lp_nl: 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
)

Value

A list containing:

irf_s1_mean: A three-dimensional array, containing all impulse responses for all endogenous variables of the first state. The last dimension denotes the shock variable. The row in each matrix denotes the responses of the ith variable, ordered as in endog_data. The columns are the horizons. For example, if the results are saved in results_nl, results_nl\$irf_s1_mean[, , 1] returns a KxH matrix, where K is the number of variables and H is the number of horizons. '1' is the shock variable, corresponding to the variable in the first column of endog_data.
irf_s1_low: A three-dimensional array, 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 three-dimensional array, 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 three-dimensional array, containing all impulse responses for all endogenous variables of the second state. The last dimension denotes the shock variable. The row in each matrix denotes the responses of the ith variable, ordered as in endog_data. The columns denote the horizon. For example, if the results are saved in results_nl, results_nl\$irf_s2_mean[, , 1] returns a KxH matrix, where K is the number of variables and H is the number of horizons. '1' is the first shock variable corresponding to the variable in the first column of endog_data.
irf_s2_low: A three-dimensional array, 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 three-dimensional array, 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 IRF estimations, and the selected lag lengths when an information criterion has been used.
fz: A vector containing the values of the transition function F(z\_{t-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: $$ F_{z_t} = \frac{exp(-\gamma z_t)}{1 + exp(-\gamma z_t)}. $$ Important: F_{z_t} will be lagged by one and then multiplied with the data. If the variable shall not be lagged, use 'lag_switching = FALSE':
Regime 1 = (1-F(z_{t-1}))*y_{(t-p)},
Regime 2 = F(z_{t-1})*y_{(t-p)}.
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 $\lambda$ for the Hodrick-Prescott filter (if use_hp = TRUE).
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.

Author

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.

Examples

Run this code

# \donttest{
                  ## 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)



# }

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