Calculating standard errors for long-run (cumulative) multiplier in a Distributed Lag model

I have a distributed lag model of the form:

lm(wellbeing ~ temperature + temperature_lag1 + temperature_lag2 + time + individual, df)


where I'm interested in finding out the long-run multiplier for the effect of daily temperatures on an individual's wellbeing.

I understand that the coefficient for the multiplier would simply be the sum of the beta coefficients for temperature, temperature_lag1 and temperature_lag2.

However, I'm not entirely sure how to go about calculating the standard error for the multiplier.

I've seen suggestions for doing so by regressing:

dif1 <- temperature_lag1 - temperature
dif2 <- temperature_lag2 - temperature
lm(wellbeing ~ temperature + dif1 + dif2 + time + individual, df)


With the beta for temperature acting as the SE for the long-run multiplier. However, I'm not sure how valid this approach is?

Any guidance would be much appreciated.

• I'd look into the dlnm package that explicitly fits distributed lag models. – COOLSerdash Sep 18 '19 at 11:30
• Thanks. I'll certainly take a look at dlnm. Though at this stage, I'd be especially keen to understand the theory/practice behind how the SEs are calculated. – Shida Sep 18 '19 at 12:05