lp_nl_iv: Compute nonlinear impulse responses with with identified shock (instrument variable approach)

Description

Compute nonlinear impulse responses with local projections and identified shock, i.e. instrument variable approach (see e.g. Jord<U+00E0> et al., 2015; and Ramey and Zubairy, 2018). The data are separated into two states via a smooth transition function as in Auerbach and Gorodnichenko (2012).

Usage

lp_nl_iv(endog_data, lags_endog_nl = NULL, instr = NULL,
  exog_data = NULL, lags_exog = NULL, contemp_data = NULL,
  lags_criterion = NULL, max_lags = NULL, trend = NULL,
  confint = NULL, hor = NULL, switching = NULL, use_hp = NULL,
  lambda = NULL, gamma = NULL, num_cores = NULL)

Arguments

endog_data

A data.frame, containing all endogenous variables for the VAR. The column order is used for the Cholesky decomposition.

lags_endog_nl

NaN or integer. Number of lags for nonlinear VAR. NaN if lag length criterion is given.

instr

One column data.frame, including the instrument to shock with. The row length has to be the same as endog_data.

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

Null or an integer, indicating the number of lags for exogenous 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 and lags_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 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.

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: $$ F_{z_t} = \frac{exp(-\gamma z_t)}{1 + exp(-\gamma z_t)}. $$ Warning: $F_{z_t}$ will be lagged in create_nl_data by one and then multiplied with the data. If the variable shall not be lagged, the vector has to be given with a lead of one. The data for the two regimes are: Regime 1 = (1-$F(z_{t-1})$)*y_(t-p), Regime 2 = $F(z_{t-1})$*y_(t-p).

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.

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 instrument 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 three 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 three 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 irfs.

A vector containing the values of the transition function F(z_t-1).

References

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

Jord<U+00E0>, <U+00D2>, Schularick, M., Taylor, A.M. (2015), "Betting the house", Journal of International Economics, 96, S2-S18.

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.

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<U+2013>464.

Examples

Run this code

# NOT RUN {
# 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,
                           instr             = shock,
                           exog_data         = exog_data,
                           lags_exog         = 4,
                           contemp_data      = NULL,
                           lags_criterion    = NaN,
                           max_lags          = NaN,
                           trend             = 0,
                           confint           = 1.96,
                           hor               = 20,
                           switching         = switching_variable,
                           use_hp            = 0,
                           lambda            = NaN, # Ravn and Uhlig (2002):
                                                    # Annual data    = 6.25
                                                    # Quarterly data = 1600
                                                    # Monthly data   = 129,600
                           gamma             = 3,
                           num_cores         = NULL)

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

 s1_plots <- sapply(plots_nl_iv$gg_s1, ggplotGrob)
 s2_plots <- sapply(plots_nl_iv$gg_s2, ggplotGrob)

# Show all responses of state 1
 marrangeGrob(s1_plots, nrow = ncol(endog_data), ncol = 1, top = NULL)

# Show all responses of state 2
 marrangeGrob(s2_plots, nrow = ncol(endog_data), ncol = 1, top = NULL)

# }