DiSCo_weights_reg: DiSCo_weights_reg
In DiSCos: Distributional Synthetic Controls Estimation

DiSCo_weights_reg

R Documentation

DiSCo_weights_reg

Description

Function for obtaining the weights in the DiSCo method at every time period

Usage

DiSCo_weights_reg(
  controls,
  target,
  M = 500,
  qmethod = NULL,
  qtype = 7,
  simplex = FALSE,
  q_min = 0,
  q_max = 1
)

Arguments

`controls`	List with matrices of control distributions
`target`	Matrix containing the target distribution
`M`	Integer indicating the number of control quantiles to use in the DiSCo method. Default is 1000.
`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.
`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.
`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.

Details

Estimate the optimal weights for the distributional synthetic controls method. solving the convex minimization problem in Eq. (2) in \insertCitegunsilius2023distributional;textualDiSCos.. using a regression of the simulated target quantile on the simulated control quantiles, as in Eq. (3), \underset{\vec{\lambda} \in \Delta^J}{\operatorname{argmin}}\left\|\mathbb{Y}_t \vec{\lambda}_t-\vec{Y}_{1 t}\right\|_2^2. For the constrained optimization we rely on the package pracma the control distributions can be given in list form, where each list element contains a vector of observations for the given control unit, in matrix form; in matrix- each column corresponds to one unit and each row is one observation. The list-form is useful, because the number of draws for each control group can be different. The target must be given as a vector.