ptm3 {PanelTM}

Three-way panel threshold regression model.

Description

Three-way panel threshold regression model and its estimation through the 2-step GMM estimator.

Usage

ptm3(data., nameI, nameT, nameJ, nameY, nameTV=NULL, nameXendo=NULL, 
    nameXexo=NULL, nameIV=NULL, trimrate=0.4, ngrid=100, h0=1.5,
    Iweight=FALSE, test.lin=TRUE, B=1000)

Arguments

data.

a data.frame with the following variables (by cols): I (statistical units ID), T (time), J (third-level), Y (dependent variable), and if not null, TV (threshold variable), Xendo (endogenous regressor(s)), Xexo (exogenous regressor(s)), IV (instruments).

nameI

the name of the (numerical) variable that identifies the statistical units.

nameT

the name of the (numerical) time variable.

nameJ

the name of the (numerical) variable that indicates the third dimension.

nameY

the name of the (numerical) dependent variable.

nameTV

the name of the (numerical) transition variable. If not specified, the first lag of Y is taken.

nameXendo

the names of the (numerical) independent endogenous variables (if any).

nameXexo

the names of the (numerical) independent exogenous variables (if any).

nameIV

the names of the (numerical) instrumental variables (if any).

trimrate

the trim rate when constructing the grid for estimating the threshold. The default value is set to 0.4.

ngrid

the number of grid points to estimate the threshold. The default is set to 100.

h0

the parameter for Silverman's rule of thumb for kernel estimation. The default is set to 1.5.

Iweight

the 1-st step weight matrix. If TRUE, the identity matrix is used. If FALSE, the 1-st step weight matrix is constructed from the instrumental variables. The default is set to FALSE.

test.lin

if TRUE (default), the linearity test is performed; if FALSE, not.

B

if test.lin=TRUE, the number of bootstrap iterations for the linearity test.

Details

ptm3 performs the first-difference 2-step GMM estimation of the three-way panel threshold regression model in Di Lascio and Perazzini (202X).

Value

An object of S4 class "ptm3", which is a list with the following elements:

threshold

the matrix of the estimated thresholds and the associated p-values.

param

the matrix of the estimated first-differenced parameters of the model and the associated p-values.

cov.

the array containing the estimated covariance matrix per each value of the third way.

residuals.

the list containing the estimated first-differenced residuals per each value of the third way.

test.lin.

the list of the linearity test results containing: the name of the test; the number of bootstrap iterations carried out; the p-value of the test per each value of the third way.

Note

The estimation method requires at least t\geq6: four lags of the dependent and independent variables are used as instruments, and two more are necessary to identify the regime switch (i.e., one per regime). Note that the instant times in the nameT variable are automatically ordered increasingly.

Author(s)

Francesca Marta Lilja Di Lascio <[e-mail]>

Selene Perazzini <[e-mail]>

References

Di Lascio, F.M.L. and Perazzini, S. (202x) A three-way dynamic panel threshold regression model for change point detection in bioimpedance data. WP BEMPS <https://repec.unibz.it/bemps104.pdf>.

Di Lascio, F.M.L. and Perazzini, S. (2022) Change point detection in fruit bioimpedance using a three-way panel model. Book of short papers - SIS2022, p.1184-1189, Eds. A. Balzanella, M. Bini, C. Cavicchia, R. Verde. Pearson. ISBN: 978-88-9193-231-0.

See Also

See also ptm2 and simptm.

Examples

# Import data
data(banana)

## NOT RUN
## Model on bioimpedance y_{ijt} with transition variable y_{ij(t-1)}
## y_{ijt} = (phi1_{jc})1(y_{ijt-1}<=gamma_j) + 
##           (phi2_{jc})1(y_{ijt-1}>gamma_j)
#
#ptm3(data.=banana, nameI="i", nameT="t", nameJ="j", 
#    nameY="bioimpedance", nameTV=NULL, nameXendo=NULL, nameXexo=NULL, 
#    nameIV=NULL, trimrate=0.4, ngrid=100, h0=1.4, Iweight=FALSE, 
#    test.lin=FALSE)
##

# Model on bioimpedance y_{ijt} with transition variable y_{ij(t-1)} 
# and time-varying regressor x_{ijt}: 
# y_{it}=(phi1_{jc}+phi1_{jX}*x_{ijt})1(y_{ijt-1}<=gamma_j) + 
# (phi2_{jc}+phi2_{jX}*x_{ijt})1(y_{ijt-1}>gamma_j)

ptm3(data.=banana, nameI="i", nameT="t", nameJ="j",nameY="bioimpedance", 
    nameTV=NULL, nameXendo="weight", nameXexo=NULL, nameIV=NULL,
    trimrate=0.4, ngrid=100, h0=1.5, Iweight=FALSE, test.lin=FALSE)