DiSCo_iter {DiSCos}

Estimate DiSCo in a single period

Description

This function implements the DiSCo method for a single time period, as well as the mixture of distributions approach. Its return values contain valuable period-specific estimation outputs.

Usage

DiSCo_iter(
  yy,
  df,
  evgrid,
  id_col.target,
  M,
  G,
  T0,
  qmethod = NULL,
  qtype = 7,
  q_min = 0,
  q_max = 1,
  simplex = FALSE,
  controls.id,
  grid.cat,
  mixture
)

Arguments

yy

Integer indicating the current year being processed.

df

Data frame or data table containing the distributional data for the target and control units. The data table should contain the following columns:

• y_col A numeric vector containing the outcome variable for each unit. Units can be individuals, states, etc., but they should be nested within a larger unit (e.g. individuals or counties within a state)

• id_col A numeric vector containing the aggregate IDs of the units. This could be, for example, the state if the units are counties or individuals

• time_col A vector containing the time period of the observation for each unit. This should be a monotonically increasing integer.

evgrid

A vector of grid points on which to evaluate the quantile functions.

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.

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.

T0

Integer indicating the last pre-treatment period starting from 1.

qmethod

Character, indicating the method to use for computing the quantiles of the target distribution. The default is NULL, which uses the quantile function from the stats package. Other options are "qkden" (based on smoothed kernel density function) and "extreme" (based on parametric extreme value distributions). Both are substantially slower than the default method but may be useful for fat-tailed distributions with few data points at the upper quantiles. Alternatively, one could use the q_max option to restrict the range of quantiles used.

qtype

Integer, indicating the type of quantile to compute when using quantile in the qmethod argument. The default 7. See the documentation for the quantile function for more information.

q_min

Numeric, minimum quantile to use. Set this together with q_max to restrict the range of quantiles used to construct the synthetic control. Default is 0 (all quantiles). Currently NOT implemented for the mixture approach.

q_max

Numeric, maximum quantile to use. Set this together with q_min to restrict the range of quantiles used to construct the synthetic control. Default is 1 (all quantiles). Currently NOT implemented for the mixture approach.

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.

controls.id

List of strings specifying the column names for the control units' identifiers.

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.

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 parameter. When that is provided, this parameter is automatically set to TRUE. Default is FALSE.

Details

This function is part of the DiSCo method, called for each time period. It calculates the optimal weights for the DiSCo method and the mixture of distributions approach for a single time period. The function processes data f or both the target and control units, computes the quantile functions, and evaluates these on a specified grid. The function is designed to be used within the broader context of the DiSCo function, which aggregates results across multiple time periods.

Value

A list with the following elements:

• DiSCo_weights Weights calculated using the DiSCo method.

• mixture

  • weights Optimal weights for the mixture approach.

  • distance Value of the objective function for the mixture approach.

  • mean Weighted mixture of the controls' CDFs.

• target

  • cdf Empirical CDF of the target. Only computed when mixture=TRUE.

  • grid Grid on which the quantile and CDF functions were evaluated.

  • data Original data for the target unit.

  • quantiles Quantiles for the target unit, evaluated on the specified grid.

• controls

  • data Original data for the control units.

  • cdf Empirical CDFs of the control units. Only computed when mixture=TRUE.

  • quantiles Quantiles for the control units, evaluated on the specified grid. .

• controls.q Quantiles for the control units, evaluated on the specified grid.