xtpqardl (version 1.0.1)

wald_test: Wald Test for Parameter Equality Across Quantiles

Description

Performs Wald tests for the null hypothesis that parameters are equal across different quantiles. Tests both long-run coefficients (beta) and ECT speed of adjustment (rho).

Usage

wald_test(object, joint = TRUE)
# S3 method for xtpqardl
wald_test(object, joint = TRUE)

Value

An object of class "wald_test.xtpqardl" containing:

beta_test

Wald test result for long-run coefficients

rho_test

Wald test result for ECT coefficients

individual_beta

Individual tests for each long-run variable (if joint = FALSE)

tau

Quantiles tested

Arguments

object

An object of class "xtpqardl".

joint

Logical. If TRUE (default), performs joint test for all coefficients. If FALSE, performs individual tests for each variable.

Details

The Wald test statistic is computed as: $$W = (R\theta)'[R V R']^{-1}(R\theta)$$

where \(\theta\) is the vector of coefficients, \(V\) is the variance-covariance matrix, and \(R\) is a restriction matrix testing equality of coefficients across quantiles.

Under the null hypothesis of equal coefficients, \(W\) follows a chi-squared distribution with degrees of freedom equal to the number of restrictions.

References

Koenker R, Bassett G (1982). "Tests of Linear Hypotheses and L1 Estimation." Econometrica, 50(6), 1577-1583. tools:::Rd_expr_doi("10.2307/1913398")

Examples

# \donttest{
data(pqardl_sample)
fit <- xtpqardl(
  formula = d_y ~ d_x1 + d_x2,
  data = pqardl_sample,
  id = "country",
  time = "year",
  lr = c("L_y", "x1", "x2"),
  tau = c(0.25, 0.50, 0.75)
)
wald_test(fit)
# }