| Type: | Package |
| Title: | Local Projections Impulse Response Functions |
| Version: | 0.2.4 |
| Maintainer: | Philipp Adämmer <philipp.adaemmer@uni-greifswald.de> |
| BugReports: | https://github.com/adaemmerp/lpirfs/issues |
| Description: | Provides functions to estimate and visualize linear as well as nonlinear impulse responses based on local projections by Jordà (2005) <doi:10.1257/0002828053828518>. The methods and the package are explained in detail in Adämmer (2019) <doi:10.32614/RJ-2019-052>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Depends: | R (≥ 3.1.2) |
| Encoding: | UTF-8 |
| LazyData: | true |
| NeedsCompilation: | yes |
| Imports: | doParallel(≥ 1.0.15), dplyr(≥ 1.0.0), foreach(≥ 1.5.0), ggplot2(≥ 3.3.0), gridExtra(≥ 2.3), lmtest(≥ 0.9-36), plm(≥ 2.2-3), sandwich(≥ 2.5-1), Rcpp(≥ 1.0.4.6) |
| RoxygenNote: | 7.3.1 |
| LinkingTo: | Rcpp, RcppArmadillo |
| Suggests: | testthat (≥ 3.0.0), AER(≥ 1.2-12), readxl, knitr, ggpubr, rmarkdown, zoo, vars |
| VignetteBuilder: | knitr |
| Config/testthat/edition: | 3 |
| Packaged: | 2025-03-18 13:04:37 UTC; adaemmerp |
| Author: | Philipp Adämmer 
[aut, cre],
James P. LeSage [ctb],
Mehmet Balcilar [ctb],
Jon Danielsson [ctb] |
| Repository: | CRAN |
| Date/Publication: | 2025-03-18 13:30:02 UTC |
Local Projection Impulse Response Functions
Description
lpirfs provides functions to estimate and plot linear as well as nonlinear impulse responses based on local projections by Jordà (2005) <doi:10.1257/0002828053828518>. The methods and the package are explained in detail in Adämmer (2019) <doi:10.32614/RJ-2019-052>. Please cite the paper when using the package.
Author(s)
Philipp Adämmer
See Also
Useful links:
Report bugs at https://github.com/adaemmerp/lpirfs/issues
Data to estimate fiscal multipliers
Description
A tibble, containing data to estimate fiscal multipliers. This data was originally used by Auerbach and Gorodnichenko (2012). Sarah and Zubairy (2018) use this data to re-evaluate their results with local projections.
Usage
ag_data
Format
A tibble with 248 quarterly observations (rows) and 7 variables (columns):
- Year
Year of observation.
- Quarter
Quarter of observation.
- Gov
Logs of real government (federal, state, and local) purchases (consumption and investment).
- Tax
Logs of real government receipts of direct and indirect taxes net of transfers to businesses and individuals.
- GDP
Logs of real gross domestic product.
- GDP_MA
7-quarter moving average growth rate of GDP.
- Gov_shock_mean
Identified government spending shock. For details see Supplementary Appendix of Ramey and Zubairy (2018).
Sample: 1948:IV - 2008:IV
Source
References
Auerbach, A. J., and Gorodnichenko Y. (2012). "Measuring the Output Responses to Fiscal Policy." American Economic Journal: Economic Policy, 4 (2): 1-27.
Jordà, Ò. (2005) "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Ramey, V.A., Zubairy, S. (2018). "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data." Journal of Political Economy, 126(2): 850 - 901.
Compute a data frame with lagged exogenous variables
Description
Create a data.frame() with lagged exogenous variables.
Usage
create_lags(data, lags)
Arguments
data |
A data.frame(). |
lags |
Integer for the number of lags. |
Value
Returns a data.frame with lagged values.
Author(s)
Philipp Adämmer
Compute data for linear model
Description
Function to create data for linear model.
Usage
create_lin_data(specs, endog_data)
Arguments
specs |
|
endog_data |
A data.frame with dependent variables. |
Value
List with filled matrices of lagged left (y_lin) and right hand side (x_lin) variables.
Author(s)
Philipp Adämmer
Compute data for nonlinear model with instrument variable approach
Description
Function to create data for nonlinear model with instrument variable approach.
Usage
create_nl_data(specs, endog_data)
Arguments
specs |
|
endog_data |
A data.frame with dependent variables. |
Value
List with filled matrices of lagged left (y_nl) and right hand side (x_nl) variables.
Author(s)
Philipp Adämmer
Prepare data sets for linear and nonlinear panel model
Description
Function to create panel data for linear and nonlinear model.
Usage
create_panel_data(specs, data_set)
Arguments
specs |
A list with specifications created in lp_lin_panel or lp_nl_panel. |
data_set |
A data.frame consisting of a panel data set. |
Value
A list with prepared endogenous and exogenous data as well as the updated list specs.
Compute structural shock matrix via Cholesky decomposition
Description
Compute structural shock matrix via Cholesky decomposition with input variables created in lp_lin or lp_nl.
Usage
get_mat_chol(y_lin, x_lin, endog_data, specs)
Arguments
y_lin |
A matrix with all endogenous variables. |
x_lin |
A matrix with lagged endogenous variables. |
endog_data |
A data.frame with all endogenous variables. |
specs |
Value
Shock matrix (d)
Author(s)
Philipp Adämmer
Compute residuals from OLS model
Description
Estimate residuals from OLS model.
Usage
get_resids_ols(y_data, x_data)
Arguments
y_data |
A vector for the left hand variable. |
x_data |
A matrix with right hand variables. |
Value
A numeric vector with residuals from OLS regression.
Author(s)
Philipp Adämmer
Function to get robust covariance matrix for panel data
Description
Function to get robust covariance matrix for panel data
Usage
get_robust_cov_panel(panel_results, specs)
Arguments
panel_results |
Plm object from estimation |
specs |
List with specifications |
Value
Object with robust covariance matrix
Create and returns a function to estimate hc and clustered standard errors for panel data.
Description
Create and returns a function to estimate hc and clustered standard errors for panel data.
Usage
get_robust_vcxt_panel(func_name)
Arguments
func_name |
A character. |
Value
A function.
References
Croissant, Y., Millo, G. (2017). "Robust Standard Error Estimators for Panel Models: A Unifying Approach." Journal of Statistical Software, 27(2), 1-43. doi:10.18637/jss.v082.i03.
Compute standard errors by standard OLS or Newey and West
Description
Compute standard errors by standard OLS or Newey and West (1987).
Usage
get_std_err(yy, xx, lag_nw, k, specs)
Arguments
yy |
A matrix with all endogenous variables. |
xx |
A matrix with lagged endogenous variables. |
lag_nw |
Integer. Number of lags for Newey and West |
k |
Integer. Value of column to choose from |
specs |
Value
List. First element contains the estimated standard errors, the second element contains the OLS point estimates.
Author(s)
Philipp Adämmer
Compute standard errors for 2SLS
Description
Compute 2SLS standard errors.#'
Usage
get_std_err_tsls(yy, xx, lag_nw, k, zz, specs)
Arguments
yy |
A matrix with all endogenous variables. |
xx |
A matrix with lagged endogenous variables. |
lag_nw |
Integer. Number of lags for Newey and West |
k |
Integer. Value of column to choose from |
specs |
Value
List. First element contains the estimated standard errors, the second element contains the OLS point estimates.
Author(s)
Philipp Adämmer
Compute values for lag length criteria
Description
Compute values for 'AICc', 'AIC', or 'BIC'.
Schwarz, Gideon E. (1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.
Usage
get_vals_lagcrit(y, x, lag_crit, h, k, max_lags, n_obs)
Arguments
y |
List with left (endogenous) variables. |
x |
List with right (exogenous) variables. |
lag_crit |
Integer: 'AICc'= 1, 'AIC' = 2, 'BIC' = 3. |
h |
Integer. |
k |
Integer. |
max_lags |
Integer. |
References
Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Compute values of transition function to separate regimes
Description
Computes transition values by using a smooth transition function as used in Auerbach and Gorodnichenko (2012). The time series used in the transition function can be detrended via the Hodrick-Prescott filter (see Auerbach and Gorodnichenko, 2013).
Usage
get_vals_switching(data_set, specs)
Arguments
data_set |
A numeric vector or a panel data set, depending on the model to estimate. |
specs |
Value
fz |
A numeric vector with values from the smooth transition function |
Author(s)
Philipp Adämmer
References
Auerbach, A. J., and Gorodnichenko Y. (2012). "Measuring the Output Responses to Fiscal Policy." American Economic Journal: Economic Policy, 4 (2): 1-27.
Auerbach, A. J., and Gorodnichenko Y. (2013). "Fiscal Multipliers in Recession and Expansion." NBER Working Paper Series. Nr 17447.
Computes AICc, AIC and BIC for VAR
Description
Computes AICc, AIC and BIC for VAR models.
Usage
get_var_lagcrit(endog_data, specs = NULL)
Arguments
endog_data |
A data.frame with endogenous variables for the VAR |
specs |
Value
A list with lag length criteria
References
Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Hamilton, J. D. (1994). "Time Series Analysis." Princeton: Princeton University Press.
Hurvich, C. M., and Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika, 76(2): 297–307
Lütkepohl, H. (2005). "New Introduction to Multiple Time Series Analysis.", New York: Springer.
Schwarz, Gideon E. (1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.
Decompose a times series via the Hodrick-Prescott filter
Description
Estimate cyclical and trend component with filter by Hodrick and Prescott (1997). The function is based on the function hpfilter from the archived mFilter-package.
Usage
hp_filter(x, lambda)
Arguments
x |
One column matrix with numeric values. |
lambda |
Numeric value. |
Value
A list. The first element contains the cyclical component and the second element the trend component.
Author(s)
Philipp Adämmer
References
Hodrick, R.J., and Prescott, E. C. (1997). "Postwar U.S. Business Cycles: An Empirical Investigation." Journal of Money, Credit and Banking, 29(1), 1-16.
Ravn, M.O., Uhlig, H. (2002). "On Adjusting the Hodrick-Prescott Filter for the Frequency of Observations." Review of Economics and Statistics, 84(2), 371-376.
Examples
library(lpirfs)
# Decompose the Federal Funds Rate
data_set <- as.matrix(interest_rules_var_data$FF)
hp_results <- hp_filter(data_set, 1600)
# Extract results and save as data.frame
hp_cyc <- as.data.frame(hp_results[[1]])
hp_trend <- as.data.frame(hp_results[[2]])
# Make data.frames for plots
cyc_df <- data.frame(yy = hp_cyc$V1, xx = seq(as.Date('1955-01-01'),
as.Date('2003-01-01') , "quarter"))
trend_df <- data.frame(yy = hp_trend$V1, xx = seq(as.Date('1955-01-01'),
as.Date('2003-01-01') , "quarter"))
# Make plots
library(ggplot2)
# Plot cyclical part
ggplot(data = cyc_df) +
geom_line(aes(y = yy, x = xx))
# Plot trend component
ggplot(trend_df) +
geom_line(aes(y = yy, x = xx))
Data to estimate the effects of interest rate rules for monetary policy
Description
A tibble, containing data to estimate the effects of interest rate rules for monetary policy. The data are used by Jordà (2005).
Usage
interest_rules_var_data
Format
A tibble with 193 quarterly observations (rows) and 3 variables (columns):
- GDP_gap
Percentage difference between real GDP and potential GDP (Congressional Budget Office).
- Infl
Inflation: Percentage change in the GDP, chain weighted price index at annual rate.
- FF
Federal funds rate: quarterly average of daily rates.
Sample: 1955:I - 2003:I
Source
https://www.aeaweb.org/articles?id=10.1257/0002828053828518
References
Jordà, Ò. (2005) "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Compute linear impulse responses
Description
Compute linear impulse responses with local projections by Jordà (2005).
Usage
lp_lin(
endog_data,
lags_endog_lin = NULL,
lags_criterion = NaN,
max_lags = NaN,
trend = NULL,
shock_type = NULL,
confint = NULL,
use_nw = TRUE,
nw_lag = NULL,
nw_prewhite = FALSE,
adjust_se = FALSE,
hor = NULL,
exog_data = NULL,
lags_exog = NULL,
contemp_data = NULL,
num_cores = 1
)
Arguments
endog_data |
A data.frame, containing the endogenous variables for the VAR. The Cholesky decomposition is based on the column order. |
lags_endog_lin |
NaN or integer. NaN if lag length criterion is used. Integer for number of lags for endog_data. |
lags_criterion |
NaN or character. NaN (default) means that the number of lags has to be given at lags_endog_lin. The character specifies the lag length criterion ('AICc', 'AIC' or 'BIC'). |
max_lags |
NaN or integer. Maximum number of lags if lags_criterion is given. NaN (default) otherwise. |
trend |
Integer. No trend = 0 , include trend = 1, include trend and quadratic trend = 2. |
shock_type |
Integer. Standard deviation shock = 0, unit shock = 1. |
confint |
Double. Width of confidence bands. 68% = 1; 90% = 1.65; 95% = 1.96. |
use_nw |
Boolean. Use Newey-West (1987) standard errors for impulse responses? TRUE (default) or FALSE. |
nw_lag |
Integer. Specifies the maximum lag with positive weight for the Newey-West estimator. If set to NULL (default), the lag increases with with the number of horizon. |
nw_prewhite |
Boolean. Should the estimators be pre-whitened? TRUE or FALSE (default). |
adjust_se |
Boolen. Should a finite sample adjsutment be made to the covariance matrix estimators? TRUE or FALSE (default). |
hor |
Integer. Number of horizons for impulse responses. |
exog_data |
A data.frame, containing exogenous variables for the VAR. The row length has to be the same as endog_data. Lag lengths for exogenous variables have to be given and will not be determined via a lag length criterion. |
lags_exog |
NULL or Integer. Integer for the number of lags for the exogenous data. The value cannot be 0. If you want to to include exogenous data with contemporaneous impact use contemp_data. |
contemp_data |
A data.frame, containing exogenous data with contemporaneous impact. This data will not be lagged. The row length has to be the same as endog_data. |
num_cores |
NULL or Integer. The number of cores to use for the estimation. If NULL, the function will use the maximum number of cores minus one. |
Value
A list containing:
irf_lin_mean |
A three 3D array, containing all impulse responses for all endogenous variables. The last dimension denotes the shock variable. The row in each matrix gives the responses of the ith variable, ordered as in endog_data. The columns denote the horizons. For example, if results_lin contains the list with results, results_lin$irf_lin_mean[, , 1] returns a KXH matrix, where K is the number of variables and H the number of horizons. '1' is the shock variable, corresponding to the first variable in endog_data. |
irf_lin_low |
A three 3D array containing all lower confidence bands of the responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_lin_mean. |
irf_lin_up |
A three 3D array containing all upper confidence bands of the responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_lin_mean. |
diagnostic_list |
A list OLS diagnostics. To see everything you can simply use summary() or results$diagnostic_list. The first entry the shock variable. The rows of each shown matrix then denotes the endogenous variable that reacts to the shock. |
specs |
A list with properties of endog_data for the plot function. It also contains lagged data (y_lin and x_lin) used for the irf estimations, and the selected lag lengths when an information criterion has been used. |
Author(s)
Philipp Adämmer
References
Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Hurvich, C. M., and Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika, 76(2): 297–307
Jordà, Ò. (2005). "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55: 703–708.
Schwarz, Gideon E. (1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.
See Also
https://adaemmerp.github.io/lpirfs/README_docs.html
Examples
## Example without exogenous variables
# Load package
library(lpirfs)
# Load (endogenous) data
endog_data <- interest_rules_var_data
# Estimate linear model
results_lin <- lp_lin(endog_data,
lags_endog_lin = 4,
trend = 0,
shock_type = 1,
confint = 1.96,
hor = 12)
# Show all impule responses
# Compare with Figure 5 in Jordà (2005)
plot(results_lin)
# Make individual plots
linear_plots <- plot_lin(results_lin)
# Show single plots
# * The first element of 'linear_plots' shows the response of the first
# variable (GDP_gap) to a shock in the first variable (GDP_gap).
# * The second element of 'linear_plots' shows the response of the first
# variable (GDP_gap) to a shock in the second variable (inflation).
# * ...
linear_plots[[1]]
linear_plots[[2]]
# Show diagnostics. The first element correponds to the first shock variable.
summary(results_lin)
## Example with exogenous variables ##
# Load (endogenous) data
endog_data <- interest_rules_var_data
# Create exogenous data and data with contemporaneous impact (for illustration purposes only)
exog_data <- endog_data$GDP_gap*endog_data$Infl*endog_data$FF + rnorm(dim(endog_data)[1])
contemp_data <- endog_data$GDP_gap*endog_data$Infl*endog_data$FF + rnorm(dim(endog_data)[1])
# Exogenous data has to be a data.frame
exog_data <- data.frame(xx = exog_data )
contemp_data <- data.frame(cc = contemp_data)
# Estimate linear model
results_lin <- lp_lin(endog_data,
lags_endog_lin = 4,
trend = 0,
shock_type = 1,
confint = 1.96,
hor = 12,
exog_data = exog_data,
lags_exog = 4,
contemp_data = contemp_data)
# Show all impulse responses
plot(results_lin)
# Show diagnostics. The first element correponds to the first shock variable.
summary(results_lin)
Compute linear impulse responses with identified shock and/or with 2SLS
Description
Compute linear impulse responses with identified shock and/or with 2SLS.
Usage
lp_lin_iv(
endog_data,
shock = NULL,
cumul_mult = FALSE,
instr = NULL,
use_twosls = FALSE,
instrum = NULL,
lags_endog_lin = NULL,
exog_data = NULL,
lags_exog = NULL,
contemp_data = NULL,
lags_criterion = NaN,
max_lags = NaN,
trend = NULL,
confint = NULL,
use_nw = TRUE,
nw_lag = NULL,
nw_prewhite = FALSE,
adjust_se = FALSE,
hor = NULL,
num_cores = 1
)
Arguments
endog_data |
A data.frame, containing the values of the dependent variable(s). |
shock |
A one column data.frame, including the variable to shock with. The row length has to be the same as endog_data. When use_twosls = TRUE, this variable will be approximated/regressed on the instrument variable(s) given in instrum. |
cumul_mult |
Boolean. Estimate cumulative multipliers? TRUE or FALSE (default). If TRUE, cumulative responses are estimated via:
where h = 0,..., H-1. This option is only available for lags_criterion = NaN. |
instr |
Deprecated input name. Use shock instead. See shock for details. |
use_twosls |
Boolean. Use two stage least squares? TRUE or FALSE (default). |
instrum |
A data.frame, containing the instrument(s) to use for 2SLS. This instrument will be used for the variable in shock. |
lags_endog_lin |
NaN or integer. NaN if lags are chosen by a lag length criterion. Integer for number of lags for endog_data. |
exog_data |
A data.frame, containing exogenous variables. The row length has to be the same as endog_data. Lag lengths for exogenous variables have to be given and will not be determined via a lag length criterion. |
lags_exog |
NULL or Integer. Integer for the number of lags for the exogenous data. The value cannot be 0. If you want to to include exogenous data with contemporaneous impact use 'contemp_data'. |
contemp_data |
A data.frame, containing exogenous data with contemporaneous impact. The row length has to be the same as endog_data. |
lags_criterion |
NaN or character. NaN means that the number of lags will be given at lags_endog_lin. Possible lag length criteria are 'AICc', 'AIC' or 'BIC'. Note that when use_twosls = TRUE, the lag lengths are chosen based on normal OLS regressions, without using the instruments. |
max_lags |
NaN or integer. Maximum number of lags if lags_criterion is a character denoting the lag length criterion. NaN otherwise. |
trend |
Integer. No trend = 0 , include trend = 1, include trend and quadratic trend = 2. |
confint |
Double. Width of confidence bands. 68% = 1; 90% = 1.65; 95% = 1.96. |
use_nw |
Boolean. Use Newey-West (1987) standard errors for impulse responses? TRUE (default) or FALSE. |
nw_lag |
Integer. Specifies the maximum lag with positive weight for the Newey-West estimator. If set to NULL (default), the lag increases with with the number of horizon. |
nw_prewhite |
Boolean. Should the estimators be pre-whitened? TRUE of FALSE (default). |
adjust_se |
Boolen. Should a finite sample adjsutment be made to the covariance matrix estimators? TRUE or FALSE (default). |
hor |
Integer. Number of horizons for impulse responses. |
num_cores |
NULL or Integer. The number of cores to use for the estimation. If NULL, the function will use the maximum number of cores minus one. |
Value
A list containing:
irf_lin_mean |
A matrix, containing the impulse responses. The row in each matrix denotes the response of the ith variable to the shock. The columns are the horizons. |
irf_lin_low |
A matrix, containing all lower confidence bands of the impulse responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_lin_mean. |
irf_lin_up |
A matrix, containing all upper confidence bands of the impulse responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_lin_mean. |
specs |
A list with properties of endog_data for the plot function. It also contains lagged data (y_lin and x_lin) used for the estimations of the impulse responses, and the selected lag lengths when an information criterion has been used. |
Author(s)
Philipp Adämmer
References
Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Auerbach, A. J., and Gorodnichenko, Y. (2012). "Measuring the Output Responses to Fiscal Policy." American Economic Journal: Economic Policy, 4 (2): 1-27.
Blanchard, O., and Perotti, R. (2002). “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output.” Quarterly Journal of Economics, 117(4): 1329–1368.
Hurvich, C. M., and Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika, 76(2): 297–307
Jordà, Ò. (2005). "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Jordà, Ò, Schularick, M., Taylor, A.M. (2015), "Betting the house", Journal of International Economics, 96, S2-S18.
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55: 703–708.
Ramey, V.A., and Zubairy, S. (2018). "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data." Journal of Political Economy, 126(2): 850 - 901.
Schwarz, Gideon E. (1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.
See Also
https://adaemmerp.github.io/lpirfs/README_docs.html
Examples
# This example replicates a result from the Supplementary Appendix
# by Ramey and Zubairy (2018) (RZ-18)
# Load data
ag_data <- ag_data
sample_start <- 7
sample_end <- dim(ag_data)[1]
# Endogenous data
endog_data <- ag_data[sample_start:sample_end,3:5]
# Variable to shock with. Here government spending due to
# Blanchard and Perotti (2002) framework
shock <- ag_data[sample_start:sample_end, 3]
# Estimate linear model
results_lin_iv <- lp_lin_iv(endog_data,
lags_endog_lin = 4,
shock = shock,
trend = 0,
confint = 1.96,
hor = 20)
# Show all impulse responses
plot(results_lin_iv)
# Make and save plots
iv_lin_plots <- plot_lin(results_lin_iv)
# * The first element of 'iv_lin_plots' shows the response of the first
# variable (Gov) to the shock (Gov).
# * The second element of 'iv_lin_plots' shows the response of the second
# variable (Tax) to the shock (Gov).
# * ...
# This plot replicates the left plot in the mid-panel of Figure 12 in the
# Supplementary Appendix by RZ-18.
iv_lin_plots[[1]]
# Show diagnostics. The first element shows the reaction of the first given endogenous variable.
summary(results_lin_iv)
## Add lags of the identified shock ##
# Endogenous data but now exclude government spending
endog_data <- ag_data[sample_start:sample_end, 4:5]
# Variable to shock with (government spending)
shock <- ag_data[sample_start:sample_end, 3]
# Add the shock variable to exogenous data
exog_data <- shock
# Estimate linear model with lagged shock variable
results_lin_iv <- lp_lin_iv(endog_data,
lags_endog_lin = 4,
shock = shock,
exog_data = exog_data,
lags_exog = 2,
trend = 0,
confint = 1.96,
hor = 20)
# Show all responses
plot(results_lin_iv)
# Show diagnostics. The first element shows the reaction of the first endogenous variable.
summary(results_lin_iv)
##############################################################################
##### Use 2SLS #########
##############################################################################
# Set seed
set.seed(007)
# Load data
ag_data <- ag_data
sample_start <- 7
sample_end <- dim(ag_data)[1]
# Endogenous data
endog_data <- ag_data[sample_start:sample_end,3:5]
# Variable to shock with (government spending)
shock <- ag_data[sample_start:sample_end, 3]
# Generate instrument variable that is correlated with government spending
instrum <- as.data.frame(0.9*shock$Gov + rnorm(length(shock$Gov), 0, 0.02) )
# Estimate linear model via 2SLS
results_lin_iv <- lp_lin_iv(endog_data,
lags_endog_lin = 4,
shock = shock,
instrum = instrum,
use_twosls = TRUE,
trend = 0,
confint = 1.96,
hor = 20)
# Show all responses
plot(results_lin_iv)
Compute linear impulse responses with local projections for panel data
Description
This function estimates impulse responses with local projections for panel data, either with an identified shock or by an instrument variable approach.
Usage
lp_lin_panel(
data_set = NULL,
data_sample = "Full",
endog_data = NULL,
cumul_mult = TRUE,
shock = NULL,
diff_shock = TRUE,
iv_reg = FALSE,
instrum = NULL,
panel_model = "within",
panel_effect = "individual",
robust_cov = NULL,
robust_method = NULL,
robust_type = NULL,
robust_cluster = NULL,
robust_maxlag = NULL,
use_gmm = FALSE,
gmm_model = "onestep",
gmm_effect = "twoways",
gmm_transformation = "d",
c_exog_data = NULL,
l_exog_data = NULL,
lags_exog_data = NaN,
c_fd_exog_data = NULL,
l_fd_exog_data = NULL,
lags_fd_exog_data = NaN,
confint = NULL,
hor = NULL
)
Arguments
data_set |
A data.frame, containing the panel data set. The first column has to be the variable denoting the cross section. The second column has to be the variable denoting the time section. |
data_sample |
Character or numeric. To use the full sample set value to "Full" (default). To estimate a subset, you have to provide a sequence of dates. This sequence has to be in the same format as the second column (time-section). |
endog_data |
Character. The column name of the endogenous variable. You can only provide one endogenous variable at a time. |
cumul_mult |
Boolean. Estimate cumulative multipliers? TRUE (default) or FALSE. If TRUE, cumulative responses are estimated via:
where h = 0,..., H-1. |
shock |
Character. The column name of the variable to shock with. |
diff_shock |
Boolean. Take first differences of the shock variable? TRUE (default) or FALSE. Note that when using this option both shock and instrument are used in first differences |
iv_reg |
Boolean. Use instrument variable approach? TRUE or FALSE. |
instrum |
NULL or Character. The name(s) of the instrument variable(s) if iv_reg = TRUE. |
panel_model |
Character. Type of panel model. The default is "within" (fixed effects). Other options are "random", "ht", "between", "pooling" or "fd". See vignette of the plm package for details. |
panel_effect |
Character. The effects introduced in the model. Options are "individual" (default), "time", "twoways", or "nested". See the vignette of the plm-package for details. |
robust_cov |
NULL or Character. The character specifies the method how to estimate robust standard errors: Options are "vcovBK", "vcovDC", "vcovG", "vcovHC", "vcovNW", "vcovSCC". For these options see vignette of plm package. Another option is "Vcxt". For details see Miller (2017) If "use_gmm = TRUE", this option has to be NULL. |
robust_method |
NULL (default) or Character. The character is an option when robust_cov = "vcovHC". See vignette of the plm package for details. |
robust_type |
NULL (default) or Character. The character is an option when robust_cov = "vcovBK", "vcovDC", "vcovHC", "vcovNW" or "vcovSCC". See vignette of the plm package for details. |
robust_cluster |
NULL (default) or Character. The character is an option when robust_cov = "vcovBK", "vcovG" or "vcovHC". See vignette of the plm package for details. |
robust_maxlag |
NULL (default) or Character. The character is an option when robust_cov = "vcovNW" or "vcovSCC". See vignette of the plm package for details. |
use_gmm |
Boolean. Use GMM for estimation? TRUE or FALSE (default). See vignette of plm package for details. If TRUE, the option "robust_cov" has to be set to NULL. |
gmm_model |
Character. Either "onestep" (default) or "twosteps". See vignette of the plm package for details. |
gmm_effect |
Character. The effects introduced in the model: "twoways" (default) or "individual". See vignette of the plm-package for details. |
gmm_transformation |
Character. Either "d" (default) for the "difference GMM" model or "ld" for the "system GMM". See vignette of the plm package for details. |
c_exog_data |
NULL or Character. Name(s) of the exogenous variable(s) with contemporaneous impact. |
l_exog_data |
NULL or Character. Name(s) of the exogenous variable(s) with lagged impact. |
lags_exog_data |
Integer. Lag length for the exogenous variable(s) with lagged impact. |
c_fd_exog_data |
NULL or Character. Name(s) of the exogenous variable(s) with contemporaneous impact of first differences. |
l_fd_exog_data |
NULL or Character. Name(s) of exogenous variable(s) with lagged impact of first differences. |
lags_fd_exog_data |
NaN or Integer. Number of lags for variable(s) with impact of first differences. |
confint |
Double. Width of confidence bands. 68% = 1; 90% = 1.65; 95% = 1.96. |
hor |
Integer. Number of horizons for impulse responses. |
Value
A list containing:
irf_lin_mean |
A matrix, containing the impulse responses. The columns are the horizons. |
irf_lin_low |
A matrix, containing all lower confidence bands. The columns are the horizons. |
irf_lin_up |
A matrix, containing all upper confidence bands. The columns are the horizons. |
reg_outputs |
Full regression output (plm object) for each horizon. |
reg_summaries |
Summary of regression output for each horizon. In case of robust covariance estimators, this only includes the t-tests. |
xy_data_sets |
Data sets with endogenous and exogenous variables for each horizon. |
specs |
A list with data properties for e.g. the plot function. |
Author(s)
Philipp Adämmer
References
Croissant, Y., Millo, G. (2008). "Panel Data Econometrics in R: The plm Package." Journal of Statistical Software, 27(2), 1-43. doi: 10.18637/jss.v027.i02.
Jordà, Ò. (2005). "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Jordà, Ò., Schualrick, M., Taylor, A.M. (2018). "Large and State-Dependent Effects of Quasi-Random Monetary Experiments", NBER working paper 23074, FRBSF working paper 2017-02.
Millo G (2017). “Robust Standard Error Estimators for Panel Models: A Unifying Approach.” Journal of Statistical Software, 82(3), 1-27. doi: 10.18637/jss.v082.i03.
Examples
#--- Info
# This example is based on a STATA code that has been provided on
# Òscar Jordà's website (https://sites.google.com/site/oscarjorda/home/local-projections)
# It estimates impulse reponses of the ratio of (mortgage lending/GDP) to a
# +1% change in the short term interest rate
#--- Get data
# Go to the website of the 'The MacroFinance and MacroHistory Lab'
# Download the Excel-Sheet of the 'Jordà-Schularick-Taylor Macrohistory Database':
# URL: https://www.macrohistory.net/database/
# Then uncomment and run the code below...
#--- Code
## Load libraries to download and read excel file from the website
# library(lpirfs)
# library(readxl)
# library(dplyr)
#
# Load JST Macrohistory Database
# jst_data <- read_excel("JSTdatasetR5.xlsx", sheet = "Data")
#
## Choose years <= 2013. Swap the first two columns so that 'country' is the
## first (cross section) and 'year' the second (time section) column
# jst_data <- jst_data %>%
# dplyr::filter(year <= 2013) %>%
# dplyr::select(country, year, everything())
#
## Prepare variables
# data_set <- jst_data %>%
# mutate(stir = stir) %>%
# mutate(mortgdp = 100*(tmort/gdp)) %>%
# mutate(hpreal = hpnom/cpi) %>%
# group_by(country) %>%
# mutate(hpreal = hpreal/hpreal[year==1990][1]) %>%
# mutate(lhpreal = log(hpreal)) %>%
#
# mutate(lhpy = lhpreal - log(rgdppc)) %>%
# mutate(lhpy = lhpy - lhpy[year == 1990][1]) %>%
# mutate(lhpreal = 100*lhpreal) %>%
# mutate(lhpy = 100*lhpy) %>%
# ungroup() %>%
#
# mutate(lrgdp = 100*log(rgdppc)) %>%
# mutate(lcpi = 100*log(cpi)) %>%
# mutate(lriy = 100*log(iy*rgdppc)) %>%
# mutate(cay = 100*(ca/gdp)) %>%
# mutate(tnmort = tloans - tmort) %>%
# mutate(nmortgdp = 100*(tnmort/gdp)) %>%
# dplyr::select(country, year, mortgdp, stir, ltrate,
# lhpy, lrgdp, lcpi, lriy, cay, nmortgdp)
#
#
## Use data from 1870 to 2013 and exclude observations during WWI and WWII
# data_sample <- seq(1870, 2013)[!(seq(1870, 2016) %in%
# c(seq(1914, 1918), seq(1939, 1947)))]
#
## Estimate panel model
# results_panel <- lp_lin_panel(data_set = data_set,
# data_sample = data_sample,
# endog_data = "mortgdp",
# cumul_mult = TRUE,
#
# shock = "stir",
# diff_shock = TRUE,
# panel_model = "within",
# panel_effect = "individual",
# robust_cov = "vcovSCC",
#
# c_exog_data = "cay",
# l_exog_data = "cay",
# lags_exog_data = 2,
# c_fd_exog_data = colnames(data_set)[c(seq(4,9),11)],
# l_fd_exog_data = colnames(data_set)[c(seq(3,9),11)],
# lags_fd_exog_data = 2,
#
# confint = 1.67,
# hor = 5)
#
## Plot irfs
# plot(results_panel)
#
#
## Simulate and add instrument to data_set
# set.seed(123)
# data_set <- data_set %>%
# group_by(country) %>%
# mutate(instrument = 0.8*stir + rnorm(length(stir), 0, sd(na.omit(stir))/10)) %>%
# ungroup()
#
#
## Estimate panel model with iv approach
# results_panel <- lp_lin_panel(data_set = data_set,
# data_sample = data_sample,
# endog_data = "mortgdp",
# cumul_mult = TRUE,
#
# shock = "stir",
# diff_shock = TRUE,
# iv_reg = TRUE,
# instrum = "instrument",
# panel_model = "within",
# panel_effect = "individual",
# robust_cov = "vcovSCC",
#
# c_exog_data = "cay",
# l_exog_data = "cay",
# lags_exog_data = 2,
# c_fd_exog_data = colnames(data_set)[c(seq(4,9),11)],
# l_fd_exog_data = colnames(data_set)[c(seq(3,9),11)],
# lags_fd_exog_data = 2,
#
# confint = 1.67,
# hor = 5)
#
## Create and plot irfs
# plot(results_panel)
#
#
##############################################################################
### Use GMM ###
##############################################################################
#
#
## Use a much smaller sample to have fewer T than N
# data_sample <- seq(2000, 2012)
#
## Estimate panel model with gmm
## This example (please uncomment) gives a warning at each iteration.
## The data set is not well suited for GMM as GMM is based on N-asymptotics
## and the data set only contains 27 countries
#
# results_panel <- lp_lin_panel(data_set = data_set,
# data_sample = data_sample,
# endog_data = "mortgdp",
# cumul_mult = TRUE,
#
# shock = "stir",
# diff_shock = TRUE,
#
# use_gmm = TRUE,
# gmm_model = "onestep",
# gmm_effect = "twoways",
# gmm_transformation = "ld",
#
# l_exog_data = "mortgdp",
# lags_exog_data = 2,
# l_fd_exog_data = colnames(data_set)[c(4, 6)],
# lags_fd_exog_data = 1,
#
# confint = 1.67,
# hor = 5)
#
# Create and plot irfs
# plot(results_panel)
#
Compute nonlinear impulse responses
Description
Compute nonlinear impulse responses with local projections by Jordà (2005). The data can be separated into two states by a smooth transition function as applied in Auerbach and Gorodnichenko (2012), or by a simple dummy approach.
Usage
lp_nl(
endog_data,
lags_endog_lin = NULL,
lags_endog_nl = NULL,
lags_criterion = NaN,
max_lags = NaN,
trend = NULL,
shock_type = NULL,
confint = NULL,
use_nw = TRUE,
nw_lag = NULL,
nw_prewhite = FALSE,
adjust_se = FALSE,
hor = NULL,
switching = NULL,
lag_switching = TRUE,
use_logistic = TRUE,
use_hp = NULL,
lambda = NULL,
gamma = NULL,
exog_data = NULL,
lags_exog = NULL,
contemp_data = NULL,
num_cores = 1
)
Arguments
endog_data |
A data.frame, containing all endogenous variables for the VAR. The Cholesky decomposition is based on the column order. |
lags_endog_lin |
NaN or integer. NaN if lag length criterion is used. Integer for number of lags for linear VAR to identify shock. |
lags_endog_nl |
NaN or integer. Number of lags for nonlinear VAR. NaN if lag length criterion is given. |
lags_criterion |
NaN or character. NaN (default) means that the number of lags will be given at lags_endog_nl and lags_endog_lin. The lag length criteria are 'AICc', 'AIC' and 'BIC'. |
max_lags |
NaN or integer. Maximum number of lags (if lags_criterion = 'AICc', 'AIC', 'BIC'). NaN (default) otherwise. |
trend |
Integer. Include no trend = 0 , include trend = 1, include trend and quadratic trend = 2. |
shock_type |
Integer. Standard deviation shock = 0, unit shock = 1. |
confint |
Double. Width of confidence bands. 68% = 1; 90% = 1.65; 95% = 1.96. |
use_nw |
Boolean. Use Newey-West (1987) standard errors for impulse responses? TRUE (default) or FALSE. |
nw_lag |
Integer. Specifies the maximum lag with positive weight for the Newey-West estimator. If set to NULL (default), the lag increases with with the number of horizon. |
nw_prewhite |
Boolean. Should the estimators be pre-whitened? TRUE of FALSE (default). |
adjust_se |
Boolen. Should a finite sample adjsutment be made to the covariance matrix estimators? TRUE or FALSE (default). |
hor |
Integer. Number of horizons for impulse responses. |
switching |
Numeric vector. A column vector with the same length as endog_data. If 'use_logistic = TRUE', this series can either be decomposed via the Hodrick-Prescott filter (see Auerbach and Gorodnichenko, 2013) or directly plugged into the following logistic function:
Important: |
lag_switching |
Boolean. Use the first lag of the values of the transition function? TRUE (default) or FALSE. |
use_logistic |
Boolean. Use logistic function to separate states? TRUE (default) or FALSE. If FALSE, the values of the switching variable have to be binary (0/1). |
use_hp |
Boolean. Use HP-filter? TRUE or FALSE. |
lambda |
Double. Value of |
gamma |
Double. Positive number which is used in the transition function. |
exog_data |
A data.frame, containing exogenous variables for the VAR. The row length has to be the same as endog_data. Lag lengths for exogenous variables have to be given and will not be determined via a lag length criterion. |
lags_exog |
NULL or Integer. Integer for the number of lags for the exogenous data. The value cannot be 0. If you want to to include exogenous data with contemporaneous impact use contemp_data. |
contemp_data |
A data.frame, containing exogenous data with contemporaneous impact. This data will not be lagged. The row length has to be the same as endog_data. |
num_cores |
Integer. The number of cores to use for the estimation. If NULL, the function will use the maximum number of cores minus one. |
Value
A list containing:
irf_s1_mean |
A three-dimensional |
irf_s1_low |
A three-dimensional |
irf_s1_up |
A three-dimensional |
irf_s2_mean |
A three-dimensional |
irf_s2_low |
A three-dimensional |
irf_s2_up |
A three-dimensional |
specs |
A list with properties of endog_data for the plot function. It also contains lagged data (y_nl and x_nl) used for the IRF estimations, and the selected lag lengths when an information criterion has been used. |
fz |
A vector containing the values of the transition function |
Author(s)
Philipp Adämmer
References
Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Auerbach, A. J., and Gorodnichenko Y. (2012). "Measuring the Output Responses to Fiscal Policy." American Economic Journal: Economic Policy, 4 (2): 1-27.
Auerbach, A. J., and Gorodnichenko Y. (2013). "Fiscal Multipliers in Recession and Expansion." NBER Working Paper Series. Nr. 17447.
Hurvich, C. M., and Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika, 76(2): 297–307
Jordà, Ò. (2005) "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703–708.
Schwarz, Gideon E. (1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.
Ravn, M.O., Uhlig, H. (2002). "On Adjusting the Hodrick-Prescott Filter for the Frequency of Observations." Review of Economics and Statistics, 84(2), 371-376.
See Also
https://adaemmerp.github.io/lpirfs/README_docs.html
Examples
## Example without exogenous variables ##
# Load package
library(lpirfs)
library(gridExtra)
library(ggpubr)
# Load (endogenous) data
endog_data <- interest_rules_var_data
# Choose data for switching variable (here Federal Funds Rate)
# Important: The switching variable does not have to be used within the VAR!
switching_data <- endog_data$Infl
# Estimate model and save results
results_nl <- lp_nl(endog_data,
lags_endog_lin = 4,
lags_endog_nl = 3,
trend = 0,
shock_type = 1,
confint = 1.96,
hor = 24,
switching = switching_data,
use_hp = TRUE,
lambda = 1600,
gamma = 3)
# Show all plots
plot(results_nl)
# Make and save all plots
nl_plots <- plot_nl(results_nl)
# Save plots based on states
s1_plots <- sapply(nl_plots$gg_s1, ggplotGrob)
s2_plots <- sapply(nl_plots$gg_s2, ggplotGrob)
# Show first irf of each state
plot(s1_plots[[1]])
plot(s2_plots[[1]])
# Show diagnostics. The first element correponds to the first shock variable.
summary(results_nl)
## Example with exogenous variables ##
# Load (endogenous) data
endog_data <- interest_rules_var_data
# Choose data for switching variable (here Federal Funds Rate)
# Important: The switching variable does not have to be used within the VAR!
switching_data <- endog_data$FF
# Create exogenous data and data with contemporaneous impact (for illustration purposes only)
exog_data <- endog_data$GDP_gap*endog_data$Infl*endog_data$FF + rnorm(dim(endog_data)[1])
contemp_data <- endog_data$GDP_gap*endog_data$Infl*endog_data$FF + rnorm(dim(endog_data)[1])
# Exogenous data has to be a data.frame
exog_data <- data.frame(xx = exog_data)
contemp_data <- data.frame(cc = contemp_data)
# Estimate model and save results
results_nl <- lp_nl(endog_data,
lags_endog_lin = 4,
lags_endog_nl = 3,
trend = 0,
shock_type = 1,
confint = 1.96,
hor = 24,
switching = switching_data,
use_hp = TRUE,
lambda = 1600, # Ravn and Uhlig (2002):
# Anuual data = 6.25
# Quarterly data = 1600
# Monthly data = 129 600
gamma = 3,
exog_data = exog_data,
lags_exog = 3)
# Show all plots
plot(results_nl)
# Show diagnostics. The first element correponds to the first shock variable.
summary(results_nl)
Compute nonlinear impulse responses with identified shock
Description
Compute nonlinear impulse responses with local projections and identified shock. The data can be separated into two states by a smooth transition function as applied in Auerbach and Gorodnichenko (2012), or by a simple dummy approach.
Usage
lp_nl_iv(
endog_data,
lags_endog_nl = NULL,
shock = NULL,
cumul_mult = FALSE,
instr = NULL,
exog_data = NULL,
lags_exog = NULL,
contemp_data = NULL,
lags_criterion = NaN,
max_lags = NaN,
trend = NULL,
confint = NULL,
use_nw = TRUE,
nw_lag = NULL,
nw_prewhite = FALSE,
adjust_se = FALSE,
hor = NULL,
switching = NULL,
lag_switching = TRUE,
use_logistic = TRUE,
use_hp = NULL,
lambda = NULL,
gamma = NULL,
num_cores = 1
)
Arguments
endog_data |
A data.frame, containing all endogenous variables for the VAR. |
lags_endog_nl |
NaN or integer. NaN if lags are chosen by a lag length criterion. Integer for number of lags for endog_data. |
shock |
One column data.frame, including the instrument to shock with. The row length has to be the same as endog_data. |
cumul_mult |
Boolean. Estimate cumulative multipliers? TRUE or FALSE (default). If TRUE, cumulative responses are estimated via:
where h = 0,..., H-1. This option is only available for lags_criterion = NaN. |
instr |
Deprecated input name. Use shock instead. See shock for details. |
exog_data |
A data.frame, containing exogenous variables. The row length has to be the same as endog_data. Lag lengths for exogenous variables have to be given and will not be determined via a lag length criterion. |
lags_exog |
NULL or Integer. Integer for the number of lags for the exogenous data. The value cannot be 0. If you want to to include exogenous data with contemporaneous impact use contemp_data. |
contemp_data |
A data.frame, containing exogenous data with contemporaneous impact. This data will not be lagged. The row length has to be the same as endog_data. |
lags_criterion |
NaN or character. NaN means that the number of lags will be given at lags_endog_nl. Possible lag length criteria are 'AICc', 'AIC' or 'BIC'. |
max_lags |
NaN or integer. Maximum number of lags (if lags_criterion = 'AICc', 'AIC', 'BIC'). NaN otherwise. |
trend |
Integer. Include no trend = 0 , include trend = 1, include trend and quadratic trend = 2. |
confint |
Double. Width of confidence bands. 68% = 1; 90% = 1.65; 95% = 1.96. |
use_nw |
Boolean. Use Newey-West (1987) standard errors for impulse responses? TRUE (default) or FALSE. |
nw_lag |
Integer. Specifies the maximum lag with positive weight for the Newey-West estimator. If set to NULL (default), the lag increases with with the number of horizon. |
nw_prewhite |
Boolean. Should the estimators be pre-whitened? TRUE of FALSE (default). |
adjust_se |
Boolen. Should a finite sample adjsutment be made to the covariance matrix estimators? TRUE or FALSE (default). |
hor |
Integer. Number of horizons for impulse responses. |
switching |
Numeric vector. A column vector with the same length as endog_data. This series can either be decomposed via the Hodrick-Prescott filter (see Auerbach and Gorodnichenko, 2013) or directly plugged into the following smooth transition function:
Warning: |
lag_switching |
Boolean. Use the first lag of the values of the transition function? TRUE (default) or FALSE. |
use_logistic |
Boolean. Use logistic function to separate states? TRUE (default) or FALSE. If FALSE, the values of the switching variable have to be binary (0/1). |
use_hp |
Boolean. Use HP-filter? TRUE or FALSE. |
lambda |
Double. Value of |
gamma |
Double. Positive number which is used in the transition function. |
num_cores |
Integer. The number of cores to use for the estimation. If NULL, the function will use the maximum number of cores minus one. |
Value
A list containing:
irf_s1_mean |
A matrix, containing the impulse responses of the first regime. The row in each matrix denotes the responses of the ith variable to the shock. The columns are the horizons. |
irf_s1_low |
A matrix, containing all lower confidence bands of the impulse responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_s1_mean. |
irf_s1_up |
A matrix, containing all upper confidence bands of the impulse responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_s1_mean. |
irf_s2_mean |
A matrix, containing all impulse responses for the second regime. The row in each matrix denotes the responses of the ith variable to the shock. The columns denote the horizon. |
irf_s2_low |
A matrix, containing all lower confidence bands of the responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_s2_mean. |
irf_s2_up |
A matrix, containing all upper confidence bands of the responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_s2_mean. |
specs |
A list with properties of endog_data for the plot function. It also contains lagged data (y_nl and x_nl) used for the estimations of the impulse responses, and the selected lag lengths when an information criterion has been used. |
fz |
A vector, containing the values of the transition function |
Author(s)
Philipp Adämmer
References
Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Auerbach, A. J., and Gorodnichenko Y. (2012). "Measuring the Output Responses to Fiscal Policy." American Economic Journal: Economic Policy, 4 (2): 1-27.
Auerbach, A. J., and Gorodnichenko Y. (2013). "Fiscal Multipliers in Recession and Expansion." NBER Working Paper Series. Nr 17447.
Blanchard, O., and Perotti, R. (2002). “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output.” Quarterly Journal of Economics, 117(4): 1329–1368.
Hurvich, C. M., and Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika, 76(2): 297–307
Jordà, Ò. (2005) "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Jordà, Ò, Schularick, M., Taylor, A.M. (2015), "Betting the house", Journal of International Economics, 96, S2-S18.
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703–708.
Ramey, V.A., and Zubairy, S. (2018). "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data." Journal of Political Economy, 126(2): 850 - 901.
Schwarz, Gideon E. (1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.
See Also
https://adaemmerp.github.io/lpirfs/README_docs.html
Examples
# This example replicates results from the Supplementary Appendix
# by Ramey and Zubairy (2018) (RZ-18).
# Load and prepare data
ag_data <- ag_data
sample_start <- 7
sample_end <- dim(ag_data)[1]
endog_data <- ag_data[sample_start:sample_end, 3:5]
# The shock is estimated by RZ-18
shock <- ag_data[sample_start:sample_end, 7]
# Include four lags of the 7-quarter moving average growth rate of GDP
# as exogenous variables (see RZ-18)
exog_data <- ag_data[sample_start:sample_end, 6]
# Use the 7-quarter moving average growth rate of GDP as switching variable
# and adjust it to have suffiently long recession periods.
switching_variable <- ag_data$GDP_MA[sample_start:sample_end] - 0.8
# Estimate local projections
results_nl_iv <- lp_nl_iv(endog_data,
lags_endog_nl = 3,
shock = shock,
exog_data = exog_data,
lags_exog = 4,
trend = 0,
confint = 1.96,
hor = 20,
switching = switching_variable,
use_hp = FALSE,
gamma = 3)
# Show all impulse responses
plot(results_nl_iv)
# Make and save individual plots
plots_nl_iv <- plot_nl(results_nl_iv)
# Show single impulse responses
# Compare with red line of left plot (lower panel) in Figure 12 in Supplementary Appendix of RZ-18.
plot(plots_nl_iv$gg_s1[[1]])
# Compare with blue line of left plot (lower panel) in Figure 12 in Supplementary Appendix of RZ-18.
plot(plots_nl_iv$gg_s2[[1]])
# Show diagnostics. The first element shows the reaction of the first endogenous variable.
summary(results_nl_iv)
Compute nonlinear impulse responses for panel data
Description
This function estimates nonlinear impulse responses by using local projections for panel data with an identified shock. The data can be separated into two states by a smooth transition function as applied in Auerbach and Gorodnichenko (2012), or by a simple dummy approach.
Usage
lp_nl_panel(
data_set = NULL,
data_sample = "Full",
endog_data = NULL,
cumul_mult = TRUE,
shock = NULL,
diff_shock = TRUE,
panel_model = "within",
panel_effect = "individual",
robust_cov = NULL,
robust_method = NULL,
robust_type = NULL,
robust_cluster = NULL,
robust_maxlag = NULL,
use_gmm = FALSE,
gmm_model = "onestep",
gmm_effect = "twoways",
gmm_transformation = "d",
c_exog_data = NULL,
l_exog_data = NULL,
lags_exog_data = NaN,
c_fd_exog_data = NULL,
l_fd_exog_data = NULL,
lags_fd_exog_data = NaN,
switching = NULL,
use_logistic = TRUE,
use_hp = FALSE,
lag_switching = TRUE,
lambda = NULL,
gamma = NULL,
confint = NULL,
hor = NULL
)
Arguments
data_set |
A data.frame, containing the panel data set. The first column has to be the variable denoting the cross section. The second column has to be the variable denoting the time section. |
data_sample |
Character or numeric. To use the full sample set value to "Full" (default). To estimate a subset, you have to provide a sequence of dates. This sequence has to be in the same format as the second column (time-section). |
endog_data |
Character. The column name of the endogenous variable. You can only provide one endogenous variable at a time. |
cumul_mult |
Boolean. Estimate cumulative multipliers? TRUE (default) or FALSE. If TRUE, cumulative responses are estimated via:
where h = 0,..., H-1. |
shock |
Character. The column name of the variable to shock with. |
diff_shock |
Boolean. Take first differences of the shock variable? TRUE (default) or FALSE. Note that when using this option both shock and instrument are used in first differences |
panel_model |
Character. Type of panel model. The default is "within" (fixed effects). Other options are "random", "ht", "between", "pooling" or "fd". See vignette of the plm package for details. |
panel_effect |
Character. The effects introduced in the model. Options are "individual" (default), "time", "twoways", or "nested". See the vignette of the plm-package for details. |
robust_cov |
NULL or Character. The character specifies the method how to estimate robust standard errors: Options are "vcovBK", "vcovDC", "vcovG", "vcovHC", "vcovNW", "vcovSCC". For these options see vignette of plm package. Another option is "Vcxt". For details see Miller (2017) If "use_gmm = TRUE", this option has to be NULL. |
robust_method |
NULL (default) or Character. The character is an option when robust_cov = "vcovHC". See vignette of the plm package for details. |
robust_type |
NULL (default) or Character. The character is an option when robust_cov = "vcovBK", "vcovDC", "vcovHC", "vcovNW" or "vcovSCC". See vignette of the plm package for details. |
robust_cluster |
NULL (default) or Character. The character is an option when robust_cov = "vcovBK", "vcovG" or "vcovHC". See vignette of the plm package for details. |
robust_maxlag |
NULL (default) or Character. The character is an option when robust_cov = "vcovNW" or "vcovSCC". See vignette of the plm package for details. |
use_gmm |
Boolean. Use GMM for estimation? TRUE or FALSE (default). See vignette of plm package for details. If TRUE, the option "robust_cov" has to be set to NULL. |
gmm_model |
Character. Either "onestep" (default) or "twosteps". See vignette of the plm package for details. |
gmm_effect |
Character. The effects introduced in the model: "twoways" (default) or "individual". See vignette of the plm-package for details. |
gmm_transformation |
Character. Either "d" (default) for the "difference GMM" model or "ld" for the "system GMM". See vignette of the plm package for details. |
c_exog_data |
NULL or Character. Name(s) of the exogenous variable(s) with contemporaneous impact. |
l_exog_data |
NULL or Character. Name(s) of the exogenous variable(s) with lagged impact. |
lags_exog_data |
Integer. Lag length for the exogenous variable(s) with lagged impact. |
c_fd_exog_data |
NULL or Character. Name(s) of the exogenous variable(s) with contemporaneous impact of first differences. |
l_fd_exog_data |
NULL or Character. Name(s) of exogenous variable(s) with lagged impact of first differences. |
lags_fd_exog_data |
NaN or Integer. Number of lags for variable(s) with impact of first differences. |
switching |
Character. Column name of the switching variable. If "use_logistic = TRUE", this series can either be decomposed by the Hodrick-Prescott filter (see Auerbach and Gorodnichenko, 2013) or directly plugged into the following smooth transition function:
The data for the two regimes are lagged by default: |
use_logistic |
Boolean. Use logistic function to separate states? TRUE (default) or FALSE. If FALSE, the values of the switching variable have to be binary (0/1). |
use_hp |
Boolean. Use HP-filter? TRUE or FALSE (default). |
lag_switching |
Boolean. Use the first lag of the values of the transition function? TRUE (default) or FALSE. |
lambda |
Double. Value of |
gamma |
Double. Positive value for |
confint |
Double. Width of confidence bands. 68% = 1; 90% = 1.65; 95% = 1.96. |
hor |
Integer. Number of horizons for impulse responses. |
Value
A list containing:
irf_lin_mean |
A matrix, containing the impulse responses. The columns are the horizons. |
irf_lin_low |
A matrix, containing all lower confidence bands. The columns are the horizons. |
irf_lin_up |
A matrix, containing all upper confidence bands. The columns are the horizons. |
reg_outputs |
Full regression output (plm object) for each horizon. |
reg_summaries |
Summary of regression output for each horizon. In case of robust covariance estimators, this only includes the t-tests. |
xy_data_sets |
Data sets with endogenous and exogenous variables for each horizon. |
specs |
A list with data properties for e.g. the plot function. |
Author(s)
Philipp Adämmer
References
Croissant, Y., Millo, G. (2008). “Panel Data Econometrics in R: The plm Package.” Journal of Statistical Software, 27(2), 1-43. doi: 10.18637/jss.v027.i02.
Jordà, Ò. (2005). "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Jordà, Ò., Schualrick, M., Taylor, A.M. (2018). "Large and State-Dependent Effects of Quasi-Random Monetary Experiments", NBER working paper 23074, FRBSF working paper 2017-02.
Millo, G. (2017). “Robust Standard Error Estimators for Panel Models: A Unifying Approach.” Journal of Statistical Software, 82(3), 1-27. doi: 10.18637/jss.v082.i03.
Examples
#--- Info
# This example is based on a STATA code that has been provided on
# Òscar Jordà's website (https://sites.google.com/site/oscarjorda/home/local-projections)
# It estimates impulse reponses of the ratio of (mortgage lending/GDP) to a
# +1% change in the short term interest rate
#--- Get data
# Go to the website of the 'The MacroFinance and MacroHistory Lab'
# Download the Excel-Sheet of the 'Jordà-Schularick-Taylor Macrohistory Database':
# URL: https://www.macrohistory.net/database/
# Then uncomment and run the code below...
#--- Code
## Load libraries to download and read excel file from the website
# library(lpirfs)
# library(readxl)
# library(dplyr)
#
# Load JST Macrohistory Database
# jst_data <- read_excel("JSTdatasetR5.xlsx", sheet = "Data")
#
## Choose years <= 2013. Swap the first two columns so that 'country' is the
## first (cross section) and 'year' the second (time section) column
# jst_data <- jst_data %>%
# dplyr::filter(year <= 2013) %>%
# dplyr::select(country, year, everything())
#
## Prepare variables. This is based on the 'data.do' file
# data_set <- jst_data %>%
# mutate(stir = stir) %>%
# mutate(mortgdp = 100*(tmort/gdp)) %>%
# mutate(hpreal = hpnom/cpi) %>%
# group_by(country) %>%
# mutate(hpreal = hpreal/hpreal[year==1990][1]) %>%
# mutate(lhpreal = log(hpreal)) %>%
#
# mutate(lhpy = lhpreal - log(rgdppc)) %>%
# mutate(lhpy = lhpy - lhpy[year == 1990][1]) %>%
# mutate(lhpreal = 100*lhpreal) %>%
# mutate(lhpy = 100*lhpy) %>%
# ungroup() %>%
#
# mutate(lrgdp = 100*log(rgdppc)) %>%
# mutate(lcpi = 100*log(cpi)) %>%
# mutate(lriy = 100*log(iy*rgdppc)) %>%
# mutate(cay = 100*(ca/gdp)) %>%
# mutate(tnmort = tloans - tmort) %>%
# mutate(nmortgdp = 100*(tnmort/gdp)) %>%
# dplyr::select(country, year, mortgdp, stir, ltrate, lhpy,
# lrgdp, lcpi, lriy, cay, nmortgdp)
#
#
## Use data_sample from 1870 to 2013 and exclude observations from WWI and WWII
# data_sample <- seq(1870, 2016)[!(seq(1870, 2016) %in%
# c(seq(1914, 1918),
# seq(1939, 1947)))]
#
## Estimate panel model
# results_panel <- lp_nl_panel(data_set = data_set,
# data_sample = data_sample,
# endog_data = "mortgdp",
# cumul_mult = TRUE,
#
# shock = "stir",
# diff_shock = TRUE,
# panel_model = "within",
# panel_effect = "individual",
# robust_cov = "vcovSCC",
#
# switching = "lrgdp",
# lag_switching = TRUE,
# use_hp = TRUE,
# lambda = 6.25,
# gamma = 10,
#
# c_exog_data = "cay",
# c_fd_exog_data = colnames(data_set)[c(seq(4,9),11)],
# l_fd_exog_data = colnames(data_set)[c(seq(3,9),11)],
# lags_fd_exog_data = 2,
#
# confint = 1.67,
# hor = 5)
#
## Plot irfs
# plot(results_panel)
#
#
## Plot values of the transition function for USA between 1950 and 2016
# library(ggplot2)
#
# data_set %>%
# mutate(fz = results_panel$fz$fz) %>%
# select(country, year, fz) %>%
# filter(country == "USA" & year > 1950 & year <= 2016) %>%
# ggplot()+
# geom_line(aes(x = year, y = fz)) +
# scale_x_continuous(breaks = seq(1950, 2016, 5))
#
#
##############################################################################
### Use GMM ###
##############################################################################
#
## Use a much smaller sample to have fewer T than N
# data_sample <- seq(2000, 2012)
#
#
## Estimate panel model with gmm
## This example (please uncomment) gives a warning at each iteration.
## The data set is not well suited for
## GMM as GMM is based on N-asymptotics and the data set only contains 27 countries
#
# results_panel <- lp_nl_panel(data_set = data_set,
# data_sample = data_sample,
# endog_data = "mortgdp",
# cumul_mult = TRUE,
#
# shock = "stir",
# diff_shock = TRUE,
#
# use_gmm = TRUE,
# gmm_model = "onestep",
# gmm_effect = "twoways",
# gmm_transformation = "ld",
#
# switching = "lrgdp",
# lag_switching = TRUE,
# use_hp = TRUE,
# lambda = 6.25,
# gamma = 10,
#
# l_exog_data = "mortgdp",
# lags_exog_data = 1,
#
# confint = 1.67,
# hor = 5)
#
## Create and plot irfs
# plot(results_panel)
Base methods for lpirfs_obj objects
Description
Base methods for lpirfs_obj objects
Data to estimate a standard monetary VAR
Description
A tibble, containing data to estimate a standard monetary VAR.
Usage
monetary_var_data
Format
A tibble with 494 monthly observations (rows) and 6 variables (columns):
- EM
Log of non-agricultural payroll employment.
- P
Log of personal consumption expenditures deflator (1996 = 100).
- POCM
Annual growth rate of the index of sensitive materials prices issued by the Conference Board.
- FF
Federal funds rate.
- NBRX
Ratio of nonborrowed reserves plus extended credit to total reserves.
- M2
Annual growth rate of M2 stock.
Sample: 1960:01 - 2001:02.
Source
https://www.aeaweb.org/articles?id=10.1257/0002828053828518
References
Jordà, Ò. (2005) "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review, 95 (1): 161-182.
Compute OLS parameters and robust standard errors based on Newey-West estimator
Description
Compute OLS parameters and robust standard errors based on Newey and West (1987). The function is based on the Matlab code by James P. LeSage.
Usage
newey_west(y, x, h)
Arguments
y |
Numeric vector. |
x |
Numeric matrix. |
h |
Integer. |
Value
A list. The first element contains the estimated OLS parameters, the second element the Newey West covariance matrix, the third element the estimated functions, the fourth element the unscaled covariance matrix and the last element the meat estimator.
References
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703–708.
Compute Newey-West estimator with prewhitened estimation functions
Description
Compute Newey-West estimator with prewhitened estimation functions. The function is based on the Matlab code by James P. LeSage.
Usage
newey_west_pw(hhat_mat, xpxi_mat, D_mat, h)
Arguments
hhat_mat |
Matrix. |
xpxi_mat |
Matrix. |
D_mat |
Matrix. |
h |
integer. |
Value
A list. The first element contains the pre-whitened Newey West covariance matrix.
References
Andrews, D.W. and Monahan, J.C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, pp.953-966.
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703–708.
Compute 2SLS parameters and robust standard errors based on Newey-West
Description
Compute 2SLS parameters and robust standard errors based on Newey and West (1987). Part of the function is based on the Matlab code by James P. LeSage.
Usage
newey_west_tsls(y, x, z, h)
Arguments
y |
Numeric vector. |
x |
Numeric matrix. |
z |
Numeric matrix. |
h |
Integer. |
Value
A list. The first element contains the estimated 2SLS parameters and the second element the 2SLS-Newey-West covariance matrix of these parameters. The third element contains the estimated functions, the fourth element the unscaled covariance matrix, the fifth element the meat estimator and the last element the ordinary covariance matrix of the point estimates.
References
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703–708. Wooldridge, J.M. (2002), Econometric Analysis of Cross Section and Panel Data, The MIT Press.
Compute diagnostics for OLS models
Description
Compute OLS diagnostics such as R^2, adjusted R^2, AIC, etc.
Usage
ols_diagnost(y, x)
Arguments
y |
Numeric vector. |
x |
Numeric matrix. |
Value
A list:
beta |
Point estimates of OLS regression. |
beta_cov |
Covariance matrix of point estimates. |
R^2 |
The R^2 statistic from OLS regression. |
Adj.R^2 |
The adjusted R^2 staistic from OLS regression. |
F-stat |
The computed F-statistic. |
df1 |
First degress of freedom for F-statistic. |
df2 |
Second degrees of freedom for F-staitisc. |
AIC_c |
The AIC_c criterion by Hurvich and Tsai (1989) |
AIC |
The AIC criterion by Akaike (1974) |
BIC |
The BIC criterion by Schwarz and Gideon (1978) |
References
Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716–723.
Hurvich, C. M., and Tsai, C.-L. (1989). "Regression and time series model selection in small samples", Biometrika, 76(2): 297–307,
Schwarz, G.(1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461–464.
Base print() function to plot all impulse responses from linear lpirfs object
Description
Base print() function to plot all impulse responses from linear lpirfs object
Usage
## S3 method for class 'lpirfs_lin_iv_obj'
plot(x, ...)
Arguments
x |
An object of type 'lpirfs_lin_obj |
... |
Additional arguments to be consistent with S3 print() function |
Base print() function to plot all impulse responses from linear lpirfs object
Description
Base print() function to plot all impulse responses from linear lpirfs object
Usage
## S3 method for class 'lpirfs_lin_obj'
plot(x, ...)
Arguments
x |
An object of type 'lpirfs_lin_obj |
... |
Additional arguments to be consistent with S3 print() function |
Base print() function to plot all impulse responses from linear lpirfs object
Description
Base print() function to plot all impulse responses from linear lpirfs object
Usage
## S3 method for class 'lpirfs_lin_panel_obj'
plot(x, ...)
Arguments
x |
An object of type 'lpirfs_lin_panel_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Base print() function to plot all impulse responses from linear lpirfs object
Description
Base print() function to plot all impulse responses from linear lpirfs object
Usage
## S3 method for class 'lpirfs_nl_iv_obj'
plot(x, ...)
Arguments
x |
An object of type 'lpirfs_nl_iv_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Base print() function to plot all impulse responses from nonlinear lpirfs object
Description
Base print() function to plot all impulse responses from nonlinear lpirfs object
Usage
## S3 method for class 'lpirfs_nl_obj'
plot(x, ...)
Arguments
x |
An object of type 'lpirfs_nl_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Base print() function to plot all impulse responses from linear lpirfs object
Description
Base print() function to plot all impulse responses from linear lpirfs object
Usage
## S3 method for class 'lpirfs_nl_panel_obj'
plot(x, ...)
Arguments
x |
An object of type 'lpirfs_lin_panel_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Compute and display plots of linear impulse responses
Description
Compute and display linear impulse responses, estimated with lp_lin() and lp_lin_iv().
Usage
plot_lin(results_lin)
Arguments
results_lin |
Value
A list with (gg-)plots for linear impulse responses.
Author(s)
Philipp Adämmer
Examples
# See examples for lp_lin() and lp_lin_iv().
Compute and display plots of nonlinear impulse responses
Description
Compute and display (nonlinear) impulse responses, estimated with lp_nl() and lp_nl_iv().
Usage
plot_nl(results_nl)
Arguments
results_nl |
Value
A list with (gg-)plots for nonlinear impulse responses.
Author(s)
Philipp Adämmer
Examples
# Load package
# See examples for lp_nl() and lp_nl_iv().
Summary for nonlinear lpirfs object
Description
Summary for nonlinear lpirfs object
Usage
## S3 method for class 'lpirfs_lin_iv_obj'
summary(object, ...)
Arguments
object |
An object of type 'lpirfs_lin_iv_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Summary for linear lpirfs object
Description
Summary for linear lpirfs object
Usage
## S3 method for class 'lpirfs_lin_obj'
summary(object, ...)
Arguments
object |
An object of type 'lpirfs_lin_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Summary for nonlinear lpirfs object
Description
Summary for nonlinear lpirfs object
Usage
## S3 method for class 'lpirfs_lin_panel_obj'
summary(object, ...)
Arguments
object |
An object of type 'lpirfs_lin_panel_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Summary for nonlinear lpirfs object
Description
Summary for nonlinear lpirfs object
Usage
## S3 method for class 'lpirfs_nl_iv_obj'
summary(object, ...)
Arguments
object |
An object of type 'lpirfs_nl_iv_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Summary for nonlinear lpirfs object
Description
Summary for nonlinear lpirfs object
Usage
## S3 method for class 'lpirfs_nl_obj'
summary(object, ...)
Arguments
object |
An object of type 'lpirfs_nl_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Summary for nonlinear lpirfs object
Description
Summary for nonlinear lpirfs object
Usage
## S3 method for class 'lpirfs_nl_panel_obj'
summary(object, ...)
Arguments
object |
An object of type 'lpirfs_lin_panel_obj' |
... |
Additional arguments to be consistent with S3 print() function |
Compute VAR to prewhite estimating functions for Newey West estimator.
Description
Compute Newey-West estimator with prewhitened estimation functions.
Usage
var_one(VAR_Data)
Arguments
VAR_Data |
Matrix. |
Value
A list. The first element contains the slope parameters of the VAR(1), the sedond element contains the residuals and the third element the inverted slope parameter matrix.
References
Andrews, D.W. and Monahan, J.C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, pp.953-966.
Newey, W.K., and West, K.D. (1987). “A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55, 703–708.