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_reps = 64
model_vec_baseline = Bit.ensemblerun(model, T, N_reps);

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(model, T, N_reps; 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_reps)
sem_gdp_shocked = std(data_vector_shocked.real_gdp, dims = 2) / sqrt(N_reps)

17×1 Matrix{Float64}:
   0.0
  63.88983724176731
  84.37656512352797
  90.74939654290017
 107.51313396058657
 111.66494872482971
 131.357091117824
 130.65742773904924
 143.46237543306944
 163.26740123389737
 177.54152462593822
 183.03957493930352
 206.1045792035031
 211.72267431241494
 208.54089820582178
 219.3901544457281
 227.33726320628224

Compute the ratio of shocked to baseline GDP

gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline

17×1 Matrix{Float64}:
 1.0
 1.0005280214959482
 1.0038503001069992
 1.006575160469475
 1.0072045234055664
 1.0051334989840073
 1.0040356474427807
 1.005748071574165
 1.0082342101088997
 1.0054281054505034
 1.0059300567685245
 1.0053358982823126
 1.0058650765349735
 1.004685861145325
 1.004621660981743
 1.005045800668616
 1.0057629519708766

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
 0.0012186804992545476
 0.0015866512001014726
 0.0017728811408221428
 0.002050526253215954
 0.0024080714129641576
 0.0026732803251819474
 0.0027226383598533397
 0.002861929690861746
 0.0031313062794118755
 0.0034426892957919236
 0.003587113060171621
 0.003926882693752494
 0.003999913939585363
 0.0040944399278720804
 0.004146966542825984
 0.0043462045203262675

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")