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
using Plots, StatsPlots
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 = 20
model = Bit.initialise_model(parameters, initial_conditions, T);
Simulate the model for T quarters
data_vec_baseline = Bit.run_n_sims(model, 4)
4-element Vector{BeforeIT.Data}:
BeforeIT.Data{Float64, Vector{Float64}, Matrix{Float64}}([72421.99999999999, 72486.71586201678, 72431.35075822541, 72153.26001528693, 72111.7536222626, 72304.95497883794, 72476.08964803106, 73001.95191787623, 73515.81543617704, 73791.81755388739 … 74268.38443210113, 74367.33922854363, 74235.63222392659, 74214.14368640183, 74062.58431583918, 74155.6429790381, 74377.10096945846, 74701.92206877234, 74838.01438353542, 74919.943312615], [72421.99999999999, 72413.689036453, 72285.48217714085, 71935.40698380065, 71821.59619203875, 71941.46955291957, 72039.09484857314, 72488.6839747946, 72925.3917196043, 73125.43260041132 … 73449.47832152978, 73473.24665726729, 73269.23350596722, 73174.23089897203, 72951.22631350165, 72969.3014275863, 73113.48398857054, 73358.80664999732, 73418.412015073, 73424.7403965837], [64900.92049553797, 64966.37094093059, 64911.23252742474, 64646.85964985339, 64609.20921596349, 64788.6419334339, 64932.65555297518, 65439.376531486225, 65936.5962852122, 66171.20978169127 … 66580.17876723164, 66663.40689358363, 66530.05512003058, 66498.78688086596, 66353.13305813873, 66435.13740733286, 66639.29782631702, 66934.5701131578, 67051.24053850191, 67103.2998720579], [64900.92049553797, 64900.92049553796, 64780.50861732079, 64451.67076514048, 64349.23991590876, 64462.94188819163, 64541.143911971325, 64979.28014630127, 65407.043154285304, 65573.64354720153 … 65846.04518330721, 65861.93601271276, 65663.96752775648, 65566.9841894788, 65357.46046467565, 65372.30845977715, 65507.14092277816, 65731.1090685371, 65779.34549076608, 65764.09638086773], [40512.94792630529, 40519.633345661976, 40556.5767968675, 40544.184324357644, 40512.94609604769, 40556.77382695169, 40670.086215905314, 40714.599297304754, 40711.18311338346, 40976.495036879736 … 41415.73960944828, 41503.89354346838, 41569.61882891872, 41629.27293627703, 41621.37866176548, 41646.98372996935, 41709.970776981594, 41825.81995734321, 41900.738583380036, 42022.9452692686], [40512.94792630529, 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14959.093152948022, 15055.03438992202, 14988.795266012967, 15177.767226321937, 15205.610315120606, 15489.180356367642, 15550.584470953008, 15771.576743021578, 15915.283311281517], [15944.236265986638, 16223.742332742833, 16532.040249132082, 16170.004152243748, 15745.413793636937, 15868.170203093798, 15330.428671026672, 15948.067682791865, 16237.167095828627, 16067.308941145719 … 16426.047931219306, 16740.582116976504, 16709.869066144453, 16835.811409604135, 16422.723881232956, 16038.312050702847, 16156.755974419288, 16802.26079553622, 16996.783182476538, 16254.71565644277], [15944.236265986638, 16207.397704803378, 16498.746582393374, 16121.18190328408, 15682.058673636619, 15788.399064220945, 15237.993805469869, 15835.938737186634, 16106.762386495622, 15922.211377809446 … 16244.929261057368, 16539.31593931169, 16492.34015773455, 16599.90252887135, 16176.290060779747, 15781.731226418464, 15882.263544098247, 16500.16180102852, 16674.371185567754, 15930.314740289361], [15944.236265986638, 15955.198320777621, 15959.021378013527, 15919.001220034956, 15911.464890623974, 15952.66823799256, 15998.60818604756, 16068.918543698166, 16127.629569921624, 16221.903467623373 … 16357.471133735307, 16385.409183575954, 16380.288132078025, 16376.337309503137, 16344.911768058511, 16360.89748344396, 16406.13314156445, 16463.671585315937, 16483.874028954968, 16489.61974427027], [15944.236265986638, 15939.124237812988, 15926.881706731067, 15870.936826641095, 15847.44162767653, 15872.472317661599, 15902.144530105039, 15955.93991022614, 15998.1045835811, 16075.409821770781 … 16177.108612491009, 16188.413126162399, 16167.049704972098, 16146.866729725583, 16099.645569765049, 16099.155939255063, 16127.403960698643, 16167.660310859928, 16171.1914062839, 16160.530766946793], [3173.2320350842047, 3171.3149518192704, 3175.850179943417, 3174.823582047954, 3174.57158734059, 3179.2276997043937, 3187.7021598076317, 3182.27846715603, 3150.744431793927, 3181.7346631645555 … 3224.311721226385, 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BeforeIT.Data{Float64, Vector{Float64}, Matrix{Float64}}([72421.99999999999, 72461.66822400881, 72403.67260994787, 72503.66933215446, 72712.55305233836, 72957.70248863344, 73532.12242131673, 73749.24872140557, 74151.09726838874, 74448.34708668212 … 74703.69191995163, 74894.45312178989, 75233.63939140215, 75361.31813189153, 75548.55638163532, 75626.0007870408, 75924.75252691313, 76198.67045140777, 76535.69838657463, 76928.63591992702], [72421.99999999999, 72388.66663271685, 72257.8597695359, 72284.75830644958, 72419.97817405686, 72590.93562499504, 73088.76026909122, 73230.7266243845, 73555.57144612282, 73776.03327257212 … 73879.98597477184, 73994.0232440942, 74254.24862611463, 74305.33076196112, 74414.90038683712, 74416.13645979973, 74634.84198573335, 74828.6440004228, 75083.89264858632, 75393.3448389658], [64900.92049553797, 64966.37094093059, 64896.67445301513, 64979.6651846411, 65174.82922407807, 65429.75984655628, 65949.13186801648, 66135.21452324299, 66502.0047066637, 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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.
In this case, let's define an interest rate shock that sets the interest rate for a number of epochs.
We do this by first defining a "struct" with some useful attributes
struct CustomShock
rate::Float64 # target rate for the first 10 epochs
final_time::Int # number of epochs for the shock
end
and then by making the struct a callable function that changes the interest rate in the model, this is done in Julia using the syntax below
function (s::CustomShock)(model::Bit.Model)
if model.agg.t <= s.final_time
model.cb.r_bar = s.rate
end
end
Now we define a specific shock with a rate of 0.01 for the first 10 epochs, and run a shocked simulation
custom_shock = CustomShock(0.0, 10)
data_vec_shocked = Bit.run_n_sims(model, 4; shock = custom_shock)
4-element Vector{BeforeIT.Data}:
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518.6059091613046 258.503696225116 … 137.13538556670355 505.41380923410765; … ; 531.7542152421476 273.3660100709633 … 146.0031755806213 533.339608461373; 526.785194778326 270.51610672146796 … 146.09235218422498 534.192769650112], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.0834390395163 258.2432663779743 … 136.9972283642248 504.90462950861695; … ; 521.6673690100888 268.1805299569942 … 143.23364119939703 523.2226889037785; 516.2719625930084 265.1173243182766 … 143.1767371778878 523.5317019611979])
Finally, we can plot baseline and shocked simulations
Te = T + 1
StatsPlots.errorline(
1:Te,
data_vec_baseline.real_gdp,
errortype = :sem,
label = "baseline",
titlefont = 10,
xlabel = "quarters",
ylabel = "GDP",
)
StatsPlots.errorline!(
1:Te,
data_vec_shocked.real_gdp,
errortype = :sem,
label = "shock",
titlefont = 10,
xlabel = "quarters",
ylabel = "GDP",
)
Note that, importantly, once the function centralbankrate has been changed, the model will use the new interest rate in all the simulations, unless the function is changed again. To restore the original interest rate, we can simply re-import the function centralbankrate