tjbal: Trajectory Balancing
R package for Trajectory Balancing: A General Reweighting Approach to Causal Inference with Time-Series Cross-Sectional Data
Reference: Hazlett, Chad and Yiqing Xu, 2018. ``Trajectory Balancing: A General Reweighting Approach to Causal Inference with Time-Series Cross-Sectional Data.’’ Working Paper, UCLA and Stanford. Available at SSRN: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3214231.
R source files can be found on Github. R code used in this demonstration can be downloaded from here.
Authors: Chad Hazlett (UCLA); Yiqing Xu (Stanford)
Date: March 23, 2020
Package: tjbal
Version: 0.3.1 (Github version). Please report bugs!
Contents
- Installation
- Example 1: Returns to Office of China’s National People’s Congress (Truex 2014)
- Example 2: German Reunification (Abaide, Diamond, Hainmueller 2015)
- Example 3: Election Day Registration (Xu 2017)
Installation
You can install the development version of the package from Github by typing the following commands:
install.packages('devtools', repos = 'http://cran.us.r-project.org') # if not already installed
devtools::install_github('chadhazlett/kbal')
devtools::install_github('xuyiqing/tjbal')Note that installing kbal (from Github) is required. tjbal also depends on the following packages, which will be installed AUTOMATICALLY when tjbal is being installed. You can also install them manually:
## for plotting
require(ggplot2)
## for parallel computing
require(foreach)
require(doParallel)
require(parallel)
## for data manipulation
require(plyr)We recommend researchers to plot data prior to data analysis. panelview is a package we make to help researchers visualize panel data. To install:
devtools::install_github('xuyiqing/panelview')Example 1: Returns to Office of China’s NPC (Truex 2014)
We illustrate tjbal using a dataset from Truex (2014), in which the author investigates the returns to seats in China’s National People’s Congress by CEOs of listed firms. The dataset npc is shipped with the tjbal package (we dropped one treated firm with extremely large revenue in 2007 to improve overlap between the treated and control units; see details in the paper). To load the package and the dataset:
library(tjbal)## ## Syntax has changed since v.0.3.0.## ## See http://bit.ly/tjbal4r for more info.
## ## Comments and suggestions -> yiqingxu@stanford.edu.data(tjbal)
ls()## [1] "germany" "npc"head(npc)## gvkey fyear roa treat so_portion rev2007
## 1 108893 2005 0.13556981 0 0.5286272 15110.46
## 2 108893 2006 0.10115566 0 0.5286272 15110.46
## 3 108893 2007 0.12335894 0 0.5286272 15110.46
## 4 108893 2008 0.20065501 1 0.5286272 15110.46
## 5 108893 2009 0.06594828 1 0.5286272 15110.46
## 6 108893 2010 0.12756890 1 0.5286272 15110.46First, we take a look at the data structure. The outcome variable is roa and the treatment indicator is treat; the unit and time indicators are gvkey and fyear, respectively. There are 47 treated firms whose CEOs became NPC members in 2008 and 939 control firms whose CEOs were never NPC members from 2005 to 2010.
The following plot shows the treatment status of the first 50 firms based on firm ID:
library(panelview)## ## See bit.ly/panelview4r for more info.
## ## Report bugs -> yiqingxu@stanford.edu.panelview(roa ~ treat + so_portion + rev2007, data = npc, show.id = c(1:50),
index = c("gvkey","fyear"), xlab = "Year", ylab = "Firm ID",
axis.lab.gap = c(0,1), by.timing = TRUE)
with(npc, table(fyear, treat))## treat
## fyear 0 1
## 2005 986 0
## 2006 986 0
## 2007 986 0
## 2008 939 47
## 2009 939 47
## 2010 939 47Difference-in-Differences (DID)
We then apply the difference-in-differences (DiD) method without controlling for any covariates. In the formula of tjbal, the left-hand-side variable is the outcome and the first right-hand-side variable is the dichotomous treatment indicator. We specify unit and time indicators using the index option. At the moment, we do not want to balance on pre-treatment outcomes, therefore, we set Y.match.npre = 0. Because an DID approach involves subtracting pre-treatment means from the outcome for each unit, we set demean = TRUE. Uncertainty estimates are obtained via a bootstrap procedure.
tjbal provides three balancing approaches: (1) "mean", which stands for mean-balancing; (2) "kernel", which stands for kernel-balancing; and (3) "meanfirst", which stands for kernel balancing with mean balancing constraints. "meanfirst" will prioritize balancing on covariate means over higher-order terms and interactions. The default option is "meanfirst". In this case, because we do not have any covariates to seek balance on, the estimator option is redundant.
For datasets with only one treatment timing, tjbal provides three types of uncertainty estimates: vce = "fixed.weights" which treats balancing weights as fixed; "jackknife" (or "jack"), which conducts jackknife by omitting one treated unit at a time, and "bootstrap" (or "boot"), which conducts non-parametric bootstrapping by reshuffle both the treated and control units. We show in the paper that, with reasonably large samples, these three methods yield very similar results. When "jackknife" or "bootstrap" is chosen, nsims determines the number of jackknife or bootstrap runs. With jackknife, nsims will be ignored if it is bigger than the number of treated units.
The print function present the result, which shows a non-significant effect of NPC membership on firms’ return on assets (ROA).
out.did <- tjbal(roa ~ treat, data = npc,
index = c("gvkey","fyear"), Y.match.npre = 0,
demean = TRUE, vce = "boot", nsims = 200)##
## Bootstrapping...
## Parallel computing...print(out.did)## Call:
## tjbal.formula(formula = roa ~ treat, data = npc, index = c("gvkey",
## "fyear"), Y.match.npre = 0, demean = TRUE, vce = "boot",
## nsims = 200)
##
## ~ by Period (including Pre-treatment Periods):
## ATT S.E. z-score CI.lower CI.upper p.value n.Treated
## 2005 -0.0042 0.0058 -0.7135 -0.0156 0.0073 0.4755 47
## 2006 0.0005 0.0034 0.1616 -0.0061 0.0071 0.8716 47
## 2007 0.0036 0.0051 0.7139 -0.0063 0.0135 0.4753 47
## 2008 -0.0017 0.0108 -0.1607 -0.0230 0.0195 0.8723 47
## 2009 0.0123 0.0066 1.8645 -0.0006 0.0252 0.0622 47
## 2010 0.0027 0.0061 0.4505 -0.0092 0.0147 0.6524 47
##
## Average Treatment Effect on the Treated:
## ATT S.E. z-score CI.lower CI.upper p.value
## [1,] 0.0044 0.0063 0.7009 -0.008 0.0168 0.4834The plot function visualizes the result, By default (type = gap), it plots the average treatment effect on the treated (ATT) over time (from 2008 to 2010). We add a histogram to illustrate the number of treated units at the bottom of the figure. It can be turned off by setting count == FALSE.
plot(out.did, ylab = "ATT", ylim = c(-0.06, 0.06))
We can also plot the treated and estimated \(Y(0)\) averages by specifying type = "counterfactual or simply type = "ct". Note that, with the DID approach, the estimated \(Y(0)\) averages do not fit perfectly with the treated averaged over the pre-treatment periods.
plot(out.did, type = "counterfactual", count = FALSE)
The plot function can also visualize the distribution of weights of the control units (the total weights added up to \(N_{tr}\), the number of the treated units). With the DID method, all control units are equally weighted:
plot(out.did, type = "weights")
Mean Balancing
Next, we apply the mean balancing approach (which the author uses in the original paper). In the formula, we also add two covariates, so_portion and rev2007. Note that they will not be put into regressions directly; rather, the algorithm will seek balance on them as well as the three pre-treatment outcomes. Because we do not employ the kernel transformation, we set estimator = "mean".
out.mbal <- tjbal(roa ~ treat + so_portion + rev2007, data = npc,
index = c("gvkey","fyear"), demean = FALSE, estimator = "mean",
vce = "jackknife")## Seek balance on:
## roa2005, roa2006, roa2007, so_portion, rev2007
##
## Optimization:
## bias.ratio = 0.0000; num.dims = 5 (mbal)
##
## Balance Table
## mean.tr mean.co.pre mean.co.pst sd.tr sd.co.pre sd.co.pst
## roa2005 0.0376 0.0225 0.0376 0.0675 0.0801 0.0778
## roa2006 0.0503 0.0305 0.0503 0.0424 0.0756 0.0667
## roa2007 0.0643 0.0414 0.0643 0.0564 0.1035 0.1611
## so_portion 0.3170 0.2491 0.3170 0.2397 0.2218 0.2355
## rev2007 6420.3705 2647.3412 6420.3705 9547.6633 5530.8308 14355.1192
## diff.pre diff.pst
## roa2005 0.2243 0
## roa2006 0.4682 0
## roa2007 0.4062 0
## so_portion 0.2835 0
## rev2007 0.3952 0
##
## Jackknife...
## Parallel computing...We see that NPC membership increases ROA by about 2 percentage points, and it is highly statistically significant.
print(out.mbal)## Call:
## tjbal.formula(formula = roa ~ treat + so_portion + rev2007, data = npc,
## index = c("gvkey", "fyear"), demean = FALSE, estimator = "mean",
## vce = "jackknife")
##
## ~ by Period (including Pre-treatment Periods):
## ATT S.E. z-score CI.lower CI.upper p.value n.Treated
## 2005 0.0000 0.0000 0.0001 0.0000 0.0000 0.9999 47
## 2006 0.0000 0.0000 -0.0038 0.0000 0.0000 0.9969 47
## 2007 0.0000 0.0000 -0.0054 0.0000 0.0000 0.9957 47
## 2008 0.0161 0.0076 2.1216 0.0012 0.0310 0.0339 47
## 2009 0.0260 0.0057 4.5312 0.0147 0.0372 0.0000 47
## 2010 0.0203 0.0064 3.1939 0.0079 0.0328 0.0014 47
##
## Average Treatment Effect on the Treated:
## ATT S.E. z-score CI.lower CI.upper p.value
## [1,] 0.0208 0.0057 3.628 0.0096 0.032 3e-04Alternatively, we can also specify the outcome (Y), treatment (D), and covariates (X) separately.
out.mbal <- tjbal(data = npc, Y = "roa", D = "treat", X = c("so_portion","rev2007"),
index = c("gvkey","fyear"), demean = FALSE, estimator = "mean",
vce = "jackknife", nsims = 200)We show the gap plot, the counterfactual plot, and the weightsplot again. With mean balancing, the pre-treatment outcomes are perfectly balanced between the treatment and control groups.
plot(out.mbal, ylim = c(-0.04, 0.06))
plot(out.mbal, type = "ct")
We can also add two bands that represent the ranges of the 5 to 95% quantile of the treated and control trajectories to the plot by setting raw = "band". When trim = TRUE (default), the control group data will be trimmed based on weights assigned to the control units (up to 90% of the total weight).
We can change the font size of almost all elements in the figure by setting cex.main (for title), cex.lab (for axis titles), cex.axis (for numbers on the axes), cex.legend (for legend) and cex.text for text in the figure. The numbers are all relative to the default.
A set of legend options can be used to adjust the look of the legends, including legendOff (turn off legends), legend.pos (position), legend.ncol (number of columns), and legend.labs (change label texts).
plot(out.mbal, type = "ct", raw = "band", ylim = c(-0.2, 0.3),
cex.main = 0.9, cex.lab = 1.1, cex.axis = 0.9, cex.legend= 0.8, cex.text = 1.5,
legend.pos = "top")
plot(out.mbal, type = "weights")
The plot function can also check balance in pre-treatment outcomes and covariates between the treatment and control groups before and after reweighting:
plot(out.mbal, type = "balance")
Kernel Balancing (w/ mean balancing constraints)
Finally, we apply the kernel balancing method (while respecting mean-balancing constraints) by setting estimator = "meanfirst". Note that kernel balancing is significantly more computationally intensive than mean balancing. Parallel computing with 4 cores on a 2016 iMac takes about 1 minutes to finish 47 jackknife runs.
begin.time<-Sys.time()
out.kbal <- tjbal(roa ~ treat + so_portion + rev2007, data = npc,
index = c("gvkey","fyear"), estimator = "meanfirst", demean = FALSE, vce = "jackknife")## Seek balance on:
## roa2005, roa2006, roa2007, so_portion, rev2007
##
## Optimization:
## bias.ratio = 0.0963; num.dims = 5 + 36 (mbal + kbal)
##
## Balance Table
## mean.tr mean.co.pre mean.co.pst sd.tr sd.co.pre sd.co.pst
## roa2005 0.0376 0.0225 0.0376 0.0675 0.0801 0.0663
## roa2006 0.0503 0.0305 0.0503 0.0424 0.0756 0.0429
## roa2007 0.0643 0.0414 0.0643 0.0564 0.1035 0.0544
## so_portion 0.3170 0.2491 0.3170 0.2397 0.2218 0.2389
## rev2007 6420.3705 2647.3412 6420.3704 9547.6633 5530.8308 9546.9245
## diff.pre diff.pst
## roa2005 0.2243 0
## roa2006 0.4682 0
## roa2007 0.4062 0
## so_portion 0.2835 0
## rev2007 0.3952 0
##
## Jackknife...
## Parallel computing...print(Sys.time()-begin.time) ## Time difference of 2.006553 minsWith kernel balancing with mean balancing weights, we find that NPC membership of the CEO increases a firm’s ROA by 1.4 percentage points. The estimate remains highly statistically significant.
print(out.kbal)## Call:
## tjbal.formula(formula = roa ~ treat + so_portion + rev2007, data = npc,
## index = c("gvkey", "fyear"), demean = FALSE, estimator = "meanfirst",
## vce = "jackknife")
##
## ~ by Period (including Pre-treatment Periods):
## ATT S.E. z-score CI.lower CI.upper p.value n.Treated
## 2005 0.0000 0.0000 0.3524 0.0000 0.0000 0.7245 47
## 2006 0.0000 0.0000 -0.3176 0.0000 0.0000 0.7508 47
## 2007 0.0000 0.0000 -0.3648 0.0000 0.0000 0.7153 47
## 2008 0.0060 0.0065 0.9248 -0.0068 0.0188 0.3551 47
## 2009 0.0198 0.0068 2.8975 0.0064 0.0332 0.0038 47
## 2010 0.0164 0.0059 2.7620 0.0048 0.0280 0.0057 47
##
## Average Treatment Effect on the Treated:
## ATT S.E. z-score CI.lower CI.upper p.value
## [1,] 0.0141 0.005 2.807 0.0042 0.0239 0.005Balance (in means) in the pre-treatment outcomes and covariates remain great, but no longer perfect. This is because kernel balancing also attempts to achieve balance in high-order features of these variables.
plot(out.kbal, ylim = c(-0.04, 0.06))
plot(out.kbal, type = "ct", xlab = "Year", ylab = "Return to Assets")
plot(out.kbal, type = "weights")
plot(out.kbal, type = "balance")
For example, kernel balancing also makes the standard deviations (or variance) of these variables in the treatment and reweighted control groups more similar than mean balancing.
plot(out.mbal, type = "balance", stat = "sd")
plot(out.kbal, type = "balance", stat = "sd")
For this example, setting estimator = "kernel" (i.e. kernel balancing without incorporating mean balancing constraints) yields very similar results.
Example 2: German Reunification (Abaide, Diamond, Hainmueller 2015)
In the second example, we re-investigate the effect of German reunification on West Germany’s GDP growth using data from Abaide, Diamond, Hainmueller (2015). Variable treat indicate West Germany over the post-1990 periods. Again, we look at the data structure first:
panelview(data = germany, gdp ~ treat, index = c("country","year"),
xlab = "Year", ylab = "Country", by.timing = TRUE,
axis.adjust = TRUE, axis.lab.gap = c(1,0))
Next, we implement the mean balancing method. Different from the previous example, we take averages for the covariates over different time periods (to be consistent with the original paper). Make sure that the length of the list set by X.avg.time is the the same as the length of the variable names in X.
out2.mbal <- tjbal(data = germany, Y = "gdp", D = "treat", Y.match.time = c(1960:1990),
X = c("trade","infrate","industry", "schooling", "invest80"),
X.avg.time = list(c(1981:1990),c(1981:1990),c(1981:1990),c(1980:1985),c(1980)),
index = c("country","year"), demean = TRUE)## Too few treated unit(s). Uncertainty estimates not provided.
## Seek balance on:
## gdp.dm1960, gdp.dm1961, gdp.dm1962, gdp.dm1963, gdp.dm1964, gdp.dm1965, gdp.dm1966, gdp.dm1967, gdp.dm1968, gdp.dm1969, gdp.dm1970, gdp.dm1971, gdp.dm1972, gdp.dm1973, gdp.dm1974, gdp.dm1975, gdp.dm1976, gdp.dm1977, gdp.dm1978, gdp.dm1979, gdp.dm1980, gdp.dm1981, gdp.dm1982, gdp.dm1983, gdp.dm1984, gdp.dm1985, gdp.dm1986, gdp.dm1987, gdp.dm1988, gdp.dm1989, gdp.dm1990, trade, infrate, industry, schooling, invest80
##
## Optimization:
## bias.ratio = 0.3804; num.dims = 2 (mbal)
##
## Balance Table
## mean.tr mean.co.pre mean.co.pst diff.pre diff.pst
## gdp.dm1960 -6282.4516 -5549.6673 -6669.2309 -0.1166 0.0616
## gdp.dm1961 -6178.4516 -5438.3548 -6554.7970 -0.1198 0.0609
## gdp.dm1962 -6039.4516 -5319.6673 -6401.5068 -0.1192 0.0599
## gdp.dm1963 -5956.4516 -5207.3548 -6281.0562 -0.1258 0.0545
## gdp.dm1964 -5760.4516 -5053.4798 -6088.6872 -0.1227 0.0570
## gdp.dm1965 -5561.4516 -4901.0423 -5896.5779 -0.1187 0.0603
## gdp.dm1966 -5398.4516 -4711.6673 -5671.6931 -0.1272 0.0506
## gdp.dm1967 -5325.4516 -4556.1048 -5483.9585 -0.1445 0.0298
## gdp.dm1968 -4995.4516 -4292.0423 -5168.5652 -0.1408 0.0347
## gdp.dm1969 -4568.4516 -3937.3548 -4760.4611 -0.1381 0.0420
## gdp.dm1970 -4199.4516 -3600.3548 -4332.6489 -0.1427 0.0317
## gdp.dm1971 -3880.4516 -3286.1673 -3926.6760 -0.1531 0.0119
## gdp.dm1972 -3511.4516 -2929.7298 -3505.8413 -0.1657 -0.0016
## gdp.dm1973 -3013.4516 -2434.9798 -2949.8805 -0.1920 -0.0211
## gdp.dm1974 -2492.4516 -1929.8548 -2325.7037 -0.2257 -0.0669
## gdp.dm1975 -1963.4516 -1482.7923 -1903.1728 -0.2448 -0.0307
## gdp.dm1976 -1199.4516 -921.0423 -1267.9545 -0.2321 0.0571
## gdp.dm1977 -476.4516 -381.5423 -517.1033 -0.1992 0.0853
## gdp.dm1978 361.5484 289.7702 304.8618 0.1985 0.1568
## gdp.dm1979 1500.5484 1157.7702 1357.3926 0.2284 0.0954
## gdp.dm1980 2516.5484 2083.5202 2502.9943 0.1721 0.0054
## gdp.dm1981 3548.5484 3020.6452 3698.6378 0.1488 -0.0423
## gdp.dm1982 4194.5484 3664.8327 4295.1869 0.1263 -0.0240
## gdp.dm1983 4952.5484 4284.3327 5084.0291 0.1349 -0.0265
## gdp.dm1984 5914.5484 5052.1452 6160.1870 0.1458 -0.0415
## gdp.dm1985 6724.5484 5795.8327 7091.8619 0.1381 -0.0546
## gdp.dm1986 7431.5484 6408.8952 7796.3761 0.1376 -0.0491
## gdp.dm1987 8112.5484 7075.5202 8532.6966 0.1278 -0.0518
## gdp.dm1988 9219.5484 8033.7702 9674.5296 0.1286 -0.0493
## gdp.dm1989 10427.5484 9064.5827 10997.5999 0.1307 -0.0547
## gdp.dm1990 11898.5484 10001.5827 12209.1612 0.1594 -0.0261
## trade 56.7778 59.8313 61.8666 -0.0538 -0.0896
## infrate 2.5948 7.6166 4.3595 -1.9353 -0.6801
## industry 34.5385 33.7944 32.0718 0.0215 0.0714
## schooling 55.5000 38.6594 51.7977 0.3034 0.0667
## invest80 27.0180 25.8952 25.5562 0.0416 0.0541Alternatively, we can use the following syntax:
out2.kbal <- tjbal(gdp ~ treat + trade + infrate + industry + schooling + invest80,
data = germany, Y.match.time = c(1960:1990), X.avg.time = list(c(1981:1990), c(1981:1990), c(1981:1990),c(1980:1985),c(1980)),
index = c("country","year"), estimator = "kernel", demean = TRUE)## Too few treated unit(s). Uncertainty estimates not provided.
## Seek balance on:
## gdp.dm1960, gdp.dm1961, gdp.dm1962, gdp.dm1963, gdp.dm1964, gdp.dm1965, gdp.dm1966, gdp.dm1967, gdp.dm1968, gdp.dm1969, gdp.dm1970, gdp.dm1971, gdp.dm1972, gdp.dm1973, gdp.dm1974, gdp.dm1975, gdp.dm1976, gdp.dm1977, gdp.dm1978, gdp.dm1979, gdp.dm1980, gdp.dm1981, gdp.dm1982, gdp.dm1983, gdp.dm1984, gdp.dm1985, gdp.dm1986, gdp.dm1987, gdp.dm1988, gdp.dm1989, gdp.dm1990, trade, infrate, industry, schooling, invest80
##
## Optimization:
## bias.ratio = 0.4800; num.dims = 4 (kbal)
##
## Balance Table
## mean.tr mean.co.pre mean.co.pst diff.pre diff.pst
## gdp.dm1960 -6282.4516 -5549.6673 -6398.8479 -0.1166 0.0185
## gdp.dm1961 -6178.4516 -5438.3548 -6264.2263 -0.1198 0.0139
## gdp.dm1962 -6039.4516 -5319.6673 -6140.4548 -0.1192 0.0167
## gdp.dm1963 -5956.4516 -5207.3548 -6023.8428 -0.1258 0.0113
## gdp.dm1964 -5760.4516 -5053.4798 -5852.5923 -0.1227 0.0160
## gdp.dm1965 -5561.4516 -4901.0423 -5696.9144 -0.1187 0.0244
## gdp.dm1966 -5398.4516 -4711.6673 -5487.6462 -0.1272 0.0165
## gdp.dm1967 -5325.4516 -4556.1048 -5314.9323 -0.1445 -0.0020
## gdp.dm1968 -4995.4516 -4292.0423 -5040.5969 -0.1408 0.0090
## gdp.dm1969 -4568.4516 -3937.3548 -4653.7141 -0.1381 0.0187
## gdp.dm1970 -4199.4516 -3600.3548 -4165.1740 -0.1427 -0.0082
## gdp.dm1971 -3880.4516 -3286.1673 -3756.9498 -0.1531 -0.0318
## gdp.dm1972 -3511.4516 -2929.7298 -3353.8282 -0.1657 -0.0449
## gdp.dm1973 -3013.4516 -2434.9798 -2850.5794 -0.1920 -0.0540
## gdp.dm1974 -2492.4516 -1929.8548 -2188.1696 -0.2257 -0.1221
## gdp.dm1975 -1963.4516 -1482.7923 -1774.8775 -0.2448 -0.0960
## gdp.dm1976 -1199.4516 -921.0423 -1186.8468 -0.2321 -0.0105
## gdp.dm1977 -476.4516 -381.5423 -434.0012 -0.1992 -0.0891
## gdp.dm1978 361.5484 289.7702 245.7793 0.1985 0.3202
## gdp.dm1979 1500.5484 1157.7702 1334.4443 0.2284 0.1107
## gdp.dm1980 2516.5484 2083.5202 2489.3281 0.1721 0.0108
## gdp.dm1981 3548.5484 3020.6452 3612.8163 0.1488 -0.0181
## gdp.dm1982 4194.5484 3664.8327 4437.0087 0.1263 -0.0578
## gdp.dm1983 4952.5484 4284.3327 5197.9434 0.1349 -0.0495
## gdp.dm1984 5914.5484 5052.1452 5929.4734 0.1458 -0.0025
## gdp.dm1985 6724.5484 5795.8327 6738.3946 0.1381 -0.0021
## gdp.dm1986 7431.5484 6408.8952 7357.2520 0.1376 0.0100
## gdp.dm1987 8112.5484 7075.5202 8009.6979 0.1278 0.0127
## gdp.dm1988 9219.5484 8033.7702 9126.7115 0.1286 0.0101
## gdp.dm1989 10427.5484 9064.5827 10416.4137 0.1307 0.0011
## gdp.dm1990 11898.5484 10001.5827 11688.9312 0.1594 0.0176
## trade 56.7778 59.8313 61.8002 -0.0538 -0.0885
## infrate 2.5948 7.6166 4.4796 -1.9353 -0.7264
## industry 34.5385 33.7944 33.3066 0.0215 0.0357
## schooling 55.5000 38.6594 50.7951 0.3034 0.0848
## invest80 27.0180 25.8952 27.7573 0.0416 -0.0274We plot the estimated treatment effect from both mean balancing and kernel balancing. It seems that the kernel balancing approach yield slightly better pre-treatment fit—this is not always the case.
plot(out2.mbal, ylim = c(-5000,5000))## Uncertainty estimates not available.
plot(out2.kbal, ylim = c(-5000,5000))## Uncertainty estimates not available.
The estimated counterfactual for West Germany.
plot(out2.mbal, type = "counterfactual", count = FALSE) 
plot(out2.kbal, type = "ct", count = FALSE) 
By setting raw = "all" and trim = TRUE (default), we can add to the counterfactual plot the trajectories of the heavily weighted control units, whose assigned weights add up to 90% of the total weight. The number 90% can be adjusted by the trim.wtot option. If trim = FALSE, all control trajectories will be shown.
plot(out2.mbal, type = "ct", raw = "all", trim.wtot = 0.9) 
We can see that kernel balancing put more weights on a much smaller number of control units.
plot(out2.kbal, type = "ct", raw = "all") 
By setting raw = "band" and trim = "TRUE" (default), we show the range of the trajectories of heavily weighted controls.
plot(out2.mbal, type = "ct", raw = "band") 
Finally, the weights plot confirms that kernel balancing puts more weights on fewer control units.
plot(out2.mbal, type = "weights")
plot(out2.kbal, type = "weights")