如何在 R 中进行具有交互效应和滞后的固定效应回归？

Question

I have panel data over the period 2010-2020 for 10 different regions in a country. I would like to measure the effect of X1 on Y were Y is the share of the population who voted for a extreme right party at Year s , and X1 is the share of asylum seekers in the region at Year s . I would like to measure the effect of X1 on Y during a specific year when asylum seekers in all regions increased drastically to examine if the increase in asylum seekers had any effect on the share of the population who voted on the extreme right party. X2...Xn are a bunch of control variables.

I have found the package "fixest" and can run a normal FE-regression, but cant seem to understand how to include an interaction effect with a specific year (the "treatment" year, when asylum seekers increased in all regions) for X1.

This is an example of the equation im trying to estimate: FE regression model , where (1) RHS term is region fixed effects, (2) RHS term is year fixed effects, (3) RHS term is the interaction between the year 2016 and asylum seekers in the previous year, (4) RHS term is all the control variables and (5) RHS term is the error term.

Below is a made up head of the data frame.

Year   Region   Y      X1    X2...Xn
2010   A        0.15  0.001
2011   A        0.25  0.05
.      .        .     .
.      .        .     .
2010   B        0.09  0.002
2011   B        0.14  0.04

Answer 1

you can simply use the function i() to create an interaction between a continuous variables (x1) and a factor (the year). With i 's argument keep , you can select the year you want to keep.

The second thing is the lag: just use the function l() within a fixest estimation, but it requires to specify the panel identifiers.

Here's an example of the expected behavior, it should be easy to adapt to your case:

library(fixest)

data(base_did)
est = feols(y ~ i(l(x1), period, keep = 10) | id + period, base_did, panel.id = ~id+period)
#> NOTE: 108 observations removed because of NA values (RHS: 108).
est
#> OLS estimation, Dep. Var.: y
#> Observations: 972 
#> Fixed-effects: id: 108,  period: 9
#> Standard-errors: Clustered (id) 
#>                      Estimate Std. Error t value Pr(>|t|) 
#> l(x1, 1):period::10 -0.263237   0.217412 -1.2108 0.228651 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 4.8876     Adj. R2: 0.173257
#>                Within R2: 0.002642