Scenario analysis via function overloading
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_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 = 20
model = Bit.initialise_model(parameters, initial_conditions, T);
data = Bit.initialise_data(model);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}}([72422.00000000017, 72493.96710169957, 72678.16167329914, 72813.37922795233, 73132.20296122217, 73470.88843177803, 73919.59388208514, 73963.3802541919, 74475.49588137458, 74755.97766786341 … 75112.1866490143, 74719.35451755438, 74553.92719937787, 75176.78828635807, 75820.27478425998, 76320.2656857601, 76038.7838842072, 76265.15919729398, 76599.01020563598, 76792.78484883266], [72422.00000000017, 72420.93297086642, 72531.79604283429, 72593.53309218147, 72837.93952964553, 73101.54172266122, 73473.89546952673, 73443.35262411917, 73877.3647335248, 74080.8857626671 … 74283.97651497467, 73821.02978928149, 73583.38492060901, 74123.38660881054, 74682.54147533698, 75099.29451264787, 74746.93602687106, 74893.937301035, 75146.00350568997, 75260.20499413139], [64900.92049553808, 64966.37094093028, 65137.52925866544, 65268.057429486245, 65576.09827107853, 65892.3506845774, 66304.0988731047, 66478.73060314296, 66912.12141831731, 67152.17805442108 … 67440.59598304605, 67032.22687126244, 66948.63744333234, 67550.43642854875, 68142.38904758407, 68573.29534964022, 68233.84853820741, 68429.11271566758, 68719.42462796005, 68928.46103430497], [64900.92049553808, 64900.92049553806, 65006.34961243661, 65070.992956345646, 65312.23848120062, 65561.10216695647, 65904.31811049666, 66011.32664449497, 66374.7336035017, 66545.75308032392 … 66696.97517355168, 66226.32179648681, 66077.10075055747, 66603.89768068618, 67119.86748604101, 67476.26016357374, 67074.60128924943, 67198.7802980225, 67415.8857945886, 67552.83217796529], [40512.94792630531, 40546.3512897014, 40583.64252369664, 40563.179918964735, 40580.78222226571, 40679.31253758924, 40891.32237666878, 40238.31105300312, 40602.24280934745, 40777.65521891855 … 41252.2800681735, 41400.53726827271, 40840.74821902299, 40973.12532621712, 41301.21593390515, 41645.97015509965, 42052.84464898807, 42151.47596786995, 42287.33140385421, 42107.38596600743], [40512.94792630531, 40505.50282129368, 40501.91163937341, 40440.70711995003, 40417.49655946256, 40474.81289785985, 40644.76802600795, 39955.40032795103, 40276.15614407002, 40409.40821299375 … 40797.419706241184, 40902.79305417979, 40309.083767100914, 40398.996530123884, 40681.46390582649, 40979.71816319704, 41338.39506839735, 41393.60661553203, 41485.18297285381, 41267.03447214433], [14866.888022051655, 14907.471444034272, 15102.63233498256, 15193.391437582619, 15284.937543058235, 15309.594124023424, 15197.890359767729, 15227.56768925167, 15301.483376382008, 15150.552528073053 … 14977.555786895646, 14871.746872481182, 14898.339183615277, 14945.738480864626, 14933.75598783856, 14889.787808767702, 15277.138558177987, 15569.534594828734, 15906.839920968363, 16065.845591565747], [14866.888022051655, 14892.452894720886, 15072.217334761097, 15147.517884779267, 15223.435250077464, 15232.631012125372, 15106.254634355124, 15120.504492437245, 15178.59337467862, 15013.733832230535 … 14812.408637820961, 14692.949048886161, 14704.392753101121, 14736.313918485577, 14709.665114216217, 14651.581068724156, 15017.590236854649, 15289.599602550423, 15605.103058858942, 15745.214019851817], [15944.236265986634, 16006.993513375412, 16026.893728817375, 15904.583251609734, 16042.04177705027, 16107.084564518605, 16318.906372785723, 18226.173729530983, 18326.344715352247, 18408.71976338555 … 17454.968555953372, 16748.699260385805, 17712.26487949881, 18131.036669121335, 18614.279259794253, 18156.560484954567, 16785.302493326246, 17291.70021197853, 16875.58674463276, 17137.703582231647], [15944.236265986634, 15990.867249284222, 15994.61737026612, 15856.562390526433, 15977.49310940918, 16026.112375337927, 16220.511477967348, 18098.027694326986, 18179.161303268036, 18242.477837522456 … 17262.504689671143, 16547.33549313764, 17481.686792413926, 17876.97866959386, 18334.959703175373, 17866.09193435657, 16500.131479889675, 16980.801261477674, 16555.473723072286, 16795.680574241105], [15944.236265986634, 15959.311013397168, 15978.726447067567, 15997.677192969235, 16044.945338697755, 16106.902407485864, 16194.157421353631, 17758.39275978861, 18196.09484922238, 18409.708577228776 … 16437.101303502295, 16436.457058361746, 18663.03120086422, 18720.680501946208, 18755.25698737838, 16750.679071712235, 16731.04338459221, 16783.975026993237, 16830.084019100144, 19071.549246513852], [15944.236265986634, 15943.232787095618, 15946.547091995746, 15949.375252453985, 15980.384987940615, 16025.931134029795, 16096.514700711301, 17633.535636317043, 18049.957506063434, 18243.457721775805 … 16255.860755448384, 16238.847270160908, 18420.07604731513, 18458.36022071168, 18473.821966829237, 16482.70180390734, 16446.794196963187, 16482.204804449706, 16510.83413878506, 18690.931819620364], [3173.232035084206, 3175.4276444388274, 3168.372939697924, 3161.146374188216, 3154.0949032821304, 3150.9738605096545, 3160.050698365898, 2627.296985519405, 2989.753003299205, 3130.589917074072 … 3227.294655495158, 3242.706041992152, 3203.639666985967, 3176.3167982170135, 3130.0916811936786, 3281.192930203565, 3287.7981103505663, 3296.597313733401, 3309.344747104528, 3301.6162183104743], [3173.232035084206, 3172.2285561931917, 3161.9921935124153, 3151.6018945563264, 3141.4037118209926, 3135.133548098387, 3140.997163221852, 2608.82477643187, 2965.741556655075, 3102.3187877619357 … 3191.7095093496687, 3203.7201186949246, 3161.934717836427, 3131.8092112352433, 3083.122587823743, 3228.7004245079934, 3231.940629112063, 3237.325603462029, 3246.5697833410964, 3235.72473496216], [34195.564496956766, 34151.49068377491, 33767.87979504818, 34388.64138790022, 34520.15154876501, 35407.77780803837, 35708.641042203366, 35046.133798803945, 34584.757934594345, 35311.43015650366 … 34197.05082680029, 34661.056111955404, 34105.141963396854, 33854.60219142597, 34201.13069330515, 35428.78422994657, 35707.8716102173, 36069.93503255158, 36703.12939473381, 36643.30744407344], [34195.564496956766, 34117.084725065935, 33699.8750890694, 34284.81143242093, 34381.252160506985, 35229.778787069925, 35493.33568416082, 34799.728647498545, 34306.99918029905, 34992.54648454546 … 33819.983598264334, 34244.33832826391, 33661.16156635679, 33380.22046331451, 33687.92013447606, 34861.99474284907, 35101.21885916919, 35421.409739562434, 36006.90769713801, 35912.00443287319], [33097.63671130043, 33118.33982918603, 32802.886709244965, 33236.41676810441, 33295.71012991704, 34032.880602391095, 34197.16626933982, 34774.80601639765, 34339.332954300895, 34892.37999901715 … 32769.66858880817, 32962.68499554026, 33002.56704615597, 32727.71438127072, 33230.10709058276, 33800.8369930078, 33784.37342650175, 34817.48660993387, 35173.87725855316, 35161.4577350455], [33097.63671130043, 33084.97471949801, 32736.825390635233, 33136.06573549457, 33161.73754981038, 33861.79334973139, 33990.9743529642, 34530.30853809431, 34063.54526879058, 34577.280604624684 … 32408.340117022533, 32566.38613518537, 32572.939958363117, 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BeforeIT.Data{Float64, Vector{Float64}, Matrix{Float64}}([72422.00000000017, 72487.48275676479, 72694.27080109638, 72986.84461801818, 73207.83690720517, 73482.15798115992, 74048.81942236157, 74517.34833533257, 74931.76590500025, 75362.13911404676 … 75966.5238504768, 75902.01093720722, 76095.7092528793, 76462.66819748963, 76584.23941402546, 76759.23145358372, 77345.46336085639, 77703.91732856855, 78131.29525651722, 78573.64960371067], [72422.00000000017, 72414.45515859242, 72547.87272866262, 72766.4747365278, 72913.2691458859, 73112.75461870575, 73602.34184402003, 73993.42582231294, 74329.97033961499, 74681.57320264481 … 75128.89353098099, 74989.46754345177, 75105.09607075356, 75391.24835121575, 75435.04231116716, 75531.23770863102, 76031.41589700263, 76306.82704530322, 76649.2226399312, 77005.52842240143], [64900.92049553808, 64966.37094093028, 65162.31405656382, 65430.233968467204, 65639.82075870497, 65911.82735918561, 66439.02327151054, 66857.21824347794, 67226.66324526326, 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0.0008909853555348076], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.6059091613056 258.50369622511647 … 137.13538556670355 505.4138092341077; … ; 539.0799357104687 271.29991393580974 … 142.1493215407563 521.4714047505063; 546.3222557235674 274.90580261024763 … 142.8772882820406 523.9255921686716], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.0834390395163 258.2432663779743 … 136.9972283642248 504.90462950861695; … ; 528.8541278796398 266.1536256014616 … 139.4528909206057 511.57961316078; 535.4191157352755 269.41941354582417 … 140.025837404896 513.4694300500374])
BeforeIT.Data{Float64, Vector{Float64}, Matrix{Float64}}([72422.00000000017, 72484.65950782453, 72325.12553231721, 72355.84182954181, 72552.66837064592, 72809.32974700363, 73241.53478284585, 73648.9791737542, 74075.82820355576, 74662.16109275653 … 75451.78690236107, 75882.34127229832, 76153.02937393876, 76127.01971847634, 75958.84326291754, 76093.19294174798, 76073.32709818143, 75881.99088553361, 75971.4656462703, 75907.65316864463], [72422.00000000017, 72411.63475393756, 72179.4708768711, 72137.37714083589, 72260.73682338874, 72443.30877040887, 72799.92472965567, 73131.16205986086, 73480.90688578557, 73987.9164082423 … 74619.83223119682, 74970.03436006156, 75161.66999905104, 75060.30308816835, 74819.03064243497, 74875.85447709172, 74780.89237484362, 74517.65822656795, 74530.3628396864, 74392.73818941804], [64900.92049553808, 64966.37094093028, 64825.5701748665, 64855.89772383799, 65023.996384697166, 65271.170038854834, 65695.5546422475, 66062.53357951314, 66462.10633549573, 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33702.10531671389, 33157.02171786423, 33865.64468902749, 33255.00061199929, 32064.498072995993, 33032.32743318984, 31822.123093964296], [29576.14777688495, 29605.97434991655, 29592.615072189586, 29640.290913389825, 29722.697348139303, 29815.132100445506, 29965.88249923163, 30129.766232861875, 30293.85856050683, 30519.555009459913 … 30874.852207921802, 31056.49895065232, 31210.10271716883, 31172.06487154427, 31141.107156940263, 31187.84272742597, 31206.96743918902, 31133.694735436922, 31157.701039458883, 31145.581370434837], [34346.710946882784, 34381.34847608996, 34260.13000986009, 34245.645022902056, 34332.15490688423, 34481.646370049966, 34744.88099298299, 34948.26907579087, 35177.12704945517, 35489.15422290778 … 35853.28427982925, 36064.64076951749, 36124.695356791904, 36114.64331386771, 35982.39250345339, 36058.67278721935, 36021.359447946284, 35904.98264665361, 35965.21560111584, 35906.47427667528], [28335.329312139693, 28363.904560528455, 28263.901821848536, 28251.952005862582, 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0.0023916094830027657, 0.0009131166614464448, -0.0008201536369335516, 0.003909269574506435, 0.0012623084469975954, 0.0060183122122274835, 0.0055841454115592715], [2.3548476e6, 2.340685494862696e6, 2.3385630133402785e6, 2.342639654766581e6, 2.3540881404785034e6, 2.3748204141006977e6, 2.350997070095161e6, 2.3531480909131155e6, 2.378346286230121e6, 2.394873543391766e6 … 2.400206344434906e6, 2.419071891927272e6, 2.40771943328037e6, 2.4052065397819704e6, 2.404392393331838e6, 2.4048332281330475e6, 2.3928050067851776e6, 2.3794113053900884e6, 2.395477991289756e6, 2.371213140548911e6], [0.0016459319014481277, 0.0010205681510567827, 0.0010855539517081354, 0.0013470651232251156, 0.0018569218346373506, 0.002789368403336227, 0.0017198356941402707, 0.00174442428626325, 0.002701451013792416, 0.0032594202487394057 … 0.0029847813748338373, 0.003492586275257361, 0.002804102830052846, 0.002548732536788276, 0.0023477019094645672, 0.0021731071081508195, 0.0016099697233811967, 0.0009691774330682411, 0.0016996980693013194, 0.0007056782699523801], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.6059091613056 258.50369622511636 … 137.13538556670355 505.4138092341077; … ; 556.8764092371811 276.57525893948565 … 143.6849044910822 526.53064328301; 551.7587879492049 278.47353501589515 … 143.54451259144216 526.5687549174529], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.0834390395163 258.2432663779743 … 136.9972283642248 504.90462950861695; … ; 546.313020082516 271.3289025805726 … 140.95934539643596 516.5428829925825; 540.7471492290998 272.91594349641406 … 140.6797456906998 516.0598422964172])Now, apply a shock to the model and simulate it again Here, we do this by overloading the centralbankrate function with the wanted behaviour
import BeforeIT: central_bank_rate
function central_bank_rate(cb::Bit.CentralBank, model::Bit.Model)
gamma_EA = model.rotw.gamma_EA
pi_EA = model.rotw.pi_EA
taylor_rate = Bit.taylor_rule(cb.rho, cb.r_bar, cb.r_star, cb.pi_star, cb.xi_pi, cb.xi_gamma, gamma_EA, pi_EA)
if model.agg.t < 10
return 0.01
else
return taylor_rate
end
end
data_vec_shocked = Bit.run_n_sims(model, 4)4-element Vector{BeforeIT.Data}:
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0.006700968653839068, 0.00399273250491583, -0.00016164270883201048, 0.0026640482926796327, 0.002930348045554698, 0.0015011146133947495, -0.0018194230417055701], [2.3548476e6, 2.3461216237325454e6, 2.340038181429603e6, 2.380982462131816e6, 2.389501172146929e6, 2.395449296938976e6, 2.3870941824034876e6, 2.368648531091481e6, 2.3859996285436284e6, 2.4214741190047353e6 … 2.411229716632751e6, 2.3987657252233885e6, 2.3792282885524547e6, 2.3784255963564613e6, 2.3618941717425785e6, 2.3686006625365033e6, 2.3491631492793593e6, 2.339961655357318e6, 2.352227121434333e6, 2.348126822878076e6], [0.0016459319014481277, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01 … 0.00833930126912169, 0.007257385716761685, 0.006040676591538585, 0.005714056199216719, 0.004698994024250506, 0.0046266918733940616, 0.003538124225804789, 0.002958163129971774, 0.003289185613943668, 0.0028324680032542236], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.6059091613056 258.50369622511636 … 137.13538556670355 505.4138092341077; … ; 557.5543406573823 276.4342966044195 … 142.95937820244276 527.1028944659823; 559.9704809061084 274.7854600035847 … 143.24880551874048 528.5452941123779], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 518.0834390395163 258.2432663779743 … 136.9972283642248 504.90462950861695; … ; 546.9780918209385 271.19061416017814 … 140.2475816166793 517.1042791423008; 548.7949586229361 269.30147265769347 … 140.38994014511937 517.9969350230548])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, you need to close and restart the Julia session.
function central_bank_rate(cb::Bit.CentralBank, model::Bit.Model)
gamma_EA = model.rotw.gamma_EA
pi_EA = model.rotw.pi_EA
taylor_rate = Bit.taylor_rule(cb.rho, cb.r_bar, cb.r_star, cb.pi_star, cb.xi_pi, cb.xi_gamma, gamma_EA, pi_EA)
return taylor_rate
endcentral_bank_rate (generic function with 2 methods)