Cross-sectional causal variance decomposition

Decomposes the treatment effect on total variance (or CV^2) into between-group and within-group components at a single timepoint.

Usage

causal_decompose_cross(params, ref = NULL)

Arguments

params

An ineqx_params object. For cross-sectional decomposition, this should contain a single time period (or no time column).

Value

An object of class "ineqx_causal_cross" containing:

tau_B

Scalar, between-group treatment effect on inequality

tau_W

Scalar, within-group treatment effect on inequality

tau_total

Scalar, total treatment effect (tau_B + tau_W)

components

List of sub-components for interpretive analysis

by_group

data.frame of group-level contributions

params

The input ineqx_params object

Details

The between-group treatment effect is: $$\delta_B^D = \text{Var}_\pi(\beta_D) + 2\,\text{Cov}_\pi(\mu(0), \beta_D)$$

The within-group treatment effect is: $$\delta_W^D = \sum_j \pi_j \sigma_j^2(0) [\exp(2\lambda_{D,j}) - 1]$$