Sampling weights

Pass sampling weights as [iw=varname]. They enter the propensity score, the outcome regression, and the aggregation weights. A weighted run answers a question about the weighted population.

For county data, weighting by population changes the estimand from the effect on the average county to the effect on the average resident, which is a real difference whenever small rural counties behave differently from large urban ones (and in mortality data they usually do).

The data

Let’s build the sample once (the same block used elsewhere on this site) and run it both ways, weighted and unweighted.

import delimited using ///
    "https://raw.githubusercontent.com/pedrohcgs/JEL-DiD/50f4f18/data/county_mortality_data.csv", ///
    clear varnames(1) bindquote(strict) stringcols(_all)
destring deaths population_20_64 year yaca county_code stfips unemp_rate poverty_rate, ///
    replace force
generate double mrate = 100000 * deaths / population_20_64
drop if missing(mrate) | population_20_64 <= 0
generate int gvar = yaca
replace gvar = 0 if missing(gvar) | gvar > 2016
bysort county_code: generate byte nyears = _N
keep if nyears == 11
save "jel_weighted.dta", replace

Unweighted and weighted

We run the same specification twice, once without weights and once with county population as the weight (everything else about the two commands is identical).

use "jel_weighted.dta", clear
csdid mrate, ivar(county_code) time(year) gvar(gvar) analytical
estat simple

use "jel_weighted.dta", clear
csdid mrate [iw=population_20_64], ivar(county_code) time(year) gvar(gvar) analytical
estat simple

The two runs differ only in the weight expression. The estimates they produce need not agree, and when they disagree it is because the counties that carry most of the population are not the counties that carry most of the rows in the dataset.

If these differ materially, that is a finding about heterogeneity across county size. We recommend reporting the one that matches the question you are asking, and saying in the text which one it is.

Only the scale of the weights is irrelevant. Multiplying every weight by a constant leaves every ATT(g,t) unchanged:

use "jel_weighted.dta", clear
quietly csdid mrate [iw=population_20_64], ivar(county_code) time(year) gvar(gvar) analytical
matrix A = e(attgt)
generate double w2 = population_20_64 * 1000
quietly csdid mrate [iw=w2], ivar(county_code) time(year) gvar(gvar) analytical
matrix B = e(attgt)
mata: printf("largest difference after rescaling weights: %g\n", ///
             max(abs(st_matrix("A")[.,4] - st_matrix("B")[.,4])))

The largest difference across all cells comes back at numerical noise (machine precision), which is what we wanted to see!

Weights that change over time

A unit’s weight can move between periods; county population changes every year. Each 2×2 comparison then has two candidate weights for the same unit, and something has to decide which of them to use. fix_weights() makes that choice explicit, so it is never left to the order of your data:


`fix_weights(varying)`	use each observation’s own weight
`fix_weights(base_period)`	fix every unit’s weight at its base-period value
`fix_weights(first_period)`	fix every unit’s weight at its first-period value

use "jel_weighted.dta", clear
csdid mrate [iw=population_20_64], ivar(county_code) time(year) gvar(gvar) ///
    fix_weights(base_period) analytical
estat simple

use "jel_weighted.dta", clear
csdid mrate [iw=population_20_64], ivar(county_code) time(year) gvar(gvar) ///
    fix_weights(varying) analytical
estat simple

Compare the two overall numbers before deciding which convention to adopt. Fixing the weights keeps the target population constant across periods, so a change in the estimate reflects a change in the outcome and not a change in who is being counted. Letting the weights vary instead tracks the population as it actually was over the sample window, migration included. Neither is universally right. However, whichever you use, state which one it was and why.

None of this changes what parallel trends means. Weighting changes the population the assumption is applied to (and therefore the estimand), and it does not change the assumption itself.

When the weights happen to be constant within unit, the choice cannot matter and the modes agree exactly. Check that before spending time on the decision.

Weights are not clustering

Weights say how much of the population each observation represents. Clustering says which observations share correlated shocks. They are separate options answering separate questions, and using one of them does not address the other:

use "jel_weighted.dta", clear
csdid mrate [iw=population_20_64], ivar(county_code) time(year) gvar(gvar) ///
    cluster(stfips) analytical
estat simple
display "clusters: " e(N_clusters)

Treatment here is assigned at the state level, so clustering on state is the relevant choice regardless of how the observations are weighted, and a weighted run with the wrong cluster variable is no safer than an unweighted one. See Inference.

capture erase "jel_weighted.dta"