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}:
   1.8333689901882087e-12
  54.45416808182842
  79.68394965459767
  88.41524987290627
  95.49500478021626
 112.36130474852348
 126.14454765069188
 148.4427705474358
 170.33365312049492
 192.59660367499382
 209.61338321989257
 211.570250114503
 218.2802665268977
 220.35543119919004
 234.246412247767
 246.4277338555497
 259.98520875275767

Compute the ratio of shocked to baseline GDP

gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline

17×1 Matrix{Float64}:
 1.0
 0.9998622967809462
 1.0043886403709754
 1.009184620204802
 1.0079675526698209
 1.0033167736664022
 1.0008062382861354
 0.9990685287041411
 0.9989537797461749
 0.9974868106442034
 0.9981107949744432
 0.9979237543105981
 0.9999611740495508
 0.997757858211183
 0.9999595666157431
 0.9998626991172047
 1.0013918176241163

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}:
 3.580093467121083e-17
 0.0010625422061316047
 0.0014233670669707525
 0.001616857297786773
 0.0018427238102715602
 0.002012003230877796
 0.002405303995167028
 0.0026526665665828546
 0.0030481537111431457
 0.003318326886565313
 0.003572258600082999
 0.003678787270421965
 0.0038174849472746445
 0.0038295470775487938
 0.004109261152026839
 0.004479773610399598
 0.00469631483547442

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")