lp_lin: Compute linear impulse responses

Description

Compute linear impulse responses with local projections by Jord<U+00E0> (2005).

Usage

lp_lin(endog_data, lags_endog_lin = NULL, lags_criterion = NULL,
  max_lags = NULL, trend = NULL, shock_type = NULL, confint = NULL,
  hor = NULL, exog_data = NULL, lags_exog = NULL,
  contemp_data = NULL, num_cores = NULL)

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 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 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.

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 no be determined via a lag length criterion.

lags_exog

Integer. Number of lags for the exogenous variables.

contemp_data

A data.frame, containing exogenous data with contemporaneous impact. 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.

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.

References

Akaike, H. (1974). "A new look at the statistical model identification", IEEE Transactions on Automatic Control, 19 (6): 716<U+2013>723.

Hurvich, C. M., and Tsai, C.-L. (1989), "Regression and time series model selection in small samples", Biometrika, 76(2): 297<U+2013>307

Jord<U+00E0>, <U+00D2>. (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). <U+201C>A Simple, Positive-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.<U+201D> Econometrica, 55: 703<U+2013>708.

Schwarz, Gideon E. (1978). "Estimating the dimension of a model", Annals of Statistics, 6 (2): 461<U+2013>464.

Examples

Run this code

# NOT RUN {
          ## 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,
                             exog_data      = NULL,
                             lags_exog      = NULL,
                             lags_criterion = NaN,
                             max_lags       = NaN,
                             trend          = 0,
                             shock_type     = 1,
                             confint        = 1.96,
                             hor            = 12,
                             contemp_data   = NULL,
                             num_cores      = NULL)

# Make 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 all plots by using 'ggpubr' and 'gridExtra'
# lpirfs does not depend on those packages so they have to be installed
 library(ggpubr)
 library(gridExtra)

# Compare with Figure 5 in Jord<U+00E0> (2005)
 lin_plots_all <- sapply(linear_plots, ggplotGrob)
 marrangeGrob(lin_plots_all, nrow = ncol(endog_data), ncol = ncol(endog_data), top = NULL)


                      ## 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,
                               lags_criterion = NaN,
                               max_lags       = NaN,
                               trend          = 0,
                               shock_type     = 1,
                               confint        = 1.96,
                               hor            = 12,
                               exog_data      = exog_data,
                               lags_exog      = 4,
                               contemp_data   = contemp_data,
                               num_cores      = NULL)

# Make plots
 linear_plots <- plot_lin(results_lin)

# Show all plots
 library(ggpubr)
 library(gridExtra)

 lin_plots_all <- sapply(linear_plots, ggplotGrob)
 marrangeGrob(lin_plots_all, nrow = ncol(endog_data), ncol = ncol(endog_data), top = NULL)


 
# }