pcdid implements factor-augmented difference-in-differences (DID) estimation. It is useful in situations where the user suspects that trends may be unparallel and/or stochastic among control and treated units. The data structure is similar to that in a DID setup.
The estimation method is regression-based and can be considered as an extension of conventional DID regressions. pcdid also implements a parallel trend alpha test (based on an interactive effects structure) and a recursive procedure that determines the number of factors automatically.
For further details, please see Chan and Kwok (2022) who developed the pcdid approach and the alpha test.
You can install the development version of pcdid from GitHub with:
devtools::install_github("adamwang15/pcdid")This is a basic example which replicates Chan and Kwok (2022)
library(pcdid)
result <- pcdid(
lncase ~ treated + treated_post + afdcben + unemp + empratio + mon_d2 + mon_d3 + mon_d4,
index = c("state", "trend"),
data = welfare,
alpha = TRUE
)To access the mean-group estimates
result$mg
#>
#> z test of coefficients:
#>
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -4.4556629 0.0878986 -50.6909 < 2.2e-16 ***
#> treated_post -0.0168484 0.0071048 -2.3714 0.01772 *
#> afdcben 0.0143423 0.0075024 1.9117 0.05591 .
#> unemp 0.0206647 0.0035431 5.8324 5.465e-09 ***
#> empratio 0.0579939 0.1285858 0.4510 0.65198
#> mon_d2 0.0261549 0.0037348 7.0031 2.504e-12 ***
#> mon_d3 0.0238558 0.0049483 4.8210 1.429e-06 ***
#> mon_d4 0.0103690 0.0042303 2.4511 0.01424 *
#> fproxy1 3.1685663 0.5606270 5.6518 1.588e-08 ***
#> fproxy2 -2.2785399 0.5683153 -4.0093 6.090e-05 ***
#> fproxy3 1.7287098 0.7313678 2.3637 0.01810 *
#> fproxy4 -3.1723206 0.6918360 -4.5854 4.532e-06 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1To access the alpha test result
result$alpha
#>
#> z test of coefficients:
#>
#> Estimate Std. Error z value Pr(>|z|)
#> alpha 0.99183 0.13754 7.2111 5.552e-13 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1To access an individual treated unit estimate
result$treated$WY$coefficients
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -4.5588646 0.2935291 -15.5312 < 2.2e-16 ***
#> treated_post -0.1142959 0.0280812 -4.0702 9.121e-05 ***
#> afdcben -0.0096464 0.0194555 -0.4958 0.6210599
#> unemp -0.0303034 0.0078223 -3.8740 0.0001866 ***
#> empratio -0.6215301 0.3450325 -1.8014 0.0745152 .
#> mon_d2 -0.0185256 0.0129566 -1.4298 0.1557394
#> mon_d3 -0.0613559 0.0165974 -3.6967 0.0003492 ***
#> mon_d4 -0.0743271 0.0167155 -4.4466 2.174e-05 ***
#> fproxy1 2.7033131 0.4950210 5.4610 3.195e-07 ***
#> fproxy2 -4.8730998 1.1297026 -4.3136 3.640e-05 ***
#> fproxy3 0.0068711 1.1667167 0.0059 0.9953122
#> fproxy4 -4.8867753 2.7304968 -1.7897 0.0763845 .
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1To access an individual control unit estimate
result$control$OH$coefficients
#>
#> t test of coefficients:
#>
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -4.1981999 0.1119283 -37.5079 < 2.2e-16 ***
#> afdcben 0.0333233 0.0051964 6.4127 4.068e-09 ***
#> unemp 0.0482666 0.0055919 8.6315 6.645e-14 ***
#> empratio 0.5510229 0.1854242 2.9717 0.003665 **
#> mon_d2 0.0275807 0.0054598 5.0516 1.836e-06 ***
#> mon_d3 0.0553877 0.0071581 7.7377 6.249e-12 ***
#> mon_d4 0.0357344 0.0061858 5.7769 7.701e-08 ***
#> fproxy1 -4.5719351 0.1996360 -22.9014 < 2.2e-16 ***
#> fproxy2 -8.1910637 0.8168225 -10.0280 < 2.2e-16 ***
#> fproxy3 10.9875132 0.7484328 14.6807 < 2.2e-16 ***
#> fproxy4 -1.0994630 0.8806680 -1.2484 0.214620
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1