Did Imputation

Estimation of staggered Difference-in-Differences using the imputation approach of Borusyak, Jaravel, and Spiess (2021). The packages allows for:

• Multiple time periods

• Staggered design (i.e., units are treated at different time periods)

• Continuous controls

The package implements an imputation method to estimate the treatment effect and pre-trend testing in difference-in-differences designs with staggered adoption (i.e where units are treated at different time periods). Recent literature stress out the importance of not using the standard twoway fixed effect regression.

The standard DiD setup involves two periods and two groups (one treated and one untreated), it relies on parallel trend assumption to estimate the treatment effect of the treated. The staggered DiD setup is the generalization of this approach to multiple periods and multiple groups (i.e. individuals treated at different time periods.). Recent literature stress out the need to not use the standard two-way fixed effect (TWFE) regression to estimate those models. This package implements a method of imputation to estimate the average treatment effect. The package uses untreated observations to predict the counterfactual outcome on treated observations and provide the appropriate Standard errors. It provides ways to test for parallel trends.

Installation

You can install the github version with devtools or renv(recommended, read more about renv)

devtools::install("CdfInnovLab/didImputation")

Usage

library(didImputation)

data(did_simulated)

res <- didImputation(y0 = y ~ 0 | i + t,
                    cohort = 'g',
                    data = did_simulated)
summary(res)
#> Event Study: imputation method. Dep. Var.:  y 
#> Counterfactual model:  y ~ 0 | i + t 
#> Number of cohorts:  5 
#> Observations: 1500 
#> |-Treated:    630 
#> |-Untreated:  870 
#>       Estimate Std. Error t value Pr(>|t|))
#> k::-4 0.058    0.228       0.256  0.798    
#> k::-3 0.124    0.238       0.518  0.605    
#> k::-2 0.204    0.257       0.795  0.428    
#> k::-1 0.059    0.284       0.208  0.835    
#> k::0  0.974    0.097      10.016  <0.001***
#> k::1  2.086    0.110      18.972  <0.001***
#> k::2  2.991    0.143      20.899  <0.001***
#> k::3  3.981    0.189      21.046  <0.001***
#> k::4  4.775    0.259      18.463  <0.001***
#> ---
#> Signif. Code: 0 '***' 0.01 '**' 0.05 '*' 0.1 '' 1 
#> Wald stats for pre-trends:
#> Wald (joint nullity): stat = 0.473843, p = 0.754974, on 4 and 860 DoF, VCOV: Clustered (i).

You can print the result easily with didplot

didplot(res)

How it works

didImputation estimates the effects of a binary treatment with staggered timing. It allows for arbitrary heterogeneity of treatment and dynamic effects.

The estimation is a three step procedures

1. Estimate a linear model on non treated observations only (it ) (either not-yet-treated or never-treated).

   

2. Impute the treated observations () potential outcome and obtain treatment effect by substracting the predicted outcome from step 1

   

3. Average estimated treatment effects to the estimand of interest.

   For the overall average treatment effect, the estimate is defined by

   

TODO

• Estimation weights
• Triple differences
• Vignette
• Time invariant controls
• Unit invariant controls
• Custom cluster
• Latex export
• Allow custom period length
• Automatic panel balance
• Interactions in fixed effects
• Allow weights reuse

Reference

Borusyak, K., Jaravel, X., & Spiess, J. (2021). Revisiting event study designs: Robust and efficient estimation. Working paper.

See also

didimputation: Another implementation using sparse matrix inversion.