set scheme lean1
webuse nlswork, clear
xtset idcode year
// Model of interest:
xtreg ln_w ttl_exp age c.age#c.age tenure c.tenure#c.tenure not_smsa south i.year, fe
local b : display %4.2f _b[ttl_exp]
// Isolate relevant variation in the treatment:
reghdfe ttl_exp, absorb(idcode year) residuals(relevantvariation)
// Identify a plausible counterfactual shift in X given the data:
center ttl_exp
sum relevantvariation
local sd1 : display %4.2f r(sd)
sum ttl_exp
local sd2 : display %4.2f r(sd)
twoway (kdensity c_ttl_exp) ///
(kdensity relevantvariation), ///
ytitle("Density") xtitle(Treatment (centered around 0)) ///
title("{bf:A} Treatment distribution", span bexpand justification(left)) ///
legend(order(1 "Original distribution, {it:SD} = `sd2'" ///
2 "Distribution after FE, {it:SD} = `sd1'" ) ///
pos(2) ring(0)) ///
name(figure1A, replace)
// Calculate range within individuals
bysort idcode: egen max = max(ttl_exp)
bysort idcode: egen min = min(ttl_exp)
generate range = max - min
drop max min
qui sum range, detail
local mean : display %4.2f r(mean)
local p95 : display %4.2f r(p95)
twoway (histogram range, freq) ///
(scatteri 2000 `mean' (3) "Mean = `mean'", msymbol(i)) ///
(scatteri 2000 `p95' (3) "95th percentile = `p95'" , msymbol(i)), ///
title("{bf:B} Within-individual range of treatment", span bexpand justification(left)) ///
ylabel(, format(%7.0gc)) ytitle(Frequency) ///
xline(`mean') xline(`p95') ///
xtitle(Within-individual range) legend(off) ///
name(figure1B, replace)
graph combine figure1A figure1B, col(2)
// Calculate % of cases where treatment does not vary
egen pickone = tag(idcode)
fre range if pickone
// In 12% of cases the treatment does not vary
// Multiply the estimated coefficient of interest by the revised standard deviation
display "Estimated coefficient of interest = `b'"
display "Within-standard deviation = `sd1'"
display "Product = " _skip(1) `sd1' * `b'
Reference
Mummolo, Jonathan, and Erik Peterson. 2018. "Improving the Interpretation of Fixed Effects Regression Results."
Political Science Research and Methods 6(4):829-835. doi: 10.1017/psrm.2017.44
