Authors: In Song Kim ([email protected]), Adam Rauh ([email protected]), Erik Wang ([email protected]), Kosuke Imai ([email protected])

This R package provides a set of methodological tools that enable researchers to apply matching methods to time-series cross-sectional data. Imai, Kim, and Wang (2018) proposes a nonparametric generalization of difference-in-differences estimator, which does not rely on the linearity assumption as often done in practice. Researchers first select a method of matching each treated observation from a given unit in a particular time period with control observations from other units in the same time period that have a similar treatment and covariate history. These methods include standard matching and weighting methods based on propensity score and Mahalanobis distance. Once matching is done, both short-term and long-term average treatment effects for the treated can be estimated with standard errors. The package also offers a visualization technique that allows researchers to assess the quality of matches by examining the resulting covariate balance.

PanelMatch is available on CRAN and can be installed using:

install.packages("PanelMatch")

You can install the most recent development version of PanelMatch using the devtools package. First you have to install devtools using the following code. Note that you only have to do this once:

if(!require(devtools)) install.packages("devtools")

Then, load devtools and use the function install_github() to install PanelMatch:

library(devtools)
install_github("insongkim/PanelMatch", dependencies=TRUE)

If you encounter problems during installation, please consult the wiki page that has some ideas for handling common issues.

Users can visualize the variation of treatment across space and time. This will help users build an intuition about how comparison of treated and control observations can be made.

library(PanelMatch)
DisplayTreatment(unit.id = "wbcode2",
                 time.id = "year", legend.position = "none",
                 xlab = "year", ylab = "Country Code",
                 treatment = "dem", data = dem)

PanelMatch identifies a matched set for each treated observation. Specifically, for a given treated unit, the matched set consists of control observations that have an identical treatment history up to a chosen number (lag) of years. This number corresponds with the lag parameter, which must be chosen by the user. Users must also consider various parameters regarding the refinement of created matched sets. Please consult the function documentation for a full set of descriptions, but some important arguments are described below:

1. refinement.method -- Users may choose between standard propensity score weighting or matching (ps.weight, ps.match), covariate balanced propensity score weighting or matching (CBPS.weight, CBPS.match), and mahalanobis distance matching (mahalanobis). Users may also opt to apply the idea of marginal structural models with the CBPS.msm.weight and ps.msm.weight methods. Alternatively users can do no refinement by setting this parameter to none.
2. size.match -- This sets the maximum number of control units that can be included in a matched set.
3. covs.formula -- This parameter defines which variables are considered in measuring the similarities/distances between units. These will then affect which control units are included/excluded during refinement. This can be set to include lagged versions of any variable as well. See the PanelMatch documentation for more information about this parameter.
4. match.missing -- Should matches between treatment and control units with identical patterns of missingness in the treatment variable be considered? If set to FALSE, missing data is not permitted in the lag window of the treatment variable in either treated or control units.

PM.results <- PanelMatch(lag = 4, time.id = "year", unit.id = "wbcode2", 
                         treatment = "dem", refinement.method = "mahalanobis", 
                         data = dem, match.missing = TRUE, 
                         covs.formula = ~ I(lag(tradewb, 1:4)) + I(lag(y, 1:4)), 
                         size.match = 5, qoi = "att" ,outcome.var = "y",
                         lead = 0:4, forbid.treatment.reversal = FALSE)

The PanelMatch function will return an object of class "PanelMatch". This is a list that contains a few specific elements: First, a matched.set object(s) that has the same name as the provided qoi -- if the qoi is "att", "atc". If qoi = "ate" then two matched.set objects will be attached, named "att" and "atc." Users can extract information about individual matched sets as well as statistics about all created matched sets from this object. Consult the Wiki page on Matched Set Objects for a more detailed walkthrough and description of these objects. Put simply, matched.set objects are merely lists with some assumed structure and special attributes.

The PanelMatch object also has some additional attributes: "qoi", "lead", "forbid.treatment.reversal" (a logical value that is the same as what was specified in the function call), and "outcome.var" (character value that is the same as what was specified in the function call)

You can check covariate balance using the get_covariate_balance function:

get_covariate_balance(PM.results$att, dem, covariates = c("tradewb"), plot = FALSE, ylim = c(-2,2))
       tradewb
t_4 0.14247452
t_3 0.08363034
t_2 0.11718424
t_1 0.25036846
t_0 0.28859923

See the documentation for more information about this function.

Once proper matched sets are attained by PanelMatch, users can estimate the causal quantity of interest such as the average treatment effect using PanelEstimate. Either bootstrap or weighted fixed effects methods can be used for standard error calculation. Users can estimate the contemporaneous effect as well as long-term effects. In this example, we illustrate the use of PanelEstimate to estimate the average treatment effect on treated units (att) at time t on the outcomes from time t+0 to t+4.

PE.results <- PanelEstimate(sets = PM.results, data = dem)

The PanelEstimate function returns a PanelEstimate object, which is a named list. This object will contain the point estimates, standard errors and other information about the calculations. See the wiki page about PanelEstimate objects for more information.

Users can easily obtain and visualize important information about esimtates and standard errors using the summary and plot methods for PanelEstimate objects

summary(PE.results)
Weighted Difference-in-Differences with Mahalanobis Distance
Matches created with 4 lags

Standard errors computed with 1000 Weighted bootstrap samples

Estimate of Average Treatment Effect on the Treated (ATT) by Period:
$summary
      estimate std.error      2.5%     97.5%
t+0 -0.8913640  0.649573 -2.104339 0.3319704
t+1 -0.4709856  1.099428 -2.656029 1.6943853
t+2  0.4803681  1.464809 -2.285216 3.4092224
t+3  1.3447573  1.769004 -1.971492 4.7865140
t+4  1.0782767  1.901539 -2.615567 4.9641979

$lag
[1] 4

$iterations
[1] 1000

$qoi
[1] "att"

plot(PE.results)