pvargmm: GMM Estimation of Panel VAR Models

In panelvar: Panel Vector Autoregression

GMM Estimation of Panel VAR Models

Description

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

Usage

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

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.

y_i,t = μ_i + ∑_l=1^pA_ly_i,t-l + Bx_i,t + Cs_i,t + ε_i,t

Let y_i,t ∈ ℜ^m be an m×1 vector of endogenous variables for the ith cross-sectional unit at time t. Let y_i,t-l ∈ ℜ^m be an m×1 vector of lagged endogenous variables. Let x_i,t ∈ ℜ^k be an k×1 vector of predetermined variables that are potentially correlated with past errors. Let s_i,t ∈ ℜⁿ be an n×1 vector of strictly exogenous variables that neither depend on ε_i,t nor on ε_i,t-s for s = 1,…,T. The idiosyncratic error vector ε_i,t ∈ ℜ^m is assumed to be well-behaved and independent from both the regressors x_i,t and s_i,t and the individual error component μ_i. Stationarity requires that all unit roots of the PVAR model fall inside the unit circle, which therefore places some constraints on the fixed effect μ_i. The cross section i and the time section t are defined as follows: i = 1,…,N and t = 1,…T. In this specification we assume parameter homogeneity for A_l (m×m), B (m×k) and C (m×n) for all i.

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.

Value

A pvargmm object containing the estimation results.

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, 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, 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, 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, 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 doi: 10.1016/j.qref.2019.01.001

See Also

stability for stability tests

oirf and girf for orthogonal and generalized impulse response functions (including bootstrapped confidence intervals)

coef.pvargmm, se, pvalue, fixedeffects for extrator functions for the most important results

fevd_orthogonal for forecast error variance decomposition

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)

panelvar documentation built on Jan. 6, 2023, 1:17 a.m.