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three dimensional panel data

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Hello,

I investigate the influence of changes in the VAT rate on consumption expenditures. I have annual panel data of 8 countries for 10 years.

My dependent variable, the consumption expenditure, is divided into 48 subgroups for each country, which sum up to aggregate consumption expenditures.
The VAT rate as main independent variable is assigned in accordance with these groups, all my other control variables (income tax, income, interest rate) are on a country level.

I am intersted in the overall effect of a change in the VAT rate on consumption expenditures. Is it possible to estimate this using a fixed effects model? If doing so, how do I take into account the dimensions (year, country, subgroup) of my dependent variable?

Many thanks in advance for your help!

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