Hausman specification test (fixed vs. random effects)

Tests the null that the random-effects estimator is consistent (i.e. individual effects are uncorrelated with the regressors) against the alternative that only the fixed-effects estimator is consistent.

Usage

panhausman(
  fe,
  re = NULL,
  method = c("classical", "mundlak"),
  data = NULL,
  vcov = c("cluster", "HC1", "classical")
)

Arguments

fe

a "panglm" fit with model = "within"

re

a "panglm" fit with model = "random", same formula/data/family; required for method = "classical", ignored for "mundlak"

method

"classical" (default) or "mundlak"

data

for method = "mundlak": the data fe was fit on

vcov

for method = "mundlak": covariance of the pooled fit, one of "cluster" (default), "HC1", "classical"

Value

a list with class "panglm_hausman": statistic, parameter (df; two values for an F reference), p.value, method, distribution ("chisq" or "F"), pos_def ("classical" only: whether V_fe - V_re is positive definite), and the compared coefficient vectors (coef_fe, coef_re for "classical"; coef_mean for "mundlak")

Details

method = "classical" computes the Hausman (1978) statistic t(b_fe - b_re) %*% solve(V_fe - V_re) %*% (b_fe - b_re) over the coefficients common to both models (the random-effects intercept is dropped), with a chi-square reference. It always uses the model-based (classical) covariances, also when fe was fit with a robust vcov: the contrast variance V_fe - V_re relies on the random-effects estimator being efficient under the null, which holds only for model-based covariances and independent, homoskedastic idiosyncratic errors. In finite samples V_fe - V_re need not be positive definite and the statistic can then be negative. The signed value is returned, with p.value = NA and a warning (plm::phtest() reports its absolute value instead); the regression-based method = "mundlak" has no such problem.

method = "mundlak" is the regression-based (correlated random effects) version of the same test (Mundlak 1978; Wooldridge 2010, section 10.7.3), valid under heteroskedasticity and serial correlation. The pooled model y ~ x + xbar is fit with the individual means xbar of the time-varying regressors of fe, and the null coef(xbar) = 0 is tested with a Wald statistic using the vcov covariance. With vcov = "cluster" the reference is F(k, G - 1) (G individuals), otherwise chi-square(k). Gaussian family only.

Validation

Numerical accuracy is checked in the package tests and in the validation suite; see the validation article on the package website.

See also

panglm() with cre = TRUE, whose summary reports the Mundlak test.

Other tests: jointtest(), lineartest(), pandispersiontest()

Examples

data(copd)
fit_fe <- panglm(fev1 ~ crp, data = copd, index = c("id", "visit"),
                  model = "within", family = "gaussian")
fit_re <- panglm(fev1 ~ crp, data = copd, index = c("id", "visit"),
                  model = "random", family = "gaussian")
panhausman(fit_fe, fit_re)
#> 
#> 	Hausman specification test (fixed vs. random effects)
#> 
#> chisq = 0.08488, df = 1, p-value = 0.7708
#> alternative hypothesis: one model is inconsistent
#> 
panhausman(fit_fe, method = "mundlak", data = copd)
#> 
#> 	Mundlak specification test (fixed vs. random effects), vcov: cluster
#> 
#> F = 0.1647, df = 1, 59, p-value = 0.6864
#> alternative hypothesis: one model is inconsistent
#>