DRDID: Doubly Robust Difference-in-Differences Estimators

Description

Implements the locally efficient doubly robust difference-in-differences (DiD) estimators for the average treatment effect proposed by Sant'Anna and Zhao (2020) doi:10.1016/j.jeconom.2020.06.003. The estimator combines inverse probability weighting and outcome regression estimators (also implemented in the package) to form estimators with more attractive statistical properties. Two different estimation methods can be used to estimate the nuisance functions.

Author(s)

Maintainer: Pedro H. C. Sant'Anna pedrohcgs@gmail.com [copyright holder]

Authors:

• Jun Zhao beanzhaojun11@gmail.com

See Also

Useful links:

• https://psantanna.com/DRDID/

• https://github.com/pedrohcgs/DRDID

• Report bugs at https://github.com/pedrohcgs/DRDID/issues

Locally efficient doubly robust DiD estimators for the ATT

Description

drdid is used to compute the locally efficient doubly robust estimators for the ATT in difference-in-differences (DiD) setups. It can be used with panel or stationary repeated cross section data. Data should be store in "long" format.

Usage

drdid(
  yname,
  tname,
  idname,
  dname,
  xformla = NULL,
  data,
  panel = TRUE,
  estMethod = c("imp", "trad"),
  weightsname = NULL,
  boot = FALSE,
  boot.type = c("weighted", "multiplier"),
  nboot = 999,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

When panel data are available (panel = TRUE), the drdid function implements the locally efficient doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.1) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of a linear regression model for the outcome evolution among the comparison units.

When only stationary repeated cross-section data are available (panel = FALSE), the drdid function implements the locally efficient doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.4) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of (separate) linear regression models for the outcome of both treated and comparison units, in both pre and post-treatment periods.

When one sets estMethod = "imp" (the default), the nuisance parameters (propensity score and outcome regression parameters) are estimated using the methods described in Sections 3.1 and 3.2 of Sant'Anna and Zhao (2020). In short, the propensity score parameters are estimated using the inverse probability tilting estimator proposed by Graham, Pinto and Pinto (2012), and the outcome regression coefficients are estimated using weighted least squares,where the weights depend on the propensity score estimates; see Sant'Anna and Zhao (2020) for details.

When one sets estMethod = "trad", the propensity score parameters are estimated using maximum likelihood, and the outcome regression coefficients are estimated using ordinary least squares.

The main advantage of using estMethod = "imp" is that the resulting estimator is not only locally efficient and doubly robust for the ATT, but it is also doubly robust for inference; see Sant'Anna and Zhao (2020) for details.

Value

A list containing the following components:

References

Graham, Bryan, Pinto, Cristine, and Egel, Daniel (2012), "Inverse Probability Tilting for Moment Condition Models with Missing Data." Review of Economic Studies, vol. 79 (3), pp. 1053-1079, doi:10.1093/restud/rdr047

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# -----------------------------------------------
# Panel data case
# -----------------------------------------------
# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw_long, nsw_long$treated == 0 | nsw_long$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(unique(eval_lalonde_cps$id), 5000)
eval_lalonde_cps <- eval_lalonde_cps[eval_lalonde_cps$id %in% unit_random,]
# -----------------------------------------------
# Implement improved DR locally efficient DiD with panel data
drdid(yname="re", tname = "year", idname = "id", dname = "experimental",
      xformla= ~ age+ educ+ black+ married+ nodegree+ hisp+ re74,
      data = eval_lalonde_cps, panel = TRUE)

#Implement "traditional" DR locally efficient DiD with panel data
drdid(yname="re", tname = "year", idname = "id", dname = "experimental",
      xformla= ~ age+ educ+ black+ married+ nodegree+ hisp+ re74,
      data = eval_lalonde_cps, panel = TRUE, estMethod = "trad")

# -----------------------------------------------
# Repeated cross section case
# -----------------------------------------------
# use the simulated data provided in the package
#Implement "improved" DR locally efficient DiD with repeated cross-section data
drdid(yname="y", tname = "post", idname = "id", dname = "d",
      xformla= ~ x1 + x2 + x3 + x4,
      data = sim_rc, panel = FALSE, estMethod = "imp")

#Implement "traditional" DR locally efficient DiD with repeated cross-section data
drdid(yname="y", tname = "post", idname = "id", dname = "d",
      xformla= ~ x1 + x2 + x3 + x4,
      data = sim_rc, panel = FALSE, estMethod = "trad")

Improved locally efficient doubly robust DiD estimator for the ATT, with panel data

Description

drdid_imp_panel is used to compute the locally efficient doubly robust estimators for the ATT in difference-in-differences (DiD) setups with panel data. The resulting estimator is also doubly robust for inference; see Section 3.1 of Sant'Anna and Zhao (2020).

Usage

drdid_imp_panel(
  y1,
  y0,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

The drdid_imp_panel function implements the locally efficient doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.1) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of a linear regression model for the outcome evolution among the comparison units.

The nuisance parameters (propensity score and outcome regression parameters) are estimated using the methods described in Sections 3.1 of Sant'Anna and Zhao (2020). In short, the propensity score parameters are estimated using the inverse probability tilting estimator proposed by Graham, Pinto and Pinto (2012), and the outcome regression coefficients are estimated using weighted least squares,where the weights depend on the propensity score estimates; see Sant'Anna and Zhao (2020) for details.

The resulting estimator is not only locally efficient and doubly robust for the ATT, but it is also doubly robust for inference; see Sant'Anna and Zhao (2020) for details.

Value

A list containing the following components:

References

Graham, Bryan, Pinto, Cristine, and Egel, Daniel (2012), "Inverse Probability Tilting for Moment Condition Models with Missing Data." Review of Economic Studies, vol. 79 (3), pp. 1053-1079, doi:10.1093/restud/rdr047

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
# Select some covariates
covX = as.matrix(cbind(1, eval_lalonde_cps$age, eval_lalonde_cps$educ,
                             eval_lalonde_cps$black, eval_lalonde_cps$married,
                             eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
                             eval_lalonde_cps$re74))

# Implement improved DR locally efficient DiD with panel data
drdid_imp_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
                D = eval_lalonde_cps$experimental,
                covariates = covX)

Improved locally efficient doubly robust DiD estimator for the ATT, with repeated cross-section data

Description

drdid_imp_rc is used to compute the locally efficient doubly robust estimators for the ATT in difference-in-differences (DiD) setups with stationary repeated cross-sectional data. The resulting estimator is also doubly robust for inference; see Section 3.2 of Sant'Anna and Zhao (2020).

Usage

drdid_imp_rc(
  y,
  post,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

The drdid_imp_rc function implements the locally efficient doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.4) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of (separate) linear regression models for the outcome of both treated and comparison units, in both pre and post-treatment periods.

The nuisance parameters (propensity score and outcome regression parameters) are estimated using the methods described in Sections 3.2 of Sant'Anna and Zhao (2020). In short, the propensity score parameters are estimated using the inverse probability tilting estimator proposed by Graham, Pinto and Pinto (2012), and the outcome regression coefficients are estimated using weighted least squares,where the weights depend on the propensity score estimates; see Sant'Anna and Zhao (2020) for details.

The resulting estimator is not only locally efficient and doubly robust for the ATT, but it is also doubly robust for inference; see Sant'Anna and Zhao (2020) for details.

Value

A list containing the following components:

References

Graham, Bryan, Pinto, Cristine, and Egel, Daniel (2012), "Inverse Probability Tilting for Moment Condition Models with Missing Data." Review of Economic Studies, vol. 79 (3), pp. 1053-1079, doi:10.1093/restud/rdr047

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement the improved, locally efficient DR DiD estimator
drdid_imp_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
             covariates= covX)

Improved doubly robust DiD estimator for the ATT, with repeated cross-section data

Description

drdid_imp_rc1 is used to compute the doubly robust estimators for the ATT in difference-in-differences (DiD) setups with stationary repeated cross-sectional data. The resulting estimator is also doubly robust for inference, though it is not locally efficient; see Section 3.2 of Sant'Anna and Zhao (2020).

Usage

drdid_imp_rc1(
  y,
  post,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

The drdid_imp_rc1 function implements the doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.3) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of (separate) linear regression models for the outcome among the comparison units in both pre and post-treatment time periods. Importantly, this estimator is not locally efficient for the ATT.

The nuisance parameters (propensity score and outcome regression parameters) are estimated using the methods described in Sections 3.2 of Sant'Anna and Zhao (2020). In short, the propensity score parameters are estimated using the inverse probability tilting estimator proposed by Graham, Pinto and Pinto (2012), and the outcome regression coefficients are estimated using weighted least squares,where the weights depend on the propensity score estimates; see Sant'Anna and Zhao (2020) for details.

The resulting estimator is not only doubly robust for the ATT, but it is also doubly robust for inference. However, we stress that it is not locally efficient; see Sant'Anna and Zhao (2020) for details.

Value

A list containing the following components:

References

Graham, Bryan, Pinto, Cristine, and Egel, Daniel (2012), "Inverse Probability Tilting for Moment Condition Models with Missing Data." Review of Economic Studies, vol. 79 (3), pp. 1053-1079, doi:10.1093/restud/rdr047

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data provided in the package
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement the improved DR DiD estimator (but not locally efficient!)
drdid_imp_rc1(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
             covariates= covX)

Locally efficient doubly robust DiD estimator for the ATT, with panel data

Description

drdid_panel is used to compute the locally efficient doubly robust estimators for the ATT in difference-in-differences (DiD) setups with panel data.

Usage

drdid_panel(
  y1,
  y0,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

The drdid_panel function implements the locally efficient doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.1) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of a linear regression model for the outcome evolution among the comparison units.

The propensity score parameters are estimated using maximum likelihood, and the outcome regression coefficients are estimated using ordinary least squares.

Value

A list containing the following components:

References

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# Form the Lalonde sample with CPS comparison group (data in wide format)
eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
# Select some covariates
covX = as.matrix(cbind(1, eval_lalonde_cps$age, eval_lalonde_cps$educ,
                       eval_lalonde_cps$black, eval_lalonde_cps$married,
                       eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
                       eval_lalonde_cps$re74))

# Implement traditional DR locally efficient DiD with panel data
drdid_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
             D = eval_lalonde_cps$experimental,
             covariates = covX)

Locally efficient doubly robust DiD estimator for the ATT, with repeated cross-section data

Description

drdid_rc is used to compute the locally efficient doubly robust estimators for the ATT in difference-in-differences (DiD) setups with stationary repeated cross-sectional data.

Usage

drdid_rc(
  y,
  post,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

The drdid_rc function implements the locally efficient doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.4) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of (separate) linear regression models for the outcome of both treated and comparison units, in both pre and post-treatment periods.

The propensity score parameters are estimated using maximum likelihood, and the outcome regression coefficients are estimated using ordinary least squares; see Sant'Anna and Zhao (2020) for details.

Value

A list containing the following components:

References

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data provided in the package
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement the 'traditional' locally efficient DR DiD estimator
drdid_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
         covariates= covX)

Doubly robust DiD estimator for the ATT, with repeated cross-section data

Description

drdid_rc1 is used to compute the doubly robust estimators for the ATT in difference-in-differences (DiD) setups with stationary repeated cross-sectional data. The resulting estimator is not locally efficient; see Section 3.2 of Sant'Anna and Zhao (2020).

Usage

drdid_rc1(
  y,
  post,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

The drdid_rc1 function implements the doubly robust difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (3.3) in Sant'Anna and Zhao (2020). This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and of (separate) linear regression models for the outcome among the comparison units in both pre and post-treatment time periods. Importantly, this estimator is not locally efficient for the ATT.

The propensity score parameters are estimated using maximum likelihood, and the outcome regression coefficients are estimated using ordinary least squares.

The resulting estimator is not not locally efficient; see Sant'Anna and Zhao (2020) for details.

Value

A list containing the following components:

References

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data provided in the package
covX = as.matrix(cbind( 1, sim_rc[,5:8]))
# Implement the 'traditional' DR DiD estimator (not locally efficient!)
drdid_rc1(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
          covariates= covX)

Inverse probability weighted DiD estimator, with panel data

Description

ipw_did_panel is used to compute inverse probability weighted (IPW) estimators for the ATT in difference-in-differences (DiD) setups with panel data. IPW weights are not normalized to sum up to one, that is, the estimator is of the Horwitz-Thompson type.

Usage

ipw_did_panel(
  y1,
  y0,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Value

A list containing the following components:

References

Abadie, Alberto (2005), "Semiparametric Difference-in-Differences Estimators", Review of Economic Studies, vol. 72(1), p. 1-19, doi:10.1111/0034-6527.00321

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
# Select some covariates
covX = as.matrix(cbind(1, eval_lalonde_cps$age, eval_lalonde_cps$educ,
                             eval_lalonde_cps$black, eval_lalonde_cps$married,
                             eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
                             eval_lalonde_cps$re74))
# Implement (unnormalized) IPW DiD with panel data
ipw_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
                D = eval_lalonde_cps$experimental,
                covariates = covX)

Inverse probability weighted DiD estimator, with repeated cross-section data

Description

ipw_did_rc is used to compute inverse probability weighted (IPW) estimators for the ATT in difference-in-differences (DiD) setups with stationary cross-sectional data. IPW weights are not normalized to sum up to one, that is, the estimator is of the Horwitz-Thompson type.

Usage

ipw_did_rc(
  y,
  post,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Value

A list containing the following components:

References

Abadie, Alberto (2005), "Semiparametric Difference-in-Differences Estimators", Review of Economic Studies, vol. 72(1), p. 1-19, doi:10.1111/0034-6527.00321

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data provided in the package
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement unnormalized IPW DiD estimator
ipw_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
           covariates= covX)

Inverse probability weighted DiD estimators for the ATT

Description

ipwdid computes the inverse probability weighted estimators for the average treatment effect on the treated in difference-in-differences (DiD) setups. It can be used with panel or stationary repeated cross-sectional data, with or without normalized (stabilized) weights. See Abadie (2005) and Sant'Anna and Zhao (2020) for details.

Usage

ipwdid(
  yname,
  tname,
  idname,
  dname,
  xformla = NULL,
  data,
  panel = TRUE,
  normalized = TRUE,
  weightsname = NULL,
  boot = FALSE,
  boot.type = c("weighted", "multiplier"),
  nboot = 999,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Details

The ipwdid function implements the inverse probability weighted (IPW) difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) proposed by Abadie (2005) (normalized = FALSE) or Hajek-type version defined in equations (4.1) and (4.2) in Sant'Anna and Zhao (2020), when either panel data or stationary repeated cross-sectional data are available. This estimator makes use of a logistic propensity score model for the probability of being in the treated group, and the propensity score parameters are estimated via maximum likelihood.

Value

A list containing the following components:

References

Abadie, Alberto (2005), "Semiparametric Difference-in-Differences Estimators", Review of Economic Studies, vol. 72(1), p. 1-19, doi:10.1111/0034-6527.00321

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# -----------------------------------------------
# Panel data case
# -----------------------------------------------
# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw_long, nsw_long$treated == 0 | nsw_long$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(unique(eval_lalonde_cps$id), 5000)
eval_lalonde_cps <- eval_lalonde_cps[eval_lalonde_cps$id %in% unit_random,]

# Implement IPW DiD with panel data (normalized weights)
ipwdid(yname="re", tname = "year", idname = "id", dname = "experimental",
      xformla= ~ age+ educ+ black+ married+ nodegree+ hisp+ re74,
      data = eval_lalonde_cps, panel = TRUE)

# -----------------------------------------------
# Repeated cross section case
# -----------------------------------------------
# use the simulated data provided in the package
#Implement IPW DiD with repeated cross-section data (normalized weights)
# use Bootstrap to make inference with 199 bootstrap draws (just for illustration)
ipwdid(yname="y", tname = "post", idname = "id", dname = "d",
      xformla= ~ x1 + x2 + x3 + x4,
      data = sim_rc, panel = FALSE,
      boot = TRUE, nboot = 199)

National Supported Work Demonstration dataset

Description

nsw contains all the subsamples of from the National Supported Work (NSW) Demonstration analyzed used by Smith and Todd (2005) in their paper "Does matching overcome LaLonde's critique of nonexperimental estimators?".

Usage

nsw

Format

A data frame in "wide" format with 19204 observations on the following and 14 variables:

treated

an indicator variable for treatment status. Missing if not part of the NSW experimental sample

age

age in years.

educ

years of schooling.

black

indicator variable for blacks.

married

indicator variable for martial status.

nodegree

indicator variable for high school diploma.

dwincl

indicator variable for inclusion in Dehejia and Wahba sample. Missing if not part of the experimental sample

re74

real earnings in 1974 (pre-treatment).

re75

real earnings in 1975 (pre-treatment).

re78

real earnings in 1978 (post-treatment).

hisp

indicator variable for Hispanics.

early_ra

indicator variable for inclusion in the early random assignment sample in Smith and Todd (2005). Missing if not part of the experimental sample

sample

1 if NSW (experimental sample), 2 if CPS comparison group, 3 if PSID comparison group.

experimental

1 if in experimental sample, 0 otherwise.

Source

https://dataverse.harvard.edu/file.xhtml?persistentId=doi:10.7910/DVN/23407/DYEWLO&version=1.0.

References

Diamond, Alexis, and Sekhon, Jasjeet S. (2013), 'Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies' Review of Economics and Statistics, vol. 95 , pp. 932-945, doi:10.1162/REST_a_00318

Smith, Jeffrey, and Todd, Petra (2005), Does matching overcome LaLonde's critique of nonexperimental estimators?' Journal of Econometrics, vol. 125, pp. 305-353, doi:10.1016/j.jeconom.2004.04.011

National Supported Work Demonstration dataset, in long format

Description

nsw_long is the same dataset as nsw but in a long format.

Usage

nsw_long

Format

A data frame in "long" format with 38408 observations on the following and 15 variables:

id

unique identifier for each cross-sectional unit (worker).

year

year. 1975 is the pre-treatment and 1978 is the post-treatment

treated

an indicator variable for treatment status. Missing if not part of the NSW experimental sample.

age

age in years.

educ

years of schooling.

black

indicator variable for blacks.

married

indicator variable for martial status.

nodegree

indicator variable for high school diploma.

dwincl

indicator variable for inclusion in Dehejia and Wahba sample. Missing if not part of the experimental sample

re74

real earnings in 1974 (pre-treatment).

hisp

indicator variable for Hispanics.

early_ra

indicator variable for inclusion in the early random assignment sample in Smith and Todd (2005). Missing if not part of the experimental sample

sample

1 if NSW (experimental sample), 2 if CPS comparison group, 3 if PSID comparison group.

re

real earnings (outcome of interest).

experimental

1 if in experimental sample, 0 otherwise.

Source

https://dataverse.harvard.edu/file.xhtml?persistentId=doi:10.7910/DVN/23407/DYEWLO&version=1.0.

References

Diamond, Alexis, and Sekhon, Jasjeet S. (2013), 'Genetic Matching for Estimating Causal Effects: A General Multivariate Matching Method for Achieving Balance in Observational Studies' Review of Economics and Statistics, vol. 95 , pp. 932-945, doi:10.1162/REST_a_00318

Smith, Jeffrey, and Todd, Petra (2005), Does matching overcome LaLonde's critique of nonexperimental estimators?' Journal of Econometrics, vol. 125, pp. 305-353, doi:10.1016/j.jeconom.2004.04.011

Outcome regression DiD estimators for the ATT

Description

ordid computes the outcome regressions estimators for the average treatment effect on the treated in difference-in-differences (DiD) setups. It can be used with panel or repeated cross section data. See Sant'Anna and Zhao (2020) for details.

Usage

ordid(
  yname,
  tname,
  idname,
  dname,
  xformla = NULL,
  data,
  panel = TRUE,
  weightsname = NULL,
  boot = FALSE,
  boot.type = c("weighted", "multiplier"),
  nboot = 999,
  inffunc = FALSE
)

Arguments

Details

The ordid function implements outcome regression difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (2.2) of Sant'Anna and Zhao (2020). The estimator follows the same spirit of the nonparametric estimators proposed by Heckman, Ichimura and Todd (1997), though here the the outcome regression models are assumed to be linear in covariates (parametric).

The nuisance parameters (outcome regression coefficients) are estimated via ordinary least squares.

Value

A list containing the following components:

References

Heckman, James J., Ichimura, Hidehiko, and Todd, Petra E. (1997),"Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme", Review of Economic Studies, vol. 64(4), p. 605–654, doi:10.2307/2971733.

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# -----------------------------------------------
# Panel data case
# -----------------------------------------------
# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw_long, nsw_long$treated == 0 | nsw_long$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(unique(eval_lalonde_cps$id), 5000)
eval_lalonde_cps <- eval_lalonde_cps[eval_lalonde_cps$id %in% unit_random,]
# Implement OR DiD with panel data
ordid(yname="re", tname = "year", idname = "id", dname = "experimental",
      xformla= ~ age+ educ+ black+ married+ nodegree+ hisp+ re74,
      data = eval_lalonde_cps, panel = TRUE)

# -----------------------------------------------
# Repeated cross section case
# -----------------------------------------------
# use the simulated data provided in the package
# Implement OR DiD with repeated cross-section data
# use Bootstrap to make inference with 199 bootstrap draws (just for illustration)
ordid(yname="y", tname = "post", idname = "id", dname = "d",
      xformla= ~ x1 + x2 + x3 + x4,
      data = sim_rc, panel = FALSE,
      boot = TRUE, nboot = 199)

Outcome regression DiD estimator for the ATT, with panel data

Description

reg_did_panel computes the outcome regressions estimators for the average treatment effect on the treated in difference-in-differences (DiD) setups with panel data.

Usage

reg_did_panel(
  y1,
  y0,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE
)

Arguments

Details

The reg_did_panel function implements outcome regression difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (2.2) of Sant'Anna and Zhao (2020) when panel data are available. The estimator follows the same spirit of the nonparametric estimators proposed by Heckman, Ichimura and Todd (1997), though here the the outcome regression models are assumed to be linear in covariates (parametric),

The nuisance parameters (outcome regression coefficients) are estimated via ordinary least squares.

Value

A list containing the following components:

References

Heckman, James J., Ichimura, Hidehiko, and Todd, Petra E. (1997),"Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme", Review of Economic Studies, vol. 64(4), p. 605–654, doi:10.2307/2971733.

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
# Select some covariates
covX = as.matrix(cbind(1, eval_lalonde_cps$age, eval_lalonde_cps$educ,
                       eval_lalonde_cps$black, eval_lalonde_cps$married,
                       eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
                       eval_lalonde_cps$re74))
# Implement OR DiD with panel data
reg_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
               D = eval_lalonde_cps$experimental,
               covariates = covX)

Outcome regression DiD estimator for the ATT, with repeated cross-section data

Description

reg_did_rc computes the outcome regressions estimators for the average treatment effect on the treated in difference-in-differences (DiD) setups with stationary repeated cross-sectional data.

Usage

reg_did_rc(
  y,
  post,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE
)

Arguments

Details

The reg_did_rc function implements outcome regression difference-in-differences (DiD) estimator for the average treatment effect on the treated (ATT) defined in equation (2.2) of Sant'Anna and Zhao (2020) when stationary repeated cross-sectional data are available. The estimator follows the same spirit of the nonparametric estimators proposed by Heckman, Ichimura and Todd (1997), though here the the outcome regression models are assumed to be linear in covariates (parametric),

The nuisance parameters (outcome regression coefficients) are estimated via ordinary least squares.

Value

A list containing the following components:

References

Heckman, James J., Ichimura, Hidehiko, and Todd, Petra E. (1997),"Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme", Review of Economic Studies, vol. 64(4), p. 605–654, doi:10.2307/2971733.

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data provided in the package
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement OR DiD estimator
reg_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
           covariates= covX)

Simulated repeated cross-section data

Description

sim_rc contains a simulated dataset following the DGP1 in Sant'Anna and Zhao (2020).

Usage

sim_rc

Format

A data frame in "long" format with 1000 observations on the following and 8 variables:

id

unique identifier for each cross-sectional unit.

post

an indicator variable for post-treatment period (1 if post, 0 if pre treatment period).

y

outcome of interest

d

an indicator variable for treatment group. Equal to 1 if experience treatment in the post-treatment period; equal to 0 if never experience treatment.

x1

Covariate z1 in Sant'Anna and Zhao(2020)

x2

Covariate z2 in Sant'Anna and Zhao(2020)

x3

Covariate z3 in Sant'Anna and Zhao(2020)

x4

Covariate z4 in Sant'Anna and Zhao(2020)

Source

Sant'Anna and Zhao (2020)

References

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Standardized inverse probability weighted DiD estimator, with panel data

Description

std_ipw_did_panel is used to compute inverse probability weighted (IPW) estimators for the ATT in difference-in-differences (DiD) setups with panel data. IPW weights are normalized to sum up to one, that is, the estimator is of the Hajek type.

Usage

std_ipw_did_panel(
  y1,
  y0,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Value

A list containing the following components:

References

Abadie, Alberto (2005), "Semiparametric Difference-in-Differences Estimators", Review of Economic Studies, vol. 72(1), p. 1-19, doi:10.1111/0034-6527.00321.

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
# Select some covariates
covX = as.matrix(cbind(1, eval_lalonde_cps$age, eval_lalonde_cps$educ,
                       eval_lalonde_cps$black, eval_lalonde_cps$married,
                       eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
                       eval_lalonde_cps$re74))
# Implement normalized IPW DiD with panel data
std_ipw_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
                D = eval_lalonde_cps$experimental,
                covariates = covX)

Standardized inverse probability weighted DiD estimator, with repeated cross-section data

Description

std_ipw_did_rc is used to compute inverse probability weighted (IPW) estimators for the ATT in DID setups with stationary repeated cross-sectional data. IPW weights are normalized to sum up to one, that is, the estimator is of the Hajek type.

Usage

std_ipw_did_rc(
  y,
  post,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE,
  trim.level = 0.995
)

Arguments

Value

A list containing the following components:

References

Abadie, Alberto (2005), "Semiparametric Difference-in-Differences Estimators", Review of Economic Studies, vol. 72(1), p. 1-19, doi:10.1111/0034-6527.00321.

Sant'Anna, Pedro H. C. and Zhao, Jun. (2020), "Doubly Robust Difference-in-Differences Estimators." Journal of Econometrics, Vol. 219 (1), pp. 101-122, doi:10.1016/j.jeconom.2020.06.003

Examples

# use the simulated data provided in the package
covX = as.matrix(cbind(1, sim_rc[,5:8]))
# Implement normalized IPW DID estimator
std_ipw_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
               covariates= covX)

Two-way fixed effects DiD estimator, with panel data

Description

twfe_did_panel is used to compute linear two-way fixed effects estimators for the ATT in difference-in-differences (DiD) setups with panel data. As illustrated by Sant'Anna and Zhao (2020), this estimator generally do not recover the ATT. We encourage empiricists to adopt alternative specifications.

Usage

twfe_did_panel(
  y1,
  y0,
  D,
  covariates,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE
)

Arguments

Value

A list containing the following components:

Examples

# Form the Lalonde sample with CPS comparison group
eval_lalonde_cps <- subset(nsw, nsw$treated == 0 | nsw$sample == 2)
# Further reduce sample to speed example
set.seed(123)
unit_random <- sample(1:nrow(eval_lalonde_cps), 5000)
eval_lalonde_cps <- eval_lalonde_cps[unit_random,]
# Select some covariates
covX = as.matrix(cbind(1, eval_lalonde_cps$age, eval_lalonde_cps$educ,
                       eval_lalonde_cps$black, eval_lalonde_cps$married,
                       eval_lalonde_cps$nodegree, eval_lalonde_cps$hisp,
                       eval_lalonde_cps$re74))
# Implement TWFE DiD with panel data
twfe_did_panel(y1 = eval_lalonde_cps$re78, y0 = eval_lalonde_cps$re75,
               D = eval_lalonde_cps$experimental,
               covariates = covX)

Two-way fixed effects DiD estimator, with repeated cross-section data

Description

twfe_did_rc is used to compute linear two-way fixed effects estimators for the ATT in difference-in-differences (DiD) setups with stationary repeated cross-sectional data. As illustrated by Sant'Anna and Zhao (2020),this estimator generally do not recover the ATT. We encourage empiricists to adopt alternative specifications.

Usage

twfe_did_rc(
  y,
  post,
  D,
  covariates = NULL,
  i.weights = NULL,
  boot = FALSE,
  boot.type = "weighted",
  nboot = NULL,
  inffunc = FALSE
)

Arguments

Value

A list containing the following components:

Examples

# use the simulated data provided in the package
covX = as.matrix(sim_rc[,5:8])
# Implement TWFE DiD estimator (you probably should consider something else....)
twfe_did_rc(y = sim_rc$y, post = sim_rc$post, D = sim_rc$d,
           covariates= covX)