# lp_nl: Compute nonlinear impulse responses In lpirfs: Local Projections Impulse Response Functions

## 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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 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: F_{z_t} = \frac{exp(-γ z_t)}{1 + exp(-γ 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 λ 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 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. 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 3D 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$irf_s1_mean[, , 1] returns a KXH matrix, where K is the number of variables and H the number of horizons. '1' is the shock variable, corresponding to the variable in the first column of endog_data. irf_s1_low A three 3D array, containing all lower confidence bands of the impulse responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_s1_mean. irf_s1_up A three 3D array, containing all upper confidence bands of the impulse responses, based on robust standard errors by Newey and West (1987). Properties are equal to irf_s1_mean. irf_s2_mean A three 3D array, containing all impulse responses for all endogenous variables of the second state. The last dimension denotes the shock variable. The row in each matrix denotes the responses of the ith variable, ordered as in endog_data. The columns denote the horizon. For example, if the results are saved in results_nl, results_nl$irf_s2_mean[, , 1] returns a KXH matrix, where K is the number of variables and H 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 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_s2_mean. irf_s2_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_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).

## 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.

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88  ## 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)