pleas,e sir: greetings

In your case it's better to use the panal data econometric,than other methods,due to precise results,and accurate signs for targeting variables,but do not mind if you use other methods ,you should care ,and be aware of spriuose regression results.

Dear Christophe,

terms of b1FII , b3IT*FII and b4IT*FII2 are colinear, specially b3IT*FII and b4IT*FII2 . but colinearity is not problem necessarily .

but I'd suggest you using the Quantile regression instead of quadratic form (and term b4IT*FII2 ). using this model provide some insights about sigh changing in different quantiles.

but it is just a suggestion and depends on your research question and data (T and N).

https://www.amazon.com/Interaction-Multiple-Regression-Quantitative-Applications/dp/0761927425

Besets.

Ehsan.

Your first equation has a constant dummy and a slope dummy. Thus the equation specifies that inflation targeting can change the Y growth rate (measured by the constant dummy), and it can change the effect of financial instability on the growth rate (measured by the slope dummy). This seems reasonable. Then you say that what you call the "interaction" effect could be positive or negative, leading you to add the term with squared FI. This addition is puzzling, because the possibility of positive or negative effects of IT on the slope is already allowed in b3, which can be positive or negative. Instead, what the squared term with the dummy gives you is a nonlinear effect of FI on growth, but only when there is inflation targeting. Perhaps what you mean is that you think the impact of IT on FI's effect could change sign for higher values of FI compared with lower values. In that case, the squared term could catch that. Anyway, if you do have some reason for expected the nonlinear effect, then you almost surely also need to have the variable FI2 itself in the regression. I would also point out that the collinearity among the variables, mentioned by another commenter, is not an issue, because it is not perfect collinearity.

@ Sir Mohammad Mousa Alalaya,

Thank you for your suggestion. But I considered a GMM estimate because of possible endogenous regressors in equations. That's why I did not choose panel data econometrics.

@ Ehsan Khalili

Thank you for your suggestion.

After your suggestion, I searched for and obtained the book you recommended to me and started to read it. However, with respect to quantile regression, if I understand correctly, it allows us to determine the effects of the independent variables on the dependent variable for different levels (quantiles) of the latter. However, I rather want to assess the role of inflation targeting on the relationship between financial instability and economic growth for low and high values ​​of financial instability, which is an independent variable in our regression.

@David O. Cushman,

Thank you for your comments!

Indeed, I think that the role that inflation targeting can play in the relationship between economic growth and financial instability depends on the level of financial instability, so the relationship is (in my opinion) non-linear. So, if I understand your comment correctly, in this case I have to estimate the following relation :

Y = aY0 + b1FII + b2IT + b3IT*FII +b4FII2 + b5IT*FII2 + cX + e

is this correct relative to my idea?

Kind regards!

Yes, Christophe.

Ok.

Thank you very much!