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
  54.178551573201446
  82.91933796143158
  95.11942722585636
 106.36328736732303
 119.65557363749025
 134.53889233145634
 135.40442517823536
 154.44872798962763
 162.90936102108964
 173.61614793717027
 179.57079506301835
 194.29748701890023
 195.54496731119104
 196.74230501594982
 201.77516716809902
 203.73629321955215

Compute the ratio of shocked to baseline GDP

gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline

17×1 Matrix{Float64}:
 1.0
 1.0005044948991615
 1.0063228078231257
 1.0119629778508967
 1.0128090350859247
 1.0084721785895934
 1.0067764435811717
 1.0050759659874198
 1.0037874749479425
 1.0040913781022742
 1.0056582190115584
 1.005460938301129
 1.006862965949022
 1.007394219366327
 1.0066704173154808
 1.0066019695818653
 1.00636219805734

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
 0.0010015840821505971
 0.0015186606337788894
 0.001972656522190506
 0.0022077710288480037
 0.0024376803738066907
 0.0025593084173382453
 0.00267851290378329
 0.002942307216345477
 0.003146175065308616
 0.0033990800945012476
 0.0035383788140848377
 0.003639491259613024
 0.003702705391577889
 0.0037627583911360014
 0.0038701871644736363
 0.004112044116890584

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")