Mean Difference-in-Differences

Computes Quantile Treatment effects on the Treated (QTT) and the Average Treatment Effect on the Treated (ATT) using the Mean Difference-in-Differences identification strategy. Handles two-period data and staggered treatment adoption uniformly. Supports both panel and repeated cross sections data.

Identification. MDiD assumes the counterfactual distribution of untreated potential outcomes is a location shift of the treated group's pre-treatment distribution. The size of the shift is the mean DiD \(\Delta = E[Y_{\text{post}}|D=0] - E[Y_{\text{pre}}|D=0]\), so \(Q_{Y(0),\text{post}|D=1}(\tau) = Q_{Y,\text{pre}|D=1}(\tau) + \Delta\). This is stronger than parallel trends in means alone: it additionally requires that the shape of the treated group's outcome distribution is unchanged in the counterfactual. MDiD is a special case of QDiD that applies a single mean shift rather than a rank-specific distributional shift.

Covariate adjustment. When xformula is specified, the scalar shift is replaced by a unit-specific conditional mean shift \(\Delta(X_i) = E[Y_{\text{post}}|D=0,X_i] - E[Y_{\text{pre}}|D=0,X_i]\), estimated by weighted OLS. The counterfactual for treated unit \(i\) is \(Y_{\text{pre},i} + \Delta(X_i)\), and the unconditional counterfactual distribution is the empirical CDF of these values. By the law of iterated expectations, this consistently estimates \(F_{Y(0),\text{post}|D=1}\).

Usage

mdid(
  yname,
  gname,
  tname,
  idname = NULL,
  data,
  panel = TRUE,
  xformula = ~1,
  weightsname = NULL,
  control_group = "notyettreated",
  anticipation = 0,
  alp = 0.05,
  cband = TRUE,
  biters = 100,
  cl = 1,
  ret_quantile = NULL,
  gt_type = "att",
  probs = NULL
)

Arguments

yname: Name of the outcome variable in data.
gname: Name of the treatment group variable (first treatment period; 0 for never-treated units).
tname: Name of the time period variable.
idname: Name of the unit id variable. Required when panel = TRUE.
data: A data frame.
panel: Logical; TRUE (default) for panel data, FALSE for repeated cross sections.
xformula: One-sided formula for covariates. Default ~1 uses no covariates.
weightsname: Name of the column in data containing sampling weights. Default NULL uses equal weights.
control_group: Which units to use as the comparison group: "notyettreated" (default) or "nevertreated".
anticipation: Number of periods of anticipation. Default 0.
alp: Significance level for confidence bands. Default 0.05.
cband: Logical; if TRUE (default) compute a uniform confidence band rather than pointwise intervals.
biters: Number of bootstrap iterations. Default 100.
cl: Number of clusters for parallel computation. Default 1.
ret_quantile: Passed through to ptetools for the "qott" case.
gt_type: Type of group-time effect to compute. "att" (default) returns ATT(g,t). "qtt" returns the full QTT curve over probs using mixture-CDF aggregation. "qott" returns the quantile of the individual treatment effect distribution (panel only).
probs: For gt_type = "qtt", the quantile grid at which to evaluate the QTT curve. Default is seq(0.05, 0.95, 0.05).

Value

For gt_type = "att", a pte_results object from ptetools. For gt_type = "qtt", a pte_qtt object with overall, group-specific, and dynamic QTT curves and bootstrap SEs.

References

Athey, Susan and Guido Imbens. “Identification and Inference in Nonlinear Difference-in-Differences Models.” Econometrica 74(2), pp. 431-497, 2006.

Thuysbaert, Bram. “Distributional Comparisons in Difference in Differences Models.” Working Paper, 2007.

Examples

# \donttest{
data(mpdta, package = "did")

## ATT aggregated across all groups and periods
res_att <- mdid(yname = "lemp", gname = "first.treat", tname = "year",
                idname = "countyreal", data = mpdta,
                gt_type = "att", biters = 20)
summary(res_att)
#> 
#> Overall ATT:  
#>      ATT    Std. Error     [ 95%  Conf. Int.]  
#>  -0.0305         0.013    -0.0535     -0.0074 *
#> 
#> 
#> Dynamic Effects:
#>  Event Time Estimate Std. Error [95% Simult.  Conf. Band]  
#>          -3   0.0298     0.0140        0.0024      0.0571 *
#>          -2  -0.0024     0.0139       -0.0296      0.0247  
#>          -1  -0.0243     0.0170       -0.0576      0.0090  
#>           0  -0.0189     0.0124       -0.0433      0.0055  
#>           1  -0.0536     0.0140       -0.0811     -0.0261 *
#>           2  -0.1363     0.0317       -0.1984     -0.0742 *
#>           3  -0.1008     0.0295       -0.1587     -0.0430 *
#> ---
#> Signif. codes: `*' confidence band does not cover 0
#> 

## Full QTT curve at selected quantiles
res_qtt <- mdid(yname = "lemp", gname = "first.treat", tname = "year",
                idname = "countyreal", data = mpdta,
                gt_type = "qtt", probs = seq(0.1, 0.9, 0.1), biters = 20)
summary(res_qtt)
#> 
#> Overall QTT Curve:
#>  Quantile     QTT Std. Error 95% CB Lower 95% CB Upper
#>       0.1  0.0474     0.1146      -0.4434       0.5381
#>       0.2 -0.0724     0.0783      -0.4077       0.2629
#>       0.3 -0.0465     0.0251      -0.1539       0.0609
#>       0.4 -0.0195     0.0373      -0.1792       0.1402
#>       0.5 -0.0384     0.0415      -0.2162       0.1395
#>       0.6 -0.0305     0.0418      -0.2093       0.1483
#>       0.7 -0.0301     0.0353      -0.1812       0.1211
#>       0.8 -0.0540     0.0422      -0.2348       0.1268
#>       0.9 -0.0185     0.0387      -0.1841       0.1471
#> 
# }