DiSCo {DiSCos}  R Documentation 
Distributional Synthetic Controls
Description
This function implements the distributional synthetic controls (DiSCo) method from Gunsilius (2023). as well as the alternative mixture of distributions approach.
Usage
DiSCo(
df,
id_col.target,
t0,
M = 1000,
G = 1000,
num.cores = 1,
permutation = FALSE,
q_min = 0,
q_max = 1,
CI = FALSE,
boots = 500,
replace = TRUE,
uniform = FALSE,
cl = 0.95,
graph = FALSE,
qmethod = NULL,
qtype = 7,
seed = NULL,
simplex = FALSE,
mixture = FALSE,
grid.cat = NULL
)
Arguments
df 
Data frame or data table containing the distributional data for the target and control units. The data table should contain the following columns:

id_col.target 
Variable indicating the name of the target unit, as specified in the id_col column of the data table. This variable can be any type, as long as it is the same type as the id_col column of the data table. 
t0 
Integer indicating period of treatment. 
M 
Integer indicating the number of control quantiles to use in the DiSCo method. Default is 1000. 
G 
Integer indicating the number of grid points for the grid on which the estimated functions are evaluated. Default is 1000. 
num.cores 
Integer, number of cores to use for parallel computation. Default is 1. If the 
permutation 
Logical, indicating whether to use the permutation method for computing the optimal weights. Default is FALSE. 
q_min 
Numeric, minimum quantile to use. Set this together with 
q_max 
Numeric, maximum quantile to use. Set this together with 
CI 
Logical, indicating whether to compute confidence intervals for the counterfactual quantiles. Default is FALSE. The confidence intervals are computed using the bootstrap procedure described in Van Dijcke et al. (2024). 
boots 
Integer, number of bootstrap samples to use for computing confidence intervals. Default is 500. 
replace 
Logical, indicating whether to sample with replacement when computing the bootstrap samples. Default is TRUE. 
uniform 
Logical, indicating whether to construct uniform bootstrap confidence intervals. Default is FALSE If FALSE, the confidence intervals are pointwise. 
cl 
Numeric, confidence level for the (twosided) confidence intervals. 
graph 
Logical, indicating whether to plot the permutation graph as in Figure 3 of the paper. Default is FALSE. 
qmethod 
Character, indicating the method to use for computing the quantiles of the target distribution. The default is NULL, which uses the 
qtype 
Integer, indicating the type of quantile to compute when using 
seed 
Integer, seed for the random number generator. This needs to be set explicitly in the function call, since it will invoke 
simplex 
Logical, indicating whether to use to constrain the optimal weights to the unit simplex. Default is FALSE, which only constrains the weights to sum up to 1 but allows them to be negative. 
mixture 
Logical, indicating whether to use the mixture of distributions approach instead.
See Section 4.3. in Gunsilius (2023). This approach minimizes the distance between the CDFs
instead of the quantile functions, and is preferred for categorical variables. When working with such variables, one should
also provide a list of support points in the 
grid.cat 
List, containing the discrete support points for a discrete grid to be used with the mixture of distributions approach. This is useful for constructing synthetic distributions for categorical variables. Default is NULL, which uses a continuous grid based on the other parameters. 
Details
This function is called for every time period in the DiSCo function. It implements the DiSCo method for a single time period, as well as the mixture of distributions approach.
The corresponding results for each time period can be accessed in the results.periods
list of the output of the DiSCo function. The DiSCo function returns the average weight for each unit across all periods,
calculated as a uniform mean, as well as the counterfactual target distribution produced as the weighted average of the control distributions for each period, using these averaged weights.
Value
A list containing the following elements:

results.periods
A list containing, for each time period, the elements described in the return argument ofDiSCo_iter
, as well as the following additional elements:
DiSco

quantile
The counterfactual quantiles for the target unit. 
weights
The optimal weights for the target unit. 
cdf
The counterfactual CDF for the target unit.



weights
A numeric vector containing the synthetic control weights for the control units, averaged over time. Whenmixture
is TRUE, these are the weights for the mixture of distributions, otherwise they are the weights for the quantilebased approach. 
CI
A list containing the confidence intervals for the counterfactual quantiles and CDFs, ifCI
is TRUE. Each element contains two named subelements calledupper
,lower
,se
which are the upper and lower confidence bands and the standard error of the estimate, respectively. They are G x T matrices where G is the specified number of grid points and T is the number of time periods. The elements are:
cdf
The bootstrapped CDF 
quantile
The bootstrapped quantile 
quantile_diff
The bootstrapped quantile difference 
cdf_diff
The bootstrapped CDF difference 
bootmat
A list containing the raw bootstrapped samples for the counterfactual quantiles and CDFs, ifCI
is TRUE. These are not meant to be accessed directly, but are used byDiSCoTEA
to compute aggregated standard errors. Advanced users may wish to access these directly for further analysis. The element names should be selfexplanatory. #' 
control_ids
A list containing the control unit IDs used for each time period, which can be used to identify the weights associated with each control as the returned weights have the same order as the control IDs. 
perm
Apermut
object containing the results of the permutation method, ifpermutation
is TRUE. Callsummary
on this object to print the overall results of the permutation test. #' 
evgrid
A numeric vector containing the grid points on which the quantiles were evaluated. 
params
A list containing the parameters used in the function call.

References
Gunsilius FF (2023).
“Distributional synthetic controls.”
Econometrica, 91(3), 1105–1117.
Van Dijcke D, Gunsilius F, Wright AL (2024).
“Return to Office and the Tenure Distribution.”
Working Paper 202456, University of Chicago, Becker Friedman Institute for Economics.()