cfact_hist: Simulate historical counterfactual for structural STVAR models.

Description

cfact_hist simulates historical counterfactual for structural STVAR models.

Usage

cfact_hist(
  stvar,
  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 cfacthist
plot(x, ...)
# S3 method for cfacthist
print(x, ..., digits = 3)

Value

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

cfact_data: A matrix of size \((T+p \times d)\) containing the counterfactual time series. Note that the first \(p\) rows are for the initial values prior the time period \(t=1\).
cfact_shocks: A matrix of size \((T \times d)\) containing the counterfactual shocks.
cfact_weights: A matrix of size \((T \times M)\) containing the counterfactual transition weights.
stvar: The original STVAR model object.
input: A list containing the arguments used to calculate the counterfactual.

Returns the input object x invisibly.

Arguments

stvar: an object of class 'stvar' defining a structural or reduced form STVAR model. For a reduced form model (that is not readily identified statiscally), the shocks are automatically identified by the lower triangular Cholesky decomposition.
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 points of time 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.
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 \(1\) and \(T\) indicating the starting period for the counterfactual behavior of the specified policy variable. It is assumed that the observed time series in indexed as \(y_{t-p+1},...,y_{0},y_1,...,y_T\), i.e., that the first \(p\) observations are the initial values, and the "time period one" observation is the \(p+1\)th row in the data matrix.
cfact_end: a positive integer between cfact_start and \(T\) 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 'cfacthist' created by the function cfact_hist.
...: arguments passed to the function window to select the time periods to print.
digits: how many significant digits to print?

Functions

plot(cfacthist): plot method
print(cfacthist): print method

Details

Two types of historical counterfactuals are accommodated where in given historical points of time 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 \(i_1\)th variable, the shock to it that is manipulated is the \(i_1\)th 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 \(i_2\)th variable, the shock to it is the \(i_2\)th shock. If it is not clear whether the \(i_2\)th 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 \(i_1\)th variable does not react to lagged movements of the \(i_2\)th variable nor to the \(i_2\)th 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 the historical 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.

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.

Examples

Run this code

# 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")

# Simulate historical counterfactual where the first variable takes the values 5 and -5
# in the first and second time periods, respectively.
cfact1 <- cfact_hist(mod32logt, cfact_type="fixed_path", policy_var=1, cfact_start=1,
  cfact_end=2, cfact_path=c(5, -5))
print(cfact1, start=c(1959, 1), end=c(1960, 4)) # Print cfact data from 1959Q1 to 1960Q4
plot(cfact1) # Plot the observed and counterfactual data

# Simulate historical counterfactual where the first variable does not respond to lagged
# movements of the second variable nor to the second shock in time periods from 10 to 100.
cfact2 <- cfact_hist(mod32logt, cfact_type="muted_response", policy_var=1, mute_var=2,
 cfact_start=10, cfact_end=100)
print(cfact2, start=c(1960, 4), end=c(1963, 4)) # Print cfact data from 1960Q4 to 1963Q4
plot(cfact2) # plot the observed and counterfactual data

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