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Difference-in-differences with a Continuous Treatment

Source: R/cont_did.R
cont_did.Rd

A function for difference-in-differences with a continuous treatment in a staggered treatment adoption setting.

cont_did currently supports staggered treatment with continuous treatments using B-splines under the hood.

Usage

cont_did(
  yname,
  dname,
  gname = NULL,
  tname,
  idname,
  xformula = ~1,
  data,
  target_parameter = c("level", "slope"),
  aggregation = c("dose", "eventstudy", "none"),
  treatment_type = c("continuous", "discrete"),
  dose_est_method = c("parametric", "cck"),
  dvals = NULL,
  degree = 3,
  num_knots = 0,
  allow_unbalanced_panel = FALSE,
  control_group = c("notyettreated", "nevertreated", "eventuallytreated"),
  anticipation = 0,
  weightsname = NULL,
  alp = 0.05,
  bstrap = TRUE,
  cband = FALSE,
  boot_type = "multiplier",
  biters = 1000,
  clustervars = NULL,
  est_method = NULL,
  base_period = "varying",
  print_details = FALSE,
  cl = 1,
  ...
)

Arguments

yname

The name of the outcome variable

dname

The name of the treatment variable in the data. The functionality of cont_did is different from the did package in that the treatment variable is the "amount" of the treatment in a particular period, rather than gname which gives the time period when a unit becomes treated. The dname variable should, for a particular unit, be constant across time periods—even in pre-treatment periods. For units that never participate in the treatment, the amount of the treatment may not be defined in some applications—it is ignored in this function.

gname

The name of the timing-group variable, i.e., when treatment starts for a particular unit. The value of this variable should be set to be 0 for units that do not participate in the treatment in any time period.

tname

The name of the column containing the time periods

idname

The individual (cross-sectional unit) id name

xformula

A formula for additional covariates. This is not currently supported.

data

The name of the data.frame that contains the data

target_parameter

Two options are "level" and "slope". In the first case, the function will report level effects, i.e., ATT's. In the second case, the function will report slope effects, i.e., ACRT's

aggregation

"dose" averages across timing-groups and time periods and provides results as a function of the dose. "eventstudy" averages across timing-groups and doses and reports results as a function of the length of exposure to the treatment.

"none" is a stub for reporting fully disaggregated results that can be processed as desired by the user. This is not currently supported though.

The combination of the arguments target_parameter and aggregation strongly affects the behavior of the function (and target of the analysis). For example, setting target_parameter="level" and aggregation="eventstudy" is effectively the same thing as binarizing the treatment (i.e., where units are considered treated if they experience any positive amount of the treatment) and reporting an event study.

treatment_type

"continuous" or "discrete" depending on the nature of the treatment. Default is "continuous". "discrete" is not yet supported.

dose_est_method

The method used to estimate the dose-specific effects. The default is "parametric", where the user needs to specify the number of knots and degree for a B-spline which is assumed to be correctly specified. The other option is "cck" which uses the a data-driven nonparametric method to estimate the dose-specific effects based on the npiv package and Chen, Christensen, and Kankanala (ReStud, 2025).

dvals

The values of the treatment at which to compute dose-specific effects. If it is not specified, the default choice will be use the percentiles of the dose among all ever-treated units.

degree

The degree of the B-Spline used in estimation. The default is 3, which in combination with the default choice for the num-knots, leads to fitting models for the group of treated units that only that is a cubic polynomial in the dose. Setting degree=1 will lead to a linear model, while setting degree=2 will lead to a quadratic model.

num_knots

The number of knots to include for the B-Spline. The default is 0 so that the spline is global (i.e., this will amount to fitting a global polynomial). There is a bias-variance tradeoff for including more or less knots.

allow_unbalanced_panel

Whether or not function should "balance" the panel with respect to time and id. The default value is FALSE which means that att_gt() will drop all units where data is not observed in all periods. The advantage of this is that the computations are faster (sometimes substantially).

control_group

Which units to use as the control group. The default is "nevertreated" which sets the control group to be the group of units that never participate in the treatment. This group does not change across groups or time periods. The other option is to set group="notyettreated". In this case, the control group is set to the group of units that have not yet participated in the treatment in that time period. This includes all never treated units, but it includes additional units that eventually participate in the treatment, but have not participated yet.

anticipation

The number of time periods before participating in the treatment where units can anticipate participating in the treatment and therefore it can affect their untreated potential outcomes

weightsname

The name of the column containing the sampling weights. If not set, all observations have same weight. When weights are time-invariant (constant within each unit across periods), all fix_weights options produce identical results and no special handling is needed.

When weights vary across time (e.g., time-varying population sizes), the default behavior differs by panel type:

Balanced panel

Each 2x2 DiD comparison uses the weight from the earlier of the two time periods involved. For post-treatment cells, this is the base period (g-1). For pre-treatment cells with base_period="varying", this is the pre-treatment period itself. The panel DRDID estimators are used.

Repeated cross sections and unbalanced panels

Both periods' per-observation weights are passed directly to the RC DRDID estimators, so each observation carries its own period-specific weight.

Use the fix_weights argument to override the default behavior.

alp

the significance level, default is 0.05

bstrap

Boolean for whether or not to compute standard errors using the multiplier bootstrap. Default is TRUE (in addition, cband is also by default TRUE indicating that uniform confidence bands will be returned). If bstrap=FALSE, analytical standard errors are reported; these are cluster-robust when clustervars is supplied.

cband

Boolean for whether or not to compute a uniform confidence band that covers all of the group-time average treatment effects with fixed probability 1-alp. In order to compute uniform confidence bands, bstrap must also be set to TRUE. The default is TRUE.

boot_type

should be one of "multiplier" (the default) or "empirical". The multiplier bootstrap is generally much faster, but attgt_fun needs to provide an expression for the influence function (which could be challenging to figure out). If no influence function is provided, then the pte package will use the empirical bootstrap no matter what the value of this parameter.

biters

The number of bootstrap iterations to use. The default is 1000, and this is only applicable if bstrap=TRUE.

clustervars

A vector of variables names to cluster on. At most, there can be two variables (otherwise will throw an error) and one of these must be the same as idname which allows for clustering at the individual level. Clustered standard errors are available with the multiplier bootstrap (bstrap=TRUE) or analytically (bstrap=FALSE).

est_method

the method to compute group-time average treatment effects. The default is "dr" which uses the doubly robust approach in the DRDID package. Other built-in methods include "ipw" for inverse probability weighting and "reg" for first step regression estimators. The user can also pass their own function for estimating group time average treatment effects. The required signature depends on the data structure:

Panel data (panel=TRUE): f(y1, y0, D, covariates, i.weights, inffunc, ...) where y1 is an n x 1 vector of post-treatment outcomes, y0 is an n x 1 vector of pre-treatment outcomes, D is a binary vector indicating treatment group membership, covariates is an n x k matrix, i.weights is a vector of sampling weights, and inffunc is a logical requesting influence-function computation.

Repeated cross sections / unbalanced panel (panel=FALSE): f(y, post, D, covariates, i.weights, inffunc, ...) where y is the outcome vector (length n), post is a binary indicator for the post-treatment period, D is a binary treatment indicator, covariates is an n x k matrix, i.weights is a vector of sampling weights, and inffunc is a logical.

In both cases the function should return a list that includes ATT (the estimated group-time average treatment effect) and att.inf.func (an n x 1 influence function — one entry per observation passed into the estimator). The function can return other things as well, but these are the only two that are required. With no covariates (xformla = NULL), the built-in methods ("dr", "ipw", "reg") all reduce to the unconditional difference-in-differences estimator, so the choice among them is irrelevant; a custom est_method function is still called (with an intercept-only covariates matrix) and determines the estimates.

base_period

Whether to use a "varying" base period or a "universal" base period. Either choice results in the same post-treatment estimates of ATT(g,t)'s. In pre-treatment periods, using a varying base period amounts to computing a pseudo-ATT in each treatment period by comparing the change in outcomes for a particular group relative to its comparison group in the pre-treatment periods (i.e., in pre-treatment periods this setting computes changes from period t-1 to period t, but repeatedly changes the value of t)

A universal base period fixes the base period to always be (g-anticipation-1). This does not compute pseudo-ATT(g,t)'s in pre-treatment periods, but rather reports average changes in outcomes from period t to (g-anticipation-1) for a particular group relative to its comparison group. This is analogous to what is often reported in event study regressions.

Using a varying base period results in an estimate of ATT(g,t) being reported in the period immediately before treatment. Using a universal base period normalizes the estimate in the period right before treatment (or earlier when the user allows for anticipation) to be equal to 0, but one extra estimate in an earlier period.

print_details

Whether or not to show details/progress of computations. Default is FALSE.

cl

number of clusters to be used when bootstrapping; default is 1

...

Additional arguments to be passed to a custom est_method function. These are ignored when using built-in estimation methods ("dr", "ipw", "reg").

Value

cont_did_obj

Examples

# build small simulated data
set.seed(1234)
df <- simulate_contdid_data(
  n = 1000,
  num_time_periods = 4,
  num_groups = 4,
  dose_linear_effect = 0,
  dose_quadratic_effect = 0
)

# estimate effects of continuous treatment
cd_res <- cont_did(
  yname = "Y",
  tname = "time_period",
  idname = "id",
  dname = "D",
  data = df,
  gname = "G",
  target_parameter = "slope",
  aggregation = "dose",
  treatment_type = "continuous",
  control_group = "notyettreated",
  biters = 50,
  cband = TRUE,
  num_knots = 1,
  degree = 3,
)
#> Warning: critical value for uniform confidence band is somehow smaller than
#>             critical value for pointwise confidence interval...using pointwise
#>             confidence interal

summary(cd_res)
#> 
#> Overall ATT:  
#>      ATT    Std. Error     [ 95%  Conf. Int.] 
#>  -0.0332        0.0726    -0.1754      0.1091 
#> 
#> 
#> Overall ACRT:  
#>     ACRT    Std. Error     [ 95%  Conf. Int.]  
#>  -0.2988         0.143     -0.579     -0.0186 *
#> ---
#> Signif. codes: `*' confidence band does not cover 0
#>