficient of CIT#GLOB in the south asian sample estimates the difference between the effect of CIT when GLOB = 1 and the effect of CIT when GLOB = 0. Or, if you prefer, it is also the difference between the effect of GLOB when CIT = 1 and the effect of GLOB when CIT = 0.

As for why it is not "significant", the reasons are the usual ones. A non-significant result, in any context, simply means that the data were not able to identify this difference with sufficient precision to determine whether it is positive or negative. This may be because of insufficient sample size (overall, or perhaps in one of the CIT # GLOB groups), or noisiness of the data that exceeds the strength of the difference you are trying to detect. This, in turn, may indicate that the data are very noisy, or the effect is very small, or both to some extent. The only way to justify any finding, whether "significant" or not, is that the data were properly collected and managed, the model a reasonable approximation to the real world data generating process, and the calculations performed correctly. At that point the data have spoken.

I am not an economist and I have no ideas about how to improve your model. There are several economists who are active on the Forum, and one of them may join in. Or you could ask one of your colleagues in your discipline. My remark about the importance of including GLOB*SA was based purely on statistics: any model that omitted that, in any context, would be invalid (or, at least, would not be subject to interpretation as an interaction model). But there are no other statistical violations that I can see in your model, so any further improvements would be based on content, where I have no expertise.

Thank you. Can you please tell me why sargan test does not work with vce(robust) command? what should I do in this case to perform sargan test?

xtdpdsys GDPPCG year1990- year2015 timeperiod, lags(1) maxldep(2) pre(GDPPCi0 GI UNEM   INFL URBAN  EDUCE HEALE  shadow  LFPART GDSPGDP INV, lagstruct(0,3)) pre(PIT_SA PIT_SHADOW  PIT_SHADOW_SA CIT_SA CIT_GLOB  CIT_GLOB_SA GTGS_SA, lagstruct(0,3)) endog(PIT  CIT GTGS  GOVTS , lagstruct(0,3)) vce(robust) artests(2)

when i put the above command following output appears for sargan tests:

. estat sargan
Sargan test of overidentifying restrictions
H0: overidentifying restrictions are valid
cannot calculate Sargan test with vce(robust)

chi2(928) = .
Prob > chi2 = .


How to perform sargan test in this case?

[Clyde Schechter]

Hopefully, somebody else can answer you. In my field we take a very different approach to these issues. I have heard of the Sargan test only because I see people refer to it on this Forum. I have never seen it used in the epidemiological or medical literature, and I don't even know what it is. I'm sorry I can't help you with this question.