cfact_girf: Simulate counterfactual generalized impulse response...

In sstvars: Toolkit for Reduced Form and Structural Smooth Transition Vector Autoregressive Models

Simulate counterfactual generalized impulse response functions for structural STVAR models.

Description

cfact_girf simulates counterfactual generalized impulse response functions for structural STVAR models.

Usage

cfact_girf(
  stvar,
  which_shocks,
  shock_size = 1,
  N = 30,
  R1 = 200,
  R2 = 250,
  init_regime = 1,
  init_values = NULL,
  which_cumulative = numeric(0),
  scale = NULL,
  scale_type = c("instant", "peak"),
  scale_horizon = N,
  ci = c(0.95, 0.8),
  use_data_shocks = FALSE,
  data_girf_pars = c(0, 0.75, 0, 0, 1.5),
  ncores = 2,
  burn_in = 1000,
  exo_weights = NULL,
  seeds = NULL,
  use_parallel = TRUE,
  cfact_type = c("fixed_path", "muted_response"),
  policy_var = 1,
  mute_var = NULL,
  cfact_start = 1,
  cfact_end = 1,
  cfact_path = NULL
)

## S3 method for class 'cfactgirf'
plot(x, ...)

## S3 method for class 'cfactgirf'
print(x, ..., digits = 3)

Arguments

stvar	an object of class 'stvar', created by, e.g., fitSTVAR or fitSSTVAR.
which_shocks	a numeric vector of length at most d (=ncol(data)) and elements in 1,...,d specifying the structural shocks for which the GIRF should be estimated.
shock_size	a non-zero scalar value specifying the common size for all scalar components of the structural shock. Note that the conditional covariance matrix of the structural shock is normalized to an identity matrix and that the (generalized) impulse responses may not be symmetric with respect to the sign and size of the shock.
N	a positive integer specifying the horizon how far ahead should the generalized impulse responses be calculated.
R1	the number of repetitions used to estimate GIRF for each initial value.
R2	the number of initial values to use, i.e., to draw from init_regime if init_values are not specified. The confidence bounds will be sample quantiles of the GIRFs based on different initial values. Ignored if the argument init_value is specified. @param init_regime an integer in 1,...,M specifying the regime from which the initial values should be generated from (see ?simulate.stvar). If use_data_shocks=TRUE this is argument not used and data_girf_pars should be specified instead.
init_regime	an integer in 1,...,M specifying the regime from which the initial values should be generated from (using a simulation procedure with a burn-in period). For models with Gaussian conditional distribution, it is also possible to generate the starting values from the stationary distribution of a regime. See the details section.
init_values	a size [p, d, R2] array specifying the initial values in each slice for each Monte Carlo repetition, where d is the number of time series in the system and R2 is an argument of this function. In each slice, the last row will be used as initial values for the first lag, the second last row for second lag etc. If not specified, initial values will be drawn from the regime specified in init_regimes.
which_cumulative	a numeric vector with values in 1,...,d (d=ncol(data)) specifying which the variables for which the impulse responses should be cumulative. Default is none.
scale	should the GIRFs to some of the shocks be scaled so that they correspond to a specific magnitude of instantaneous or peak response of some specific variable (see the argument scale_type)? Provide a length three vector where the shock of interest is given in the first element (an integer in 1,...,d), the variable of interest is given in the second element (an integer in 1,...,d), and the magnitude of its instantaneous or peak response in the third element (a non-zero real number). If the GIRFs of multiple shocks should be scaled, provide a matrix which has one column for each of the shocks with the columns being the length three vectors described above.
scale_type	If argument scale is specified, should the GIRFs be scaled to match an instantaneous response ("instant") or peak response ("peak"). If "peak", the scale is based on the largest magnitude of peak response in absolute value. Ignored if scale is not specified.
scale_horizon	If scale_type == "peak" what the maximum horizon up to which peak response is expected? Scaling won't based on values after this.
ci	a numeric vector with elements in (0, 1) specifying the confidence levels of the "confidence intervals" that do not quantify uncertainty about the true parameter value but only uncertainty about the initial value (and possibly sign and size of the shock) within the given regime.
use_data_shocks	set TRUE for a special feature in which for every possible length p history in the data, or a subset of them if so specified in the argument data_girf_pars, the GIRF is estimated for a shock that has the sign and size of the corresponding structural shock recovered from the data. If used, the argument which_shocks must specify only one shock. See the details section.
data_girf_pars	a length five numeric vector with the following elements determining settings for use_data_shocks=TRUE (concerns the single shock specified in the argument which_shocks): An integer between 0 and M determining the (dominant) regime for which the GIRF should be calculated (0 for all regimes). A number between 0.5 and 1 determining how large transition weight a regime should have to be considered dominant in a given time period (i.e., determining which histories are used to calculate the GIRF if the first element is not 0). Either 0, -1, or 1, determining whether the GIRF should be calculated using shocks of all signs, only negative shocks, or only positive shocks, respectively. Either, 0, 1, or 2, determining whether the GIRF should be calculated using shocks of all sizes, only small shocks, or only large shocks, respectively. A strictly positive real number determining what size shocks are considered large and what size small "in the scale of standard deviations" (for example, if set to 2, shocks larger than that are considered large and shocks smaller than that are considered small; note that the standard deviations of the shocks are normalized to unity).
ncores	the number CPU cores to be used in parallel computing. Only single core computing is supported if an initial value is specified (and the GIRF won't thus be estimated multiple times).
burn_in	Burn-in period for simulating initial values from a regime.
exo_weights	if weight_function="exogenous", provide a size (N+1 \times M) matrix of exogenous transition weights for the regimes: [h, m] for the (after-the-impact) period h-1 and regime m weight ([1, m] is for the impact period). Ignored if weight_function != "exogenous".
seeds	A numeric vector initializing the seeds for the random number generator for estimation of each GIRF. Should have the length of at least (extra seeds are removed from the end of the vector)... If initial values are drawn using init_regime: R2 If initial values are specified in init_values: dim(init_values)[3] If use_data_shocks=TRUE: 1 (the vector of seeds are generated according on the number of histories in the data that satisfy the conditions given in the argument data_girf_pars). Set NULL for not initializing the seed.
use_parallel	employ parallel computing? If FALSE, does not print anything.
cfact_type	a character string indicating the type of counterfactual to be computed: should the path of the policy variable be fixed to some hypothetical path (cfact_type="fixed_path") in given impulse response horizons or should the responses of the policy variable to lagged and contemporaneous movements of some given variable be muted (cfact_type="muted_response")? See details for more information.
policy_var	a positive integer between 1 and d indicating the index of the policy variable considered in the counterfactual scenario. Note that policy_var is assumed to satisfy !(policy_var %in% which_shocks).
mute_var	a positive integer between 1 and d indicating the index of the variable to whose movements the policy variable specified in the argument policy_var should not react to in the counterfactual scenario. This indicates also the index of the shock to which the policy variable should not react to. It is assumed that mute_var != policy_var. This argument is only used when cfact_type="muted_response".
cfact_start	a positive integer between 0 and N indicating the starting impulse response horizon period for the counterfactual behavior of the specified policy variable.
cfact_end	a positive integer between cfact_start and N indicating the ending period for the counterfactual behavior of the specified policy variable.
cfact_path	a numeric vector of length cfact_end-cfact_start+1 indicating the hypothetical path of the policy variable specified in the argument policy_var. This argument is only used when cfact_type="fixed_path".
x	object of class 'cfactgirf' created by the function cfact_girf.
...	parameters passed to print.stvargirf printing the girf.
digits	how many significant digits to print?

Details

Two types of counterfactual generalized impulse response functions (GIRFs) are accommodated where in given impulse response horizons either (1) the policy variable of interest takes some hypothetical path (cfact_type="fixed_path"), or (2) its responses to lagged and contemporaneous movements of some given variable are shut off (cfact_type="muted_response"). In both cases, the counterfactual scenarios are simulated by creating hypothetical shocks to the policy variable of interest that yield the counterfactual outcome. This approach has the appealing feature that the counterfactual deviations from the policy reaction function are treated as policy surprises, allowing them to propagate normally, so that the dynamics of the model are not, per se, tampered but just the policy surprises are.

Important: This function assumes that when the policy variable of interest is the i_1th variable, the shock to it that is manipulated is the i_1th shock. This should be automatically satisfied for recursively identified models, whereas for model identified by heteroskedasticity or non-Gaussianity, the ordering of the shocks can be generally changed without loss of generality with the function reorder_B_columns. In Type (2) counterfactuals it is additionally assumed that, if the variable to whose movements the policy variable should not react to is the i_2th variable, the shock to it is the i_2th shock. If it is not clear whether the i_2th shock can be interpreted as a shock to a variable (but has a broader definition such as "a demand shock"), the Type (2) counterfactual scenario is interpreted as follows: the i_1th variable does not react to lagged movements of the i_2th variable nor to the i_2th shock.

See the seminal paper of Bernanke et al (1997) for discussing about the "Type (1)" counterfactuals and Kilian and Lewis (2011) for discussion about the "Type (2)" counterfactuals. See Kilian and Lütkepohl (2017), Section 4.5 for further discussion about counterfactuals. The literature cited about considers linear models, but it is explained in the vignette of this package how this function computes the historical counterfactuals for the STVAR models in a way that accommodates nonlinear time-varying dynamics.

Value

Returns a class 'cfactgirf' list with the following elements:

$girf

An object of class 'girf' containing the counterfactual GIRFs (see ?GIRF).

$stvar

The original STVAR model object.

$input

A list containing the arguments used to calculate the counterfactual.

Returns the input object x invisibly.

Functions

• plot(cfactgirf): plot method

• print(cfactgirf): print method

References

• Bernanke B., Gertler M., Watson M. 1997. Systematic monetary policy and the effects of oilprice shocks. Brookings Papers on Economic Activity, 1, 91—142.

• Kilian L., Lewis L. 2011. Does the fed respond to oil price shocks? The Economic Journal, 121:555.

• Kilian L., Lütkepohl H. 2017. Structural Vector Autoregressive Analysis. 1st edition. Cambridge University Press, Cambridge.

See Also

GIRF, GFEVD, linear_IRF, hist_decomp, cfact_hist, cfact_fore, fitSSTVAR

Examples

# Recursively identified logistic Student's t STVAR(p=3, M=2) model with the first
# lag of the second variable as the switching variable:
params32logt <- c(0.5959, 0.0447, 2.6279, 0.2897, 0.2837, 0.0504, -0.2188, 0.4008,
  0.3128, 0.0271, -0.1194, 0.1559, -0.0972, 0.0082, -0.1118, 0.2391, 0.164, -0.0363,
  -1.073, 0.6759, 3e-04, 0.0069, 0.4271, 0.0533, -0.0498, 0.0355, -0.4686, 0.0812,
  0.3368, 0.0035, 0.0325, 1.2289, -0.047, 0.1666, 1.2067, 7.2392, 11.6091)
mod32logt <- STVAR(gdpdef, p=3, M=2, params=params32logt, weight_function="logistic",
  weightfun_pars=c(2, 1), cond_dist="Student", identification="recursive")

# Counterfactual GIRFs for Shock 2 with horizon N=5 (using only R1=R2=10 Monte Carlo repetitions
# to save computation time), where the first variable takes values 1, -2, and 3 in the
# horizons 1, 2, and 3, respectively:
cfact1 <- cfact_girf(mod32logt, which_shocks=2, N=5, R1=10, R2=10, init_regime=1, seeds=1:10,
 cfact_type="fixed_path", policy_var=1, cfact_start=1, cfact_end=3, cfact_path=c(1, -2, 3))
cfact1 # Print the results
plot(cfact1) # Plot the counterfactual GIRF

# Counterfactual GIRFs for Shock 2 with horizon N=5 (using only R1=R2=10 Monte Carlo repetitions
# to save computation time), where the first variable does not respond to lagged movements
# of the second variable nor to the second shock in time periods from 1 to 3:
cfact2 <- cfact_girf(mod32logt, which_shocks=2, N=5, R1=10, R2=10, init_regime=1, seeds=1:20,
 cfact_type="muted_response", policy_var=1, mute_var=2, cfact_start=1, cfact_end=3)
cfact2 # Print the results
plot(cfact2) # Plot the counterfactual GIRF

sstvars documentation built on June 8, 2025, 10:07 a.m.