Essential use of BeforeIT
We start by importing the BeforeIT library and other useful libraries.
import BeforeIT as Bit
using FileIO, Plots, StatsPlots
We then initialise the model loading some precomputed set of parameters and by specifying a number of epochs. In another tutorial we will illustrate how to compute parameters and initial conditions.
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
⋮ => ⋮
We can now initialise the model, by specifying in advance the maximum number of epochs.
T = 16
model = Bit.initialise_model(parameters, initial_conditions, T)
Model(Workers{Vector{Float64}, Vector{Int64}}([0.7661282859097249, 0.7661282859097249, 0.7661282859097249, 0.7661282859097249, 0.7661282859097249, 0.7661282859097249, 0.7661282859097249, 0.7661282859097249, 0.7661282859097249, 0.7661282859097249 … 4.655745607447569, 4.655745607447569, 4.655745607447569, 4.655745607447569, 4.655745607447569, 4.655745607447569, 4.655745607447569, 4.655745607447569, 4.655745607447569, 4.655745607447569], [3.7818066335944898, 3.7818066335944898, 3.7818066335944898, 3.7818066335944898, 3.7818066335944898, 3.7818066335944898, 3.7818066335944898, 3.7818066335944898, 3.7818066335944898, 3.7818066335944898 … 22.981960001210975, 22.981960001210975, 22.981960001210975, 22.981960001210975, 22.981960001210975, 22.981960001210975, 22.981960001210975, 22.981960001210975, 22.981960001210975, 22.981960001210975], [6.9734810591562555, 6.9734810591562555, 6.9734810591562555, 6.9734810591562555, 6.9734810591562555, 6.9734810591562555, 6.9734810591562555, 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0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0 … 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [1.3061857958470853, 1.3061857958470853, 1.3061857958470853, 1.3061857958470853, 1.3061857958470853, 1.3061857958470853, 1.3061857958470853, 1.3061857958470853, 1.3061857958470853, 14.192383842657284 … 4.671824563850786, 10.794132553090519, 8.753363223343941, 4.671824563850786, 2.631055234104208, 4.671824563850786, 14.875671212583672, 2.631055234104208, 4.671824563850786, 4.671824563850786], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [11.889212387273595, 11.889212387273595, 11.889212387273595, 11.889212387273595, 11.889212387273595, 11.889212387273595, 11.889212387273595, 11.889212387273595, 11.889212387273595, 129.1824381520196 … 42.524053356193726, 98.25075028996942, 79.67518464537751, 42.524053356193726, 23.948487711601828, 42.524053356193726, 135.40188157915318, 23.948487711601828, 42.524053356193726, 42.524053356193726], [6.447669663541792, 6.447669663541792, 6.447669663541792, 6.447669663541792, 6.447669663541792, 6.447669663541792, 6.447669663541792, 6.447669663541792, 6.447669663541792, 70.05726371132184 … 23.061329873209313, 53.28261969169227, 43.20885641886461, 23.061329873209313, 12.987566600381662, 23.061329873209313, 73.43014623734756, 12.987566600381662, 23.061329873209313, 23.061329873209313]), Bank{Float64}(89460.0, 6476.292527744366, 0.0, 126430.99999999919, 0.028359903595743693, 3695.369633667526, 0.0, 0.0, 0.0, 0.0, 33636.12938055414, 18241.29672694819), CentralBank{Float64}(0.0016459319014481277, 0.0089810924595537, 0.9259668580654086, -0.003424572940686137, 0.0049629315732038215, 0.30996974466133875, 1.328593153520194, 106179.90000000002), Government{Float64}(0.9905949533296431, 0.09373211872949586, 0.011235005057648862, 0.0, 14732.121510837034, 232610.9, 2.238468336136841, 0.5902859043576301, [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 0.0, 0.0), RestOfTheWorld{Float64}(0.962809216044625, 0.39260026877953946, 0.020320381298662014, 0.9662360466537488, 0.35492769963078624, 0.02122821278168188, 2.3548476e6, 0.0, 0.0019383188997990075, 0.38456173629534834, 0.0026219533879005877, 0.0025327891562467505, 0.9635784504324201, 0.5360029623199525, 0.006618207536795881, 0.0, 33097.63671130043, 34095.03119997918, [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 0.0, [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 0.0), Aggregates{Float64, Int64}([104531.39273728609, 105062.38754395355, 105399.12953350678, 106689.88106040593, 107938.33111423723, 108890.48532381697, 110110.17779727321, 110374.00540561741, 110808.89423399912, 111932.48072916963 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [-0.007497362866886709, -0.007895434153021436, -0.0019938777296781562, -0.0035311300388783107, 0.001212170001002849, -0.001672412335241874, 0.001839696090252002, 0.004290005139261838, 0.00600429551344886, 0.0036060572293247772 … 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], 1.0, [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 … 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1), MutableNamedTuple(tau_VAT = 0.1528683933530887, tau_EXPORT = 0.0029486201783457183, tau_SIW = 0.17114894621657745, psi_H = 0.07125099957246343, tau_FIRM = 0.07701197259426128, H_inact = 4130, theta_DIV = 0.7858074440019603, I_s = [48, 2, 1, 1, 5, 2, 4, 1, 1, 1 … 14, 10, 13, 41, 20, 16, 7, 7, 2, 19], psi = 0.9096681249468772, tau_INC = 0.21340742230566648, zeta_b = 0.5, tau_CF = 0.08761417854834112, H_act = 4743, zeta = 0.03, mu = 0.026713971694295565, tau_G = 0.009147800682711324, theta_UB = 0.3585824478060919, T_prime = 54, tau_SIF = 0.21215146534992413, T = 16, zeta_LTV = 0.6, I = 624, products = MutableNamedTuple(a_sg = [0.37790282216028437 0.0 … 0.0 0.0; 0.0006712800413285777 0.8149348034258406 … 2.4029219530949635e-5 0.00019143106686926454; … ; 0.00037430822580994426 0.000357977071568566 … 0.3197327950788158 0.0011366219595362582; 0.0 5.36965607352849e-5 … 0.0 0.05594572929254256], b_CF_g = [0.0033476048872100555, 0.0, 0.0, 0.0008050086095806136, 0.0, 0.003306696048303853, 0.0030629933432974495, 0.0, 0.0, 0.0 … 0.0017883064872300512, 0.0, 0.0, 0.0, 0.0, 0.002291709084994238, 0.0, 0.0, 0.0, 0.0], b_CFH_g = [0.0006092803753845975, 0.0, 0.0, 0.004372477702289994, 0.0, 0.0, 0.06710603871527036, 0.0, 0.0, 0.0 … 0.0041711096896454745, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], c_E_g = [0.005090338238241512, 0.0005933402816643566, 1.793599921320476e-5, 0.007268146142708006, 0.05434404438533037, 0.02138421321578873, 0.023894091259534518, 0.028037089231640524, 0.005923381894006229, 0.011927802553688313 … 0.0014618202435669027, 0.0009447261124040238, 0.0001280209174610526, 0.0010477673386531637, 0.0, 0.0013030104043795392, 5.5260305268213854e-5, 0.0, 1.307076865739618e-5, 8.641230390167474e-6], b_HH_g = [0.011287997598927976, 0.0020040637862256817, 0.0003326837475323491, 0.00034402684015257527, 0.06305103828047173, 0.03068200872784047, 0.0003505790613555631, 0.0020473225369636873, 0.0, 0.0191077565617325 … 0.005591228759882936, 0.0004356874830029748, 0.014434120586233577, 0.03514505772295519, 0.024907176866291014, 0.013342154173060372, 0.009686226103767459, 0.011051272187723254, 0.0021206651420422927, 0.01721782824162338], c_G_g = [0.0, 0.0, 0.0, 0.0, 8.57086390274792e-6, 0.0, 0.0, 0.0, 2.4536198623552867e-5, 0.0 … 0.008555738848801895, 0.3324338967920097, 0.22067672180252998, 0.2370889178393625, 0.0477595425645907, 0.012942508661614227, 0.004667927760053456, 0.021757222045203074, 0.0, 0.002000708524749294], c_I_g = [0.016810689305736877, 0.004087420487057966, 0.00036885674795364003, 0.05818437780960789, 0.04895082866561155, 0.04689140072807505, 0.010101572733480902, 0.016066325760592727, 0.00037371898454196314, 0.041008926225895866 … 0.0018123421762754539, 0.000401097116716159, 0.0003479865324437806, 0.0006664256271585853, 0.0028556289501379516, 0.001307065586721844, 6.418152296577174e-5, 0.0, 3.538212163497461e-5, 0.00020458795490837936]), J = 156, G = 62, H = 8873, L = 312, theta = 0.05, C = [4.3800671000101816e-5 0.00010629745355671226 9.959785873214212e-5; 0.00010629745355671226 0.0004129178961230129 0.0003596689472264872; 9.959785873214212e-5 0.0003596689472264872 0.0004506370179043619]))
Note that the it is very simple to inspect the model by typing
fieldnames(typeof(model))
(:w_act, :w_inact, :firms, :bank, :cb, :gov, :rotw, :agg, :prop)
and to inspect the specific attributes of one agent type by typing
fieldnames(typeof(model.bank))
(:E_k, :Pi_k, :Pi_e_k, :D_k, :r, :Y_h, :C_d_h, :I_d_h, :C_h, :I_h, :K_h, :D_h)
We can now define a data tracker, which will store the time series of the model.
data = Bit.initialise_data(model);
We can run now the model for a number of epochs and progressively update the data tracker.
for t in 1:T
println(t)
Bit.one_epoch!(model; multi_threading = true)
Bit.update_data!(data, model)
end
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Note that we can equivalently run the model for a number of epochs in the single command data = BeforeIT.run_one_sim!(model)
, but writing the loop explicitely is more instructive.
We can then plot any time series stored in the data tracker, for example
p1 = plot(data.real_gdp, title = "gdp", titlefont = 10)
p2 = plot(data.real_household_consumption, title = "household cons.", titlefont = 10)
p3 = plot(data.real_government_consumption, title = "gov. cons.", titlefont = 10)
p4 = plot(data.real_capitalformation, title = "capital form.", titlefont = 10)
p5 = plot(data.real_exports, title = "exports", titlefont = 10)
p6 = plot(data.real_imports, title = "imports", titlefont = 10)
p7 = plot(data.wages, title = "wages", titlefont = 10)
p8 = plot(data.euribor, title = "euribor", titlefont = 10)
p9 = plot(data.nominal_gdp ./ data.real_gdp, title = "gdp deflator", titlefont = 10)
plot(p1, p2, p3, p4, p5, p6, p7, p8, p9, layout = (3, 3), legend = false)
To run multiple monte-carlo repetitions in parallel we can use
model = Bit.initialise_model(parameters, initial_conditions, T)
data_vector = Bit.run_n_sims(model, 4)
4-element Vector{BeforeIT.Data}:
BeforeIT.Data{Float64, Vector{Float64}, Matrix{Float64}}([72422.00000000003, 73225.18156893371, 73412.99791812907, 73365.83329706342, 73889.95664260068, 74756.8994299326, 75750.51437686989, 76640.85923673584, 77022.66166468708, 77478.89076897944, 78002.34847598129, 79326.39350272245, 80144.88454245192, 81752.72424811132, 82567.3834299692, 83518.88048343814, 84582.92121595745], [72422.00000000003, 72676.48278594555, 72651.65815610507, 72893.78489668258, 73124.71939364908, 73496.88066296565, 74290.07342264922, 74469.69107542225, 75200.79554860739, 75407.17312660841, 75526.04419257087, 76322.2291797264, 76703.36274771286, 77646.87777370683, 78077.33130730741, 78821.27468460391, 79524.94009806962], [64900.92049553808, 65649.45319624289, 65804.0154097198, 65770.85340066566, 66240.89757264985, 67040.60571314876, 67942.98028309477, 68735.82804161041, 69093.46574924413, 69491.12554843526, 69976.92250252025, 71180.6278135297, 71920.47350492452, 73399.85048145037, 74139.66067756648, 75003.32310355394, 75958.52010157796], [64900.92049553808, 65157.521673496114, 65121.585664947175, 65347.67240831252, 65554.87738086976, 65910.64417125024, 66633.06560101651, 66788.60246413494, 67459.15395878609, 67632.99374817261, 67755.39768540238, 68484.95121556954, 68832.11822849956, 69713.508281936, 70107.91197765664, 70784.68363540444, 71416.27026090915], [40512.94792630531, 40781.75008091306, 40943.32616742323, 40857.94013859464, 41128.766608893035, 41408.42944391175, 41889.74824551517, 42444.23138972847, 42545.01749541781, 42836.52153808539, 43001.89105231976, 43587.544033287115, 43950.1471080672, 44600.95117858597, 45036.072516677625, 45536.81888821736, 46191.56504645681], [40512.94792630531, 40476.15989789019, 40518.71767730915, 40595.053118594675, 40702.81881243138, 40710.49522502587, 41082.129915752324, 41241.82363043953, 41538.67307537722, 41691.11049092863, 41636.73001437478, 41936.843189219064, 42062.87270474224, 42360.96884361269, 42586.9902689478, 42975.55342067826, 43429.3518188699], [14866.888022051655, 15054.461661670894, 15240.455962320133, 15210.604810516665, 15405.656533087687, 15750.078664996205, 15946.32027591992, 16070.807860322895, 16302.47110621157, 16250.502339342773, 16559.133865825137, 16900.6770658453, 17273.358195811954, 17227.571550617675, 17369.32839947141, 17376.165809875387, 17319.339152453977], [14866.888022051655, 14941.653955150887, 15082.402682321623, 15112.737160863477, 15246.108703323815, 15484.612937411985, 15638.881318024467, 15615.536002720904, 15916.858364781183, 15815.978147531758, 16033.438743528392, 16260.632701872753, 16531.61854469631, 16362.355564677031, 16424.77636682285, 16398.82539537872, 16283.658554668278], [15944.236265986623, 16280.464051176357, 16128.955212174138, 16098.748483882651, 16166.546099129795, 16423.34785117346, 16726.49941891103, 17015.167409251855, 17023.62439720147, 17024.054769049413, 16886.234538605957, 17427.856480869512, 17637.35667445668, 18036.900433759623, 18157.947892083866, 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2.3544453647151245e6, 2.3548963606062103e6, 2.3729556534649716e6, 2.369337376183663e6, 2.3665289334075074e6, 2.3645619205888854e6, 2.3830237969468483e6, 2.380940987670386e6], [0.0016459319014481277, 0.000829184707799764, 0.00040093821591899757, 0.0003797755830507073, 0.0006943242240241604, 0.0007393459996482003, 0.0014818579538485822, 0.0017884070989414467, 0.0026310310079305293, 0.001951148054538492, 0.0019319961922866348, 0.002628622066165438, 0.0024160377733784748, 0.0022285310154946916, 0.0020822083127071318, 0.0027696859252318187, 0.0025106037377049337], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 523.1706102630087 260.77901180889194 … 138.34243321988407 509.86239520482536; … ; 556.3739991958122 278.56114861678407 … 148.5335235095041 547.7556502306107; 552.9369861622199 285.19807288493405 … 149.9019855912123 553.5534665291294], [518.0834390395164 258.24326637797435 … 136.99722836422484 504.90462950861706; 520.4577491953551 259.42676224723994 … 137.62506914452456 507.21854286549797; … ; 524.4051910964895 262.55524626166243 … 139.99890521990935 516.2820456177915; 516.1948978068684 266.2469571973316 … 139.94115436257158 516.7704136937779])
Note that this will use the number of threads specified when activating the Julia environment. To discover the number of threads available, you can use the command
Threads.nthreads()
1
To activate Julia with a specific number of threads, say 8, you can use the command julia -t 8
in the terminal.
We can then plot the results of the monte-carlo repetitions. Since we are saving the initial data point, we effectively have T+1 data points in our time series.
Te = T + 1
p1 = errorline(1:Te, data_vector.real_gdp, errorstyle = :ribbon, title = "gdp", titlefont = 10)
p2 = errorline(
1:Te,
data_vector.real_household_consumption,
errorstyle = :ribbon,
title = "household cons.",
titlefont = 10,
)
p3 =
errorline(1:Te, data_vector.real_government_consumption, errorstyle = :ribbon, title = "gov. cons.", titlefont = 10)
p4 = errorline(1:Te, data_vector.real_capitalformation, errorstyle = :ribbon, title = "capital form.", titlefont = 10)
p5 = errorline(1:Te, data_vector.real_exports, errorstyle = :ribbon, title = "exports", titlefont = 10)
p6 = errorline(1:Te, data_vector.real_imports, errorstyle = :ribbon, title = "imports", titlefont = 10)
p7 = errorline(1:Te, data_vector.wages, errorstyle = :ribbon, title = "wages", titlefont = 10)
p8 = errorline(1:Te, data_vector.euribor, errorstyle = :ribbon, title = "euribor", titlefont = 10)
p9 = errorline(
1:Te,
data_vector.nominal_gdp ./ data.real_gdp,
errorstyle = :ribbon,
title = "gdp deflator",
titlefont = 10,
)
plot(p1, p2, p3, p4, p5, p6, p7, p8, p9, layout = (3, 3), legend = false)