Doubly robust DiD with a spatial lag of treatment

With a non-negative neighbour matrix W the row-standardised spatial lag (W z)_i = sum_j w_ij z_j / sum_j w_ij is the neighbourhood average of z. The lag of the treatment is appended to the covariate block of the doubly robust moment of Sant'Anna and Zhao (2020), equation (2.6), so that both the propensity score and the outcome regression condition on how treated a unit's neighbourhood is. A W with no off-diagonal mass makes the lag constant and the two estimates coincide.

Usage

Drspa(y, D, X = NULL, W_neighbors = NULL)

Arguments

y: Outcome change, one entry per unit.
D: Binary treatment indicator.
X: Optional baseline covariates.
W_neighbors: Optional non-negative n x n neighbour weights.

Value

List with estimate, tau_nospatial, spatial_shift, se, wd_mean, wd_sd, n.

References

Anselin, L. (2003). Spatial externalities, spatial multipliers, and spatial econometrics. International Regional Science Review 26(2), 153-166. Sant'Anna, P. H. C. and Zhao, J. (2020). Journal of Econometrics 219(1), 101-122.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Drspa(V, V)
#> $estimate
#> [1] 5.666667
#> 
#> $tau_nospatial
#> [1] 5.666667
#> 
#> $spatial_shift
#> [1] 0
#> 
#> $se
#> [1] 1.659708
#> 
#> $wd_mean
#> [1] 0
#> 
#> $wd_sd
#> [1] 0
#> 
#> $n
#> [1] 8
#> 
#> $method
#> [1] "Spatial DR-DiD with neighbor effects"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"