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_conditionsDict{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)BeforeIT.DataVector(BeforeIT.Data[BeforeIT.Data{Float64, Vector{Float64}, Matrix{Float64}}([72422.0, 72492.93135048292, 72377.18138216024, 72243.86559257144, 72399.38575975278, 72504.51345883342, 72433.88245859685, 72516.92100518077, 72642.71649862379, 72860.48808620566, 73054.43950533542, 73251.84255939518, 73754.10329695114, 74024.77367107378, 74205.13373522303, 74535.18362316652, 74400.349368608], [72422.0, 72419.89826311855, 72231.42189209613, 72025.73899479314, 72108.07097864267, 72140.02482920302, 71997.14214751197, 72007.06325610275, 72059.30485579857, 72202.51360375955, 72321.77938601439, 72444.14515300175, 72867.38344730502, 73061.1199076424, 73165.34719816314, 73416.73395602529, 73210.09300573253], [64900.92049553801, 64966.37094093018, 64863.289070504645, 64726.57687319233, 64872.34466962954, 64963.43312081654, 64881.33966549816, 64950.397402548784, 65069.1288028081, 65273.50840764331, 65437.93594298452, 65627.22005417707, 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139.6555936020336 517.4250246831089])])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
endand 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
endA 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
endDefine 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{Float64, Vector{Float64}, Matrix{Float64}}([72422.0, 72508.62233139476, 73251.15839290792, 73723.76687736598, 74056.05655446695, 74028.46566742261, 74497.5527715304, 74808.71835034869, 75089.03887209907, 75386.92790440762, 75524.6737369489, 75584.81953906853, 75742.40647738171, 76098.0477103788, 76255.23443255122, 76645.28449096109, 76815.23340198369], [72422.0, 72435.57343613355, 73103.63881159708, 73501.17199941436, 73758.07579567155, 73656.31595263208, 74048.36955411673, 74282.74724980006, 74485.98020857348, 74706.13813516534, 74767.23973503977, 74751.39800902485, 74831.78195235724, 75107.40408623648, 75186.72121584868, 75495.17136639688, 75586.34373818072], [64900.92049553801, 64966.37094093018, 65638.55468101487, 66061.44589925966, 66428.28907627793, 66376.69846871866, 66820.51589055915, 67093.59290754607, 67345.69292775865, 67617.55344359086, 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2.366530722012705e6, 2.387759885949106e6, 2.3641668222907376e6, 2.389565055613911e6], [0.0016459319014481277, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.009163479454832472, 0.007794532752166506, 0.007795506729503041, 0.007706564872038709, 0.008125883691737754, 0.0066166536005655315, 0.00729237878988878], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.6059091613047 258.50369622511613 … 137.13538556670352 505.4138092341077; … ; 525.5185156067253 264.55180147693983 … 141.3857359562174 520.1867299939037; 533.2294889332621 267.41953838464894 … 141.87765625873632 522.6311223845726], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.0834390395163 258.2432663779743 … 136.99722836422478 504.90462950861695; … ; 517.6327631300433 260.5820269366482 … 139.26414959080265 512.3809844824434; 524.6988866247901 263.14136214192405 … 139.60789832688866 514.2700726834161])])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
1.4726828245004053
17.469118151198717
33.33665531195546
52.538411041690864
66.42081264366784
79.97964513218773
94.1584491407305
107.47523799606581
122.94644598321045
137.7705830402362
153.5309948454033
166.45169156145724
178.5340606458416
190.06930704191464
203.03031917426057
214.33136175071542Compute the ratio of shocked to baseline GDP
gdp_ratio = mean_gdp_shocked ./ mean_gdp_baseline17×1 Matrix{Float64}:
1.0
1.0004973770755758
1.005868833195798
1.0081920799916582
1.0091990824029278
1.0065109446702831
1.006027768981873
1.0054104646402537
1.0053920074981486
1.0051033569134404
1.0051555531792933
1.0038775978753522
1.0033325745832984
1.0035925080126677
1.0032403546248494
1.0037096061718875
1.0039899047684657the 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).^0.517×1 Matrix{Float64}:
0.0
2.7139855957660794e-5
0.0003674652725352239
0.0007175853274266766
0.0010668915096419382
0.0013223000622202595
0.0015917992138638896
0.0018546513364306968
0.002069350151154063
0.0023269171838006834
0.0025678820871797062
0.0027933372130039863
0.0029997501293237646
0.003189035106995814
0.003348413528225271
0.00352892923558482
0.0037116291028179735Finally, 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")