Introduction
The package DynBalancing implements the methods for estimating treatment effect with panel data of the following paper:
“Viviano, Davide, and Jelena Bradic.”Dynamic covariate balancing: estimating treatment effects over time." arXiv preprint arXiv:2103.01280 (2021)."
The package estimates treatment effects when units are exposed to treatments that change over time. The method estimates the effects of treatment histories, consisting of arbitrary sequences of treatments specified by the user.
The package works for balanced and unbalanced panels with high-dimensional (and time-varying) covariates. Effects are estimated through penalized regression with dynamic balancing weights.
In the regression, by default, all coefficients are penalized, except the ones corresponding to the treatment assignments. Parameters are chosen via cross-validation. The user may also specify regularization = F to avoid regularization of the parameters.
Standard errors assume cross-sectionally independent observations. Clustered standard errors can also be computed (see params list).
Illustration
We first discuss estimation of the ATE. We estimate the ATE on the outcome in the last period.
## Define the inputs
Time_name = 'Time'
unit_name = 'Unit'
## Define which covariates to include in the regression
## (Note: fixed effects are not included here and should pass to the argument "fixed_effects")
covariates_names = c(paste0('V', c(1:158)), 'lag1.Value1',
'lag2.Value1', 'lag3.Value1', 'lag4.Value1')
outcome_name = 'Y'
treatment_name = 'D'
## Consider the effect over two periods only
## Always treated in two periods
ds1 = c(1,1)
## Never treated in two periods
ds2 = c(0,0)
my_first_result = DynBalancing_ATE(panel_example, covariates_names , Time_name, unit_name, outcome_name, treatment_name,
ds1 = ds1, ds2 = ds2,
pooled = F,
fixed_effects = c('region'))
After running the regression we can now explore the results.
my_first_result$summaries
#> ATE SE_ATE Robust_Quantile_ATE Gaussian_Quantile_ATE
#> 1 -0.02079539 0.01777009 2.789165 1.644854
#> Mu1 SE_mu1 Mu2 Variance_mu2 Robust_Quantile_mu
#> 1 7.818412 0.009662629 7.839208 0.01491341 2.145966
#> Gaussian_Quantile_ATE
#> 1 1.644854
The above table reports the estimated ATE for being under treatment over two consecutive periods, its standard error and the critical quantile to use for a test with size \(10\%\) (see below for details). Robust quantiles impose weaker conditions than Gaussian quantiles, but are larger in absolute terms.
Pooled regression
By default the R command considers as the main outcome the outcome in the last period of the panel only (in this case of the outcome at time 5). However, we can also consider a pooled regression, with time fixed effects. In such a case, standard errors are automatically clustered at the unit level (same units in different times form a same cluster), unless a larger cluster (e.g., region) is passed to the function.
## Here Time fixed effect is necessary since regression is pooled
my_second_result = DynBalancing_ATE(panel_example, covariates_names , Time_name, unit_name, outcome_name, treatment_name,
ds1 = ds1, ds2 = ds2,
## You can run the regression pooled or not pooled. If pooled select a time fixed effect
## if pooled = F, the regression considers as end-line outcome the last period
pooled = T,
fixed_effects = c('region', 'Time'))
my_second_result$summaries
#> ATE SE_ATE Robust_Quantile_ATE Gaussian_Quantile_ATE
#> 1 -0.01475476 0.01266926 2.789165 1.644854
#> Mu1 SE_mu1 Mu2 Variance_mu2 Robust_Quantile_mu
#> 1 7.828838 0.006013551 7.843592 0.01115112 2.145966
#> Gaussian_Quantile_ATE
#> 1 1.644854
Time varying effects
The function DynBalancing_History computes treatment effects that vary in the exposure length. For example, it computes the effect of being one, two, three, … periods under treatment.
## Look at the 1 to 5 lag effect of the treatment
histories_length = c(1:5)
## consider the case where I am always treated
ds1 = rep(1, 5)
## never treated
ds2 = rep(0, 5)
## Study the effect of the treatment over 2, ..., 5 periods
res1 <- DynBalancing_History(panel_example, covariates_names,
Time_name, unit_name, outcome_name,
treatment_name, ds1, ds2, histories_length = histories_length,
## Choose fixed effects
fixed_effects = c('region'),
pooled = T,
## Optional: run computations in parallel
params = list(numcores = 6, initial_period = 0))
res1$plots$ATE
The plot reports the standard errors with robust quantile (light gray area), and standard errors with Gaussian quantile (dark-gray area). Each element corresponds to the effect of being exposed to treatment since \(t\) periods.
Additional features
Clustered standard errors
In applications, we may be concerned with correlations and control for those using clustered standard errors. These are implemented as follows.
my_third_result = DynBalancing_ATE(panel_example, covariates_names , Time_name, unit_name, outcome_name, treatment_name,
ds1 = c(1,1), ds2 = c(0,0),
fixed_effects = c('region'), params = list(cluster_SE = 'region'))
my_third_result$summaries
#> ATE SE_ATE Robust_Quantile_ATE Gaussian_Quantile_ATE
#> 1 -0.02079532 0.03163238 2.789165 1.644854
#> Mu1 SE_mu1 Mu2 Variance_mu2 Robust_Quantile_mu
#> 1 7.818412 0.02445404 7.839208 0.02006508 2.145966
#> Gaussian_Quantile_ATE
#> 1 1.644854
Plots
The function DynBalancing_ATE reports imbalance plots of the following form:
my_third_result$plots$imbalance1
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
#> Warning: Removed 2 rows containing non-finite values (stat_bin).
The plot reports the imbalance, based on the covariate balancing method in the first and second period across all covariates (imbalance for each covariate is rescaled by its standard deviation).
We can also plot the ATE
my_third_result$plots$ATE
#> $mus
#>
#> $ATE
Additional parameters
We indicate below a list of some default settings that the user may change. To change the settings pass the params list to the above functions. More options will be added.
## Examples of params to pass
params = list(
## Do regularized regression
regularization = T,
## pass identity of final period. If missing, the last period in the panel is considered.
final_period = NA,
## size
alpha = 0.1,
## lb for balancing (balancing is lb * sqrt(log(p)/sqrt(n)))
lb = 0.0005,
## ub for balancing
ub = 2,
## method for estimation either lasso_plain or lasso_subsample
method = 'lasso_plain',
## use a robust quantile for CI with chisquared dist
robust_quantile = T,
## use open source software
open_source = T,
## numcores
numcores = 1,
## nfolds for cross validation
nfolds = 10,
##cluster_SE pass a string indicating the column of clustering
cluster_SE = NA,
## use function to compute tuning parameters in a fast way
fast_adaptive = F,
## Beginning of the panel to consider
initial_period = 0
)