Type:	Package
Title:	Dynamic Panel Multiple Threshold Model with Fixed Effects
Version:	3.0.2
Date:	2025-3-21
Description:	Compute the fixed effects dynamic panel threshold model suggested by Ramírez-Rondán (2020) <doi:10.1080/07474938.2019.1624401>, and dynamic panel linear model suggested by Hsiao et al. (2002) <doi:10.1016/S0304-4076(01)00143-9>, where maximum likelihood type estimators are used. Multiple thresholds estimation based on Markov Chain Monte Carlo (MCMC) is allowed, and model selection of linear model, threshold model and multiple threshold model is also allowed.
License:	GPL (≥ 3)
URL:	https://github.com/HujieBai/DPTM
Encoding:	UTF-8
Imports:	Rcpp (≥ 1.0.12),R6,BayesianTools, purrr, MASS,stats,coda,parabar,utils
LinkingTo:	Rcpp,RcppEigen
RoxygenNote:	7.3.2
Depends:	R (≥ 4.3.0)
LazyData:	true
BugReports:	https://github.com/HujieBai/DPTM/issues
NeedsCompilation:	yes
Packaged:	2025-03-21 14:44:10 UTC; baimbp2024
Author:	Bai Hujie [aut, cre, cph]
Maintainer:	Bai Hujie <hujiebai@163.com>
Repository:	CRAN
Date/Publication:	2025-03-21 15:00:02 UTC

Dynamic panel model with fixed effects.

Description

Use a MLE procedure to estimate the dynamic panel model with fixed effects.

Usage

DPML(formula, data, index=NULL, timeFE = FALSE, y1 = NULL,...)

## S6 method for class 'DPTM' 
#print(...)

Arguments

Details

DPML can fit the dynamic panel model with fixed effects proposed by Hsiao et al. (2002), which is based on the first difference and the maximum likelihood (MLE) method.

For a classical dynamic panel model with fixed effects having following form:

y_{it}=\rho y_{it-1}+\beta_1x_{1,it}+\beta_2x_{2,it}+\alpha_i+u_{it}

, can use y~x1+x2.

For a special dynamic panel model with fixed effects having the following form:

\Delta y_{it}=\rho y_{it-1}+\beta_1x_{1,it}+\beta_2x_{2,it}+\alpha_i+u_{it}

, can use dy~x1+x2 with y1= y_{it-1}.

We assume the exogenous regressor x is weakly exogenous, and thus the first period after difference is given by

\Delta y_{i1}=\delta_0 + {\boldsymbol\delta}'_1 \Delta {\bf x}_{i1}+ v_{i1},

where E(v_{i1}| \Delta {\bf x}_{i1} )=0. E(v_{i1}^2)=\sigma^2_v, E(v_{i1}\Delta u_{i2})=-\sigma^2_u and E(v_{i1} \Delta u_{it})=0 for t=3,4,...,T and i=1,...,N. For more details, see Hsiao et al. (2002).

In addition, we solve the log-likelihood function by stats::nlm who uses iterlim to set the maximum number of iterations, and thus iterlim is allowed by ... in DPML.

Value

DPML returns an object of class "DPTM". The function print are used to obtain and print a print of the results. An object of class "DPTM" is a list containing at least the following components:

Author(s)

Hujie Bai

References

Hsiao, C., Pesaran, M. H., & Tahmiscioglu, A. K. (2002). Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods. Journal of econometrics, 109(1), 107-150.

Examples

data(d1)

# No time fixed effects
model1 <- DPML(y~x+z, data = d1)
print(model1)

# With time fixed effects
model2 <- DPML(y~x+z, data = d1, timeFE = TRUE)
print(model2)

Dynamic Panel Multiple Threshold Model with Fixed Effects (DPTM)

Description

Use a MCMC-MLE based on two-step procedure to estimate the dynamic panel multiple threshold model with fixed effects.

Format

[R6::R6Class] object.

Public fields

Methods

Public methods

• DPTM$new()

• DPTM$capture_input()

• DPTM$MLE()

• DPTM$TModel_fit()

• DPTM$MCMC_process()

• DPTM$print()

• DPTM$clone()

Method new()

initialize Initializing method

Usage

DPTM$new(
  data,
  index = NULL,
  Th = NULL,
  iterations = NULL,
  sro = NULL,
  w = NULL,
  var_u = NULL,
  iterlim = NULL,
  restart = FALSE,
  delty0 = NULL
)

Arguments

Method capture_input()

Identify and capturing inputs

Usage

DPTM$capture_input(
  formula = NULL,
  formula_cv = NULL,
  timeFE,
  y1 = NULL,
  q = NULL,
  r0x = NULL,
  r1x = NULL,
  NoY = FALSE
)

Arguments

Method MLE()

Maximum likelihood estimation method

Usage

DPTM$MLE(ny = 1)

Arguments

Method TModel_fit()

Compute coefficients given thresholds

Usage

DPTM$TModel_fit(ga)

Arguments

Method MCMC_process()

Use MCMC to compute thresholds

Usage

DPTM$MCMC_process(
  proportion = 0.5,
  types = "DREAMzs",
  ADs = FALSE,
  nCR = 3,
  ...
)

Arguments

Method print()

print and print estimated results

Usage

DPTM$print(...)

Arguments

Method clone()

The objects of this class are cloneable with this method.

Usage

DPTM$clone(deep = FALSE)

Arguments

Dynamic panel multiple threshold model with fixed effects.

Description

Use a MCMC-MLE based on two-step procedure to estimate the dynamic panel multiple threshold model with fixed effects.

Usage

DPTS(formula = NULL, formula_cv = NULL, data, index=NULL, Th = 1, q, timeFE = FALSE, 
NoY = FALSE, y1 = NULL, iterations = 2000, sro = 0.1, r0x = NULL, r1x = NULL,
...)

## S6 method for class 'DPTM' 
#print(...)

Arguments

Details

DPTS can fit the dynamic panel threshold model with fixed effects proposed by Ramírez-Rondán (2020), and also allow a multiple threshold model by setting Th > 1.

Given the diverse forms and versatile applications of threshold models, we advocate for aligning model selection with specific research objectives, thereby granting users autonomy in specifying the model structure.

Take the model with one threshold (Ramírez-Rondán, 2020) as example.

For a standard threshold model

\begin{aligned}y_{i t} &=\left(\rho_1 y_{i t-1}+\beta_1 x_{i t}\right) I\left(q_{i t}\leq \gamma\right)+\left(\rho_2 y_{i t-1}+\beta_2 x_{i t}\right) I\left(q_{i t}> \gamma\right)\\&+\alpha_i+u_{i t},\end{aligned}

, can use DPTS(y~x,data = data, q = q, Th = 1).

For a threshold model who has regressors with threshold effects (x) and regressors without threshold effects (z)

\begin{aligned}y_{i t} &=\left(\rho_1 y_{i t-1}+\beta_1 x_{i t}\right) I\left(q_{i t}\leq \gamma\right)+\left(\rho_2 y_{i t-1}+\beta_2 x_{i t}\right) I\left(q_{i t}> \gamma\right)\\&+\theta z_{i t}+\alpha_i+u_{i t},\end{aligned}

, can use DPTS(y~x,y~z,data = data, q = q, Th = 1).

If user only cares about the regressors with threshold effects (thus hopes there is no threshold effects in the lag of dependent variable y_1), like

\begin{aligned}y_{i t} &= \rho y_{i t-1}+ \beta_1 x_{i t} I\left(q_{i t}\leq \gamma\right)+\beta_2 x_{i t} I\left(q_{i t}> \gamma\right)\\&+\theta z_{i t}+\alpha_i+u_{i t},\end{aligned}

, can use DPTS(y~x,y~z,data = data, q = q, Th = 1, NoY = TRUE).

And, the threshold model with the following form

\begin{aligned}y_{i t} &=\rho_1 y_{i t-1}I\left(q_{i t}\leq \gamma\right)+\rho_2 y_{i t-1}I\left(q_{i t}> \gamma\right)+\beta x_{i t}\\&+\theta z_{i t}+\alpha_i+u_{i t},\end{aligned}

, is also allowed by DPTS(NULL,y~x+z,data = data, q = q, Th = 1).

In addition, a special threshold model having the following form

\begin{aligned}\Delta y_{i t} &=\left(\rho_1 y_{i t-1}+\beta_1 x_{i t}\right) I\left(q_{i t}\leq \gamma\right)+\left(\rho_2 y_{i t-1}+\beta_2 x_{i t}\right) I\left(q_{i t}> \gamma\right)\\&+\theta z_{i t}+\alpha_i+u_{i t},\end{aligned}

, can use DPTS(dy~x,dy~z,data = data, q = q, Th = 1) with y1= y_{it-1}.

The MCMC we used is based on BayesianTools, and the default method is "DREAMzs" (see Vrugt et al., 2009). If user wants to use other MCMC, can use ... (see BayesianTools::applySettingsDefault). As for the length of iterations, it can be set by iterations (50% used for burnining) and default length is 2000. The trace plot and the Gelman and Rubin's convergence diagnostic are supplied by DPTS (print) to test the convergence of MCMC sample.

Additionally, we assume the exogenous regressor x is weakly exogenous, and thus the first period after difference is given by

\Delta y_{i1}=\delta_0 + {\boldsymbol\delta}'_1 \Delta {\bf x}_{i1}+ v_{i1},

where E(v_{i1}| \Delta {\bf x}_{i1} )=0. E(v_{i1}^2)=\sigma^2_v, E(v_{i1}\Delta u_{i2})=-\sigma^2_u and E(v_{i1} \Delta u_{it})=0 for t=3,4,...,T and i=1,...,N. For more details, see Hsiao et al. (2002).

Finally, we solve the log-likelihood function by stats::nlm who uses iterlim to set the maximum number of iterations, and thus iterlim is allowed by ... in DPTS.

Value

DPTS returns an object of class "DPTM". The function print are used to obtain and print a print of the results. An object of class "DPTM" is a list containing at least the following components:

Author(s)

Hujie Bai

References

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

Vrugt, Jasper A., et al. (2009)."Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling." International Journal of Nonlinear Sciences and Numerical Simulation 10.3: 273-290.

Hsiao, C., Pesaran, M. H., & Tahmiscioglu, A. K. (2002). Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods. Journal of econometrics, 109(1), 107-150.

Examples

data(d1)

# single threshold

## standard form 
#Model1_1 <- DPTS(y~x,data = d1, index = c('id','year'), q = d1$q, Th = 1, 
#iterations = 1000)
#print(Model1_1)


### Examples elapsed time > 15s
## with x \& z
#Model2_1 <- DPTS(y~x,y~z,data = d1, index = c('id','year'), q = d1$q, Th = 1, 
#iterations = 1000)
#print(Model2_1)

## with x \& z (y1 no threshold effects)
#Model3_1 <- DPTS(y~x,y~z,data = d1, index = c('id','year'), q = d1$q, Th = 1,
#NoY = TRUE, iterations = 1000)
#print(Model3_1)

## only y1 with threshold effects
#Model4_1 <- DPTS(NULL,y~x+z,data = d1, index = c('id','year'), q = d1$q, Th = 1, 
#iterations = 1000)
#print(Model4_1)

# two thresholds (Th = 2)
## with x \& z
#Model2_2 <- DPTS(y~x,y~z,data = d1, index = c('id','year'), q = d1$q, Th = 2, 
#iterations = 1000)
#print(Model2_2)

# Adding time fixed effects (timeFE = TRUE)
#Model2_2T <- DPTS(y~x,y~z,data = d1, index = c('id','year'), q = d1$q, Th = 2,
#timeFE = TRUE, iterations = 1000)
#print(Model2_2T)

Example Dataset Growth_Inflation

Description

A dataset for economic growth of 74 countries from 1961 to 2015 (five-year average).

Usage

Growth_Inflation

Format

## 'Growth_Inflation' A data.frame with 814 rows and 15 columns:

ncountry

country id

countryname

country name

code

country code

Period

Period

years

years

GDP per capita growth

the difference of ln(GDP per capita)

Inflation rate-semilog

the semi-log of Inflation rate

Transitional convergence

the lag of ln(GDP per capita)

Human capital

Human capital

Financial depth

Financial depth

Governance

Governance

Public infrastructure

Public infrastructure

Trade openness

Trade openness

Economic instability

Economic instability

Inflation rate

Inflation rate

Source

https://doi.org/10.1080/07474938.2019.1624401

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

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:

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

Example Dataset d1

Description

A simulated dataset for demonstrating the package

Usage

d1

Format

## 'd1' A data.frame with 1000 rows and 7 columns:

id

individuals

year

periods

y

dependent variable

y1

the first lag of y

q

threshold variable

x

regressor with threshold effects

z

regressor without threshold effects

Source

Simulated data with two thresholds