Package 'panelvar'

Title: Panel Vector Autoregression
Description: We extend two general methods of moment estimators to panel vector autoregression models (PVAR) with p lags of endogenous variables, predetermined and strictly exogenous variables. This general PVAR model contains the first difference GMM estimator by Holtz-Eakin et al. (1988) <doi:10.2307/1913103>, Arellano and Bond (1991) <doi:10.2307/2297968> and the system GMM estimator by Blundell and Bond (1998) <doi:10.1016/S0304-4076(98)00009-8>. We also provide 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.
Authors: Michael Sigmund [aut], Robert Ferstl [aut, cre]
Maintainer: Robert Ferstl <[email protected]>
License: GPL (>= 2)
Version: 0.5.6
Built: 2024-11-25 19:33:02 UTC
Source: CRAN

Help Index

Employment UK data

Description

This data set contains labor demand data from a panel of firms in the United Kingdom. The panel is unlanced.

Usage

abdata

Format

The variables are:

c1

Record ID

ind

Firm index

year

Year

emp

Employment

wage

Wage

cap

Capital

indoutpt

Industrial output

n, w, k, ys

Logs of variables

rec

Record number

yearm1

Lagged year

id

ID

nL1, nL2, wL1, kL1, kL2, ysL1, ysL2

Lags of log variables

yr1976 - yr1984

Time dummies

Source

https://www.stata-press.com/data/r13/abdata.dta

References

Arellano, M. and Bond, S. (1991) "Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations", The Review of Economic Studies, 58(2), 227-297, doi:10.2307/2297968

Andrews Lu MMSC Criteria based on Hansen-J-Statistic

Description

...

Usage

Andrews_Lu_MMSC(model, HQ_criterion = 2.1)

## S3 method for class 'pvargmm'
Andrews_Lu_MMSC(model, HQ_criterion = 2.1)

Arguments

model

A PVAR model
HQ_criterion

Hannan Quinn criterion

Value

BIC, AIC and HQIC

References

Andrews, D., Lu, B. (2001) Consistent Model and Momement Selection Procedures for GMM Estimation with Application to Dynamic Panel Data Models, Journal of Econometrics, 101(1), 123–164, doi:10.1016/S0304-4076(00)00077-4

Examples

data("ex3_abdata")
Andrews_Lu_MMSC(ex3_abdata)

Empirical estimation of PVAR Impulse Response Confidence Bands

Description

Uses blockwise sampling of individuals (bootstrapping).

Usage

bootstrap_irf(
  model,
  typeof_irf,
  n.ahead,
  nof_Nstar_draws,
  confidence.band,
  mc.cores
)

## S3 method for class 'pvargmm'
bootstrap_irf(
  model,
  typeof_irf = c("OIRF", "GIRF"),
  n.ahead,
  nof_Nstar_draws,
  confidence.band = 0.95,
  mc.cores = getOption("mc.cores", 2L)
)

## S3 method for class 'pvarfeols'
bootstrap_irf(
  model,
  typeof_irf = c("OIRF", "GIRF"),
  n.ahead,
  nof_Nstar_draws,
  confidence.band = 0.95,
  mc.cores = getOption("mc.cores", 2L)
)

Arguments

model

A PVAR model
typeof_irf

"OIRF" or GIRF
n.ahead

n ahead steps
nof_Nstar_draws

Number of draws
confidence.band

Confidence band
mc.cores

Number of cores to use

Examples

## Not run: 
data("ex1_dahlberg_data")
ex1_dahlberg_data_bs <-  bootstrap_irf(ex1_dahlberg_data, typeof_irf = c("GIRF"),
                                       n.ahead = 8,
                                       nof_Nstar_draws = 500,
                                       confidence.band = 0.95,
                                       mc.cores = 100)
                                           
                                           

## End(Not run)
data("ex1_dahlberg_data")
ex1_dahlberg_data_girf <-  girf(ex1_dahlberg_data, n.ahead = 8, ma_approx_steps= 8)
data("ex1_dahlberg_data_bs")
plot(ex1_dahlberg_data_girf, ex1_dahlberg_data_bs)

Cigar data

Description

This panel data set consists of 46 U.S. States over the period 1963-1992.

Usage

Cigar

Format

The variables are:

state

State abbreviation

year

Year

price

Price per pack of cigarettes

pop

Population

pop16

Population above the age of 16.

cpi

Consumer price index with (1983=100

ndi

Per capita disposable income

sales

Cigarette sales in packs per capita

pimin

Minimum price in adjoining states per pack of cigarettes

All variables all also available as logs.

Source

https://www.wiley.com/legacy/wileychi/baltagi/supp/Cigar.txt

References

Baltagi, B.H. and D. Levin (1992) "Cigarette taxation: raising revenues and reducing consumption", Structural Change and Economic Dynamics, 3(2), 321-335, doi:10.1016/0954-349X(92)90010-4.

Baltagi, B.H., J.M. Griffin and W. Xiong (2000) "To pool or not to pool: homogeneous versus heterogeneous estimators applied to cigarette demand", Review of Economics and Statistics, 82(1), 117-126, doi:10.1162/003465300558551.

Baltagi, B.H. (2013) "Econometric analysis of panel data", 5th edition, John Wiley and Sons Cigar

Extract PVARFEOLS(p) Model Coefficients

Description

Extract PVARFEOLS(p) Model Coefficients

Usage

## S3 method for class 'pvarfeols'
coef(object, ...)

Arguments

object

object
...

further arguments

Extract PVAR(p) Model Coefficients

Description

Extract PVAR(p) Model Coefficients

Usage

## S3 method for class 'pvargmm'
coef(object, ...)

Arguments

object

object
...

further arguments

Examples

data("ex1_dahlberg_data")
coef(ex1_dahlberg_data)

Extract PVARHK(p) Model Coefficients

Description

Extract PVARHK(p) Model Coefficients

Usage

## S3 method for class 'pvarhk'
coef(object, ...)

Arguments

object

object
...

further arguments

Swedish municipalities data

Description

The panel data set consists of 265 Swedish municipalities and covers 9 years (1979-1987).

Usage

Dahlberg

Format

The variables are:

id

ID number for municipality

year

Year

expenditures

Total expenditures

revenues

Total own-source revenues

grants

Intergovernmental grants received by the municipality

Total expenditures contains both capital and current expenditures.

Expenditures, revenues, and grants are expressed in million SEK. The series are deflated and in per capita form. The implicit deflator is a municipality-specific price index obtained by dividing total local consumption expenditures at current prices by total local consumption expenditures at fixed (1985) prices.

The data are gathered by Statistics Sweden and obtained from Financial Accounts for the Municipalities (Kommunernas Finanser).

Source

http://qed.econ.queensu.ca/jae/2000-v15.4/dahlberg-johansson/

References

M. Dahlberg and E. Johansson (2000) "An examination of the dynamic behavior of local governments using GMM bootstrapping methods", Journal of Applied Econometrics, 15(4), 401-416, https://www.jstor.org/stable/2678589.

Dahlberg results example 1

Description

Dahlberg results example 1

Usage

ex1_dahlberg_data

Format

An object of class pvargmm of length 35.

Dahlberg bootstrap results example 1

Description

Dahlberg bootstrap results example 1

Usage

ex1_dahlberg_data_bs

Format

An object of class list of length 4.

NLS Work 2 bootstrap results example 2

Description

NLS Work 2 bootstrap results example 2

Usage

ex2_nlswork2_data_bs

Format

An object of class list of length 4.

Example results for Employment UK data

Description

Example results for Employment UK data

Usage

ex3_abdata

Format

An object of class pvargmm of length 36.

Extract Coefficients and GOF Measures from a Statistical Object

Description

Extract Coefficients and GOF Measures from a Statistical Object

Usage

extract(model, ...)

## S3 method for class 'pvargmm'
extract(model, ...)

## S3 method for class 'pvarfeols'
extract(model, ...)

## S3 method for class 'pvarhk'
extract(model, ...)

Arguments

model

Model
...

Further arguments passed to or from other methods

Examples

data("ex1_dahlberg_data")
extract(ex1_dahlberg_data)

Forcast Error Variance Decomposition for PVAR

Description

Computes the forecast error variance decomposition of a PVAR(p) model.

Usage

fevd_orthogonal(model, n.ahead = 10)

## S3 method for class 'pvargmm'
fevd_orthogonal(model, n.ahead = 10)

## S3 method for class 'pvarfeols'
fevd_orthogonal(model, n.ahead = 10)

Arguments

model

A PVAR model
n.ahead

Number of steps

Details

The estimation is based on orthogonalised impulse response functions.

Value

A list with forecast error variances as matrices for each variable.

Note

A plot method will be provided in future versions.

References

Pfaff, B. (2008) VAR, SVAR and SVEC Models: Implementation Within R Package vars, Journal of Statistical Software 27(4) https://www.jstatsoft.org/v27/i04/

See Also

pvargmm for model estimaion

oirf for orthogonal impulse response function

Examples

data("ex1_dahlberg_data")
fevd_orthogonal(ex1_dahlberg_data, n.ahead = 8)

Extracting Fixed Effects

Description

Extracting Fixed Effects

Usage

fixedeffects(model, ...)

## S3 method for class 'pvargmm'
fixedeffects(model, Only_Non_NA_rows = TRUE, ...)

Arguments

model

Model
...

Further arguments passed to or from other methods
Only_Non_NA_rows

Filter NA rows

Examples

data("ex1_dahlberg_data")
fixedeffects(ex1_dahlberg_data)

Generalized Impulse Response Function

Description

Generalized Impulse Response Function

Usage

girf(model, n.ahead, ma_approx_steps)

## S3 method for class 'pvargmm'
girf(model, n.ahead, ma_approx_steps)

Arguments

model

A PVAR model
n.ahead

Any stable AR() model has an infinite MA representation. Hence any shock can be simulated infinitely into the future. For each forecast step t you need an additional MA term.
ma_approx_steps

MA approximation steps

Examples

data("ex1_dahlberg_data")
girf(ex1_dahlberg_data, n.ahead = 8, ma_approx_steps= 8)

Sargan-Hansen-J-Test for Overidentification

Description

Sargan-Hansen-J-Test for Overidentification

Usage

hansen_j_test(model, ...)

## S3 method for class 'pvargmm'
hansen_j_test(model, ...)

Arguments

model

A PVAR model
...

Further arguments passed to or from other methods

Examples

data("ex1_dahlberg_data")
hansen_j_test(ex1_dahlberg_data)

Knit Print Method for pvarfeols

Description

Knit Print Method for pvarfeols

Usage

## S3 method for class 'pvarfeols'
knit_print(x, ...)

Arguments

x

object
...

further arguments

Knit Print Method for pvargmm

Description

Knit Print Method for pvargmm

Usage

## S3 method for class 'pvargmm'
knit_print(x, ...)

Arguments

x

object
...

further arguments

Knit Print Method for pvarhk

Description

Knit Print Method for pvarhk

Usage

## S3 method for class 'pvarhk'
knit_print(x, ...)

Arguments

x

object
...

further arguments

Knit Print summary Method

Description

Knit Print summary Method

Usage

## S3 method for class 'summary.pvarfeols'
knit_print(x, ...)

Arguments

x

object
...

further arguments

Knit Print summary Method

Description

Knit Print summary Method

Usage

## S3 method for class 'summary.pvargmm'
knit_print(x, ...)

Arguments

x

object
...

further arguments

Knit Print summary Method

Description

Knit Print summary Method

Usage

## S3 method for class 'summary.pvarhk'
knit_print(x, ...)

Arguments

x

object
...

further arguments

NLS Work 2 data

Description

NLS Work 2 data

Usage

nlswork2

Format

An object of class data.frame with 16094 rows and 21 columns.

Orthogonal Impulse Response Function

Description

Orthogonal Impulse Response Function

Usage

oirf(model, n.ahead)

Arguments

model

A PVAR model
n.ahead

Any stable AR() model has an infinite MA representation. Hence any shock can be simulated infinitely into the future. For each forecast step t you need an addtional MA term.

Examples

data("ex1_dahlberg_data")
oirf(ex1_dahlberg_data, n.ahead = 8)

S3 plot method for pvarstability object, returns a ggplot object

Description

S3 plot method for pvarstability object, returns a ggplot object

Usage

## S3 method for class 'pvarstability'
plot(x, ...)

Arguments

x

object
...

further arguments

S3 Print Method for pvarfeols

Description

S3 Print Method for pvarfeols

Usage

## S3 method for class 'pvarfeols'
print(x, ...)

Arguments

x

object
...

further arguments

S3 Print Method for pvargamm

Description

S3 Print Method for pvargamm

Usage

## S3 method for class 'pvargmm'
print(x, ...)

Arguments

x

object
...

further arguments

S3 Print Method for pvarhk

Description

S3 Print Method for pvarhk

Usage

## S3 method for class 'pvarhk'
print(x, ...)

Arguments

x

object
...

further arguments

S3 print method for pvarstability object

Description

S3 print method for pvarstability object

Usage

## S3 method for class 'pvarstability'
print(x, ...)

Arguments

x

object
...

further arguments

S3 Print Method for summary.pvarfeols

Description

S3 Print Method for summary.pvarfeols

Usage

## S3 method for class 'summary.pvarfeols'
print(x, ...)

Arguments

x

object
...

further arguments

S3 Print Method for summary.pvargmm

Description

S3 Print Method for summary.pvargmm

Usage

## S3 method for class 'summary.pvargmm'
print(x, ...)

Arguments

x

object
...

further arguments

S3 Print Method for summary.pvarhk

Description

S3 Print Method for summary.pvarhk

Usage

## S3 method for class 'summary.pvarhk'
print(x, ...)

Arguments

x

object
...

further arguments

P-value S3 Method

Description

P-value S3 Method

Usage

pvalue(object, ...)

## S3 method for class 'pvargmm'
pvalue(object, ...)

## S3 method for class 'pvarfeols'
pvalue(object, ...)

## S3 method for class 'pvarhk'
pvalue(object, ...)

Arguments

object

Object
...

Further arguments

Examples

data("ex1_dahlberg_data")
pvalue(ex1_dahlberg_data)

Fixed Effects Estimator for PVAR Model

Description

This function estimates a stationary PVAR with fixed effects.

Usage

pvarfeols(
  dependent_vars,
  lags,
  exog_vars,
  transformation = c("demean"),
  data,
  panel_identifier = c(1, 2)
)

Arguments

dependent_vars

Dependent variables
lags

Number of lags of dependent variables
exog_vars

Exogenous variables
transformation

Demeaning "demean"
data

Data set
panel_identifier

Vector of panel identifiers

Examples

data(Cigar)
ex1_feols <-
pvarfeols(dependent_vars = c("log_sales", "log_price"),
          lags = 1,
          exog_vars = c("cpi"),
          transformation = "demean",
          data = Cigar,
          panel_identifier= c("state", "year"))
          
summary(ex1_feols)

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 pp lags of mm endogenous variables, kk predetermined variables and nn strictly exogenous variables.

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

yi,t = μi + ∑l=1pAlyi,t-l + Bxi,t + Csi,t + εi,t

Let yi,t ∈ ℜm be an m×1 vector of endogenous variables for the ith cross-sectional unit at time t. Let yi,t-l ∈ ℜm be an m×1 vector of lagged endogenous variables. Let xi,t ∈ ℜk be an k×1 vector of predetermined variables that are potentially correlated with past errors. Let si,t ∈ ℜn be an n×1 vector of strictly exogenous variables that neither depend on εi,t nor on εi,t-s for s = 1,…,T. The idiosyncratic error vector εi,t ∈ ℜm is assumed to be well-behaved and independent from both the regressors xi,t and si,t and the individual error component μi. Stationarity requires that all unit roots of the PVAR model fall inside the unit circle, which therefore places some constraints on the fixed effect μi. 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 Al(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)

Hahn Kuehrsteiner Estimator for PVAR Model

Description

This function estimates a stationary PVAR with fixed effects.

Usage

pvarhk(
  dependent_vars,
  exog_vars,
  transformation = c("demean"),
  data,
  panel_identifier = c(1, 2)
)

Arguments

dependent_vars

Dependent variables
exog_vars

Exogenous variables
transformation

Demeaning "demean"
data

Data set
panel_identifier

Vector of panel identifiers

References

Hahn J., Kuehrsteiner G. (2002) Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects When Both n and T Are Large, Econometrica, 70(4), 1639–1657

Examples

data(Dahlberg)
ex1_hk <-
pvarhk(dependent_vars = c("expenditures", "revenues", "grants"),
        transformation = "demean",
        data = Dahlberg,
        panel_identifier= c("id", "year"))

summary(ex1_hk)

Extracting Level Residuals

Description

Extracting Level Residuals

Usage

residuals_level(model, ...)

## S3 method for class 'pvargmm'
residuals_level(model, ...)

Arguments

model

Model
...

Further arguments passed to or from other methods

Examples

data("ex1_dahlberg_data")
residuals_level(ex1_dahlberg_data)

Standard Error S3 Method

Description

Standard Error S3 Method

Usage

se(object, ...)

## S3 method for class 'pvargmm'
se(object, ...)

## S3 method for class 'pvarfeols'
se(object, ...)

## S3 method for class 'pvarhk'
se(object, ...)

Arguments

object

Object
...

Further arguments

Examples

data("ex1_dahlberg_data")
se(ex1_dahlberg_data)

Stability of PVAR(p) model

Description

Stability of PVAR(p) model

Usage

stability(model, ...)

## S3 method for class 'pvargmm'
stability(model, ...)

## S3 method for class 'pvarfeols'
stability(model, ...)

Arguments

model

PVAR model
...

Further arguments

Value

A pvarstability object containing eigenvalue stability conditions

Examples

data("ex1_dahlberg_data")
stability_info <- stability(ex1_dahlberg_data)
print(stability_info)
plot(stability_info)

S3 Summary Method for pvarfeols

Description

S3 Summary Method for pvarfeols

Usage

## S3 method for class 'pvarfeols'
summary(object, ...)

Arguments

object

object
...

further arguments

S3 Summary Method for pvargmm

Description

S3 Summary Method for pvargmm

Usage

## S3 method for class 'pvargmm'
summary(object, ...)

Arguments

object

object
...

further arguments

S3 Summary Method for pvarhk

Description

S3 Summary Method for pvarhk

Usage

## S3 method for class 'pvarhk'
summary(object, ...)

Arguments

object

object
...

further arguments