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
  62.38034349862752
  66.74306221818445
  90.50682909387842
  94.9223915538385
 101.23178284808925
 125.3209776045712
 143.15927980218254
 159.0638847101627
 169.26884579231952
 179.7914852245972
 183.0584029670968
 177.597233942538
 181.62262849014647
 201.3340124914622
 204.16078749232594
 217.1217757813231

Compute the ratio of shocked to baseline GDP

gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline

17×1 Matrix{Float64}:
 1.0
 0.9997667919001694
 1.0047638964767707
 1.0085135101048244
 1.0079072296942388
 1.0039113825297838
 1.0024587265848417
 1.0010625269256113
 1.0005976474556584
 0.9992281563802026
 0.998505414725525
 1.0012944570818023
 1.002225161704196
 1.0041971304502935
 1.0021243487409304
 1.0035467943500556
 1.0043203674546137

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
 0.0011054420793262835
 0.001310732277949278
 0.001611931988660452
 0.0018940443573763042
 0.002237879888223368
 0.002568526975882533
 0.002687407022488961
 0.0029547263338137028
 0.003208374274696713
 0.0033702731571916334
 0.0034400773561801055
 0.003504414386293318
 0.003504869138164534
 0.003849726429477901
 0.004132578429535682
 0.0043064026611760306

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")