simptm {PanelTM}

Data simulation from two- or three-way panel threshold regression model.

Description

Random generation of data from two- or three-way panel threshold regression model with or without a time-varying regressor.

Usage

simptm(n, T., J=2, CP, gamma.=c(0,0), 
        phi_c=matrix(c(-1,1,-0.7,1.8), nrow=2, byrow=TRUE), 
        phi_X=matrix(c(-0.2,0.2,-0.5,0.8), nrow=2, byrow=TRUE), 
        sigmau=1, parAR=c(0.7,0.5), B=200, seedstart=1) 

Arguments

n

number of statistical units.

T.

number of times.

J

number of third way's values.

CP

vector of times of regime switch (one per each j). If vector of length 1, the same change point is taken for all the js.

gamma.

vector of length J of threshold values.

phi_c

matrix J\times 2 of the constant parameters of the two regimes; first column for lower (upper) regime and second column for upper (lower) regime.

phi_X

matrix J\times 2 of the regressor parameter of the two regimes; first column for lower (upper) regime and second column for upper (lower) regime.

sigmau

possible constant to be applied to the error term distributed as a Gaussian white noise.

B

number of datasets to be drawn.

parAR

vector of autoregressive parameter(s) (one for each j) to generate a (exogenous) time-varying regressor.

seedstart

number of the initial seed.

Details

simptm generates B datasets from a two- or three-way panel threshold regression model with n statistical units, T. times of observations and J values/levels for the third dimension. The data generating process is constituted by two regimes with a change point at time CP and a threshold value y_{t-1} = \gamma_j for each value/level j of the third way. The two regimes are defined by the constant parameters phi_c or phi_c and parameters for the time-varying regressor phi_X. In the current version of the package, it is thus possible to generate data from a model without regressors or with a time-varying regressor. The (exogenous) time-varying regressor is assumed to be distributed as an autoregressive stochastic process with the j-th parameter of the parAR. The error component is generated from a Gaussian white noise and can be rescaled through the constant sigmau.

Value

An object of S4 class "simptm", which is a list of simulated data matrices.

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). The output is a list of B dataframes. Each dataframe contains columns: i, j, t, Y and possibly X.

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.

Seo, M.H. and Shin, Y. (2016) Dynamic panels with threshold effect and endogeneity, Journal of Econometrics, 195(2), p.169-186.

See Also

See also ptm2 and ptm3.

Examples

## NOT RUN
#
## Simulation of 10 two-way panels  
## y_{it} = (-1-0.2*x_{it})1(y_{it-1}<=0) + (1+0.2*x_{it})1(y_{it-1}>0) 
## with 50 statistical units observed for 50 times with change point at 
## time 20, autoregressive parameter 0.7, and sigmau=1. 
#
DB1 <- simptm(n=50, T.=11, J=1, CP=8, gamma.=0, phi_c=matrix(c(-1,1), 
     nrow=1, byrow=TRUE), phi_X=matrix(c(-0.2,0.2), nrow=1, byrow=TRUE), 
     sigmau=1, parAR=0.7, B=10, seedstart=1)
#head(DB1@simulation)
#str(DB1@simulation)
    
## Simulation of 10 three-way panels 
## y_{i1t} = (-1-0.2*x_{i1t})1(y_{i1t-1}<=0) + 
##           (1+0.2*x_{i1t})1(y_{i1t-1}>0)
## y_{i2t} = (-0.7-0.5*x_{i2t})1(y_{i2t-1}<=0) + 
##           (1.8+0.8*x_{i2t})1(y_{i2t-1}>0)
## with 50 statistical units, 50 times, J=2, change point corresponding to 
## time 20, with autoregressive parameter 0.7, and sigmau=1. 
#
#DB2 <- simptm(n=50, T.=20, J=2, CP=10, gamma.=c(0,0), 
#    phi_c=matrix(c(-1,1,-0.7,1.8), nrow=2, byrow=TRUE), 
#    phi_X=matrix(c(-0.2,0.2,-0.5,0.8), nrow=2, byrow=TRUE), sigmau=1, 
#    parAR=rep(0.7,2), B=5, seedstart=1)
#head(DB2@simulation)
#str(DB2@simulation)
#
##