DPML: Dynamic panel model with fixed effects.

In DPTM: Dynamic Panel Multiple Threshold Model with Fixed Effects

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

formula	formula of the covariates with threshold effects.
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'.
timeFE	logicals. If TRUE the time fixed effects will be allowed. 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'.
...	additional arguments, seestats::nlm.

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:

coefficients	a named vector of coefficients
NNLL	the negative log-likelihood function value
Zvalues	a vector of t statistics
Ses	a vector of standard errors
covariance_matrix	a covariance matrix
Th	the number of thresholds
thresholds	a named vector of thresholds

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)

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