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, 40478.811794277804, 40474.90041986949, 40421.7688789245, 40349.93338675208, 40352.89020358631, 40424.86580933871, 40428.339846896866, 40384.22152155088, 40606.45238657089  …  40959.07689220516, 41004.90671294294, 41028.46594668649, 41045.94998585991, 40996.82238046128, 40980.71552290285, 41001.346393143445, 41073.805790479986, 41105.92343197254, 41184.27898725274], [14866.888022051655, 14805.688627359314, 14471.821612775566, 14521.12611140604, 14687.862651358295, 14685.297916404896, 14971.701644292876, 15058.67944164096, 15228.309197646731, 15445.583376254337  …  15394.18539812938, 15141.12967194757, 15253.605676082221, 15201.807957418134, 15408.989289568703, 15452.82451313394, 15756.879148035216, 15835.297796151357, 16076.532503903272, 16239.378131201327], [14866.888022051655, 14790.772619262116, 14442.676994288273, 14477.28233576374, 14628.762819939386, 14611.473214218971, 14881.42972441742, 14952.803677781505, 15106.006875891238, 15306.10037257208  …  15224.444362476093, 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, 3240.2817998263845, 3250.534180690302, 3256.7673623168484, 3252.409995331262, 3255.7784233187963, 3263.401778465545, 3274.5135694052974, 3281.9059951443137, 3288.893926070683], [3173.2320350842047, 3168.12000691056, 3169.4543754383767, 3165.237806690933, 3161.7980034575803, 3163.2453519544233, 3168.4819000940915, 3159.9042500256614, 3125.4400231254763, 3153.0016657162064  …  3188.75946583414, 3201.325022346909, 3208.218759230348, 3211.132475790808, 3203.6054348560265, 3203.692498758802, 3207.958774517035, 3215.6389174250176, 3219.651517093898, 3223.256345857097], [34195.564496956766, 33316.60150423536, 33081.35378145896, 32916.80834988196, 32351.683676831424, 32488.99664392109, 34742.6419754771, 33567.12143746159, 33108.22943923296, 33315.007224631554  …  32499.29281531485, 32605.13991064592, 32026.59603907452, 31980.032306765832, 31397.82277094411, 31566.61108614618, 31619.718060347474, 31442.659552086447, 31101.770710434983, 32141.158718320065], [34195.564496956766, 33283.036655594005, 33014.73166153511, 32817.42231404145, 32221.50959386217, 32325.67067564926, 34533.1611116992, 33331.11504417, 32842.32905087879, 33014.15246491219  …  32140.945590190393, 32213.139690092747, 31609.674132093303, 31531.917663299133, 30926.677699315802, 31061.60862287302, 31082.520291798333, 30877.331114983783, 30511.801191232706, 31499.706628057167], [33097.63671130043, 32378.949947983405, 32210.441682008543, 31998.862922602224, 31186.152595611937, 31294.283611533898, 33238.7688586709, 32286.515941322956, 31769.073409914785, 32012.57702502442  …  31466.881322010802, 31623.406014494914, 31324.057386293684, 31432.780923663704, 30788.330287672376, 30549.08840091416, 30866.22299032479, 31204.116032344846, 31237.810596659594, 31738.254462618137], [33097.63671130043, 32346.32973748464, 32145.57348094529, 31902.248448213417, 31060.668282151648, 31136.96360475605, 33038.35560235198, 32059.513331240447, 31513.928115212333, 31723.484001453347  …  31119.917784399644, 31243.208838028404, 30916.281120469146, 30992.334545071546, 30326.331053377493, 30060.364259728733, 30341.826596837116, 30643.076527448196, 30645.260536721747, 31104.843270297362], [29576.1477768849, 29605.974349916607, 29598.48717629355, 29533.271743793215, 29507.022896228234, 29570.51845917554, 29651.272966496494, 29831.019142874826, 29993.24726268078, 30148.305638370504  …  30360.615675900757, 30377.010893260907, 30362.55715141906, 30327.197911232768, 30276.934500885505, 30283.052898641607, 30363.935983634532, 30450.365893734972, 30470.372642360195, 30460.5476335904], [34346.71094688273, 34381.34847608991, 34337.6977489476, 34144.533443720626, 34133.97780502115, 34250.58668106632, 34316.1456243924, 34631.48860484354, 34955.34662461725, 35034.810141256705  …  35229.16798412023, 35293.9014041599, 35177.94780435882, 35180.76710321812, 35087.46823808329, 35167.43190264369, 35286.48315781733, 35487.48089939955, 35582.81783086957, 35641.91413013709], [28335.32931213965, 28363.904560528415, 28327.89360943022, 28168.537034984958, 28159.82885040472, 28256.02877209644, 28310.11355044314, 28570.265016217352, 28837.441214103004, 28902.99697912987  …  29063.338197549645, 29116.741936183076, 29021.082603900195, 29023.408467408095, 28946.43882475053, 29012.40720151384, 29110.622035696524, 29276.441033839787, 29355.092039258903, 29403.845269326946], [978.0617717704334, 979.0481149238866, 975.0476021837654, 969.0544623398886, 968.2085147140399, 967.536793191839, 965.2369620863507, 976.8687837678432, 988.0023979143425, 988.0940020636501  …  990.3951072109838, 992.494596162937, 989.550164252602, 990.8218664149316, 988.7303191700108, 984.6526060477331, 988.8786848653792, 996.7233200234223, 998.0500652721132, 1000.8381083303934], [0.0019383188997990075, 0.005520097121087586, 0.005197197172589929, 0.005105265915127832, 0.0061190320698054634, 0.006309794340298103, 0.0028480755259372437, 0.00685178363862482, 0.004781820547621329, 0.00018414295375790424  …  0.00031631978901813795, 0.0022272893185713016, 0.0016202458795202546, 0.0019430472825245904, 0.0024049878705258987, 0.0047246955530986234, 0.0015998634926353006, 0.006647094482979954, 0.007681061882070184, 0.006073362661699111], [2.3548476e6, 2.3481433177803312e6, 2.341418407985875e6, 2.35653403221599e6, 2.348429025498789e6, 2.357427289604897e6, 2.40847446339157e6, 2.3822878785096346e6, 2.3844204798930027e6, 2.365846405557099e6  …  2.350317073813967e6, 2.3810295849561957e6, 2.368225136235816e6, 2.3646311118460475e6, 2.343413683582957e6, 2.3375877765111667e6, 2.3437679942443725e6, 2.3462204128091605e6, 2.333977368586387e6, 2.367812516274818e6], [0.0016459319014481277, 0.0013707217613104104, 0.0011068127866682746, 0.0017770153824584402, 0.0014475803347245289, 0.0018620856628627084, 0.003919449942734016, 0.0027170791977117028, 0.002713709535841248, 0.0017508301418900703  …  0.0008801687718815064, 0.0021514265855204413, 0.001500381583631932, 0.001284621467243411, 0.00036213995327654, 0.00019922171198301326, 0.0004812347368734719, 0.0007010647864669194, 0.0003121663957909551, 0.0018543293023790446], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.6059091613046 258.5036962251161 … 137.13538556670355 505.41380923410765; … ; 549.3496231629182 259.6351681133864 … 140.65460723048056 524.1209591822778; 547.2353742381588 269.20703716100036 … 140.89677844371784 525.9559631321567], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.0834390395163 258.2432663779743 … 136.9972283642248 504.90462950861695; … ; 538.9290096207242 254.71014835403042 … 137.98652984755824 514.1789081919515; 536.3140108315931 263.834380306474 … 138.0848532783529 515.4592802062527])
 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, 66769.10532701261  …  66972.31667551612, 67165.08383411526, 67460.23760943934, 67574.48261422625, 67741.17777413143, 67805.36739918479, 68081.82388068747, 68346.1085531864, 68676.00718989965, 69051.6415312075], [64900.92049553797, 64900.92049553796, 64765.97986123299, 64783.471456978026, 64912.58402807281, 65100.836826930296, 65551.49138002844, 65670.22578483463, 65967.91064070645, 66166.13973242595  …  66233.85925808085, 66357.58146643221, 66582.04091081812, 66627.60692336688, 66724.67665278108, 66720.61752006908, 66925.15942853382, 67117.2685224477, 67373.29194195323, 67673.55431958787], [40512.94792630529, 40359.64887607413, 40490.217209359806, 40600.389508225446, 40638.57747275217, 40496.698458622355, 40771.71938622019, 40980.45946719161, 41122.10596546767, 41273.473145376265  …  41578.46472539287, 41493.11247670698, 41764.21324703791, 41812.85528340943, 41968.56168689163, 42052.97188825295, 42107.120765306994, 42085.67621333584, 42066.82704051361, 42170.05304217563], [40512.94792630529, 40318.988501228494, 40408.67447309561, 40477.80436194046, 40475.05925810422, 40293.11684112698, 40525.886182148715, 40692.33078590716, 40791.84415046342, 40900.74860228297  …  41120.00775083747, 40994.25526318469, 41220.527136615405, 41226.9599172651, 41338.79569495029, 41380.208684955374, 41391.74906996105, 41328.98991844005, 41268.861356998015, 41328.45088005366], [14866.888022051655, 14582.12551307391, 14501.43608336645, 14678.637113358724, 14835.63434858899, 14941.699500186947, 14952.62992562028, 15138.928452886887, 15232.962664224371, 15345.1664473697  …  15512.51905458658, 15573.699155695804, 15641.241600071122, 15553.870472631585, 15494.516883151071, 15731.32918452027, 15874.109960155418, 15992.3651627008, 15923.035342646122, 15972.611693163111], [14866.888022051655, 14567.434733894239, 14472.23182467144, 14634.317763234274, 14775.939925390328, 14866.58583739081, 14862.472998729583, 15032.48846788176, 15110.622969326412, 15206.590269575234  …  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 BeforeIT.Data{Float64, Vector{Float64}, Matrix{Float64}}([72421.99999999999, 72489.22579204952, 72527.1278343526, 72504.48157951208, 72811.1001158258, 73072.25048035703, 73552.03649126377, 73779.27867111871, 74275.4350645291, 74442.54307348262  …  74726.08960145077, 75241.7682754494, 75783.7197176668, 76313.05595875713, 76481.35439874424, 76788.55753523215, 77234.52648351538, 78505.99915219407, 79143.18406308976, 79768.67857654924], [72421.99999999999, 72416.19643785381, 72381.06636902588, 72285.56810138088, 72518.12871185673, 72704.90777062924, 73108.55426709374, 73260.54543713332, 73678.91065463565, 73770.28167313883  …  73902.13669252816, 74337.16274884703, 74797.1680121932, 75243.73252797313, 75333.70115350705, 75560.094631796, 75922.36376268526, 77094.48770767306, 77641.91692673948, 78176.70779357555], [64900.92049553797, 64966.37094093059, 65004.78827791556, 64980.09078653339, 65255.50486226994, 65502.466821777314, 65952.93399847954, 66168.39256681105, 66606.25230494852, 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0.0025698175100661996, 0.002784413741267725, 0.0029252593971660548, 0.003395123439117592, 0.0034719788686598694], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.6059091613046 258.5036962251161 … 137.13538556670355 505.41380923410765; … ; 582.7884051330489 284.28765010431056 … 146.71281361456937 534.7712899782745; 588.473116462272 288.6802625492379 … 147.77087011783362 538.4672862062782], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.0834390395163 258.2432663779743 … 136.9972283642248 504.90462950861695; … ; 571.7334913027571 278.89499738981146 … 143.9298181087846 524.6272128525907; 576.72875733923 282.91897187976053 … 144.82175635538783 527.7209105294514])

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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504.90462950861706; 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",
)
Example block output

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