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Principal Components Difference-in-Differences

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.

Installation

You can install the development version of pcdid from GitHub with:

devtools::install_github("adamwang15/pcdid")

Example

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 ' ' 1

To 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 ' ' 1

To 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 ' ' 1

To 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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.