Interpreting an interaction term in a panel linear regression model

[Megan Moreton]

Hi,

I am exploring the link between the introduction of a stewardship policy and the consumption of antibiotics. I have time-series data for ~150 antibiotics for 8 counties (not every antibiotic is used in every county). Antibiotics are categorized into 4 classes - this is a categorical variable in the dataset.

I xtset where the panelvar is the antibiotic-county (~650 groups). The timevar is quarterly data between 2013 and 2018. Overall, there are ~14,000 observations.

The policy was introduced at the same time in all counties (q3 2017) & is expected to have a differential effect on the 4 different classes of antibiotics included.

I want to explore the effect using a linear regression model with an interaction term.

egen panel = group(product county)
gen policy = qdate>= tq(2017q3)
xtset panel qdate, q

xtreg vol_percap policy##class i.county i.year, re robust
contrast policy@class, effects

Is this suitable for a baseline specification? Is it correct to interpret the results of the contrast command as the effect of the policy on each antibiotic class? Though I appreciate I cannot say this is causal.

Could I also create a variable that would enable me to extract this directly from the regression output as follows:

gen polintensity  = policy
replace polintensity = class if policy!=0

xtreg vol_percap i.polintensity i.class i.county i.year, re robust

I also have some reservations about whether my SE are clustered appropriately. I'm not sure whether they should alternatively be clustered at the product or county level. In subsequent models, I will also try using a time trend instead of year FE & will try interacting this with county.

I really appreciate any advice on this to check I'm on the right lines. I can paste the full Stata output if useful.