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.init_model(parameters, initial_conditions, T);
data = Bit.init_data(model);Simulate the model for T quarters
data_vec_baseline = Bit.ensemblerun(model, 4)BeforeIT.DataVector{BeforeIT.Data}(BeforeIT.Data[BeforeIT.Data{Float64}([72422.0, 72492.46477816327, 72448.02976911361, 72816.1559237421, 73173.98504608909, 73548.00242314098, 73949.84569260138, 74297.52813473548, 74906.01649969361, 75317.83718128318 … 75767.5583369466, 76058.23236703314, 76751.51174549668, 77271.16207720309, 77875.84680605077, 78512.56998595702, 79048.86639154273, 79507.22672687951, 79662.85226752918, 80467.68714451285], [72422.0, 72419.43216084767, 72302.1275983794, 72596.30140426647, 72879.5534951452, 73178.26805301158, 73503.9648766594, 73775.15115110556, 74304.42773415787, 74637.67134325481 … 74932.12187256207, 75143.81077753552, 75752.36133307945, 76188.41335098288, 76707.26828105669, 77256.52634120939, 77705.87925449762, 78077.713547513, 78151.72754449387, 78861.76600862629], [64900.92049553802, 64966.37094093021, 64934.592026839324, 65284.68170469612, 65627.28121304217, 65957.07689029197, 66346.84939055654, 66674.25361479213, 67225.21617902753, 67597.39585432988 … 68029.13805148638, 68315.54308846593, 68972.75846866897, 69460.35802838251, 70034.39194033417, 70614.39834574437, 71091.73400848002, 71524.89221375942, 71683.08515154442, 72447.73365988904], [64900.92049553802, 64900.920495538, 64803.821073334446, 65087.56703772113, 65363.21547739013, 65625.50298649908, 65946.81086357421, 66205.47495736614, 66685.31382266367, 66986.95029295333 … 67279.02779564161, 67494.20915058407, 68074.87178862494, 68487.05683610993, 68983.47962555297, 69484.70960563926, 69883.93320523111, 70238.89872258196, 70323.32863878277, 71001.86947688414], [40512.94792630534, 40542.44514417396, 40465.60309201002, 40514.58155523012, 40552.91225306137, 40778.325952936546, 40764.757516503945, 40858.96112852201, 41150.9997250641, 41377.8490289921 … 41519.12384774425, 41471.42904036138, 41596.44218172588, 41748.39322833686, 41860.13500781279, 42113.95682833692, 42424.3813108187, 42524.204494397694, 42667.315381314234, 42680.62752229289], [40512.94792630534, 40501.600611017035, 40384.109925805096, 40392.25548972202, 40389.73873118136, 40573.32856124129, 40518.96628904565, 40571.686687441535, 40820.5058571214, 41004.18190824257 … 41061.32118400462, 40972.83251922707, 41054.9401133526, 41163.401125531964, 41231.99602981477, 41440.21798831593, 41703.619571930285, 41759.633608588316, 41857.959033869825, 41828.83565075747], [14866.888022051655, 14707.303929988817, 14901.10516391379, 14986.262162100631, 15185.33043256929, 15374.831072516181, 15412.63954074574, 15569.025334293781, 15695.670693837583, 15502.608254862196 … 15453.423830222197, 15798.223899184373, 15850.326782443524, 15971.549653292132, 16111.617730771059, 16369.626351956027, 16522.270150587105, 16520.094779073348, 16666.810513470842, 16851.882184994993], [14866.888022051655, 14692.48703966853, 14871.096016712938, 14941.013996709507, 15124.228930607323, 15297.540006883448, 15319.708984503415, 15459.56138984819, 15569.614876185062, 15362.610281873234 … 15283.02961334718, 15608.287365563407, 15643.987386886853, 15747.751090180232, 15869.852263616865, 16107.745163377633, 16241.567879954713, 16223.069034581056, 16350.657768443936, 16515.563412321044], [15944.236265986641, 16136.3632016077, 15791.855861635446, 15992.025136507695, 16104.680811202574, 16092.948398737162, 16312.800807124093, 16193.80242148493, 16404.546468219578, 16742.02975524415 … 16612.26139412151, 16392.713074527786, 16804.881943038406, 16880.891930728165, 16999.663210396106, 17143.914735013233, 17301.592526410404, 17484.792566521348, 18149.21249605001, 18571.65977149275], [15944.236265986641, 16120.106603874701, 15760.052842871837, 15943.740261300753, 16039.880101692024, 16012.047273707281, 16214.44272583188, 16079.945744488989, 16272.797493702552, 16590.839052949264 … 16429.0894768899, 16195.629204980927, 16586.11615794629, 16644.351367028663, 16744.572034190012, 16869.646485319478, 17007.650092141026, 17170.421880467948, 17804.940066357165, 18201.01880971175], [15944.236265986641, 15960.004604142443, 15952.264154401513, 16002.945117968848, 16060.539189259991, 16140.062699018054, 16211.713227715925, 16297.969712112295, 16405.038082479212, 16493.259368246712 … 16616.633091495773, 16689.544395320798, 16804.984823364743, 16881.667031844176, 17027.638889352344, 17165.212426896178, 17276.031387532035, 17387.852975247955, 18319.01618759648, 18592.53011432452], [15944.236265986641, 15943.925679082025, 15920.13809140616, 15954.627271956919, 15995.916093230535, 16058.92472491594, 16113.96465428632, 16183.380647425445, 16273.28515968634, 16344.31521371635 … 16433.412970580714, 16488.891826374474, 16586.217698977565, 16645.115607175027, 16772.12791960318, 16890.603456849716, 16982.5232198409, 17075.22523042182, 17971.52275151164, 18221.472635978225], [3173.2320350842083, 3176.1212351840504, 3171.062153200024, 3160.6461071842573, 3149.646206737345, 3156.302999600741, 3159.1433410293635, 3175.111218241362, 3182.347946455056, 3195.6134763461464 … 3209.5952912063576, 3214.622762681308, 3212.952265822965, 3185.7679023561054, 3216.690980485595, 3246.6510974654166, 3257.8833655156777, 3292.618379874192, 3005.8499608877178, 3227.9811350015734], [3173.2320350842083, 3172.921448179603, 3164.6759912414554, 3151.1031380133104, 3136.972915580788, 3140.435896986844, 3140.09527679903, 3152.787393175924, 3156.7897221351036, 3166.755144780917 … 3174.2053037097817, 3175.9744748523003, 3171.1260853547687, 3141.1278834204136, 3168.422407423407, 3194.7111918119203, 3202.534115695836, 3233.4182094944167, 2948.831990022471, 3163.559212178909], [34195.564496956766, 34414.84385571856, 34504.23661158909, 34264.208338207696, 33550.02770109073, 34204.837119604024, 34656.00000187822, 35175.75819686894, 35303.29815688552, 35482.01213914202 … 34782.63946204291, 35184.06550167711, 34568.97819732683, 34735.17957463381, 34208.14107893254, 34723.17092211263, 35835.831682923475, 34899.19060711266, 34630.57076434725, 34378.06967012931], 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0.002112466284585445, 0.002085660993826706, 0.0008472982326339839, 0.0004442580459939429, 0.0008091422713830549, 0.0010318206112488822 … 0.002829548431070722, 0.0020708123928684942, 0.0025806991102408686, 0.002067825566510074, 0.0016299792982310502, 0.0010597357596693053, 0.0005854369023931946, 0.0005473501507919763, 0.0004119878849245615, 0.0], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.6059091613043 258.50369622511613 … 137.13538556670355 505.41380923410753; … ; 581.8069148707513 284.89205346134065 … 145.51865196970635 528.8150849453245; 583.0548659077145 286.45890463832757 … 146.7689150421452 532.9682707664736], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.0834390395163 258.24326637797435 … 136.9972283642248 504.904629508617; … ; 570.7706189301841 279.48793581895507 … 142.75830851733156 518.7839910787471; 571.4186406629029 280.7419463679184 … 143.83979763960335 522.3316408203]), BeforeIT.Data{Float64}([72422.0, 72485.73151741322, 72518.52425247895, 72686.86295563477, 72720.99603023783, 72763.04037866712, 72855.16343676993, 73123.18839925966, 73085.36540575571, 73321.69780644611 … 73222.49308467793, 73352.57374717169, 73670.61524170214, 73812.19477087002, 73942.32770160878, 74402.05695814271, 74759.57432906172, 75173.74031575487, 75404.64706076292, 75755.49395780248], [72422.0, 72412.70568352895, 72372.48011379638, 72467.39881166049, 72428.38717978528, 72397.25210411537, 72415.88301076641, 72609.06805705783, 72498.39873995628, 72659.5583199643 … 72415.11929464484, 72470.68134720181, 72711.57190916374, 72777.9142227428, 72832.77422920348, 73211.77327726058, 73489.45938272521, 73822.14176367912, 73974.29623648431, 74243.61567195276], [64900.92049553802, 64966.37094093021, 64986.97749284444, 65138.66395190699, 65164.05533168824, 65188.705887595366, 65277.35002736114, 65517.42141055815, 65472.46653076667, 65690.1136840872 … 65577.90766793583, 65691.8977850167, 65992.47000546071, 66111.60798880526, 66221.28279298749, 66660.4069876102, 66981.90412802843, 67371.83005387761, 67575.53420460096, 67899.74358127161], [64900.92049553802, 64900.920495538, 64856.10104091219, 64941.9901577365, 64901.853486797336, 64860.994674281676, 64883.760049990684, 65056.77630121388, 64946.6409408162, 65096.89203970392 … 64854.82543424198, 64902.107019175455, 65133.38069082919, 65185.23057433473, 65227.58869984773, 65593.97417859589, 65843.92657357336, 66160.50722267306, 66293.69382979316, 66544.64519075131], [40512.94792630534, 40504.27235241091, 40574.60292285779, 40632.75455997365, 40686.93301026493, 40760.21825448139, 40762.48366947408, 40887.39414522995, 40960.4893153374, 41039.998250596334 … 41164.02751847219, 41235.14298253374, 41279.48704068517, 41409.941264854424, 41529.29567862018, 41555.291025792205, 41742.81193449831, 41843.006816857654, 41988.18115571652, 42069.14693573797], [40512.94792630534, 40463.4662764771, 40492.89024327232, 40510.07169357646, 40523.22022652327, 40555.311892294376, 40516.70615218351, 40599.919795029164, 40631.52548366661, 40669.38212767735 … 40710.14025636843, 40739.38724622779, 40742.11109116866, 40829.691661353485, 40906.12116330457, 40890.489718079305, 41033.62960145353, 41090.683636041955, 41191.707306065786, 41229.558591270295], [14866.888022051655, 14842.041981419392, 14923.223779292734, 15027.871138346238, 15091.160255665905, 15232.165195482678, 15312.91994372993, 15237.140965808147, 15504.843335097086, 15394.009609232497 … 15317.48890838018, 15504.708640498991, 15474.574259880184, 15433.281489076231, 15685.94283044312, 15806.08893612776, 15928.863853902756, 15895.71424956377, 16071.65029387546, 16259.58234444184], [14866.888022051655, 14827.089349093669, 14893.17008769215, 14982.497342573199, 15030.437668030132, 15155.591327822016, 15220.590647096378, 15130.010460437596, 15380.320099212337, 15254.992348005677 … 15148.593551874801, 15318.300938419832, 15273.126406904905, 15217.02531504597, 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16000.313425317763, 15998.274945738647, 16024.909880912288, 16069.878552961682, 16074.882738624474, 16106.591906349018 … 16108.208738756313, 16135.814686487029, 16201.20878071993, 16212.408799967434, 16226.703259842372, 16280.858995634715, 16341.366086025579, 16441.06524247286, 16518.06206862393, 16555.004778956878], [15944.236265986641, 15938.992356310617, 15942.179857945277, 15951.674622234883, 15935.932660836519, 15917.84975517827, 15928.287638821446, 15956.893169779532, 15945.781375145973, 15961.139593965387 … 15930.594661548977, 15941.81941662257, 15990.301606818415, 15985.235239932452, 15983.210858300663, 16020.397906714174, 16063.737253923604, 16145.460422452317, 16204.730932993734, 16224.610890146854], [3173.2320350842083, 3171.1829373187575, 3178.9030996948964, 3182.94088573236, 3187.897639605134, 3191.7217086787673, 3190.959941097948, 3205.0035668724518, 3208.0763970752478, 3213.810345572707 … 3223.859990910431, 3229.302931695057, 3237.6278347373373, 3237.194379797533, 3245.041279460208, 3222.8066997305964, 3227.572363555235, 3230.4877484869353, 3266.8072623201156, 3269.396838707655], [3173.2320350842083, 3167.988125408193, 3172.501146953363, 3173.330601722247, 3175.070435432933, 3175.6765520911445, 3171.7200385822916, 3182.469572299325, 3182.3115411979206, 3184.787685220723 … 3188.312716435802, 3190.478149316211, 3195.480427959769, 3191.833756286404, 3196.347291434113, 3171.2482566154445, 3172.73807729659, 3172.404665950221, 3204.8391921472803, 3204.1483685304142], [34195.564496956766, 33566.12704668554, 34010.541823692496, 34391.53892443988, 34209.34528125539, 34528.06096906069, 35058.378571864545, 34624.15963216198, 35082.47158229052, 34799.27323153096 … 35982.00915907253, 35998.099336402236, 36882.76643697077, 37966.44130759879, 38000.79627689138, 38508.58039867984, 38676.906183384745, 39000.03113222018, 39511.8871798683, 39400.04105455501], [34195.564496956766, 33532.31081324842, 33942.04842372376, 34287.700220400424, 34071.69649006829, 34354.48438705197, 34846.993973332865, 34380.72133046566, 34800.715566454295, 34485.01464782645 … 35585.26042949603, 35565.30674854358, 36402.62695230789, 37434.443148650105, 37430.56922597487, 37892.5203501214, 38019.81152945657, 38298.82369744564, 38762.38615308162, 38613.720968448135], [33097.63671130043, 32501.666671040275, 32965.05446398422, 33563.42484705959, 33756.54874852897, 33731.716799458234, 34480.696620882176, 33558.98803521428, 34508.58883753418, 33910.856039898485 … 35355.71239912697, 35030.226843650285, 36511.82403222785, 37339.13942806099, 36714.75686276264, 37986.585090600536, 37619.60114045997, 38138.264882763666, 38867.59212205209, 38240.693092239744], [33097.63671130043, 32468.92282943724, 32898.66655778449, 33462.086475813645, 33620.72188333521, 33562.14353229497, 34272.795157402994, 33323.03882689466, 34231.441816116756, 33604.62040329758 … 34965.869410771, 34609.07064906175, 36036.51347208063, 36815.93122765266, 36163.82768279434, 37378.875919989616, 36980.46938894138, 37452.55171513746, 38130.31272885096, 37477.51050967743], [29576.147776884885, 29605.974349916614, 29626.459587767375, 29668.038846530584, 29664.315241539098, 29636.7453811213, 29710.01045244616, 29762.241518163923, 29785.269566973042, 29833.367837350874 … 29849.076093989992, 29902.328964003376, 30013.16869782268, 30078.575999199547, 30106.694348969915, 30239.045969987714, 30376.269064743956, 30589.036617824393, 30709.11402036138, 30768.548893974817], [34346.71094688274, 34381.34847608992, 34383.83572150592, 34489.79771171822, 34513.726290148654, 34559.545226230686, 34584.89272821686, 34763.20162247331, 34689.52633971307, 34851.04749767039 … 34726.90775509014, 34798.20996156711, 34983.01117453455, 35033.61344355363, 35093.30178810287, 35386.12295761976, 35564.90404322457, 35755.67449512256, 35837.21778232603, 36076.06156797298], [28335.329312139656, 28363.904560528423, 28365.956486782776, 28453.372946888037, 28473.113531389597, 28510.913210218354, 28531.82437743693, 28678.925543713183, 28618.14495245352, 28751.396581952395 … 28648.983850434215, 28707.806702623217, 28860.263898155372, 28902.009728165543, 28951.25138340045, 29192.822818891273, 29340.313533307224, 29497.69522804694, 29564.966760965413, 29762.00796618972], [978.0617717704337, 979.048114923888, 976.682183571137, 980.8273936581186, 986.0138000005664, 992.4152802434148, 982.446846698154, 991.9782699209236, 997.6706240806022, 1005.6983490659181 … 1001.9238188557825, 991.3588594461642, 996.2901331035395, 999.4185460521275, 1021.2866559147221, 1035.2380600026358, 1040.7310200599227, 1027.1189409306603, 1029.2024019136259, 1055.1331193237972], [0.0019383188997990075, 0.004138178016411365, 0.0031077463464894706, 0.007993767017814069, 0.009055790680427833, 0.006184677325595578, 0.003957667853867086, 0.0034032696281172115, 0.0023488267442401956, 0.0014810245577463466 … 0.00566307910427577, 0.005162064407832734, 0.0024479772690495505, 0.002548763582743252, 0.006002914328512299, 0.0031312255880917572, 0.005467011350218209, 0.00348520672735142, 0.006363590886309112, 0.005730550449986493], [2.3548476e6, 2.340245462813872e6, 2.3465300379486815e6, 2.355957403437064e6, 2.35751655433788e6, 2.3586513633907107e6, 2.3595996676609945e6, 2.366057293770595e6, 2.37770246424063e6, 2.369498742850168e6 … 2.4134485290068383e6, 2.418763703348714e6, 2.43781499212361e6, 2.4581453832244943e6, 2.463155756493583e6, 2.4682893920707316e6, 2.464962559559667e6, 2.4628543581875414e6, 2.47047815686862e6, 2.4620887977231382e6], [0.0016459319014481277, 0.0010091229373832477, 0.001269870169904373, 0.001754467519796655, 0.0018974850626099816, 0.0019462807881316254, 0.0019325581652571134, 0.002136769340741489, 0.0025165826757986122, 0.0020248902107977205 … 0.0037697456655474016, 0.003825738337169262, 0.004373410916692625, 0.00492840467788539, 0.004901778934224795, 0.004815739125926525, 0.004452099611111895, 0.004118351323592882, 0.004263963204140915, 0.0037457784866774344], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.6059091613041 258.5036962251161 … 137.13538556670355 505.41380923410753; … ; 529.9020347494384 263.9846693493359 … 142.0552493053394 524.808874491735; 504.6761636005783 260.3371720754693 … 142.69502808127584 526.6115154503658], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.0834390395163 258.24326637797435 … 136.9972283642248 504.904629508617; … ; 519.8503225309585 258.9771438967403 … 139.36060314151248 514.8537744351944; 494.60416890724764 255.1415341501241 … 139.84721463325096 516.1017494427506])])Now, apply a shock to the model and simulate it again Here, we do this by overloading the centralbankrate function with the wanted behaviour
function Bit.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.ensemblerun(model, 4)BeforeIT.DataVector{BeforeIT.Data}(BeforeIT.Data[BeforeIT.Data{Float64}([72422.0, 72454.87426442056, 72859.09551877515, 73029.98378768955, 73340.67712631005, 73850.53875875934, 74210.85359803677, 74664.0301013356, 75024.81360334624, 75269.23903928412 … 75885.73001516366, 76037.77731676337, 76318.03390215457, 76747.7185260047, 77051.51920033633, 77383.66929881793, 77556.35496007583, 77681.01926281399, 77664.46321759827, 77741.47548036547], [72422.0, 72381.87951771144, 72712.3655079274, 72809.48365568914, 73045.57485328273, 73479.2835032519, 73763.39903414817, 74139.07628646247, 74422.27074885662, 74589.51207200983 … 75048.99055341202, 75123.60165119814, 75324.52649996753, 75672.3044615534, 75895.31025560517, 76145.68580079483, 76238.7245896218, 76284.3406790638, 76191.2459384172, 76189.9622824692], [64900.92049553802, 64966.37094093021, 65350.20047724094, 65511.25287940049, 65814.5372526895, 66283.04852978954, 66603.8722825399, 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2.400401078099344e6, 2.4072324604440625e6], [0.0016459319014481277, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01 … 0.011017537054101096, 0.009993470925667406, 0.008503119244192458, 0.010038278193793874, 0.008813984285374457, 0.007196356175284156, 0.007526565613398886, 0.005950510606811666, 0.00648013004845661, 0.006398491532112223], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.6059091613043 258.5036962251161 … 137.13538556670355 505.41380923410753; … ; 573.6946024492528 285.11953211995547 … 145.58161072427964 532.9252828956436; 572.3937357386769 285.4070657978254 … 146.01050934321265 534.2304392784673], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.9046295086171; 518.0834390395163 258.24326637797435 … 136.9972283642248 504.904629508617; … ; 562.8121889709915 279.7110994346712 … 142.82007300722748 522.8162226801037; 560.9702783125824 279.7110994346711 … 143.09652770242482 523.5686198038966])])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 central_bank_rate 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 could close and restart the Julia session.