I'm currently trying to figure out whether a specific difference-in-difference (DiD) model makes sense. Suppose I have a set of 20 countries, where one country (A) introduced a tax for a specific good in 2005 and started to substantially increase this tax from 2010 onward. The other countries introduced the same tax between 2005 and 2009, but stayed on a low level compared country A's level before the severe increase that started 2010. From 2010 onward, country A continued to strongly increase the tax each year.
I want to analyze the effect of that tax on consumption of the taxed good. Does it make sense to take the year 2010 as the treatment intervention, and run the following model:
$Y = \alpha + {\beta_1}*{Treatment_i} + {\beta_2}*{Year_t} + {\beta_3}*({Treatment_i}*{Year_t}) + {\epsilon_i},$
where ${Treatment_i}$ is a country A dummy, and $Y$ is the consumption of the taxed good?
My problem is that I don't have a single intervention, but rather a spike that becomes increasingly more intense. So, I wonder if I have to treat every single tax increase as its own intervention.
With the equation above, I'd have a regression output with just a lot of interaction variables that span the time of my data set, 2000-2016. Now, supposing that all the ‘country A’ times ‘year’ interaction terms are significant from 2010 onward, but insignificant before - do I have a proper DiD model that suggests causality if the parallel-trend assumption is valid?
