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Elliott-Muller Test for Time-Varying Coefficients

Source: R/qll_hat.R
qll_hat.Rd

Computes the \(\hat{qLL}\) statistic of Elliott and Muller (2006) for testing the null hypothesis that regression coefficients are constant over time against the alternative of general time variation.

Usage

qll_hat(y, X, Z = NULL, L = 0L)

Arguments

y

Numeric vector of length T; the dependent variable.

X

A T x k matrix of regressors linked to potentially time-varying coefficients.

Z

A T x d matrix of regressors with constant coefficients. Use NULL (default) if all coefficients may vary.

L

Integer; lag truncation for the Newey-West estimator of the variance. Default 0 (no correction).

Value

A list with class "qll_hat" containing:

statistic

The \(\hat{qLL}\) test statistic.

k

Number of potentially time-varying coefficients.

n

Number of observations.

Details

The test is based on optimal invariant statistics for the null of constant coefficients against local alternatives. The \(\hat{qLL}\) statistic has non-standard critical values that depend on k; see Table 1 in Elliott and Muller (2006).

Selected critical values (5\

  • k = 1: -5.91

  • k = 2: -10.64

  • k = 3: -15.78

  • k = 4: -20.62

  • k = 5: -25.87

Reject the null when \(\hat{qLL}\) is below the critical value.

References

Elliott, G. and Muller, U.K. (2006). Efficient Tests for General Persistent Time Variation in Regression Coefficients. Review of Economic Studies, 73(4), 907-940.

Examples

if (FALSE) { # \dontrun{
set.seed(42)
n <- 200
x <- matrix(rnorm(n * 2), n, 2)
y <- x %*% c(0.5, -0.3) + rnorm(n)
qll_hat(y, x)
} # }