maxTestIU_func: An internal function of the EquiTrends Maximum Equivalence Testing procedure using the Intersection Union approach.

Description

This is a supporting function of the maxEquivTest function. It calculates the placebo coefficients and the absolute value of the placebo coefficients. It then calculates the critical value and p-values if an equivalence threshold is supplied for the test, according to Dette & Schumann (2024). If no equivalence threshold is supplied, it calculates the minimum equivalence threshold for which the null of non-negligible pre-trend differences can be rejected.

Usage

maxTestIU_func(
  data,
  equiv_threshold,
  vcov,
  cluster,
  alpha,
  n,
  no_periods,
  base_period,
  is_panel_balanced
)

Value

An object of class "maxEquivTestIU" containing:

placebo_coefficients: A numeric vector of the estimated placebo coefficients,
abs_placebo_coefficients: a numeric vector with the absolute values of estimated placebo coefficients,
placebo_coefficient_se: a numeric vector with the standard errors of the placebo coefficients,
significance_level: the chosen significance level of the test,
num_individuals: the number of cross-sectional individuals (n),
num_periods: the number of periods (T),
num_observations: the total number of observations (N),
base_period: the base period in the data,
placebo_names: the names corresponding to the placebo coefficients,
equiv_threshold_specified: a logical value indicating whether an equivalence threshold was specified.
is_panel_balanced: a logical value indicating whether the panel data is balanced.

Additionally, if !(is.null(equiv_threshold))

IU_critical_values: a numeric vector with the individual critical values for each of the placebo coefficients,
reject_null_hypothesis: a logical value indicating whether the null hypothesis of negligible pre-trend differences can be rejected at the specified significance level alpha,
equiv_threshold: the equivalence threshold employed,

if is.null(equiv_threshold)

minimum_equiv_thresholds: a numeric vector including for each placebo coefficient the minimum equivalence threshold for which the null hypothesis of negligible pre-trend differences can be rejected for the corresponding placebo coefficient individually,
minimum_equiv_threshold: a numeric scalar minimum equivalence threshold for which the null hypothesis of negligible pre-trend differences can be rejected for all placebo coefficients individually.

Arguments

data: The data.frame object containing the data for the test. Should be of the form what is returned by the EquiTrends_dataconstr function.
equiv_threshold: The equivalence threshold for the test. If NULL, the minimum equivalence threshold for which the null hypothesis of non-negligible can be rejected is calculated.
vcov: The variance-covariance matrix estimator. See maxEquivTest for more information.
cluster: The cluster variable for the cluster-robust variance-covariance matrix estimator. See maxEquivTest for more information.
alpha: The significance level for the test.
n: The number of cross-sectional individuals in the data.
no_periods: The number of periods in the data.
base_period: The base period for the test. Must be one of the unique periods in the data.
is_panel_balanced: A logical value indicating whether the panel data is balanced.

References

Dette, H., & Schumann, M. (2024). "Testing for Equivalence of Pre-Trends in Difference-in-Differences Estimation." Journal of Business & Economic Statistics, 1–13. DOI: tools:::Rd_expr_doi("10.1080/07350015.2024.2308121")