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
  50.713831878554544
  78.27842716651006
  93.41589507514584
 102.36192989403186
 121.02517311947649
 152.90849307418225
 157.98908101348385
 174.76134820876788
 188.91834777044585
 187.94307962403042
 195.90336580677968
 212.10667100518464
 220.99787680517605
 239.9663848494646
 252.10317760584334
 266.2727581279288

Compute the ratio of shocked to baseline GDP

gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline

17×1 Matrix{Float64}:
 1.0
 1.0008147553643534
 1.0060467200759853
 1.0107499862014764
 1.0104208484342372
 1.0050580484667873
 1.0053225083944883
 1.0044332184086244
 1.003632014295706
 1.0027355226733037
 1.0024111171611838
 1.001981272970507
 1.0017126707723931
 1.0003542583112328
 0.9981943684728605
 0.9982932666211456
 0.9992238032174349

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
 0.0010141736200250553
 0.0014788641674407341
 0.0018365369311206356
 0.0019473956182025885
 0.002201299217411755
 0.0026777557717321803
 0.0028193097948589338
 0.002939281315225711
 0.0031621540483486445
 0.003263105035845009
 0.003338188279345011
 0.0035616637277342982
 0.0036593034391925617
 0.003826713721213004
 0.004077920682742194
 0.004374388959133427

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")