# Setting up a 3-dimensional panel with interaction term

I am a new member and this is the first time I am posting a question here. I have yet to familiarise myself with writing equation here. Apologies for the poor representation of my equation.

I have a query related to a using a 3-dimensional panel. I have a dataset on 2 donor countries j; 4 recipient countries i; and 5 years t.

My aim is to compare the role of corruption in foreign aid allocation decision of United States vs United Kingdom.

For this purpose, the dependent variable is the absolute amount of aid received by a recipient country i from donor j (i.e., U.S amd U.K) in year t. Corruption in a recipient country is my key explanatory variable. I am having some recipient specific control variables i.e., GDP and some donor-recipient specific control variables i.e., Trade between donor j and recipient i in a year. I intend to estimate the following equation:

Aidijt = beta0 + beta1 Corruptionit + beta2 Corruption*DonorDummy + beta3 GDPit + beta4 Tradejit + uijt

DonorDummy takes a value 1 for US and 0 for UK. Standard error will be clustered by donor-recipient pairs.

I have the following question in this regard:

Question: I am assuming that the coefficient beta2 will indicate the influence of recipient’s corruption on aid allocation decisions of US in comparison with UK i.e., a positive significant coefficient will tell: U.S will give more aid to corrupt countries than U.K. Whereas, beta1, beta3, and beta4 will be same for both the donors.

Earlier studies on this topic have estimated separate equations as follows for each donor and through the following equations:

USAidit = beta0+ beta1Corruptionit+ beta2GDPit+ beta3Tradejit + uijt

UKAidit = beta0+ beta1Corruptionit+ beta2GDPit+ beta3Tradejit + uijt

They have then compared the magnitude of coefficient beta1 in the two equations to tell how different is US from UK in giving aid to corrupt countries.

But as per my understanding, separate equations will not serve the purpose of comparison and U.S.and UK’s aid should be estimated within one equation. I am wondering if my strategy of setting the 3-dimensional panel and interacting donor dummy with the key explanatory variable makes any sense at all?

I am a bit unsure if my strategy i.e., setting the panel and coefficient interpretation is appropriate or is there any alternate way of doing it

Looking forward to the feedback.

Best regards, Shazmeen Maroof.