Threshold_Test: Tests for multiple thresholds.

In DPTM: Dynamic Panel Multiple Threshold Model with Fixed Effects

Tests for multiple thresholds.

Description

Tests for models with different thresholds, using bootstrap method.

Usage

Threshold_Test(formula = NULL, formula_cv = NULL, data, index=NULL, Th = 1, q, 
timeFE = FALSE, bt = 100,NoY = FALSE, y1 = NULL, iterations = 2000, sro = 0.1,
r0x = NULL, r1x = NULL, parallel=TRUE, seed = NULL,...)

Arguments

formula	formula of the covariates with threshold effects; If a setting is not provided, defaults (no covariates with threshold effects) will be used. Defaults to 'NULL'.
formula_cv	formula of the covariates without threshold effects; If a setting is not provided, defaults (no covariates without threshold effects) will be used. Defaults to 'NULL'.
data	data frame of the observed data.
index	variable names of individuals and period; If a setting is not provided, defaults (the first variables in data will be as "id", while the second will be "year") will be used.Defaults to 'NULL'.
q	threshold variable.
timeFE	logicals. If TRUE the time fixed effects will be allowed. Defaults to 'FALSE'.
bt	the number of bootstrap; If a setting is not provided, defaults (bt = 100) will be used. Defaults to '100'.
NoY	logicals. If TRUE the lags of dependent variables will be without threshold effects. Defaults to 'FALSE'.
y1	lags of dependent variables; If a setting is not provided, defaults (the first-order lag) will be used. Defaults to 'NULL'.
iterations	MCMC iterations (50% used for burnining). Defaults to '2000'.
sro	regime (subsample) proportion; If a setting is not provided, defaults (10%) will be used. Defaults to '0.1'.
r0x	lower bound of threshold parameter space; If a setting is not provided, defaults (15% quantile of threshold variable) will be used.
r1x	upper bound of threshold parameter space; If a setting is not provided, defaults (85% quantile of threshold variable) will be used.
parallel	logicals. If TRUE test will run in parallel for saving time. Defaults to 'TRUE'.
seed	set seeds to guarantee the replication the test (see set.seed);
...	additional arguments to be passed to the settings of MCMC (see BayesianTools::applySettingsDefault)
Th	number of thresholds; Defaults to '1'.

Details

Threshold_Test can run the Test for multiple thresholds (Th is H1). The statistic is

F_s=\frac{S\left(\hat{\gamma}_{s-1}\right)-S\left(\hat{\gamma}_s\right)}{S\left(\hat{\gamma}_s\right) / N(T-1)},

where s is the number of thresholds in H1, S\left(\hat{\gamma}_{s-1}\right)=-\ln L\left(\hat{\gamma}_{s-1}\right) and S\left(\hat{\gamma}_s\right)=-\ln L\left(\left(\hat{\gamma}_{s-1}^{\prime}, \hat{\gamma}_s\right)^{\prime}\right). And the p-value is computed by bootstrap method (see Ramírez-Rondán, 2020).

Take the two threshold model as example. User must set Th = 1 firstly to reject the null hypothesis of no threshold effects; Then he should set Th = 2 to reject the null hypothesis of only one threshold; Lastly, set Th = 3 to accept the null hypothesis of two thresholds. In other words, p-values of the first test (Th = 1) and the second test (Th = 1) should be less than significant level while the third test (Th = 3) is not.

Threshold_Test contains all augments in DPTS, but with three new augments: bt, parallel and seed. bt is the number of bootstrap (by default is 100); parallel can allow user to run test in parallel to save time; seed is used to guarantee the replication of tests.

It is worthy noting that the test shrinks to the so-called threshold existence test when Th = 1.

Value

A list with class "htest" containing the following components:

statistic	the value of the F-statistic.
parameter	the degrees of freedom for the F-statistic.
p.value	the p-value for the test.
null.value	the specified hypothesized value of the null hypothesis.
alternative	a character string describing the alternative hypothesis.
method	a character string indicating what type of test was performed.
data.name	a character string giving the name(s) of the data.
estimate	the critical value of the statistic (5% significance level).
LRs	a vector of statistics from bootstrap.

Author(s)

Hujie Bai

References

Ramírez-Rondán, N. R. (2020). Maximum likelihood estimation of dynamic panel threshold models. Econometric Reviews, 39(3), 260-276.

Examples

### Examples elapsed time > 15s

#data(d1)

# H0: no threshold effects (no threshold)
#test0 <- Threshold_Test(y~x,y~z,data = d1, index = c('id','year'), q = d1$q, Th = 1,
#bt = 50, iterations = 500)
#test0

# H0: one threshold 
#test1 <- Threshold_Test(y~x,y~z,data = d1, index = c('id','year'), q = d1$q, Th = 2,
#bt = 50, iterations = 500)
#test1

# H0: two threshold 
#test2 <- Threshold_Test(y~x,y~z,data = d1, index = c('id','year'), q = d1$q, Th = 3,
#bt = 50, iterations = 500)
#test2

DPTM documentation built on April 3, 2025, 6:28 p.m.