Margins for state-specific linear time trends

[Dany Shakeel]

My individual-level data includes an outcome variable (svar) with state (FIPS) pooled across years with background characteristics.

I first estimate state adjusted scores with controls using margins command

reg svar i.FIPS i.YEAR `cntrls'
margins FIPS, post
estimates store mar1, title(Adjusted)

Next I want to estimate state-specific linear time trend after adjusting for national trend. Is the following code correct, and does the margins command below produce the trend coefficients for each state?

reg svar i.FIPS##c.YEAR `cntrls'
margins FIPS, post
estimates store mar2, title(Adjusted trends)

[George Ford]

reg svar YEAR i.FIPS#c.YEAR `cntrols' , absorb(FIPS)
margins, dydx(YEAR) over(FIPS)

the first line gets you the difference in the trends by FIPS.
the second makes all the computations to get you the actual trend value by FIPS.

[Dany Shakeel]

Thanks, could you shed light on why the term in first line is YEAR and not i.YEAR or c.YEAR? Stata returned "not estimable" with the suggested code.

[George Ford]

What this does is compute the time trend of the first and then the differences from that trend for each FIPS. The margins gets you the trend for all of them.

With i.YEAR, you are centering the data on a FIPS before estimating the trend. This means you'll not have a trend for that FIPS since it is being estimated using dummies.

[George Ford]

I suppose you could detrend the sample with a mean trend first, then work with the detrended series.

reg svar year , absorb(FIPS)
predict svar_dt, resid

[Dany Shakeel]

So you're suggesting something like

reg svar YEAR, absorb(FIPS)
predict svar_dt, resid

reg svar_dt YEAR i.FIPS#c.YEAR `cntrls', absorb(FIPS)
margins, dydx(YEAR) over(FIPS)

Unfortunately, the last step is always resulting in "not estimable" margins for each FIPS

[George Ford]

reg svar YEAR, absorb(FIPS) predict svar_dt, resid reg svar_dt i.FIPS#c.YEAR `cntrls', absorb(FIPS) the coefficients should give you what you want