Use a MLE procedure to estimate the dynamic panel model with fixed effects.
DPML(formula, data, index=NULL, timeFE = FALSE, y1 = NULL,...)## S6 method for class 'DPTM'
#print(...)
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:
a named vector of coefficients
the negative log-likelihood function value
a vector of t statistics
a vector of standard errors
a covariance matrix
the number of thresholds
a named vector of thresholds
formula of the covariates with threshold effects.
data frame of the observed data.
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`.
logicals. If TRUE the time fixed effects will be allowed. Defaults to `FALSE`.
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.
Hujie Bai
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.
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.
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)
Run the code above in your browser using DataLab