Scenario analysis via custom shocks

In this tutorial we will illustrate how to perform a scenario analysis by running the model multiple times under a specific shock and comparing the results with the unshocked model.

import BeforeIT as Bit
import StatsBase: mean, std
using Plots

parameters = Bit.AUSTRIA2010Q1.parameters;
initial_conditions = Bit.AUSTRIA2010Q1.initial_conditions;

Initialise the model

model = Bit.Model(parameters, initial_conditions);

Simulate the baseline model for T quarters, N_reps times, and collect the data

T = 16
n_sims = 64
model_vec_baseline = Bit.ensemblerun!((deepcopy(model) for _ in 1:n_sims), T);

Now, apply a shock to the model and simulate it again. A shock is simply a function that takes the model and changes some of its parameters for a specific time period. We do this by first defining a "struct" with useful attributes. For example, we can define an productivity and a consumption shock with the following structs

struct ProductivityShock
    productivity_multiplier::Float64    # productivity multiplier
end

struct ConsumptionShock
    consumption_multiplier::Float64    # productivity multiplier
    final_time::Int
end

and then by making the structs callable functions that change the parameters of the model, this is done in Julia using the syntax below

A permanent change in the labour productivities by the factor s.productivity_multiplier

function (s::ProductivityShock)(model::Bit.Model)
    return model.firms.alpha_bar_i .= model.firms.alpha_bar_i .* s.productivity_multiplier
end

A temporary change in the propensity to consume model.prop.psi by the factor s.consumption_multiplier

function (s::ConsumptionShock)(model::Bit.Model)
    return if model.agg.t == 1
        model.prop.psi = model.prop.psi * s.consumption_multiplier
    elseif model.agg.t == s.final_time
        model.prop.psi = model.prop.psi / s.consumption_multiplier
    end
end

Define specific shocks, for example a 2% increase in productivity

productivity_shock = ProductivityShock(1.02)

Main.ProductivityShock(1.02)

or a 4 quarters long 2% increase in consumption

consumption_shock = ConsumptionShock(1.02, 4)

Main.ConsumptionShock(1.02, 4)

Simulate the model with the shock

model_vec_shocked = Bit.ensemblerun!((deepcopy(model) for _ in 1:n_sims), T; shock! = consumption_shock);

extract the data vectors from the model vectors

data_vector_baseline = Bit.DataVector(model_vec_baseline);
data_vector_shocked = Bit.DataVector(model_vec_shocked);

Compute mean and standard error of GDP for the baseline and shocked simulations

mean_gdp_baseline = mean(data_vector_baseline.real_gdp, dims = 2)
mean_gdp_shocked = mean(data_vector_shocked.real_gdp, dims = 2)
sem_gdp_baseline = std(data_vector_baseline.real_gdp, dims = 2) / sqrt(n_sims)
sem_gdp_shocked = std(data_vector_shocked.real_gdp, dims = 2) / sqrt(n_sims)

17×1 Matrix{Float64}:
   0.0
  52.908878562919156
  73.0793055281963
  93.41561565475078
 116.74976518086554
 130.305076541754
 150.56260689310656
 157.7817753672868
 161.89779542159988
 175.998599367303
 198.30675201715457
 208.48435702640842
 225.21780105736994
 242.31753435305976
 253.31116464296392
 249.20547549757626
 245.00220578846157

Compute the ratio of shocked to baseline GDP

gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline

17×1 Matrix{Float64}:
 1.0
 1.000229298683889
 1.0049190342695247
 1.0082898150350634
 1.0086184533052573
 1.007843084415859
 1.0071786757058623
 1.0076663748688628
 1.0069173283354664
 1.0053597899914253
 1.006895385983945
 1.0049609652306912
 1.0041784512377394
 1.0032866568346266
 1.0040494975167515
 1.002727769722409
 1.005525057828365

the standard error on a ratio of two variables is computed with the error propagation formula

sem_gdp_ratio = gdp_ratio .* ((sem_gdp_baseline ./ mean_gdp_baseline) .^ 2 .+ (sem_gdp_shocked ./ mean_gdp_shocked) .^ 2) .^ 0.5

17×1 Matrix{Float64}:
 0.0
 0.0010698267115297707
 0.001382545181815747
 0.001796028922378768
 0.002159543616920005
 0.0024831981333852827
 0.0026606477328988197
 0.0027665713404299063
 0.0028856350526197307
 0.003133019974078932
 0.0034277330045456786
 0.0035307558607374427
 0.003800307539213481
 0.00413292949707026
 0.004462358521975702
 0.004449512661256251
 0.004530721168749329

Finally, we can plot the impulse response curve

plot(
    1:(T + 1),
    gdp_ratio,
    ribbon = sem_gdp_ratio,
    fillalpha = 0.2,
    label = "",
    xlabel = "quarters",
    ylabel = "GDP change",
)

We can save the figure using: savefig("gdp_shock.png")