pvargmm() R function from [panelvar]

GMM Estimation of Panel VAR Models

Estimates a panel vector autoregressive (PVAR) model with fixed effects.


pvargmm(
  dependent_vars,
  lags,
  predet_vars,
  exog_vars,
  transformation = "fd",
  data,
  panel_identifier = c(1, 2),
  steps,
  system_instruments = FALSE,
  system_constant = TRUE,
  pca_instruments = FALSE,
  pca_eigenvalue = 1,
  max_instr_dependent_vars,
  max_instr_predet_vars,
  min_instr_dependent_vars = 2L,
  min_instr_predet_vars = 1L,
  collapse = FALSE,
  tol = 1e-09,
  progressbar = TRUE
)

Arguments

dependent_vars: Dependent variables
lags: Number of lags of dependent variables
predet_vars: Predetermined variables
exog_vars: Exogenous variables
transformation: First-difference "fd" or forward orthogonal deviations "fod"
data: Data set
panel_identifier: Vector of panel identifiers
steps: "onestep", "twostep" or "mstep" estimation
system_instruments: System GMM estimator
system_constant: Constant only available with the System GMM estimator in each equation
pca_instruments: Apply PCA to instruments matrix
pca_eigenvalue: Cut-off eigenvalue for PCA analysis
max_instr_dependent_vars: Maximum number of instruments for dependent variables
max_instr_predet_vars: Maximum number of instruments for predetermined variables
min_instr_dependent_vars: Minimum number of instruments for dependent variables
min_instr_predet_vars: Minimum number of instruments for predetermined variables
collapse: Use collapse option
tol: relative tolerance to detect zero singular values in "ginv"
progressbar: show progress bar

Returns

A pvargmm object containing the estimation results.

Details

The first vector autoregressive panel model (PVAR) was introduced by Holtz-Eakin et al. (1988). Binder et al. (2005) extend their equation-by-equation estimator for a PVAR model with only endogenous variables that are lagged by one period. We further improve this model in Sigmund and Ferstl (2021) to allow for $p$ lags of $m$ endogenous variables, $k$ predetermined variables and $n$ strictly exogenous variables.

Therefore, we consider the following stationary PVAR with fixed effects.

A PVAR model is hence a combination of a single equation dynamic panel model (DPM) and a vector autoregressive model (VAR).

First difference and system GMM estimators for single equation dynamic panel data models have been implemented in the STATA package xtabond2 by Roodman (2009) and some of the features are also available in the R package plm.

For more technical details on the estimation, please refer to our paper Sigmund and Ferstl (2021).

There we define the first difference moment conditions (see Holtz-Eakin et al., 1988; Arellano and Bond, 1991), formalize the ideas to reduce the number of moment conditions by linear transformations of the instrument matrix and define the one- and two-step GMM estimator. Furthermore, we setup the system moment conditions as defined in Blundell and Bond (1998) and present the extended GMM estimator. In addition to the GMM-estimators we contribute to the literature by providing specification tests (Hansen overidentification test, lag selection criterion and stability test of the PVAR polynomial) and classical structural analysis for PVAR models such as orthogonal and generalized impulse response functions, bootstrapped confidence intervals for impulse response analysis and forecast error variance decompositions. Finally, we implement the first difference and the forward orthogonal transformation to remove the fixed effects.

Examples


## Not run:

library(panelvar)
data(abdata)
ex3_abdata <-pvargmm(
 dependent_vars = c("emp"),
 lags = 4,
 predet_vars = c("wage"),
 exog_vars = c("cap"),
 transformation = "fd",
 data = abdata,
 panel_identifier = c("id", "year"),
 steps = c("twostep"),
 system_instruments = TRUE,
 max_instr_dependent_vars = 99,
 max_instr_predet_vars = 99,
 min_instr_dependent_vars = 2L,
 min_instr_predet_vars = 1L,
 collapse = FALSE
)
## End(Not run)

data("ex3_abdata")
summary(ex3_abdata)

data("Dahlberg")
## Not run:

ex1_dahlberg_data <- pvargmm(dependent_vars = c("expenditures", "revenues", "grants"),
                             lags = 1,
                             transformation = "fod",
                             data = Dahlberg,
                             panel_identifier=c("id", "year"),
                             steps = c("twostep"),
                             system_instruments = FALSE,
                             max_instr_dependent_vars = 99,
                             max_instr_predet_vars = 99,
                             min_instr_dependent_vars = 2L,
                             min_instr_predet_vars = 1L,
                             collapse = FALSE
)
## End(Not run)

data("ex1_dahlberg_data")
summary(ex1_dahlberg_data)

References

Arellano, M., Bond, S. (1991) Some Tests of Specification for Panel Sata: Monte Carlo Evidence and an Application to Employment Equations The Review of Economic Studies, 58 (2), 277--297, tools:::Rd_expr_doi("10.2307/2297968")

Binder M., Hsiao C., Pesaran M.H. (2005) Estimation and Inference in Short Panel Vector Autoregressions with Unit Roots and Cointegration Econometric Theory, 21 (4), 795--837, tools:::Rd_expr_doi("10.1017/S0266466605050413")

Blundell R., Bond S. (1998). Initial Conditions and Moment Restrictions in Dynamic Panel Data Models Journal of Econometrics, 87 (1), 115--143, tools:::Rd_expr_doi("10.1016/S0304-4076(98)00009-8")

Holtz-Eakin D., Newey W., Rosen H.S. (1988) Estimating Vector Autoregressions with Panel Data, Econometrica, 56 (6), 1371--1395, tools:::Rd_expr_doi("10.2307/1913103")

Roodman, D. (2009) How to Do xtabond2: An Introduction to Difference and System GMM in Stata The Stata Journal, 9 (1), 86--136, https://www.stata-journal.com/article.html?article=st0159

Sigmund, M., Ferstl, R. (2021) Panel Vector Autoregression in R with the Package panelvar The Quarterly Review of Economics and Finance tools:::Rd_expr_doi("10.1016/j.qref.2019.01.001")

pvargmm function