| pdynmc {pdynmc} | R Documentation |
Generalized Method of Moments (GMM) Estimation of Linear Dynamic Panel Data Models.
Description
pdynmc fits a linear dynamic panel data model based on moment
conditions with the Generalized Method of Moments (GMM).
Usage
pdynmc(
dat,
varname.i,
varname.t,
use.mc.diff,
use.mc.lev,
use.mc.nonlin,
use.mc.nonlinAS = NULL,
inst.stata = FALSE,
include.y,
varname.y = NULL,
lagTerms.y = NULL,
maxLags.y = NULL,
include.x = FALSE,
varname.reg.end = NULL,
lagTerms.reg.end = NULL,
maxLags.reg.end = NULL,
varname.reg.pre = NULL,
lagTerms.reg.pre = NULL,
maxLags.reg.pre = NULL,
varname.reg.ex = NULL,
lagTerms.reg.ex = NULL,
maxLags.reg.ex = NULL,
inst.reg.ex.expand = TRUE,
include.x.instr = FALSE,
varname.reg.instr = NULL,
include.x.toInstr = FALSE,
varname.reg.toInstr = NULL,
fur.con = FALSE,
fur.con.diff = NULL,
fur.con.lev = NULL,
varname.reg.fur = NULL,
lagTerms.reg.fur = NULL,
include.dum = FALSE,
dum.diff = NULL,
dum.lev = NULL,
varname.dum = NULL,
col_tol = 0.65,
w.mat = "iid.err",
w.mat.stata = FALSE,
std.err = "corrected",
estimation = "iterative",
max.iter = 100,
iter.tol = 0.01,
inst.thresh = NULL,
opt.meth = "BFGS",
hessian = FALSE,
optCtrl = list(kkt = FALSE, kkttol = .Machine$double.eps^(1/3), kkt2tol =
.Machine$double.eps^(1/3), starttests = TRUE, dowarn = TRUE, badval = (0.25) *
.Machine$double.xmax, usenumDeriv = FALSE, reltol = 1e-12, maxit = 200, trace = TRUE,
follow.on = FALSE, save.failures = TRUE, maximize = FALSE, factr = 1e+07, pgtol = 0,
all.methods = FALSE),
custom.start.val = FALSE,
start.val = NULL,
start.val.lo = -1,
start.val.up = 1,
seed.input = 42
)
Arguments
dat |
A dataset. |
varname.i |
The name of the cross-section identifier. |
varname.t |
The name of the time-series identifier. |
use.mc.diff |
A logical variable indicating whether moment conditions from equations in differences (i.e. instruments in levels) should be used. |
use.mc.lev |
A logical variable indicating whether moment conditions from equations in levels (i.e. instruments in differences) should be used. |
use.mc.nonlin |
A logical variable indicating whether nonlinear (quadratic) moment conditions should be used. |
use.mc.nonlinAS |
A logical variable indicating whether only the nonlinear (quadratic) moment conditions in the form proposed by Ahn and Schmidt (1995) should be used (is set to 'TRUE' when nonlinear moment conditions are employed). |
inst.stata |
A logical variable indicating whether to use the moment conditions from equations in levels as in Stata implementations xtabond2 Roodman (2018) and xtdpdgmm Kripfganz (2019). |
include.y |
A logical variable indicating whether instruments should be derived from the lags of the dependent variable. |
varname.y |
A character string denoting the name of the dependent variable in the dataset. |
lagTerms.y |
An integer indicating the number of lags of the dependent variable. Note that setting 'lagTerms.y' to zero excludes the dependent variable from the right-hand-side of the model specification. |
maxLags.y |
An integer indicating the maximum number of lags of the dependent variable from which instruments should be derived. |
include.x |
A logical variable indicating whether instruments should be derived from the covariates. Setting the argument to 'TRUE' requires specifying whether the covariates are endogenous, predetermined, or (strictly) exogenous (defaults to 'FALSE'). |
varname.reg.end |
One or more character strings denoting the covariate(s) in the dataset to be treated as endogenous (defaults to 'NULL'). |
lagTerms.reg.end |
One or more integers indicating the number of lags of the endogenous covariate(s). One integer per covariate needs to be given in the same order as the covariate names (defaults to 'NULL'). |
maxLags.reg.end |
One or more integers indicating the maximum number of lags of the endogenous covariate(s) used for deriving instruments. |
varname.reg.pre |
One or more character strings denoting the covariate(s) in the dataset to be treated as predetermined (defaults to 'NULL'). |
lagTerms.reg.pre |
One or more integers indicating the number of lags of the predetermined covariate(s). |
maxLags.reg.pre |
One or more integers indicating the maximum number of lags of the predetermined covariate(s) used for deriving instruments. One integer per covariate needs to be given in the same order as the covariate names (defaults to 'NULL'). |
varname.reg.ex |
One or more character strings denoting the covariate(s) in the dataset to be treated as (strictly) exogenous (defaults to 'NULL'). |
lagTerms.reg.ex |
One or more integers indicating the number of lags of the (strictly) exogenous covariate(s). One integer per covariate needs to be given in the same order as the covariate name (defaults to 'NULL'). |
maxLags.reg.ex |
One or more integers indicating the maximum number of lags of the (strictly) exogenous covariate(s) used for deriving instruments. |
inst.reg.ex.expand |
A logical variable that allows for using all past, present, and future observations of 'varname.reg.ex' to derive instruments (defaults to 'TRUE'). If set to 'FALSE', only past and present time periods are used to derive instruments. |
include.x.instr |
A logical variable that allows to include additional IV-type instruments (i.e., include covariates which are used as instruments but for which no parameters are estimated; defaults to 'FALSE'). |
varname.reg.instr |
One or more character strings denoting the covariate(s) in the dataset treated as instruments in estimation (defaults to 'NULL'). Note that the instrument type needs to be specified by including the names of the covariate(s) in any of the arguments 'varname.reg.end', 'varname.reg.pre', or 'varname.reg.ex'. |
include.x.toInstr |
A logical variable that allows to instrument covariate(s) (i.e., covariates which are not used as instruments but for which parameters are estimated; defaults to 'FALSE'). |
varname.reg.toInstr |
One or more character strings denoting the covariate(s) in the dataset to be instrumented (defaults to 'NULL'). Note that the names of the covariate(s) should not be included in any other function argument. |
fur.con |
A logical variable indicating whether further control variables (covariates) are included (defaults to 'FALSE'). |
fur.con.diff |
A logical variable indicating whether to include further control variables in equations from differences (defaults to 'NULL'). |
fur.con.lev |
A logical variable indicating whether to include further control variables in equations from level (defaults to 'NULL'). |
varname.reg.fur |
One or more character strings denoting covariate(s) in the dataset to treat as further controls (defaults to 'NULL'). |
lagTerms.reg.fur |
One or more integers indicating the number of lags of the further controls. One integer per further control needs to be given in the same order as the corresponding variable names (defaults to 'NULL'). |
include.dum |
A logical variable indicating whether dummy variables for the time periods are included (defaults to 'FALSE'). |
dum.diff |
A logical variable indicating whether dummy variables are included in the equations in first differences (defaults to 'NULL'). |
dum.lev |
A logical variable indicating whether dummy variables are included in the equations in levels (defaults to 'NULL'). |
varname.dum |
One or more character strings from which time dummies should be derived (can be different from varname.t; defaults to 'NULL'). |
col_tol |
A numeric variable in [0,1] indicating the absolute correlation threshold for collinearity checks (columns are omitted when pairwise correlations are above the threshold; defaults to 0.65). |
w.mat |
One of the character strings c('"iid.err"', '"identity"', '"zero.cov"') indicating the type of weighting matrix to use (defaults to '"iid.err"'). |
w.mat.stata |
A logical variable that slightly adjusts the weighting matrix according to the Stata function xtdpdgmm (defaults to 'FALSE'). |
std.err |
One of the character strings c('"corrected"', '"unadjusted"', '"dbl.corrected"'). The second and third options compute corrected standard error according to Windmeijer (2005) and Hwang et al. (2021), respectively (defaults to '"corrected"'). |
estimation |
One of the character strings c('"onestep"', '"twostep"', '"iterative"'). Denotes the number of iterations of the parameter procedure (defaults to '"twostep"'). |
max.iter |
An integer indicating the maximum number of iterations (defaults to 'NULL'; if estimation is set to '"iterative"', 'max.iter' defaults to 100). |
iter.tol |
A numeric variable in [0,1] indicating the tolerance for determining convergence of the iterative approach (defaults to 'NULL'; if estimation is set to '"iterative"', iter.tol defaults to 0.01). |
inst.thresh |
An integer denoting above which instrument count a generalized inverse is used to invert the weighting matrix (defaults to 'NULL'). |
opt.meth |
A character string denoting the numerical optimization procedure. When no nonlinear moment conditions are employed in estimation, closed form estimates can be computed by setting the argument to '"none"' (defaults to '"BFGS"'; for details on the further available optimizers see the documentation of package optimx). |
hessian |
A logical variable indicating if the hessian matrix should be approximated in optimization (defaults to 'FALSE'). |
optCtrl |
A list of arguments that are passed to optimx. For details on the arguments and the available options see the package documentation. |
custom.start.val |
A logical variable indicating whether prespecified starting values for the parameters are provided by the user (defaults to 'FALSE'; if set to 'TRUE', starting values need to be provided via argument 'start.val'). |
start.val |
A vector of numeric variables denoting the starting values for the parameter vector for numeric optimization (defaults to 'NULL'). |
start.val.lo |
A numeric variable denoting the lower limit for drawing starting values with uniform density (defaults to -1; ignored if 'custom.start.val' is set to 'TRUE'). |
start.val.up |
A numeric variable denoting the lower limit for drawing starting values with uniform density (defaults to 1; ignored if 'custom.start.val' is set to 'TRUE'). |
seed.input |
An integer used as seed for drawing starting values (defaults to 42; required if custom.start.val is set to 'FALSE'). |
Details
The function estimates a linear dynamic panel data model of the form
y_{i,t} = y_{i,t-1} \rho_1 + \boldsymbol{x}_{i,t}' \boldsymbol{\beta} + a_i + \varepsilon_{i,t}
where y_{i,t-1} is the lagged dependent variable, \rho_1 is
the lag parameter, \boldsymbol{x}_{i,t} are further covariates,
\boldsymbol{\beta} are the corresponding parameters, a_i
is an unobserved individual specific effect, and
\varepsilon_{i,t} is an idiosyncratic remainder component. The
model structure accounts for unobserved individual specific heterogeneity
and dynamics. Note that the specification given above is simplified for
illustatory purposes and more general lag structures are allowed in
pdynmc.
Estimation of the model parameters in pdynmc is based on
moment conditions with the generalized method of moments (GMM). Linear
dynamic panel data models The moment conditions employed in estimation can be linear and
nonlinear in parameters and estimation is carried out iteratively. In case
only linear moment conditions are used in estimation, closed form solutions
can be for computing parameter estimates – while when nonlinear moment
conditions are employed, parameter estimation relies on numerical
optimization of the objective function.
'pdynmc' provides an implementation of some of the functionality available in the Stata library xtdpdgmm Kripfganz (2019) and allows for '"onestep"', '"twostep"', and '"iterative"' GMM estimation based on the moment conditions of Holtz-Eakin et al. (1988), Arellano and Bover (1995), and Ahn and Schmidt (1995). Standard error corrections according to Windmeijer (2005) and Hwang et al. (2021) are available. For further details, please see Fritsch et al. (2021).
Value
An object of class 'pdynmc' with the following elements:
coefficients |
a vector containing the coefficient estimates |
data |
a list of elements on which computation of the model fit is based |
dep.clF |
a list of vectors containing the dependent variable for the cross-sectional observations |
dat.clF |
a list of matrices containing the covariates for the cross-sectional observations |
w.mat |
a list of weighting matrices for the different estimation steps |
H_i |
a matrix used to create the weighting matrix for the first estimation step |
par.optim |
a list of vectors containing the parameter estimates obtained from numerical optimization for the estimation steps |
ctrl.optim |
a list of control parameters used in numerical optimization for the estimation steps |
par.clForm |
a list of vectors containing the parameter estimates obtained from the closed form for the estimation steps |
iter |
a scalar denoting the number of iteration steps carried out to obtain parameter estimates |
fitted.values |
a list for each estimation step that contains a list of vectors of fitted values for each cross-sectional observation |
residuals |
a list for each estimation step that contains a list of vectors of residuals for each cross-sectional observation |
vcov |
a list of matrices containing the variance covariance matrix of the parameter estimates for each estimation step |
stderr |
a list of vectors containing the standard errors of the parameter estimates for each estimation step |
zvalue |
a list of vectors containing the z scores for the parameter estimates for each estimation step |
pvalue |
a list of vectors containing the p-values for the parameter estimates for each estimation step |
It has 'case.names', 'coef', 'dum.coef', 'fitted', 'model.matrix', 'ninst', 'nobs', 'optimIn', 'plot', 'print','residuals', 'summary', 'variable.names', 'vcov', and 'wmat' methods.
Author(s)
Markus Fritsch
References
Ahn SC, Schmidt P (1995).
“Efficient estimation of models for dynamic panel data.”
Journal of Econometrics, 68(1), 5–27.
doi:10.1016/0304-4076(94)01641-C.
Arellano M, Bover O (1995).
“Another look at the instrumental variable estimation of error-components models.”
Journal of Econometrics, 68(1), 29–51.
doi:10.1016/0304-4076(94)01642-D.
Fritsch M, Pua AAY, Schnurbus J (2021).
“pdynmc: A Package for Estimating Linear Dynamic Panel Data Models Based on Nonlinear Moment Conditions.”
The R Journal, 13(1), 218–231.
doi:10.32614/RJ-2021-035.
Holtz-Eakin D, Newey WK, Rosen HS (1988).
“Estimating Vector Autoregressions with Panel Data.”
Econometrica, 56(6), 1371–1395.
doi:10.2307/1913103.
Hwang J, Kang B, Lee S (2021).
“A doubly corrected robust variance estimator for linear GMM.”
Journal of Econometrics, forthcoming.
doi:10.1016/j.jeconom.2020.09.010.
Kripfganz S (2019).
“XTDPDGMM: Stata module to perform generalized method of moments estimation of linear dynamic panel data models.”
https://econpapers.repec.org/RePEc:boc:bocode:s458395.
Roodman D (2018).
“xtabond2: Stata module to extend xtabond dynamic panel data estimator.”
https://econpapers.repec.org/software/bocbocode/s435901.htm.
Windmeijer F (2005).
“A finite sample correction for the variance of linear efficient two-step GMM estimators.”
Journal of Econometrics, 126(1), 25–51.
doi:10.1016/j.jeconom.2004.02.005.
See Also
wald.fct for Wald tests,
jtest.fct for the Hansen J test, and
mtest.fct for serial correlation tests.
optimx for details on alternative routines and options
for numerical optimization
Examples
## Load data
data(ABdata, package = "pdynmc")
dat <- ABdata
dat[,c(4:7)] <- log(dat[,c(4:7)])
dat <- dat[c(1:140), ]
## Code example
m1 <- pdynmc(dat = dat, varname.i = "firm", varname.t = "year",
use.mc.diff = TRUE, use.mc.lev = FALSE, use.mc.nonlin = FALSE,
include.y = TRUE, varname.y = "emp", lagTerms.y = 2,
fur.con = TRUE, fur.con.diff = TRUE, fur.con.lev = FALSE,
varname.reg.fur = c("wage", "capital", "output"), lagTerms.reg.fur = c(1,2,2),
include.dum = TRUE, dum.diff = TRUE, dum.lev = FALSE, varname.dum = "year",
w.mat = "iid.err", std.err = "corrected", estimation = "onestep",
opt.meth = "none")
summary(m1)
## Load data
data(ABdata, package = "pdynmc")
dat <- ABdata
dat[,c(4:7)] <- log(dat[,c(4:7)])
## Arellano and Bond (1991) estimation in Table 4, column (a1)
m1 <- pdynmc(dat = dat, varname.i = "firm", varname.t = "year",
use.mc.diff = TRUE, use.mc.lev = FALSE, use.mc.nonlin = FALSE,
include.y = TRUE, varname.y = "emp", lagTerms.y = 2,
fur.con = TRUE, fur.con.diff = TRUE, fur.con.lev = FALSE,
varname.reg.fur = c("wage", "capital", "output"), lagTerms.reg.fur = c(1,2,2),
include.dum = TRUE, dum.diff = TRUE, dum.lev = FALSE, varname.dum = "year",
w.mat = "iid.err", std.err = "corrected", estimation = "onestep",
opt.meth = "none")
summary(m1)
## Arellano and Bond (1991) estimation in Table 4, column (a2)
m2 <- pdynmc(dat = dat, varname.i = "firm", varname.t = "year",
use.mc.diff = TRUE, use.mc.lev = FALSE, use.mc.nonlin = FALSE,
include.y = TRUE, varname.y = "emp", lagTerms.y = 2,
fur.con = TRUE, fur.con.diff = TRUE, fur.con.lev = FALSE,
varname.reg.fur = c("wage", "capital", "output"), lagTerms.reg.fur = c(1,2,2),
include.dum = TRUE, dum.diff = TRUE, dum.lev = FALSE, varname.dum = "year",
w.mat = "iid.err", std.err = "corrected", estimation = "twostep",
opt.meth = "none")
summary(m2)
## Arellano and Bond (1991) twostep estimation extended by nonlinear moment
## conditions
m3 <- pdynmc(dat = dat, varname.i = "firm", varname.t = "year",
use.mc.diff = TRUE, use.mc.lev = FALSE, use.mc.nonlin = TRUE,
include.y = TRUE, varname.y = "emp", lagTerms.y = 2,
fur.con = TRUE, fur.con.diff = TRUE, fur.con.lev = FALSE,
varname.reg.fur = c("wage", "capital", "output"), lagTerms.reg.fur = c(1,2,2),
include.dum = TRUE, dum.diff = TRUE, dum.lev = FALSE, varname.dum = "year",
w.mat = "iid.err", std.err = "corrected", estimation = "twostep",
opt.meth = "BFGS")
summary(m3)
## Arellano and Bond (1991) iterative estimation extended by nonlinear moment
## conditions
m4 <- pdynmc(dat = dat, varname.i = "firm", varname.t = "year",
use.mc.diff = TRUE, use.mc.lev = FALSE, use.mc.nonlin = TRUE,
include.y = TRUE, varname.y = "emp", lagTerms.y = 2,
fur.con = TRUE, fur.con.diff = TRUE, fur.con.lev = FALSE,
varname.reg.fur = c("wage", "capital", "output"), lagTerms.reg.fur = c(1,2,2),
include.dum = TRUE, dum.diff = TRUE, dum.lev = FALSE, varname.dum = "year",
w.mat = "iid.err", std.err = "corrected", estimation = "iterative",
max.iter = 4, opt.meth = "BFGS")
summary(m4)
## Arellano and Bond (1991) twostep estimation extended by linear moment
## conditions from equations in levels
m5 <- pdynmc(dat = dat, varname.i = "firm", varname.t = "year",
use.mc.diff = TRUE, use.mc.lev = TRUE, use.mc.nonlin = FALSE,
include.y = TRUE, varname.y = "emp", lagTerms.y = 2,
fur.con = TRUE, fur.con.diff = TRUE, fur.con.lev = FALSE,
varname.reg.fur = c("wage", "capital", "output"), lagTerms.reg.fur = c(1,2,2),
include.dum = TRUE, dum.diff = TRUE, dum.lev = FALSE, varname.dum = "year",
w.mat = "iid.err", std.err = "corrected", estimation = "twostep",
opt.meth = "none")
summary(m5)