Test for pre-trends

Jointly tests the null hypothesis of parallel (common) trends prior to treatment, following Wooldridge (2025, Sec. 7). A light wrapper around fixest::wald() that selects the relevant coefficients on your behalf. The test depends on how the etwfe model was estimated:

• trend = TRUE: tests that the cohort-specific linear trends are jointly zero.

• cgroup = "never": tests that the pre-treatment cohort-period effects (i.e., the "leads" in an event study) are jointly zero.

These are alternative tests of the same null hypothesis, and cannot be combined in a single model; cohort trends and a full set of pre-treatment effects are not separately identified. Note that the cgroup = "never" model is equivalent to augmenting the default "notyet" model with the pre-treatment effects, as per Wooldridge's test regression.

Usage

pretrends(x, interactions = FALSE, ...)

Arguments

x

An etwfe model object.

interactions

Logical. Should interactions between the tested terms and any (demeaned) controls or xvar covariates also be included in the joint null? Defaults to FALSE, following Wooldridge (2025), who notes that testing for covariate-dependent violations of parallel trends comes at a considerable cost in power.

...

Additional arguments passed to fixest::wald(), e.g. print or vcov.

Value

The result of fixest::wald(): a list containing the test statistic, p-value, degrees of freedom, and vcov type.

Details

The cgroup = "never" test involves roughly one restriction per pre-treatment period per cohort, which can be a lot. Each cohort's restrictions are informed mainly by that cohort's own units, so a cluster-robust test needs many clusters (units) per cohort. With few clusters per cohort, the cluster-robust vcov can badly underestimate the variance of some combinations of the pre-treatment effects, leading the joint test to over-reject (sometimes wildly) even when the individual estimates look unremarkable. The cohort trends test (one restriction per cohort) is much less susceptible to this problem.

References

Wooldridge, Jeffrey M. (2025). Two-way fixed effects, the two-way Mundlak regression, and difference-in-differences estimators. Empirical Economics, 69, 2545-2587. Available: https://doi.org/10.1007/s00181-025-02807-z

See also

fixest::wald(), which performs the underlying test.

Examples

#
# Option 1: cgroup = "notyet" (default) + trend = TRUE
#

# Tests whether the cohort-specific linear trends are jointly zero. Requires
# at least two pre-treatment periods per cohort, so we drop the cohort
# treated in year 2.
data("base_stagg", package = "fixest")
mod_trend = etwfe(
  y ~ x1, tvar = year, gvar = year_treated,
  data = subset(base_stagg, year_treated != 2), vcov = ~id,
  trend = TRUE # <= cohort trends (with default cgroup = "notyet")
)
pretrends(mod_trend)
#> Wald test, H0: joint nullity of year_treated::3:year, year_treated::4:year, year_treated::5:year, year_treated::6:year, year_treated::7:year, year_treated::8:year and 2 others
#>  stat = 0.511144, p-value = 0.845112, on 8 and 89 DoF, VCOV: Clustered (id).

#
# Option 2: cgroup = "never"
#

# Tests whether the pre-treatment effects (event study leads) are jointly
# zero. This involves many more restrictions, so we switch to the bundled
# walmart dataset, which has enough units per cohort for a reliable
# cluster-robust test.
mod_never = etwfe(
  log_retail_emp ~ 0, tvar = year, gvar = cohort,
  ivar = fips, wvar = n_open,
  data = walmart, vcov = ~fips,
  cgroup = "never" # <= never-treated control group
)
pretrends(mod_never)
#> Wald test, H0: joint nullity of .Dpre:cohort::1986:year::1977, .Dpre:cohort::1986:year::1978, .Dpre:cohort::1986:year::1979, .Dpre:cohort::1986:year::1980, .Dpre:cohort::1986:year::1981, .Dpre:cohort::1986:year::1982 and 197 others
#>  stat = 4.19796, p-value < 2.2e-16, on 203 and 1,287 DoF, VCOV: Clustered (fips).