Event Studies
Linear panel models, and the event-study plots that often accompany
them, are popular tools for learning about policy effects.
Data
We will use the example_data dataset to demonstrate the
basic functionality of eventstudyr. These sample data are
from the replication
archive for Freyaldenhoven et al. (2021). The documentation can be
accessed using ?example_data.
dim(example_data)
#> [1] 2000 12
head(example_data)
#> # A tibble: 6 × 12
#> id eventtime t z y_base eta_m y_jump_m y_smooth_m x_jump_m eta_r
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 32 1 0 -0.609 0.180 41.6 41.6 0.684 1
#> 2 1 32 2 0 -0.870 0.180 41.3 41.3 0.0167 1
#> 3 1 32 3 0 -0.906 0.180 41.3 41.3 0.153 1
#> 4 1 32 4 0 0.148 0.180 42.3 42.3 -0.930 1
#> 5 1 32 5 0 0.579 0.180 42.8 42.8 -0.316 1
#> 6 1 32 6 0 -0.340 0.180 41.8 41.8 1.69 1
#> # ℹ 2 more variables: y_r <dbl>, x_r <dbl>
EventStudy()
EventStudy() estimates the regression model from
Equation (2) in Freyaldenhoven et al. (2021) and returns a list object
that stores the estimation results (as an lm() object) as well as the
arguments given in the function call. It accepts variables specifying
the outcome, policy, ID and time variables. One must also specify the
number of periods in the past before which the past values of the policy
are not supposed to affect the value of the outcome and the number of
periods in the future after which the future values of the policy are
not supposed to affect the value of the outcome today. The function
optionally accepts variables specifying the controls, the time window,
whether fixed effects should be included, and the period to be used for
normalization.
Here is an example using the sample data:
results <- EventStudy(estimator = "OLS",
data = example_data,
outcomevar = "y_jump_m",
policyvar = "z",
idvar = "id",
timevar = "t",
post = 3,
pre = 0)
summary(results$output)
#>
#> Call:
#> estimatr::lm_robust(formula = prepared_model_formula, data = prepared_data,
#> clusters = get(idvar), fixed_effects = ~get(idvar) + get(timevar),
#> se_type = "stata")
#>
#> Standard error type: stata
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF
#> z_lead3 0.2390 0.1433 1.6683 1.016e-01 -0.04891 0.5270 49
#> z_fd_lead3 0.1752 0.1618 1.0829 2.842e-01 -0.14997 0.5004 49
#> z_fd_lead2 0.1238 0.1748 0.7085 4.820e-01 -0.22744 0.4751 49
#> z_fd 0.8309 0.1332 6.2355 1.014e-07 0.56309 1.0986 49
#> z_fd_lag1 0.8552 0.1766 4.8419 1.328e-05 0.50024 1.2101 49
#> z_fd_lag2 0.6326 0.1538 4.1123 1.491e-04 0.32347 0.9417 49
#> z_fd_lag3 0.2464 0.1830 1.3465 1.843e-01 -0.12132 0.6140 49
#> z_lag4 0.1428 0.1270 1.1241 2.664e-01 -0.11244 0.3979 49
#>
#> Multiple R-squared: 0.9997 , Adjusted R-squared: 0.9997
#> Multiple R-squared (proj. model): 0.05327 , Adjusted R-squared (proj. model): -0.001353
#> F-statistic (proj. model): 10.44 on 8 and 49 DF, p-value: 2.142e-08
Click for results$arguments
## Estimator
results$arguments$estimator
#> [1] "OLS"
## Data
results$arguments$data[1:5,]
#> id eventtime t z y_base eta_m y_jump_m y_smooth_m x_jump_m eta_r
#> 1 1 32 1 0 -0.6087238 0.18 41.57128 41.57128 0.68367314 1
#> 2 1 32 2 0 -0.8699341 0.18 41.31007 41.31007 0.01667022 1
#> 3 1 32 3 0 -0.9059790 0.18 41.27402 41.27402 0.15259252 1
#> 4 1 32 4 0 0.1482184 0.18 42.32822 42.32822 -0.93015540 1
#> 5 1 32 5 0 0.5785761 0.18 42.75858 42.75858 -0.31635490 1
#> y_r x_r z_fd z_fd_lag1 z_fd_lag2 z_fd_lag3 z_fd_lead3 z_fd_lead2
#> 1 1.891276 0.5520976 NA NA NA NA 0 0
#> 2 1.630066 2.3021448 0 NA NA NA 0 0
#> 3 1.594021 1.0289093 0 0 NA NA 0 0
#> 4 2.648218 0.2615794 0 0 0 NA 0 0
#> 5 3.078576 1.2146608 0 0 0 0 0 0
#> z_fd_lead1 z_lag4 z_lead3
#> 1 0 NA 1
#> 2 0 NA 1
#> 3 0 NA 1
#> 4 0 NA 1
#> 5 0 0 1
## Variables
results$arguments$outcomevar
#> [1] "y_jump_m"
results$arguments$outcomevar
#> [1] "y_jump_m"
results$arguments$policyvar
#> [1] "z"
results$arguments$idvar
#> [1] "id"
results$arguments$timevar
#> [1] "t"
results$arguments$controls
#> NULL
## Proxies
results$arguments$proxy
#> NULL
results$arguments$proxyIV
#> NULL
## Fixed effects
results$arguments$FE
#> [1] TRUE
results$arguments$TFE
#> [1] TRUE
## Periods
results$arguments$post
#> [1] 3
results$arguments$overidpost
#> [1] 1
results$arguments$pre
#> [1] 0
results$arguments$overidpre
#> [1] 3
## Normalization
results$arguments$normalize
#> [1] -1
results$arguments$normalization_column
#> [1] "z_fd_lead1"
## Cluster
results$arguments$cluster
#> [1] TRUE
## Eventstudy coefficients
results$arguments$eventstudy_coefficients
#> [1] "z_lead3" "z_fd_lead3" "z_fd_lead2" "z_fd" "z_fd_lag1"
#> [6] "z_fd_lag2" "z_fd_lag3" "z_lag4"
EventStudyPlot()
EventStudyPlot() prepares an event-study plot based on
the suggestions in Freyaldenhoven et al. (2021).
This function is designed to use the output of the
EventStudy() and returns a ggplot object. Here is an
example of using the function with some default settings:
eventstudy_estimates_ols <- EventStudy(estimator = "OLS",
data = example_data,
outcomevar = "y_jump_m",
policyvar = "z",
idvar = "id",
timevar = "t",
post = 3,
pre = 0)
EventStudyPlot(estimates = eventstudy_estimates_ols,
xtitle = "Event time",
ytitle = "Coefficient")
References
Freyaldenhoven, S., Hansen, C., Pérez, J.P. and Shapiro, J.M., 2021.
Visualization, identification, and estimation in the linear panel
event-study design (No. w29170). National Bureau of Economic
Research.