Trajectory Balancing

Implements mean balancing and kernel balancing algorithms with time-series cross-sectional data.

Usage

tjbal(formula=NULL, data, Y, D, X = NULL, X.avg.time = NULL, 
  index, index, trim.npre = 0, Y.match.time = NULL, Y.match.npre = NULL, 
  demean = TRUE, estimator = "meanfirst", sigma=NULL, 
  print.baltable = TRUE, vce = "jackknife", conf.lvl = 0.95, 
  nsims = NULL, parallel = TRUE, cores = 4, seed = 1234)

Arguments

formula: an object of class "formula": a symbolic description of the model to be fitted. The first variable on the right-hand-side is a dichotomous treatment indicator (D); the rest of the right-hand-side variables are time-invariant controls (X). If X are time-varying, they will be averaged within each unit based on values specified by X.avg.time.
data: a data frame (must be a balanced panel).
Y: outcome.
D: treatment.
X: covariates. If a covariate is time-varying, it will be averaged based on X.avg.time before balancing.
X.avg.time: a list of time periods over which covariates are being averaged. Ignored if the treatment starts at different times.
index: a two-element string vector specifying the unit (group) and time indicators. Must be of length 2.
trim.npre: a numeric value indicating the smallest number of pre-treatment periods for a treated unit to be preserved. The default is 0.
Y.match.time: a set of pre-treatment time periods in which the outcome variable is being balanced on.
Y.match.npre: a numeric value indicating the number of pre-treatment outcome periods to be balanced on. If Y.match.npre = 0, no pre-treatment outcome will be part of the balancing scheme.
demean: a logical flag indicating whether a demeaning procedure will be performed to take out the average of pre-treatment outcomes for each unit.
estimator: a string specifying the balancing approach: "mean" for mean-balancing, "kernel" for kernel-balancing, and "meanfirst" (default) for kernel balancing with mean balancing constraints. "meanfirst" will prioritize balancing on covariate means over higher-order terms and interactions.
sigma: a numeric value specifying the bandwidth of the kernel transformation (will be multiplied by the number of covariates to be balanced on). The default is 2. Ignored if estimator = "mean".
print.baltable: a logical flag that controls whether to print out the balance table after the algorithm is run. Ignored if treatment timing is different.
vce: a string specifying the variance estimator. vce = "none": no uncertainty estimates; vce = "fixed.weights": treating balancing weights as fixed; vce = "bootstrap": conducting non-parametric bootstrapping by reshuffle both the treated and control units; vce = "jackknife": conducting jackknife by omitting one treated unit at a time. When the treatment timing is different, vce = "jackknife" is the only available choice for producing uncertainty estimates.
conf.lvl: a positive number in the range of 0 and 1 specifying confidence levels for uncertainty estimates. The default value is 0.95.
nsims: an integer specifying the number of bootstrap or jackknife runs. Ignored if vce = "none" or there are too few treated units.
parallel: a logical flag indicating whether parallel computing will be used in bootstrap/jackknife simulations. .
cores: an integer indicating the number of cores to be used in parallel computing. If not specified, the algorithm will use the maximum number of logical cores of your computer (warning: this could prevent you from multi-tasking on your computer).
seed: an integer that sets the seed in random number generation. Ignored if vce = "none" or there are too few treated units.

Details

tjbal provides a general reweighting approach to causal inference with time-series cross-sectional (TSCS) data. It includes two estimators, mean balancing and kernel balancing. The former reweights control units such that the averages of the pre-treatment outcomes and covariates are approximately equal between the treatment and (reweighted) control groups. The latter relaxes the linearity assumption and seeks approximate balance on a kernel-based feature expansion of the pre-treatment outcomes and covariates. The resulting approach inherits the ability of synthetic control and latent factor models to tolerate time-varying confounders, but (1) improves feasibility and stability with reduced user discretion; (2) accommodates both short and long pre-treatment time periods with many or few treated units; and (3) balances on the high-order ``trajectory" of pre-treatment outcomes rather than their period-wise average. We illustrate this method with simulations and two empirical examples.

Value

data.wide: a matrix storing data in wide form -- each row represents one unit.
id.tr: a vector of row numbers for the treatment units.
id.co: a vector of row numbers for the control units.
Y.tr: data of the treated unit outcome.
Y.co: data of the control unit outcome.
Y.var: a vector of outcome variable names.
matchvar.list: a list of covariates to be balanced on for each subgroup.
Ttot: the set of all time periods.
N: the total number of units.
Ntr: the number of treated units.
Nco: the number of control units.
T0: a vector that stores the unique values of the timing of the treatment.
T0.all: a vector that stores the timing of the treatment for each unit.
T0.tr: a vector that stores the timing of the treatment for each treated unit.
weights.co: weights of the control unit; added up to 1.
Y.bar: average values of treated outcomes, counterfactual outcomes, and control outcomes over time.
att: average treatment effect on the treated over time (it is realigned and based on the timing of the treatment if it is different for each unit).
att.avg: average treatment effect on the treated (averaged both across unit and over time).
est.att: inference for att.
est.att.avg: inference for att.avg.
ntreated: a vector of numbers of treated units for all subgroups.
sameT0: TRUE if the timing of the treatment is the same.
Ttot: the set of all time periods.
Tpre: the set of pre-treatment periods; same timing.
Tpst: the set of post-treatment periods; same timing.
bal.type: the type of balancing scheme being used: "mbal" for mean balancing and "kbal" for kernel balancing; same timing.
ndims: the number of dimensions being balanced; same timing.
b: tunning parameter for kbal; same timing.
kbal.out: output from kbal; same timing.
success: a logical flag indicating whether convergence is achieve with balancing.
bias.ratio: the ratio of L1 measure of distance after balancing over L1 measure of distance before balancing. A smaller number indicates more improvement brought by balancing.
bal.table: balance table; same timing.
att.sims: jackknife/bootstrap results for att; same timing.
att.avg.sims: jackknife/bootstrap results for att.avg; same timing.
att.sub.att: jackknife results for att for all subgroups; different timing.
att.sub.att.avg: jackknife results for att.avg for all subgroups; different timing.
sub.weights.co: a matrix of weights for the control units for all subgroups; different timing.
sub.Ytr.avg: a matrix of average outcomes for the treated units for all subgroups; different timing.
sub.Yct.avg: a matrix of average Y(0)'s for the treated units for all subgroups; different timing.
sub.att: a matrix of ATT for all subgroups; different timing.
sub.ntr: a matrix of numbers of treated units over time for all subgroups; different timing.
sub.att.adj: a matrix of realigned ATT for all subgroups; different timing.
group.stats: statistics for all subgroups, including T0, the number of treated units, sigma, convenience, and bias ratio; different timing.
bal.table.list: a list of the balance table for all subgroups; different timing.

Author

Chad Hazlett <chazlett@ucla.edu>, UCLA

Yiqing Xu (Maintainer) <yiqingxu@stanford.edu>, Stanford

References

Hazlett, Chad and Yiqing Xu, 2020. ``Trajectory Balancing: A General Reweighting Approach to Causal Inference with Time-Series Cross-Sectional Data.'' Working Paper, UCLA and UCSD.

Examples

library(tjbal)
data(tjbal)
out <- tjbal(roa ~ treat + so_portion + rev2007, data = npc, 
       index = c("gvkey","fyear"), estimator = "mean") 
#> Seek balance on:
#> roa.dm2005, roa.dm2006, roa.dm2007, so_portion, rev2007 
#> 
#> Optimization:
#> bias.ratio = 0.0000; num.dims = 4 (mbal)
#> 
#> Balance Table
#>              mean.tr mean.co.pre mean.co.pst     sd.tr sd.co.pre  sd.co.pst
#> roa.dm2005   -0.0131     -0.0090     -0.0131    0.0377    0.0605     0.0766
#> roa.dm2006   -0.0004     -0.0010     -0.0004    0.0211    0.0513     0.0537
#> roa.dm2007    0.0135      0.0099      0.0135    0.0296    0.0756     0.0984
#> so_portion    0.3170      0.2491      0.3170    0.2397    0.2218     0.2309
#> rev2007    6420.3705   2647.3412   6420.3706 9547.6633 5530.8308 14247.7903
#>            diff.pre diff.pst
#> roa.dm2005  -0.1100        0
#> roa.dm2006   0.0258        0
#> roa.dm2007   0.1220        0
#> so_portion   0.2835        0
#> rev2007      0.3952        0
#> 
#> Jackknife... 
#> Parallel computing...
print(out) 
#> Call:
#> tjbal.formula(formula = roa ~ treat + so_portion + rev2007, data = npc, 
#>     index = c("gvkey", "fyear"), estimator = "mean")
#> 
#>    ~ by Period (including Pre-treatment Periods):
#>         ATT   S.E. z-score CI.lower CI.upper p.value n.Treated
#> 2005 0.0000 0.0000  0.8970   0.0000   0.0000  0.3697        47
#> 2006 0.0000 0.0000  1.1704   0.0000   0.0000  0.2418        47
#> 2007 0.0000 0.0000 -1.3460   0.0000   0.0000  0.1783        47
#> 2008 0.0073 0.0075  0.9707  -0.0075   0.0221  0.3317        47
#> 2009 0.0200 0.0057  3.5342   0.0089   0.0311  0.0004        47
#> 2010 0.0103 0.0054  1.8917  -0.0004   0.0209  0.0585        47
#> 
#> Average Treatment Effect on the Treated:
#>         ATT   S.E. z-score CI.lower CI.upper p.value
#> [1,] 0.0125 0.0053   2.348   0.0021    0.023  0.0189