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
Dict{String, Any} with 21 entries:
  "sb_inact" => 2.23847
  "C_G"      => [11482.3; 11556.2; … ; 14578.2; 14714.8;;]
  "E_CB"     => 1.0618e5
  "D_RoW"    => 0.0
  "sb_other" => 0.590286
  "L_I"      => 236919.0
  "omega"    => 0.85
  "r_bar"    => 0.00164593
  "N_s"      => [123.0; 18.0; … ; 5.0; 60.0;;]
  "C_E"      => [17384.5; 17752.9; … ; 38786.7; 38617.8;;]
  "D_H"      => 219841.0
  "K_H"      => 4.05377e5
  "L_G"      => 2.32611e5
  "pi"       => [-0.00749736; -0.00789543; … ; 0.00530319; 0.00100796;;]
  "w_UB"     => 4.06546
  "Y"        => [1.04531e5; 1.05062e5; … ; 1.35709e5; 1.34636e5;;]
  "Y_I"      => [19804.6; 19944.1; … ; 36883.2; 36575.9;;]
  "Y_EA"     => 2.35485e6
  "D_I"      => 54049.0
  ⋮          => ⋮

Initialise the model and the data collector

T = 16
model = Bit.init_model(parameters, initial_conditions, T);

Simulate the baseline model for T quarters, N_reps times, and collect the data

N_reps = 64
data_vec_baseline = Bit.ensemblerun(model, N_reps)
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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)
    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)
    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

data_vec_shocked = Bit.ensemblerun(model, N_reps; shock = consumption_shock)
BeforeIT.DataVector{BeforeIT.Data}(BeforeIT.Data[BeforeIT.Data{Float64}([72421.99999999999, 72513.77165435233, 73112.40260044222, 73629.46697440282, 73943.02434929145, 74012.7961605108, 74522.64896260925, 75094.87688775263, 75518.99219997157, 75682.81713676543, 75852.38300533993, 76289.87865168451, 76735.83731401897, 77281.72656425896, 77852.02775564208, 78790.57296353213, 79416.27281923174], [72421.99999999999, 72440.71757139974, 72965.16245766684, 73407.15681705452, 73645.49840032298, 73640.72521815529, 74073.31442763608, 74566.89384094666, 74912.48047481108, 74999.35530795169, 75091.66241998196, 75448.68292242913, 75813.26911667269, 76275.67382063215, 76761.13975007653, 77608.26836828918, 78145.77174173499], [64900.92049553801, 64966.370940930225, 65516.403762299466, 66000.97061491643, 66364.8467782064, 66415.63014807345, 66919.32834134485, 67415.88084959371, 67809.28984418666, 67934.64009719715, 68084.52740964147, 68500.26173634046, 68924.86764876054, 69437.73915466301, 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Compute mean and standard error of GDP for the baseline and shocked simulations

mean_gdp_baseline = mean(data_vec_baseline.real_gdp, dims = 2)
mean_gdp_shocked = mean(data_vec_shocked.real_gdp, dims = 2)
sem_gdp_baseline = std(data_vec_baseline.real_gdp, dims = 2) / sqrt(N_reps)
sem_gdp_shocked = std(data_vec_shocked.real_gdp, dims = 2) / sqrt(N_reps)
17×1 Matrix{Float64}:
   0.0
   1.7087910597059337
  19.332874342265427
  34.036728703907166
  48.680688382178325
  65.24281594318593
  82.60100789439731
  96.76491766434869
 111.29073090617283
 121.31020752152371
 133.6002922908776
 142.93970959814064
 150.33128734503097
 155.46844759371996
 166.90791879675658
 174.20864328750514
 184.54188420000017

Compute the ratio of shocked to baseline GDP

gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline
17×1 Matrix{Float64}:
 1.0
 1.000482327753667
 1.0057830194997233
 1.007892223215894
 1.0095653532135471
 1.006617820072272
 1.005378369815575
 1.0047400640497572
 1.0047363812789942
 1.004615612692966
 1.004536270723786
 1.0036412808554824
 1.0036919082392575
 1.0036166039492016
 1.003813375717866
 1.003868044123636
 1.0043098133682322

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
 2.8733493054845606e-5
 0.00038155014880086435
 0.0006475752477165653
 0.000974635442374253
 0.0013251148332801203
 0.0016127132644382738
 0.001887130834243173
 0.0021495476350544343
 0.002436122987688638
 0.0026269809671034088
 0.0027801234458659616
 0.002926965281610013
 0.0031125267464393127
 0.0033031041125758664
 0.003410951697955109
 0.0035410212636358255

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",
)
Example block output

We can save the figure using: savefig("gdp_shock.png")