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These R codes replicate the models and the experiments discussed in Canelli, Fontana, Realfonzo and Veronese Passarella (2021, 2022, 2024).

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An empirical SFC macroeconomic model for Italy using Bimets package

Authors: Rosa Canelli and Marco Veronese Passarella

Last change: 6 February 2024

Description: This repository contains two types of code. The file named Italy_SFC_model.r replicates the baseline and the experiments discussed in: Canelli, R., Fontana, G., Realfonzo, R. and Veronese Passarella, M. (2022) Is the Italian government debt sustainable? Scenarios after the Covid-19 shock, Cambridge Journal of Economics. Notice that an early version of it was used to produce the simulations discussed in: Canelli, R., Fontana, G., Realfonzo, R. and Veronese Passarella, M. (2021) Are EU policies effective to tackle the Covid-19 crisis? The case of Italy, Review of Political Economy. The other (numbered) files allow replicating the baseline and the experiments discussed in: Canelli, R., Fontana, G., Realfonzo, R. and Veronese Passarella, M. (2024) Energy crisis, economic growth and public finance in Italy, Energy Economics. A detailed description of the latter is provided below.

Table of Contents

[Warning: work in progress] 🛠️

1_Model_and_data

The model presented here is created using the R package named Bimets. You can install it from the Packages sub-pane within RStudio. We also recommend installing and loading the knitr package.

library(bimets)
library(knitr)

Once packages have been loaded, the first step in creating the model is to define the structure of the economy, determining the level of aggregation implied by the desired accounting matrices. Subsequently, the density of the original matrices, as implied by the observed series, must be consistently reduced to limit the number of equations. Additionally, in the absence of information (e.g., on cross-sector interest payments), a decision must be made regarding which sector is paying whom. Available data must be reclassified accordingly - please refer to Veronese Passarella (2019), section 2, for additional information on the method for reclassifying Eurostat time series.

In our model, we consider six sectors (households, production firms, government, commercial banks, central bank, and the foreign sector) and six financial assets (cash, deposits, securities, loans, shares, and other net financial assests). The associated simplified balance sheet of Italy in 2021 is:

$$ \begin{array}{lccccccc} \hline & Households & Firms & Government & Banks & ECB & Foreign & Total\\ \hline Cash ~ and ~ reserves & 200683 & 0 & 0 & 10817 & -211500 & 0 & 0\\ Deposits & 1428434 & 0 & 0 & -1428434 & 0 & 0 & 0\\ Securities & 233263 & 0 & -2678397 & 1366294 & 868289 & 210551 & 0\\ Loans & -763488 & -871902 & 0 & 1635390 & 0 & 0 & 0\\ Shares & 1372850 & -1372850 & 0 & 0 & 0 & 0 & 0\\ Other ~ net ~ financial ~ assets & 1583746 & 284629 & 323282 & -1563895 & -783662 & 155900 & 0\\ \hline Net ~ financial ~ wealth & 4055488 & -1960123 & -2355115 & 20172 & -126873 & 366451 & 0\\ \hline Column ~ total & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \hline \end{array} $$

Figures are all expressed at current prices, million euros.

Similarly, the simplified or riclassified transactions-flow matrix of Italy in 2021 is:

$$ \begin{array}{lcccccccc} \hline & Households & Firms ~ (current) & Firms ~ (capital) & Government & Banks & ECB & Foreign & Total\\ \hline Consumption & -1030124 & 1030124 & 0 & 0 & 0 & 0 & 0 & 0\\ Total ~ investment & 0 & 357215 & -357215 & 0 & 0 & 0 & 0 & 0\\ Government ~ spending & 0 & 352718 & 0 & -352718 & 0 & 0 & 0 & 0\\ Export & 0 & 582192 & 0 & 0 & 0 & 0 & -582192 & 0\\ Import & 0 & -540198 & 0 & 0 & 0 & 0 & 540198 & 0\\ [GDP] & 0 & [ 1782051 ] & 0 & 0 & 0 & 0 & 0 & 0\\ Taxes & -483366 & 0 & 0 & 483366 & 0 & 0 & 0 & 0\\ Transfers & 188601 & 0 & 0 & -188601 & 0 & 0 & 0 & 0\\ Wages & 692915 & -692915 & 0 & 0 & 0 & 0 & 0 & 0\\ Interest ~ payments & 10905 & -2326 & 0 & -60678 & 29134 & 13200 & 9765 & 0\\ Corporate ~ profit & 738858 & -1141970 & 403112 & 0 & 0 & 0 & 0 & 0\\ Bank ~ profit & 29134 & 0 & 0 & 0 & -29134 & 0 & 0 & 0\\ CB ~ seigniorage & 0 & 0 & 0 & 13200 & 0 & -13200 & 0 & 0\\ Other ~ payments & -60675 & 55160 & 0 & 275577 & -151307 & -5171 & -113584 & 0\\ \hline \Delta ~ in ~ cash ~ and ~ res. & 15250 & 0 & 0 & 0 & -657 & -14593 & 0 & 0\\ \Delta ~ in ~ deposits & 57376 & 0 & 0 & 0 & -57376 & 0 & 0 & 0\\ \Delta ~ in ~ securities & -30072 & 0 & 0 & -105432 & -77658 & 103317 & 109845 & 0\\ \Delta ~ in ~ loans & -27196 & 0 & 169601 & 0 & -142405 & 0 & 0 & 0\\ \Delta ~ in ~ shares & 138716 & 0 & -138716 & 0 & 0 & 0 & 0 & 0\\ \Delta ~ in ~ other ~ net ~ f.a. & -67825 & 0 & 15012 & 275577 & 126789 & -93895 & -255658 & 0\\ \hline \Delta ~ in ~ net ~ wealth & 86249 & 0 & 45897 & 170145 & -151307 & -5171 & -145813 & 0\\ \hline Column ~ total & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \hline \end{array} $$

where the entry named 'Other payments' allows aligning each sector's saving, calculated based on Eurostat's non-financial transactions, with the change in financial wealth as derived from Eurostat's financial balance sheets.

Note: The R code to create the tables above (using observed series) is presented in Section 2.

The second step to create the model is to import the data (observed series). Our code takes the observed series from a Dropbox folder, containing Eurostat data for Italy over the period 1995-2021.

#Upload data: time series for transactions-flow matrix and balance sheet
DataEE <- read.csv("https://www.dropbox.com/scl/fi/58un32aub0asx1tu1t53c/Data_Aalborg.csv?rlkey=642w2hwa8qo069nmn1rc848i2&dl=1")

Running this chunk of code allows creating the dataset used by the model to estimate the coefficients and attribute initial values to the variables. Data are already classified to fit the two tables above.

Year CONS INV GOV X IM Y TAX INVnet TR WB INTh INTlh INTgh INTm INTf INTg INTgb INTb INTcb INTrow Ff DIV FUf Fb Fcb YD OPh OPf OPg OPb OPcb OProw Yrow DEF1 Hh Hbd Hs Mh Ms Bh Deb Bb Bcb Bs Brow Lf Lh Ls Eh Es OAh OAf OAg OAb OAcb OArow Vh NVh Vf Vg Vb Vcb Vrow K Rlh Rl Rb Rstar Prod ProdR Delta Kappa KappaN Py Pc Exr Exr42 Exr42R IMen Pen Pen2 Pim Pim_en Py_row RHO w gid gkn gy Rbb Rbrow Rbh Re gw CPI PI PIen Nd Ns
1995 581704 198068 172298 243824 207651 988243 304502.9179 61690.466 32837 353786 94539 22058.98524 202553.2366 -85955.25137 32051 101685.9999 -29707.98536 110357.2512 -85955.25137 14796 594208 435525 158683 110357.2512 -85955.25137 709948 -12593.3333 -8198 -26684.6667 108193.2514 9950 -70667.25137 11869868.24 88273.33333 42951 3915 -46866 642843 -642843 407396 1179962.142 390724 106668 -1179962.142 275174.142 -480014 -166659 646673 337925 -337925 276065 104061 239854.142 -483688 -80593 -55699.142 1707180 1540521 -713878 -940108 -85219 -20791 219475 2964729 0.13236 0.066770969 0.086177341 0.086875 49.59938769 75.25206367 0.046 0.333333333 0.34940601 65.911 65.5 1.308 77.5 92.40989 15433.334 49.50860467 56.1921773 64.63870703 51.80703164 55.27815729 0.006090134 17.75633015 0.037188395 0.023283628 0.051381348 -0.076033173 0.053769587 0.497190048 1.288821484 0.074269715 0.045801527 0.045075936 0 19924.5 22560.6
1996 611812 202429 184246 247921 200535 1045873 339106.6832 66051.466 32914 378499 96012 21362.90615 196733.19 -79358.28384 28312 108261.0004 -21732.90575 107300.2842 -79358.28384 12619 677120 514076 163044 107300.2842 -79358.28384 763826 -25868.601 38058 -49285.399 -15041 976 51161 12432671.32 65672.601 43739 4488 -48227 666811 -666811 490407 1245634.743 439727 97545 -1245634.743 217955.743 -482938 -176991 659929 370549 -370549 298020 100224 190568.743 -537593 -69133 17913.257 1869526 1692535 -753263 -1055066 -100260 -19815 235869 3030780.466 0.128183333 0.058624503 0.091749554 0.084375 52.20568342 75.79002268 0.046 0.345083721 0.369781837 68.882 68.5 1.27 86.1 101.71875 19682.28 51.77617435 58.72509228 68.18104965 54.64617037 58.3075213 0.006730543 18.8931151 0.022017691 0.022279091 0.058315617 -0.055622142 0.045858233 0.482904079 1.521272472 0.064021391 0.045801527 0.045075936 0.045801527 20033.7 22737.8
1997 645631 213028 193160 263802 223262 1092359 348240.7178 73612.09856 35143 397066 79460 18600.83965 153836.1258 -55775.28619 28260 94403.00059 -10613.83906 92022.28678 -55775.28619 6956 701730 567744 133986 92022.28678 -55775.28619 914897 91702.431 34697 -29706.431 -41340 407 -55760 13182538.9 30240.569 46923 4901 -51824 638201 -638201 559168 1275875.312 441022 92006 -1275875.312 183679.312 -493212 -188351 681563 448317 -448317 457543 109224 160862.312 -630885 -59590 -37154.312 2150152 1961801 -832305 -1115013 -141600 -19408 146525 3104392.565 0.105094833 0.057297876 0.075787064 0.063958333 54.29705441 76.8524924 0.046 0.351875279 0.377800508 70.651 69.8 1.134 87.5 100.6284 20382.45 52.75878788 60.23324663 71.82719165 57.56850286 61.42565315 0.007679399 19.73665636 0.052359099 0.024288166 0.044447079 -0.024137338 0.031914736 0.313690722 1.532169834 0.044648077 0.018978102 0.0256816 0.018978102 20118.2 22865.7
1998 679941 224747 199624 274042 239497 1138857 363999.2758 81944.94203 58835 395312 62467 16279.38098 122672.1812 -43925.80025 15700 85175.00053 -1030.380451 74874.80078 -43925.80025 7459 835871 745987 89884 74874.80078 -43925.80025 958284 -15192.525 108026 -43185.475 -124795 -1730 76877 13879204.32 23560.525 50305 5521 -55826 609760 -609760 513956 1299435.837 577525 78127 -1299435.837 129827.837 -504062 -205507 709569 562925 -562925 708705 99819 117676.837 -949250 -43439 66488.163 2445651 2240144 -967168 -1181759 -266395 -21138 196316 3186337.507 0.086431083 0.031146962 0.066758091 0.047916667 56.0861343 77.52271562 0.046 0.357418823 0.384542359 72.348 71.2 1.121 90.4 102.12797 12666.42 81.00496309 61.68001765 74.8634512 60.00202299 64.02222168 0.009054382 19.4682229 0.055011548 0.02639645 0.042566592 -0.002336347 0.040608819 0.219383408 1.663972145 -0.013600757 0.020057307 0.024019476 0.535383324 20305.5 23111.2
1999 710248 237770 206206 272643 251716 1175151 356021.3367 91198.4747 62587 410340 54993 13040.49806 115548.0802 -47514.58213 13073 71724.00058 -5035.497487 68592.58271 -47514.58213 8726 560877 558925 1952 68592.58271 -47514.58213 926019 126602.754 -190861 58330.246 12396 -1685 -4783 14675566.04 32010.246 56333 5795 -62128 610642 -610642 438251 1331446.083 610011 75770 -1331446.083 207414.083 -572790 -239433 812223 750109 -750109 840013 119913 176007.083 -1071386 -36465 -28082.083 2695348 2455915 -1202986 -1155439 -253999 -22823 179332 3277535.981 0.06345525 0.022823373 0.055196262 0.027083333 57.17411294 77.83026537 0.046 0.358547094 0.386592589 73.46 72.3 1.066 91.8 101.55784 16561.2 92.65119048 62.62804911 77.66434745 62.24690268 66.41751068 0.009490012 19.96409441 0.057945156 0.028621725 0.031868795 -0.008719099 0.067212088 0.224820958 0.992894258 0.025470815 0.015449438 0.015370155 0.143771776 20553.9 23279.3
2000 751730 259037 220195 318172 307621 1241513 375224.8494 108270.3449 66311 427487 53814 16814.76105 108571.6979 -37942.93688 17088 72578.99948 -8496.761572 63348.93636 -37942.93688 10447 780481 560823 219658 63348.93636 -37942.93688 925612 129052.913 -16457 14867.087 -241870 -274 114681 17137543.71 21803.087 59394 6644 -66038 631780 -631780 503331 1353249.17 557289 85497 -1353249.17 207132.17 -641875 -273340 915215 747248 -747248 961384 146758 190874.17 -1343237 -42556 86776.83 2903137 2629797 -1242365 -1162375 -495869 -23097 293909 3385806.326 0.070227417 0.026622006 0.054511407 0.040416667 59.46968826 79.53044862 0.046 0.366681635 0.397059351 74.776 74.2 0.924 88 96.48973 34898.31 94.79664835 63.75 79.69396408 63.8736124 68.15321166 0.010516319 20.47704585 0.08944358 0.033034068 0.056471041 -0.013928866 0.050367843 0.24773862 0.747655341 0.0256937 0.026279391 0.017914511 0.02315629 20876.4 23418.8
2001 775878 271825 239959 334498 318022 1304138 343517.9719 116077.909 68186 451041 52025 19920.33585 99117.42021 -27172.08436 16530 75157.99956 -7151.336287 56471.08392 -27172.08436 10364 821681 614287 207394 56471.08392 -27172.08436 720897 -177595.112 -14886 854.112 192428 -1733 932 18063016.94 66957.112 49167 8156 -57323 690239 -690239 566966 1420206.282 534466 86879 -1420206.282 231895.282 -688808 -303134 991942 736025 -736025 835553 118037 191728.282 -1147766 -54386 56833.718 2877950 2574816 -1306796 -1228478 -303441 -24830 288729 3501884.235 0.0728775 0.023997979 0.055538922 0.0425 61.21133041 79.44880318 0.046 0.372410369 0.40375049 77.045 75.9 0.896 89.9 97.08403 34288.28 98.23146825 60.81 83.42047245 66.86035743 71.34007175 0.011816197 21.17016733 0.049367465 0.034283682 0.050442484 -0.012832366 0.050035685 0.19692294 0.822065767 0.033848705 0.022911051 0.030343961 0.036233558 21305.5 23573.9
2002 798351 291267 250419 329564 319342 1350259 391298.2531 130180.3252 71440 470108 46028 19814.37917 81591.92619 -15749.54702 17230 70159.00011 -9526.379064 43267.54713 -15749.54702 13843 811498 594283 217215 43267.54713 -15749.54702 858604 24775.706 -51423 -21476.706 -59291 -933 108348 17984691 16469.294 53408 8970 -62378 716998 -716998 637330 1436675.576 511446 65401 -1436675.576 222498.576 -716643 -336487 1053130 777177 -777177 786643 112972 170251.576 -1219280 -28786 178199.424 2971556 2635069 -1380848 -1266424 -362732 -25763 400698 3632064.56 0.065365083 0.024042654 0.04940057 0.032083333 62.23624958 78.21867053 0.046 0.347 0.404172649 79.567 77.9 0.946 92.2 99.27912 32653.125 105.7765564 63.15 86.39226109 69.24220501 73.88150563 0.012510495 21.66825684 0.071523958 0.037174366 0.035365122 -0.017824107 0.059695048 0.143909734 0.807422302 0.023527897 0.026350461 0.032734116 0.076809278 21695.7 23902.1
2003 828304 295388 264649 324994 318642 1394693 393258.1745 128313.0302 74195 490889 47510 19618.3698 90145.08292 -23016.71312 14382 66123.00043 -14327.36938 42689.71355 -23016.71312 13322 990303 724781 265522 42689.71355 -23016.71312 890185 -96621.539 100881 29264.539 -78778 -279 45533 16579854.78 34725.539 64267 8975 -73242 754034 -754034 642341 1471401.115 511490 68819 -1471401.115 248751.115 -773097 -371352 1144449 747473 -747473 860187 109856 199516.115 -1352390 -21619 204449.885 3068302 2696950 -1410714 -1271885 -441510 -26042 453201 3760377.591 0.0583035 0.018603099 0.046025005 0.0225 63.4081062 77.25912151 0.046 0.370891743 0.402510012 82.072 80.1 1.131 98.4 105.94827 34191.43 105.3707108 64.38 89.12955539 71.43610862 76.22240308 0.011902646 22.31770135 0.01414853 0.03532785 0.032907761 -0.028013455 0.059874541 0.141441769 0.932581638 0.029972162 0.028241335 0.031482901 -0.00383682 21995.5 24141.3
2004 856707 308799 278255 348699 340141 1452319 380777.1062 135821.6308 74916 509540 46295 20447.26004 84747.52034 -18005.2603 14173 64586.99987 -14956.26017 37669.26017 -18005.2603 12801 1049131 882027 167104 37669.26017 -18005.2603 1041694 -127976.154 120525 -14715.846 -22910 694 44383 16589586.29 54986.154 76070 8639 -84709 784680 -784680 718263 1526387.269 481986 74525 -1526387.269 251613.269 -806836 -421412 1228248 857892 -857892 866444 112319 184800.269 -1398613 -15164 250213.731 3303349 2881937 -1552409 -1341587 -464420 -25348 501827 3896199.221 0.055061667 0.017566147 0.043894897 0.02 64.93945681 77.06758223 0.046 0.372752757 0.404838856 84.263 81.9 1.244 100.4 107.67591 38846.224 96.41309005 68.91 91.86997485 73.632517 78.56597314 0.011009584 22.78373472 0.045401303 0.036119147 0.041318054 -0.029240572 0.051461076 0.131935406 1.180011853 0.020881782 0.02247191 0.026696072 -0.085010537 22364.2 24277.5
2005 885949 316194 292969 367451 368928 1493635 388702.5627 136968.8358 76130 531929 47503 22393.55976 90820.76384 -20924.20408 15074 64506.99964 -16365.56012 42026.20372 -20924.20408 10976 970860 915219 55641 42026.20372 -20924.20408 1219425 -4679.641 24228 9482.641 14648 -8930 -34749 17493109.5 65827.641 89146 8737 -97883 822325 -822325 735715 1592214.91 499382 82215 -1592214.91 274902.91 -876585 -479078 1355663 1057758 -1057758 989547 121381 194282.91 -1491229 -18610 204628.09 3694491 3215413 -1812962 -1397932 -449772 -34278 479531 4033168.057 0.05313935 0.017196279 0.042261228 0.020208333 66.79493773 77.70648192 0.046 0.370337903 0.401841653 85.958 83.7 1.244 99.3 105.95688 47940.26 75.45 76.69 94.2 75.5 80.55857946 0.010624753 23.78771549 0.023947616 0.035154474 0.028448295 -0.03395443 0.043622501 0.126444998 1.066823097 0.04406568 0.021978022 0.02011559 -0.217429916 22361.5 24238.8
2006 921983 340933 302522 406392 419143 1552687 412935.4616 155407.2694 84673 555830 50027 26932.7072 101583.2882 -24623.58098 19164 65618.99958 -24421.70762 46298.58056 -24623.58098 13081 681954 645212 36742 46298.58056 -24623.58098 1196782 227676.881 -295739 49413.119 -108750 -3773 131172 18391491.59 64502.119 103968 10322 -114290 879188 -879188 735374 1656717.029 487660 93789 -1656717.029 339894.029 -954392 -541251 1495643 1289471 -1289471 1023462 126710 243696.029 -1672959 -17550 296640.971 4031463 3490212 -2117153 -1413021 -558522 -38051 636535 4188575.327 0.056217792 0.020079799 0.041212401 0.027916667 68.3704904 77.88491115 0.046 0.370695733 0.403542447 87.784 85.6 1.256 99.3 105.4757 61681.2 95.70833333 78.98 98.4 95.7 82.64410275 0.011740379 24.47522886 0.078239941 0.038532307 0.039535763 -0.04890386 0.047584073 0.138074238 0.609980733 0.028902034 0.022700119 0.021242933 0.26850011 22709.9 24364.2
2007 953816 359238 307266 441837 447317 1614840 465321.4558 166563.535 78465 576340 56865 34286.6271 118836.814 -27685.1869 30044 73006.99985 -45126.62725 46889.18675 -27685.1869 26982 998664 657999 340665 46889.18675 -27685.1869 679025 -272211.731 -9792 26685.731 144725 -6743 117336 18332622.93 21101.731 112983 11364 -124347 915020 -915020 762538 1677818.76 462908 93824 -1677818.76 358548.76 -1071324 -602022 1673346 1199296 -1199296 827606 134894 270381.76 -1646395 -14271 427784.24 3817443 3215421 -2135726 -1407437 -413797 -44794 786333 4355138.862 0.063347 0.028043804 0.044067272 0.038541667 70.68339892 78.57203081 0.046 0.370789555 0.40412414 89.96 87.3 1.371 101 106.39722 59734.24 94.025 86.23 98.9 94 85.39684094 0.012419401 25.22706282 0.053690901 0.039766155 0.040029317 -0.092537069 0.079383566 0.161600511 0.510286001 0.030718159 0.019859813 0.024788116 -0.017588158 22846.1 24327
2008 973266 356666 320333 439932 452498 1637699 457702.286 156329.6124 81770 595572 65938 41162.11041 147428.9744 -40328.86402 39097 76688.00002 -57908.11039 62679.86404 -40328.86402 27496 915292 562142 353150 62679.86404 -40328.86402 760338 -150061.578 -87738 -10330.422 290011 -4201 -37680 17674323.9 61417.578 123257 13153 -136410 974991 -974991 809949 1739236.338 472953 105039 -1739236.338 351295.338 -1134965 -624988 1759953 1141864 -1141864 577420 137587 260051.338 -1394854 -17624 437419.662 3627481 3002493 -2139242 -1479185 -123786 -48995 788715 4511468.474 0.0683731 0.034447758 0.045706963 0.038541667 71.08346246 77.16398444 0.046 0.363007967 0.394170122 92.12 90.4 1.471 103.3 107.93314 76410 122.7666667 83.27 103.6 122.8 88.16565515 0.013490381 25.85048895 -0.007159599 0.035895437 0.014155582 -0.12509637 0.07668692 0.193339839 0.468726653 0.024712593 0.035509737 0.024010671 0.305681114 23039.1 24703.4
2009 953184 307703 326155 353292 363078 1577256 410194.439 100175.4502 99915 590431 45050 29728.59587 92382.19295 -17603.59708 17698 66364.99993 -29036.59594 35993.59701 -17603.59708 20623 1017050 564863 452187 35993.59701 -17603.59708 905176 -20882.158 47923 -17766.842 65986 -11416 -63844 17578903.82 99844.158 129192 11664 -140856 994220 -994220 779292 1839080.496 609381 119299 -1839080.496 331108.496 -1146281 -654677 1800958 997363 -997363 709095 148886 242284.496 -1485583 -38854 424171.504 3609162 2954485 -1994758 -1596796 -57800 -60411 755280 4611643.924 0.047566667 0.015439495 0.038157551 0.012291667 69.6378712 74.34701087 0.046 0.342015998 0.366467855 93.666 91.1 1.395 105.1 109.31352 52081.4 88.21666667 84.81 94.6 88.2 90.05561801 0.01173181 26.06828437 -0.137279696 0.022204622 -0.036907271 -0.061394253 0.05870559 0.114059272 0.494685006 0.008425195 0.007743363 0.016782458 -0.281428184 22649.4 24556
2010 978454 331599 331166 404013 433952 1611280 421807.5657 119463.3795 107096 599034 34172 26394.39438 59409.22375 1157.170637 10465 66268.00032 -14186.39406 21515.82969 1157.170637 19888 1013316 613378 399938 21515.82969 1157.170637 880005 -73383.264 11535 71182.264 4682 -22786 8770 18852954.48 81565.264 133437 11172 -144609 988877 -988877 732051 1920645.76 638344 151353 -1920645.76 398897.76 -1154988 -686301 1841289 915991 -915991 771981 144560 313466.76 -1555046 -89941 414979.24 3542337 2856036 -1926419 -1607179 -53118 -83197 813877 4731107.304 0.040316667 0.0090607 0.036033224 0.01 71.70039693 76.21620721 0.046 0.340571434 0.366240927 94.075 92.6 1.326 101 104.33731 66130.02 105.6083333 94.19 99.5 105.6 91.06593797 0.011297664 26.65643189 0.077659301 0.025904728 0.021571641 -0.023280007 0.060064904 0.076234869 0.614999754 0.022561804 0.016465423 0.004366579 0.197147175 22472.4 24528.1
2011 1007661 337468 326718 443061 466151 1648757 454145.6216 119837.064 110671 608088 38915 31564.12683 66948.11742 3531.009403 12701 73204 -20791.12682 19942.9906 3531.009403 23516 1174074 792739 381335 19942.9906 3531.009403 917706 -198504.369 146106 105275.369 111366 -12726 -151517 18926146.73 52916.369 141838 11535 -153373 984230 -984230 743323 1973562.129 523412 176406 -1973562.129 530421.129 -1175094 -704239 1879333 844950 -844950 755979 137492 418742.129 -1371802 -118956 178544.871 3470320 2766081 -1882552 -1554820 58248 -95923 708966 4850944.368 0.045991667 0.010808497 0.038114264 0.0125 73.13020337 76.50643222 0.046 0.339883716 0.365296473 95.587 95.3 1.392 101.6 104.48254 76271.13 133.8916667 103.32 107.7 133.9 92.94986771 0.011719822 26.97159078 0.017699088 0.025329602 0.023259148 -0.032570412 0.058952449 0.091452805 0.865444093 0.011822996 0.029157667 0.016072283 0.267813462 22545.5 24606.8
2012 995710 288966 321754 460981 443052 1624359 436848.3013 65822.55909 120511 600264 37724 36778.88178 69509.18801 4993.693761 12686 80829.00101 -16705.88076 27765.30725 4993.693761 23032 1032254 808402 223852 27765.30725 4993.693761 1280778 122959.994 20845 -161315.994 -83650 -3494 104655 20616647.33 81252.006 137756 13380 -151136 1046373 -1046373 736578 2054814.135 746424 192181 -2054814.135 379631.135 -1161701 -697100 1858801 912080 -912080 915462 126115 257426.135 -1597634 -140462 439092.865 3748249 3051149 -1947666 -1797388 -25402 -99417 818724 4916766.927 0.052225 0.010920194 0.040955894 0.00875 72.15909697 74.3402396 0.046 0.330371365 0.351000189 97.066 98.4 1.285 99 102.51107 83664.24 150.1916667 108.71 111 150.2 93.74142715 0.012787027 26.66560051 -0.143723257 0.01356902 -0.014797814 -0.031917267 0.043422101 0.093511418 0.95674537 -0.01134491 0.032528856 0.015472815 0.121740213 22510.8 25201.8
2013 982190 272433 319441 461783 423095 1612752 455823.3594 46261.72137 131490 594339 37854 35859.98583 85903.61056 -12189.62473 11661 74784.99964 -23152.9862 36557.62437 -12189.62473 24224 910531 727101 183430 36557.62437 -12189.62473 1111389 39870.735 -96221 -5962.735 -118788 30741 150360 20727022.91 82082.265 139992 13043 -153035 1076752 -1076752 643794 2136896.4 965725 187388 -2136896.4 339989.4 -1106952 -684676 1791628 1036255 -1036255 968231 106538 251463.4 -1837834 -103029 614630.6 3865024 3180348 -2036669 -1885433 -144190 -68676 954620 4963028.648 0.051441667 0.010534332 0.036395019 0.005416667 72.85619418 74.20675716 0.046 0.324953192 0.343826695 98.18 99.7 1.328 101.7 104.41029 72200.4 141.8083333 108.7 108.3 141.8 95.63143633 0.012113281 26.8493095 -0.057214344 0.009408972 -0.007145588 -0.031018545 0.063809308 0.116625273 0.797189939 0.006889362 0.013211382 0.011476727 -0.055817567 22136.1 25204.8
2014 986310 275995 317979 473719 426597 1627406 487469.4046 47695.68219 142072 595991 35086 33320.89867 91045.6278 -22638.72913 8050 71390.99944 -21486.89923 42522.72857 -22638.72913 24471 1090953 814731 276222 42522.72857 -22638.72913 1135780 -7153.324 67588 -144554.676 -39772 -9189 133081 21619705.53 66611.324 141353 12882 -154235 1110770 -1110770 536907 2203507.724 1273284 202850 -2203507.724 190466.724 -1082212 -679562 1761774 1057339 -1057339 1163011 103109 106908.724 -2121132 -126480 874583.276 4009380 3329818 -2036442 -2096599 -183962 -77865 1065050 5010724.33 0.048666667 0.007438469 0.033408732 0.001583333 73.27027149 73.95285635 0.046 0.324784581 0.343716797 99.077 99.9 1.329 103.4 104.6746 51756.01 130.5583333 101.85 104.9 130.6 97.87056077 0.01159736 26.83314574 0.013074774 0.009610197 0.009086332 -0.022249501 0.071975773 0.141420435 0.786226363 -0.000602018 0.002006018 0.00913628 -0.079332432 22211 25447
2015 1005936 283186 316344 491905 442016 1655355 506679.773 52692.68081 141366 609506 28901 28060.81389 76995.17867 -20033.36478 5335 65123.99918 -13475.8147 39953.36396 -20033.36478 21638 928480 694646 233834 39953.36396 -20033.36478 1134133 126440.409 -112034 -22738.409 9458 951 -2077 25354512.33 36187.591 144595 11845 -156440 1137500 -1137500 420995 2239695.315 1361780 289731 -2239695.315 167189.315 -1059755 -679918 1739673 1154348 -1154348 1280495 128309 84170.315 -2150302 -210205 867532.685 4137933 3458015 -2085794 -2155525 -174504 -76914 1034722 5063417.011 0.0412925 0.005034182 0.029554695 0.0005 73.91660601 73.91660601 0.046 0.326924485 0.346291842 100 100 1.11 100 100 44458.08 100.0083333 95.9 100 100 100 0.010413187 27.21628585 0.02605482 0.010515981 0.017173957 -0.010583511 0.113605146 0.143405056 0.656975672 0.014278613 0.001001001 0.009315987 -0.233995021 22394.9 25428.2
2016 1019579 297798 322650 497339 441578 1695788 492490.8411 64880.81749 145038 625000 22308 23771.06648 53680.81605 -7601.749576 5205 63428.00057 1081.934091 37659.75014 -7601.749576 16267 1119880 752840 367040 37659.75014 -7601.749576 1023768 -66586.909 54297 41327.909 150612 -9643 -170007 25801943.97 46226.909 150624 11441 -162065 1182519 -1182519 363801 2285922.224 1315743 417139 -2285922.224 189239.224 -1039509 -686157 1725666 1126524 -1126524 1324893 149481 125498.224 -1894223 -341631 635981.776 4148361 3462204 -2016552 -2160424 -23892 -86557 825221 5128297.829 0.034961667 0.005007172 0.028319924 0.0000833 74.77711781 73.93865348 0.046 0.330672683 0.351058495 101.134 99.9 1.107 102.1 100.84031 36762.5 80.675 98.35 96 80.7 102.3973588 0.009675109 27.55987106 0.051598596 0.012813643 0.024425576 0.0007945 0.097296888 0.127509391 0.65217768 0.012624251 -0.001 0.01134 -0.193317223 22677.9 25689.9
2017 1046342 313526 327002 533720 483997 1736593 493832.7575 77624.29988 142440 642230 21320 20590.42798 46722.17343 -4811.745452 3572 62428.001 8671.573029 37645.74646 -4811.745452 11846 1006081 689357 316724 37645.74646 -4811.745452 1218330 179170.011 -84710 39424.989 -57156 1275 -78004 26323897.53 42848.989 155752 12001 -167753 1206658 -1206658 330574 2328771.213 1248226 523682 -2328771.213 226289.213 -1009435 -697152 1706587 1157381 -1157381 1480979 153462 164923.213 -1841204 -441211 483050.787 4331344 3634192 -2013354 -2163848 -81048 -85282 709340 5205922.128 0.030008333 0.003538613 0.027309766 0 75.6682106 74.27991891 0.046 0.333580287 0.354957562 101.869 101.3 1.13 103.4 101.39634 52193.31 95.65 101.25 99.4 95.7 103.8605307 0.009945652 27.98375606 0.052814324 0.015136465 0.02406256 0.006590628 0.062598016 0.128427831 0.611932813 0.015380515 0.014014014 0.007267586 0.18562132 22950.1 25857
2018 1066167 328194 334454 555394 512818 1771391 480055.6522 88721.58209 141572 665490 16570 18683.6736 29951.57742 5302.096182 1934 61354.9994 16425.3258 31740.90322 5302.096182 9676 1326322 907171 419151 31740.90322 5302.096182 863136 -419352.251 222355 99226.251 220437 -3082 -119584 26726264.67 52023.251 162421 12232 -174653 1224330 -1224330 313141 2380794.464 1202244 541877 -2380794.464 323532.464 -1018031 -711907 1729938 1075545 -1075545 1367631 171179 264149.464 -1580695 -455588 233323.536 4143068 3431161 -1922397 -2116645 139389 -88364 556856 5294643.711 0.0268 0.001899746 0.026346512 0 76.53979104 74.34151252 0.046 0.334562833 0.356671486 102.957 102.5 1.181 106.7 103.37155 59646.3 115.1333333 106.79 102.4 115.1 106.2717832 0.00999077 28.75506624 0.046783999 0.017042434 0.020038086 0.013158936 0.04275944 0.090604758 0.783813627 0.027562782 0.011846002 0.010680384 0.203694023 23143.4 25898.9
2019 1074680 327703 334512 567784 508031 1796648 506154.8658 84149.38931 146882 681104 14113 18527.37968 29505.85369 3134.525981 3429 56871.99979 12795.62011 31617.4738 3134.525981 11436 1082293 869739 212554 31617.4738 3134.525981 1426904 189603.392 -29822 -124910.392 -98786 -18379 82294 28774461.9 28976.608 165890 12654 -178544 1286064 -1286064 289695 2409771.072 1370663 573547 -2409771.072 175866.072 -995791 -728244 1724035 1228692 -1228692 1541288 186937 139239.072 -1780685 -501746 414966.928 4511629 3783385 -2037546 -2270532 40603 -106743 590833 5378793.1 0.026025 0.003443494 0.023887824 0 77.17560137 74.26229167 0.046 0.334024374 0.3556951 103.923 103.2 1.12 105.8 101.08213 55150.68 108.25 107.02 101.5 108.3 108.7763154 0.009839324 29.25704467 -0.001496066 0.015893305 0.014258286 0.010643114 0.035347303 0.094225457 0.808649568 0.017457043 0.006829268 0.009382558 -0.059785755 23280 25861.5
2020 963726 293530 343580 488941 429156 1660621 428608.9298 46105.51741 202196 642972 10558 16955.9478 19250.6187 8263.329099 3779 54290.99891 16112.05111 28583.66981 8263.329099 10665 1126688 801632 325056 28583.66981 8263.329099 1149580 -107752.74 112818 -91533.26 130876 -14959 -29449 26993213.3 163194.74 185433 11474 -196907 1371058 -1371058 263335 2572965.812 1443952 764972 -2572965.812 100706.812 -1041503 -736292 1777795 1234134 -1234134 1651571 269617 47705.812 -1690684 -689767 411557.188 4705531 3969239 -2006020 -2525260 171479 -121702 512264 5424898.617 0.023283333 0.00362841 0.022529526 0 72.73822717 68.88024466 0.046 0.306110974 0.323621459 105.601 103 1.142 108.1 101.91719 31741.38 78.45 99.6 96.3 78.5 111.9985301 0.00836872 28.16334576 -0.1042804 0.008571722 -0.075711547 0.011754933 0.060642737 0.066451332 0.652427134 -0.037382413 -0.001937984 0.01614657 -0.275288684 22830.1 25140.6
2021 1030124 357215 352718 582192 540198 1782051 483365.7672 107669.6636 188601 692915 10905 14916.66234 12622.01724 13199.6451 2326 60678.00031 25091.33797 29134.35521 13199.6451 9765 1141970.282 738858.2821 403112 29134.35521 13199.6451 1116373 -60674.87011 55160.28211 275576.588 -151307 -5171 -113584 29441497.75 105431.588 200683 10817 -211500 1428434 -1428434 233263 2678397.4 1366294 868289 -2678397.4 210551.4 -871902 -763488 1635390 1372850 -1372850 1583746 284629 323282.4 -1563895 -783662 155899.6 4818976 4055488 -1960123 -2355115 20172 -126873 366451 5532568.281 0.020259167 0.002667731 0.023582902 0 79.33378445 74.72335354 0.046 0.322101944 0.344334175 106.17 105 1.183 109.3 101.53931 64858.995 112.4833333 125.39 105 85.59190031 114.2006256 0.007572628 30.84736029 0.216962491 0.019847314 0.073123247 0.01737685 0.096964642 0.047931408 0.598685623 0.095301693 0.019417476 0.005388207 0.433821967 22462.7 24829.5

Alternatively, simply copy and paste the https address into your browser, save the dataset in the chosen folder, and set the directory path accordingly.

The third step is to create a text file (txt) defining model equations. For a comprehensive description of the behavioral assumptions underlying the behavioral equations, please refer to Canelli, Fontana, Realfonzo, and Veronese Passarella (2024).

Note: we place the key behavioral equations at the end of the code. This arrangement is intentional, as, after estimating model coefficients, the related details are to be read in a 'last in, first out' order from the RStudio Console.

S_model.txt="MODEL

COMMENT> FIRMS SECTOR ----------------------------------------------------------

COMMENT> GDP
IDENTITY> y
EQ> y = cons + id + gov + nx                      

COMMENT> Growth rate of nominal GDP (auxiliary) 
IDENTITY> gy
EQ> gy = (y/TSLAG(y,1))-1

COMMENT> Depreciation rate (average value over the period 1996-2019)
IDENTITY> deltak
EQ> deltak = 0.046

COMMENT> Real investment net of capital depreciation 
IDENTITY> idR
EQ> idR = exp(LidR)

COMMENT> Nominal investment including capital depreciation 
IDENTITY> id
EQ> id = idR*p/100  + deltak*TSLAG(k,1)         

COMMENT> Nominal capital stock
IDENTITY> k
EQ> k = TSLAG(k,1)*(1 - deltak) + id 

COMMENT> Firms' profit
IDENTITY> ff
EQ> ff = y - intf - wb + opf

COMMENT> Interest payments on loans to firms
IDENTITY> intf
EQ> intf = rl*lf  

COMMENT> Interest rate on loans to firms
IDENTITY> rl
EQ> rl = rstar + mul 

COMMENT> Firms' undistributed profit
BEHAVIORAL> fuf
TSRANGE 1998 1 2021 1
EQ> fuf = theta*ff   
COEFF> theta
STORE> coe(3)

COMMENT> Firms' distributed profit
IDENTITY> fdf
EQ> fdf = ff - fuf

COMMENT> Firms' demand for bank loans  
IDENTITY> lf
EQ> lf = TSLAG(lf,1) + id - fuf - (es-TSLAG(es,1)) + (oaf-TSLAG(oaf,1))

COMMENT> Supply of shares  
IDENTITY> es
EQ> es = eh

COMMENT> Total wealth accumulated by firms
IDENTITY> vf
EQ> vf = oaf - (lf + es)

COMMENT> HOUSEHOLD SECTOR ------------------------------------------------------

COMMENT> Disposable income  
IDENTITY> yd
EQ> yd = wb - tax + tr + inth + fdf + fb + oph

COMMENT> Real consumption
IDENTITY> consR
EQ> consR = exp(LconsR)

COMMENT> Nominal consumption
IDENTITY> cons
EQ> cons = consR*p/100

COMMENT> Net wealth of households    
IDENTITY> vh
EQ> vh = TSLAG(vh,1) + yd - cons

COMMENT> Loans to households 
BEHAVIORAL> lh
TSRANGE 1998 1 2021 1
EQ> TSDELTALOG(lh,1) = phi1*TSLAG(cons/yd,1)
COEFF> phi1
STORE> coe(6)

COMMENT> Interests paid by households on personal loans 
IDENTITY> intlh
EQ> intlh = rlh*TSLAG(lh,1)  

COMMENT> Premium on government bills held by households
BEHAVIORAL> mubh
TSRANGE 1998 1 2021 1
EQ> mubh = mubh1*TSLAG(mubh,1) + mubh2*mub  
COEFF> mubh1 mubh2
STORE> coe(7)

COMMENT> Interest rate received households on their government debt holdings
IDENTITY> rbh
EQ> rbh = rstar + mubh 

COMMENT> Interests received by households on their government debt holdings 
IDENTITY> intgh
EQ> intgh = rbh * TSLAG(bh,1)  

COMMENT> Markup on loans to firms
BEHAVIORAL> mul
TSRANGE 1998 1 2021 1
EQ> mul = mul0 + mul1*TSLAG(mub,1)  
COEFF> mul0 mul1
STORE> coe(2)

COMMENT> Net interest payments received by households 
IDENTITY> inth
EQ> inth = intgh + intmh - intlh

COMMENT> Markup on personal loans to households
BEHAVIORAL> mulh
TSRANGE 1998 1 2021 1
EQ> mulh = mulh0 + mulh1*TSLAG(mub,1)  
COEFF> mulh0 mulh1
STORE> coe(7)

COMMENT> Interest rate on loans to households
IDENTITY> rlh
EQ> rlh = rstar + mulh 

COMMENT> Wage share (endogenous) 
IDENTITY> Omega
EQ> Omega = wb/y

COMMENT> Other assets of households 
BEHAVIORAL> oah
TSRANGE 1998 1 2021 1
EQ> oah = oah0 + lambda_oah*TSLAG(oah,1)
COEFF> oah0 lambda_oah
STORE> coe(18)

COMMENT> BANKING SECTOR --------------------------------------------------------

COMMENT> Total supply of loans  
IDENTITY> ls
EQ> ls = lf + lh

COMMENT> Supply of bank deposits  
IDENTITY> ms
EQ> ms = mh

COMMENT> Banks profit 
IDENTITY> fb
EQ> fb = intb

COMMENT> Total interests payments received by banks
IDENTITY> intb
EQ> intb = intgb + intf + intlh - intmh

COMMENT> Net interest payments received by banks on government bills 
IDENTITY> intgb
EQ> intgb = rbb*TSLAG(bb,1) 

COMMENT> Stock of bills held by banks 
BEHAVIORAL> Lbb
TSRANGE 1998 1 2021 1
EQ> Lbb = lambdabb1*TSLAG(log(ls+hbd+bb),1) + lambdabb2*dum
COEFF> lambdabb1 lambdabb2
STORE> coe(33)

COMMENT> bb
IDENTITY> bb
EQ> bb = exp(Lbb)

COMMENT> Total wealth accumulated by banks     
IDENTITY> vb
EQ> vb = oab + hbd + bb + ls - ms  

COMMENT> GOVERNMENT SECTOR -----------------------------------------------------

COMMENT> Tax revenue  
BEHAVIORAL> tax
TSRANGE 1998 1 2021 1
EQ> tax = tau1*(TSLAG(wb,1)) + tau2*(TSLAG((yd - wb),1)) + tau3*(TSLAG(vh,1))
COEFF> tau1 tau2 tau3
STORE> coe(10)

COMMENT> Transfers and benefits 
BEHAVIORAL> tr
TSRANGE 1998 1 2021 1
EQ> tr = tau4*TSLAG(tr,1) + tau5*TSDELTA(un,1)
COEFF> tau4 tau5
STORE> coe(11)

COMMENT> Government deficit
IDENTITY> def
EQ> def = gov + tr + intg - tax - fcb

COMMENT> Government debt stock
IDENTITY> deb
EQ> deb = bs 

COMMENT> Interest payments on government debt 
IDENTITY> intg
EQ> intg = rb*TSLAG(deb,1)  

COMMENT> Supply of government bills and bonds
IDENTITY> bs
EQ> bs = TSLAG(bs,1) + def

COMMENT> Net wealth of goverment sector  (Note: negative value) 
IDENTITY> vg
EQ> vg = - bs + oag

COMMENT> PORTFOLIO EQUATIONS ---------------------------------------------------

COMMENT> Holdings of government bills (log) 
BEHAVIORAL> Lbh
TSRANGE 1998 1 2021 1
EQ> Lbh = lambda20*TSLAG(log(vh),1) + lambda21*dum
COEFF> lambda20 lambda21
STORE> coe(16)

COMMENT> Holdings of shares (log) 
BEHAVIORAL> Leh
TSRANGE 1998 1 2021 1
EQ> Leh = lambda10*TSLAG(log(vh),1) 
COEFF> lambda10 
STORE> coe(15)

COMMENT> Holding of shares 
IDENTITY> eh
EQ> eh = exp(Leh)

COMMENT> Holding of government bills 
IDENTITY> bh
EQ> bh = exp(Lbh)

COMMENT> Holdings of cash (log) 
BEHAVIORAL> Lhh
TSRANGE 1998 1 2021 1
EQ> TSDELTA(Lhh,1) = lambdac*log(cons/pc)
COEFF> lambdac
STORE> coe(17)

COMMENT> Holding of cash 
IDENTITY> hh
EQ> hh = exp(Lhh)

COMMENT> Holdings of deposits 
IDENTITY> mh
EQ> mh = vh + lh - hh - bh - eh - oah

COMMENT> CENTRAL BANK ----------------------------------------------------------

COMMENT> CB holdings of government bills
IDENTITY> bcb
EQ> bcb = bs - bh - bb - brow 

COMMENT> Supply of cash  
IDENTITY> hs
EQ> hs = bcb + oacb - vcb

COMMENT> Profit realised and distributed by CB
IDENTITY> fcb
EQ> fcb = intg - intgh - intgb - introw

COMMENT> Reserve requirement: demand
IDENTITY> hbd
EQ> hbd = rho*ms

COMMENT> Reserve ratio 
BEHAVIORAL> rho
TSRANGE 1998 1 2021 1
EQ> rho = rho_1*TSLAG(rho,1)
COEFF> rho_1
STORE> coe(56)

COMMENT> Total demand for cash and reserves (auxiliary)
IDENTITY> hd
EQ> hd = hbd + hh

COMMENT> FOREIGN SECTOR --------------------------------------------------------

COMMENT> Nominal import
IDENTITY> im
EQ> im = exp(LimR) * p / 100

COMMENT> Nominal export
IDENTITY> x
EQ> x = exp(LxR) * p / 100

COMMENT> Foreign income. Note: yf1 = (1 + gF)
BEHAVIORAL> yf
TSRANGE 1998 1 2021 1
EQ> yf = yf1*TSLAG(yf,1) 
COEFF> yf1
STORE> coe(22)

COMMENT> Net export (trade balance)
IDENTITY> nx
EQ> nx = x - im

COMMENT> Stock of Italian bills debt held by foreign agents
IDENTITY> brow
EQ> brow = lambdarow*bs 

COMMENT> Total wealth accumulated by RoW
IDENTITY> vrow
EQ> vrow = brow + oarow

COMMENT> Net interest payments received by RoW on government bills 
IDENTITY> introw
EQ> introw = rbrow * TSLAG(brow,1)

COMMENT> Exchange rate: dollars per 1 euro   
BEHAVIORAL> exr
TSRANGE 1998 1 2021 1
EQ> exr = exr1*MOVAVG(exr,2) 
COEFF> exr1 
STORE> coe(58)

COMMENT> Share of government bills purchased by foreign agents
BEHAVIORAL> lambdarow
TSRANGE 1998 1 2021 1
EQ> lambdarow = lambdarow1*TSLAG(lambdarow,1) + lambdarow2*TSLAG(rbrow,1)
COEFF> lambdarow1 lambdarow2
STORE> coe(31)

COMMENT> INTEREST RATES --------------------------------------------------------

COMMENT> Return rate on shares 
IDENTITY> re
EQ> re = fdf/TSLAG(eh,1)

COMMENT> Policy rate
BEHAVIORAL> rstar
TSRANGE 1998 1 2021 1
EQ> rstar = r0
COEFF> r0
STORE> coe(25)

COMMENT> Average risk premium on government bond
IDENTITY> rb
EQ> rb = rstar + mub

COMMENT> Interest rate received by banks on their government debt holdings
IDENTITY> rbb
EQ> rbb = rstar + mubb 

COMMENT> Interest rate received by RoW on their government debt holdings
IDENTITY> rbrow
EQ> rbrow = rstar + mubrow 

COMMENT> Premium on government bills held by banks
BEHAVIORAL> mubb
TSRANGE 1998 1 2021 1
EQ> mubb = mubb1*TSLAG(mubb,1) + mubb2*mub  
COEFF> mubb1 mubb2
STORE> coe(45)

COMMENT> Premium on government bills held by RoW
BEHAVIORAL> mubrow
TSRANGE 1998 1 2021 1
EQ> mubrow = mubrow1*TSLAG(mubrow,1) + mubrow2*mub  
COEFF> mubrow1 mubrow2
STORE> coe(46)

COMMENT> Interests paid by banks to households on deposits and other A/L 
BEHAVIORAL> intmh
TSRANGE 1998 1 2021 1
EQ> intmh = intmh0 + intmh1*mh
COEFF> intmh0 intmh1
STORE> coe(47)

COMMENT> LABOUR MARKET ---------------------------------------------------------

COMMENT> Wage bill
IDENTITY> wb
EQ> wb = w*nd

COMMENT> Labour productivity (real value added per employee) 
BEHAVIORAL> prod
EQ> TSDELTALOG(prod,1) = nu0  + nu1 * TSDELTALOG(100*w/p,1) + nu2 * TSDELTALOG(100*y/p,2)
COEFF> nu0 nu1 nu2
STORE> coe(51)

COMMENT> Employment: demand for labour 
IDENTITY> nd
EQ> nd = (100*y)/(prod*p)

COMMENT> Labour force (log) 
BEHAVIORAL> Lns
TSRANGE 1998 1 2021 1
EQ> Lns = nu1*TSLAG(Lns,1) + nu2*( log(nd) -TSLAG(Lns,1))
COEFF> nu1 nu2
STORE> coe(27)

COMMENT> Labour force 
IDENTITY> ns
EQ> ns = exp(Lns)

COMMENT> Wage rate growth 
BEHAVIORAL> gw
TSRANGE 1998 1 2021 1
EQ> gw = omega1*TSDELTAP(p/100,1) + omega2*TSDELTA(un,1)
COEFF> omega1 omega2
STORE> coe(28)

COMMENT> Nominal wage rate
IDENTITY> w
EQ> w = TSLAG(w,1)*(1+gw)

COMMENT> Unemployment rate
IDENTITY> un
EQ> un = 1-(nd/ns) 

COMMENT> PRODUCTION AND PRICES -------------------------------------------------

COMMENT> Price level (GDP deflator)
IDENTITY> p
EQ> p = exp(Lp)

COMMENT> Consumer price index 
IDENTITY> pc
EQ> pc = exp(Lpc)

COMMENT> Log foreign price level --- exogenous    
BEHAVIORAL> Lp_row
TSRANGE 1998 1 2021 1
EQ> Lp_row = prow0 + prow1*TSLAG(Lp_row,1)
COEFF> prow0 prow1
STORE> coe(60)

COMMENT> Foreign price level  
IDENTITY> p_row
EQ> p_row = exp(Lp_row)

COMMENT> Price of import  
IDENTITY> p_im
EQ> p_im = exp(Lp_im)

COMMENT> Inflation rate based on GDP deflator 
IDENTITY> infl
EQ> infl = (p - TSLAG(p,1))/TSLAG(p,1)

COMMENT> Inflation rate based on CPI 
IDENTITY> inflc
EQ> inflc = (pc - TSLAG(pc,1))/TSLAG(pc,1)

COMMENT> Deficit to GDP ratio
IDENTITY> def_ratio
EQ> def_ratio = def/y

COMMENT> Debt to GDP ratio
IDENTITY> deb_ratio
EQ> deb_ratio = deb/y

COMMENT> ENERGY IMPORT ---------------------------------------------------------

COMMENT> Energy Price level  
IDENTITY> p_en
EQ> p_en = exp(Lp_en)

COMMENT> Share of energy products to total import 
BEHAVIORAL> perc_en
TSRANGE 1998 1 2021 1
EQ> perc_en = enm1*infl_en + enm2*TSLAG(log(y/p),1) 
COEFF> enm1 enm2
STORE> coe(54)

COMMENT> Import of energy products 
IDENTITY> im_en
EQ> im_en = im * perc_en

COMMENT> Energy inflation rate. Note: high values, so do not use dlog
IDENTITY> infl_en
EQ> infl_en = (p_en - TSLAG(p_en,1))/TSLAG(p_en,1)

COMMENT> Log of energy price --- exogenous
BEHAVIORAL> Lp_en
TSRANGE 1998 1 2021 1
EQ> Lp_en = ep1*TSLAG(Lp_en,1) 
COEFF> ep1
STORE> coe(53)

COMMENT> OTHER ACCOUNTING-CONSISTENCY EQUATIONS --------------------------------

COMMENT> Other payments or receipts received by firms  
IDENTITY> opf
EQ> opf = vf - TSLAG(vf,1) - (cons + gov + nx - wb - intf - fdf)

COMMENT> Other payments or receipts received by banks 
IDENTITY> opb
EQ> opb = fb - intb + (vb - tslag(vb,1))

COMMENT> Other payments or receipts by government
IDENTITY> opg
EQ> opg = vg - TSLAG(vg,1) - ( -gov + tax - tr - intg + fcb)

COMMENT> Other payments or receipts received by CB   
IDENTITY> opcb
EQ> opcb = vcb - TSLAG(vcb,1)

COMMENT> Other payments or receipts received by RoW   
IDENTITY> oprow
EQ> oprow = -(oph + opf + opg + opb + opcb) 

COMMENT> Other payments or receipts of households  
BEHAVIORAL> oph
TSRANGE 1998 1 2021 1
EQ> TSDELTAP(oph,1) = par_oph * TSDELTAP(oph,1) 
COEFF> par_oph
STORE> coe(57)

COMMENT> Other financial assets held by RoW 
IDENTITY> oarow
EQ> oarow = - (oah + oaf + oab + oacb + oag) 

COMMENT> Total wealth accumulated by central bank   
IDENTITY> vcb
EQ> vcb = -(vh + vf + vrow + vg + vb)

COMMENT> Other financial assets/liabilities of firms 
BEHAVIORAL> oaf
TSRANGE 1998 1 2021 1
EQ> oaf = oaf0 + lambda_oaf*TSLAG(oaf,1)
COEFF> oaf0 lambda_oaf
STORE> coe(38)

COMMENT> Other financial assets/liabilities of government
BEHAVIORAL> oag
TSRANGE 1998 1 2021 1
EQ> oag = oag0 + lambda_oag*TSLAG(oag,1)
COEFF> oag0 lambda_oag
STORE> coe(44)

COMMENT> Other financial assets held by banks
BEHAVIORAL> oab
TSRANGE 1998 1 2021 1
EQ> oab = oab0 + lambda_oab*TSLAG(oab,1)
COEFF> oab0 lambda_oab
STORE> coe(52)

COMMENT> Other financial assets held by ECB
BEHAVIORAL> oacb
TSRANGE 1998 1 2021 1
EQ> oacb = oacb0 + lambda_oacb*TSLAG(oacb,1)
COEFF> oacb0 lambda_oacb
STORE> coe(55)

COMMENT> ADDITIONAL CALCULATIONS --------------------------------

COMMENT> Real GDP 
IDENTITY> yR
EQ> yR = 100*y/p 

COMMENT> Real investment including depreciation (note: iddR > idR)
IDENTITY> iddR
EQ> iddR = 100*id/p 

COMMENT> Real export
IDENTITY> xR
EQ> xR = 100*x/p 

COMMENT> Real investment including depreciation (note: different from idR)
IDENTITY> imR
EQ> imR = 100*im/p 

COMMENT> KEY BEHAVIOURAL EQUATIONS --------------------------------

COMMENT> Real consumption (log). Note: yd replaced with y because the latter is more stable over time 
BEHAVIORAL> LconsR
TSRANGE 1998 1 2021 1
EQ> LconsR = alpha1*TSLAG(log(y*100/pc),1) + alpha2*TSLAG( log(vh*100/pc),1)  
COEFF> alpha1 alpha2
STORE> coe(5)

COMMENT> Government consumption 
BEHAVIORAL> gov
TSRANGE 1998 1 2021 1
EQ> gov = sigma1*TSLAG((gov/p),1)*p  
COEFF> sigma1
RESTRICT> sigma1 = 1.01
STORE> coe(12)

COMMENT> Real investment net of capital depreciation 
BEHAVIORAL> LidR
TSRANGE 1998 1 2021 1
EQ> LidR = gamma0 + gamma1*TSLAG(log(y)/log(k),1)
COEFF> gamma0 gamma1 
STORE> coe(1)

COMMENT> Log of real export    
BEHAVIORAL> LxR
TSRANGE 1998 1 2021 1
EQ> LxR = x0 + x1*TSLAG(log(yf),1) + x2*TSLAG(exr*p/p_row,1)
COEFF> x0 x1 x2
STORE> coe(21)

COMMENT> Log of real import  
BEHAVIORAL> LimR
TSRANGE 1998 1 2021 1
EQ> LimR = m0 + m1*TSLAG(log(y),1) + m2*TSLAG(p_im/p,1)
COEFF> m0 m1 m2
STORE> coe(20)

COMMENT> Log of price of import    
BEHAVIORAL> Lp_im
TSRANGE 1998 1 2021 1
EQ> Lp_im = pim0 + pim1*TSLAG(exr,1) + pim2*TSLAG(Lp_row,1)
COEFF> pim0 pim1 pim2
STORE> coe(59)

COMMENT> Log of price level (GDP deflator) 
BEHAVIORAL> Lp
TSRANGE 1998 1 2021 1
EQ> Lp = viy1*TSLAG(Lp_en,1) + viy2*TSLAG(Lp_row,1) + viy3*TSLAG(log(100*y/p),1) 
COEFF> viy1 viy2 viy3 
STORE> coe(30)

COMMENT> Log of consumer price index 
BEHAVIORAL> Lpc
TSRANGE 1998 1 2021 1
EQ> Lpc = vic1*TSLAG(Lp_en,1) + vic2*TSLAG(Lp_row,1) + vic3*TSLAG(log(100*y/p),1)
COEFF> vic1 vic2 vic3
STORE> coe(30)

COMMENT> Average premium on government bills
BEHAVIORAL> mub
TSRANGE 1998 1 2021 1
EQ> mub = mub2*TSLAG(deb/y,1) + mub3*bcb/bs + mub4*rstar
COEFF> mub2 mub3 mub4
STORE> coe(39)

END"

Notice that the two price equations have been defined including real GDP among the deflators. This choice is due to four reasons:

  1. Income effect. Real GDP can be considered a proxy for the overall volume of activity or income in an economy. Changes in income can affect the demand for goods and services, thus indirectly affecting the price level.

  2. Aggregate demand effect. Real GDP reflects the aggregate demand. When aggregate demand increases, it can put direct upward pressure on prices, particularly when supply is constrained (as it happened in recent years). Therefore, including real GDP in the price equation allows capturing this demand-pressure effect.

  3. Macroeconomic and labour market conditions. Real GDP can be taken as a key indicator of the overall health of the economy, hence labour market conditions. A higher employment rate and a lower unemployment rate are usually associated with higher nominal wages. Real GDP serves as a summary measure of these macroeconomic and labour market conditions.

  4. Medium-term trend. Real GDP can also be used to capture medium-term trend in the economy, which can in turn influence the price level.

An alternative specification of these equations, including the unit labour cost among the regressors (instead of real GDP), could be:

COMMENT> Log of price level (GDP deflator) 
BEHAVIORAL> Lp
TSRANGE 1998 1 2021 1
EQ> TSDELTA(Lp,1) = viy1*TSDELTA(Lp_en,1) + viy2*TSDELTA(Lp_row,1) + viy3*TSDELTA(log(w),1) + viy4*TSDELTA(log(prod),1)
COEFF> viy1 viy2 viy3 viy4
STORE> coe(30)

COMMENT> Log of consumer price index 
BEHAVIORAL> Lpc
TSRANGE 1998 1 2021 1
EQ> TSDELTA(Lpc,1) = vic1*TSDELTA(Lp_en,1) + vic2*TSDELTA(Lp_row,1) + vic3*TSDELTA(log(w),1) + vic4*TSDELTA(log(prod),1)
COEFF> vic1 vic2 vic3 vic4
STORE> coe(30)

While our qualitative results would not be affected, and the coefficients exhibit the correct signs, the latter are barely significant. This may be attributed to the specific situation of the Italian labour market, where workers have lost most of their bargaining power, while the goods market is characterised by an oligopolistic structure. This is why we pragmatically opted for real GDP in the final specification of the model.

Having clarified that, the fourth step is to load the model.

#Load the model
S_model=LOAD_MODEL(modelText = S_model.txt)

This allows displaying the structure of the model (including the number of behavioural equations, identities, and coefficients) in the Console.

Analyzing behaviorals...
Analyzing identities...
Optimizing...
Loaded model "S_model.txt":
   40 behaviorals
   81 identities
   77 coefficients
...LOAD MODEL OK

The fifth step is to associate the model with the imported data. Note: a time series is required for each variable defined in the model, including dummies.

#Attribute values to model variables and coefficients
S_modelData=list(  
  
  pc = TIMESERIES(c(DataEE$Pc),   
                 START=c(1995,1),FREQ=1),
  Lpc = TIMESERIES(c(log(DataEE$Pc)),   
                  START=c(1995,1),FREQ=1),
  gid = TIMESERIES(c(DataEE$gid),   
                    START=c(1995,1),FREQ=1),
  gidR = TIMESERIES(c(DataEE$gid-DataEE$PI),   
                   START=c(1995,1),FREQ=1),
  infl = TIMESERIES(c(DataEE$PI),   
                  START=c(1995,1),FREQ=1),
  inflc = TIMESERIES(c(DataEE$CPI),   
                    START=c(1995,1),FREQ=1),
  Lp = TIMESERIES(c(log(DataEE$Py)),   
                  START=c(1995,1),FREQ=1),
  p_en = TIMESERIES(c(DataEE$Pen2 ),   
                    START=c(1995,1),FREQ=1),
  Lp_en = TIMESERIES(c(log(DataEE$Pen2)),   
                     START=c(1995,1),FREQ=1),
  infl_en = TIMESERIES(c(DataEE$PIen),   
                  START=c(1995,1),FREQ=1),
  im_en = TIMESERIES(c(DataEE$IMen),   
                    START=c(1995,1),FREQ=1),
  perc_en = TIMESERIES(c(DataEE$IMen/DataEE$IM),   
                     START=c(1995,1),FREQ=1),
  Lim_en = TIMESERIES(c(log(DataEE$IMen)),   
                     START=c(1995,1),FREQ=1),
  y = TIMESERIES(c(DataEE$Y),   
                  START=c(1995,1),FREQ=1),
  gy  = TIMESERIES(c(DataEE$gy),   
                  START=c(1995,1),FREQ=1),
  cons = TIMESERIES(c(DataEE$CONS),   
                     START=c(1995,1),FREQ=1),
  id = TIMESERIES(c(DataEE$INV),   
                  START=c(1995,1),FREQ=1),
  gov = TIMESERIES(c(DataEE$GOV),   
                    START=c(1995,1),FREQ=1),
  x = TIMESERIES(c(DataEE$X),   
                  START=c(1995,1),FREQ=1),
  im = TIMESERIES(c(DataEE$IM),   
                   START=c(1995,1),FREQ=1),
  Lx = TIMESERIES(c(log(DataEE$X)),   
                   START=c(1995,1),FREQ=1),
  Lim = TIMESERIES(c(log(DataEE$IM)),   
                    START=c(1995,1),FREQ=1),
  LxR = TIMESERIES(c(log(100*DataEE$X/DataEE$Py)),   
                   START=c(1995,1),FREQ=1),
  LimR = TIMESERIES(c(log(100*DataEE$IM/DataEE$Py)),   
                   START=c(1995,1),FREQ=1),
  consR  = TIMESERIES(c(DataEE$CONS*100/DataEE$Py),   
                      START=c(1995,1),FREQ=1),
  LconsR  = TIMESERIES(c(log(DataEE$CONS*100/DataEE$Py)),   
                       START=c(1995,1),FREQ=1),
  idR = TIMESERIES(c(DataEE$INVnet*100/DataEE$Py), 
                   START=c(1995,1),FREQ=1),
  LidR  = TIMESERIES(c(log(DataEE$INVnet*100/DataEE$Py)),   
                     START=c(1995,1),FREQ=1),
  nx  = TIMESERIES(c(DataEE$X-DataEE$IM),   
                   START=c(1995,1),FREQ=1),
  wb  = TIMESERIES(c(DataEE$WB),   
                   START=c(1995,1),FREQ=1),
  yd  = TIMESERIES(c(DataEE$YD),   
                   START=c(1995,1),FREQ=1),
  vh = TIMESERIES(c(DataEE$NVh),   
                   START=c(1995,1),FREQ=1),
  k = TIMESERIES(c(DataEE$K),   
                  START=c(1995,1),FREQ=1),
  deltak = TIMESERIES(c(DataEE$Delta ),   
                 START=c(1995,1),FREQ=1),
  intf = TIMESERIES(c(DataEE$INTf),   
                    START=c(1995,1),FREQ=1),
  lf  = TIMESERIES(c(-DataEE$Lf),   
                   START=c(1995,1),FREQ=1),
  fdf  = TIMESERIES(c(DataEE$DIV),   
                    START=c(1995,1),FREQ=1),
  ff  = TIMESERIES(c(DataEE$Ff),   
                   START=c(1995,1),FREQ=1),
  fuf  = TIMESERIES(c(DataEE$FUf),   
                    START=c(1995,1),FREQ=1),
  es  = TIMESERIES(c(-DataEE$Es),   
                   START=c(1995,1),FREQ=1),
  eh = TIMESERIES(c(DataEE$Eh),   
                   START=c(1995,1),FREQ=1),
  Leh = TIMESERIES(c(log(DataEE$Eh)),   
                  START=c(1995,1),FREQ=1),
  tax  = TIMESERIES(c(DataEE$TAX),   
                    START=c(1995,1),FREQ=1),
  tr  = TIMESERIES(c(DataEE$TR),   
                   START=c(1995,1),FREQ=1),
  Ltax  = TIMESERIES(c(log(DataEE$TAX)),   
                    START=c(1995,1),FREQ=1),
  Ltr  = TIMESERIES(c(log(DataEE$TR)),   
                   START=c(1995,1),FREQ=1),
  lh  = TIMESERIES(c(-DataEE$Lh),   
                   START=c(1995,1),FREQ=1),
  ls  = TIMESERIES(c(DataEE$Ls),   
                   START=c(1995,1),FREQ=1),
  mh  = TIMESERIES(c(DataEE$Mh),   
                   START=c(1995,1),FREQ=1),
  ms  = TIMESERIES(c(-DataEE$Ms),   
                   START=c(1995,1),FREQ=1),
  inth  = TIMESERIES(c(DataEE$INTh),   
                     START=c(1995,1),FREQ=1),
  un  = TIMESERIES(c( (DataEE$Ns-DataEE$Nd)/DataEE$Ns ),   
                   START=c(1995,1),FREQ=1),
  Omega  = TIMESERIES(c(DataEE$WB/DataEE$Y),   
                      START=c(1995,1),FREQ=1),
  ns  = TIMESERIES(c(DataEE$Ns),   
                   START=c(1995,1),FREQ=1),
  Lns  = TIMESERIES(c(log(DataEE$Ns)),   
                   START=c(1995,1),FREQ=1),
  bs  = TIMESERIES(c(-DataEE$Bs),   
                   START=c(1995,1),FREQ=1),
  bh = TIMESERIES(c(DataEE$Bh),   
                  START=c(1995,1),FREQ=1),
  Lbh = TIMESERIES(c(log(DataEE$Bh)),   
                  START=c(1995,1),FREQ=1),
  rbb = TIMESERIES(c(DataEE$Rbb ),         
                   START=c(1995,1),FREQ=1),  
  mubb = TIMESERIES(c(DataEE$Rbb-DataEE$Rstar),   
                    START=c(1995,1),FREQ=1),
  rbrow = TIMESERIES(c(DataEE$Rbrow ),         
                     START=c(1995,1),FREQ=1),  
  mubrow = TIMESERIES(c(DataEE$Rbrow-DataEE$Rstar),   
                      START=c(1995,1),FREQ=1),
  rbh = TIMESERIES(c(DataEE$Rbh ),         
                   START=c(1995,1),FREQ=1),  
  mubh = TIMESERIES(c(DataEE$Rbh-DataEE$Rstar),   
                    START=c(1995,1),FREQ=1),
  introw = TIMESERIES(c(DataEE$INTrow ),         
                      START=c(1995,1),FREQ=1),  
  fcb = TIMESERIES(c(DataEE$Fcb),                       
                   START=c(1995,1),FREQ=1),
  re = TIMESERIES(c(DataEE$Re),                
                  START=c(1995,1),FREQ=1),
  hh = TIMESERIES(c(DataEE$Hh),   
                   START=c(1995,1),FREQ=1),
  Lhh = TIMESERIES(c(log(DataEE$Hh)),   
                  START=c(1995,1),FREQ=1),
  rho  = TIMESERIES(c(DataEE$RHO),   
                    START=c(1995,1),FREQ=1),
  yf  = TIMESERIES(c(DataEE$Yrow/1000),   
                   START=c(1995,1),FREQ=1),   
  rstar  = TIMESERIES(c(DataEE$Rstar),   
                      START=c(1995,1),FREQ=1),
  mub  = TIMESERIES(c(DataEE$Rb-DataEE$Rstar),   
                    START=c(1995,1),FREQ=1),
  deb  = TIMESERIES(c(DataEE$Deb),   
                    START=c(1995,1),FREQ=1),
  vg = TIMESERIES(c(DataEE$Vg),   
                  START=c(1995,1),FREQ=1),
  def  = TIMESERIES(c(DataEE$DEF1),   
                     START=c(1995,1),FREQ=1),
  nd = TIMESERIES(c(DataEE$Nd),   
                   START=c(1995,1),FREQ=1),
  ndstar = TIMESERIES(c(DataEE$Y/DataEE$Prod),   
                  START=c(1995,1),FREQ=1),
  w = TIMESERIES(c(DataEE$w),   
                 START=c(1995,1),FREQ=1),
  gw = TIMESERIES(c(DataEE$gw),   
                  START=c(1995,1),FREQ=1),
  bb = TIMESERIES(c(DataEE$Bb),   
                  START=c(1995,1),FREQ=1),
  Lbb = TIMESERIES(c(log(DataEE$Bb)),   
                  START=c(1995,1),FREQ=1),
  bcb = TIMESERIES(c(DataEE$Bcb),   
                   START=c(1995,1),FREQ=1),
  bb_not = TIMESERIES(c(-DataEE$Ms - DataEE$Ls - DataEE$Hbd),                        
                      START=c(1995,1),FREQ=1),
  hbd = TIMESERIES(c(DataEE$Hbd),   
                   START=c(1995,1),FREQ=1),
  hs = TIMESERIES(c(-DataEE$Hs ),   
                  START=c(1995,1),FREQ=1),
  hd = TIMESERIES(c(-DataEE$Hs),   
                  START=c(1995,1),FREQ=1),
  fb = TIMESERIES(c(DataEE$Fb ), 
                  START=c(1995,1),FREQ=1),
  lambdacb = TIMESERIES(c(-DataEE$Bcb/DataEE$Bs),   
                        START=c(1995,1),FREQ=1),
  lambdarow = TIMESERIES(c(-DataEE$Brow/DataEE$Bs),   
                        START=c(1995,1),FREQ=1),
  oph = TIMESERIES(c(DataEE$OPh),   
                   START=c(1995,1),FREQ=1),
  opb = TIMESERIES(c(DataEE$OPb),
                   START=c(1995,1),FREQ=1),
  opcb = TIMESERIES(c(DataEE$OPcb),   
                    START=c(1995,1),FREQ=1),
  opf = TIMESERIES(c(DataEE$OPf),   
                   START=c(1995,1),FREQ=1),
  opg = TIMESERIES(c(DataEE$OPg),   
                   START=c(1995,1),FREQ=1),
  vf = TIMESERIES(c(DataEE$Vf),   
                  START=c(1995,1),FREQ=1),
  oprow = TIMESERIES(c(DataEE$OProw),   
                     START=c(1995,1),FREQ=1),
  vb = TIMESERIES(c(DataEE$Vb),                        
                  START=c(1995,1),FREQ=1),
  vrow = TIMESERIES(c(DataEE$Vrow),   
                    START=c(1995,1),FREQ=1),
  oah = TIMESERIES(c(DataEE$OAh),   
                   START=c(1995,1),FREQ=1),
  Loah = TIMESERIES(c(log(DataEE$OAh)),   
                   START=c(1995,1),FREQ=1),
  oaf = TIMESERIES(c(DataEE$OAf),   
                   START=c(1995,1),FREQ=1),
  oab = TIMESERIES(c(DataEE$OAb),   
                   START=c(1995,1),FREQ=1),
  oag = TIMESERIES(c(DataEE$OAg),   
                   START=c(1995,1),FREQ=1),
  oacb = TIMESERIES(c(DataEE$OAcb),   
                    START=c(1995,1),FREQ=1),
  oarow = TIMESERIES(c(DataEE$OArow),   
                     START=c(1995,1),FREQ=1),
  vcb = TIMESERIES(c(DataEE$Vcb),   
                   START=c(1995,1),FREQ=1),
  p = TIMESERIES(c(DataEE$Py),   
                 START=c(1995,1),FREQ=1),
  prod = TIMESERIES(c(DataEE$ProdR),   
                    START=c(1995,1),FREQ=1),
  rl = TIMESERIES(c(DataEE$Rl ),   
                  START=c(1995,1),FREQ=1),
  mul = TIMESERIES(c(DataEE$Rl - DataEE$Rstar ),   
                   START=c(1995,1),FREQ=1),
  intgb  = TIMESERIES(c(DataEE$INTgb),   
                      START=c(1995,1),FREQ=1),   
  intgh = TIMESERIES(c(DataEE$INTgh ),   
                     START=c(1995,1),FREQ=1),            
  intb  = TIMESERIES(c(DataEE$INTb),   
                     START=c(1995,1),FREQ=1), 
  intmh = TIMESERIES(c(DataEE$INTm ),   
                     START=c(1995,1),FREQ=1),    
  intlh = TIMESERIES(c(DataEE$INTlh ),   
                     START=c(1995,1),FREQ=1),           
  rlh = TIMESERIES(c(DataEE$Rlh ),   
                   START=c(1995,1),FREQ=1),               
  mulh = TIMESERIES(c(DataEE$Rlh - DataEE$Rstar ),   
                    START=c(1995,1),FREQ=1),               
  rb = TIMESERIES(c(DataEE$Rb),         
                  START=c(1995,1),FREQ=1),   
  mub  = TIMESERIES(c(DataEE$Rb-DataEE$Rstar),   
                    START=c(1995,1),FREQ=1),
  intg = TIMESERIES(c(DataEE$INTg),             
                    START=c(1995,1),FREQ=1),
  brow = TIMESERIES(c(DataEE$Brow),   
                    START=c(1995,1),FREQ=1),
  pc = TIMESERIES(c(DataEE$Pc),   
                  START=c(1995,1),FREQ=1),
  exr = TIMESERIES(c(DataEE$Exr),   
                  START=c(1995,1),FREQ=1),
  exr42 = TIMESERIES(c(DataEE$Exr42 ),   
                   START=c(1995,1),FREQ=1),
  exr42 = TIMESERIES(c(DataEE$Exr42 ),   
                     START=c(1995,1),FREQ=1),
  dum = TIMESERIES(c(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1),   
                  START=c(1995,1),FREQ=1),
  p_im = TIMESERIES(c(DataEE$Pim ),   
                    START=c(1995,1),FREQ=1),
  Lp_im = TIMESERIES(c(log(DataEE$Pim)),   
                     START=c(1995,1),FREQ=1),
  p_im_en = TIMESERIES(c(DataEE$Pim_en ),   
                       START=c(1995,1),FREQ=1),
  Lp_im_en = TIMESERIES(c(log(DataEE$Pim_en)),   
                        START=c(1995,1),FREQ=1),
  p_row = TIMESERIES(c(DataEE$Py_row ),   
                     START=c(1995,1),FREQ=1),
  Lp_row = TIMESERIES(c(log(DataEE$Py_row)),   
                      START=c(1995,1),FREQ=1),
  yR = TIMESERIES(c(DataEE$Y*100/DataEE$Py),   
                  START=c(1995,1),FREQ=1),
  iddR = TIMESERIES(c(DataEE$INV*100/DataEE$Py),   
                    START=c(1995,1),FREQ=1),
  xR = TIMESERIES(c(DataEE$X*100/DataEE$Py),   
                  START=c(1995,1),FREQ=1),
  imR = TIMESERIES(c(DataEE$IM*100/DataEE$Py),   
                   START=c(1995,1),FREQ=1),
  def_ratio = TIMESERIES(c(DataEE$DEF1/DataEE$Y),   
                         START=c(1995,1),FREQ=1),
  deb_ratio = TIMESERIES(c(DataEE$Deb/DataEE$Y),   
                         START=c(1995,1),FREQ=1)
  
)

#Load the data into the model
S_model=LOAD_MODEL_DATA(S_model,S_modelData)

The sixth step is to estimate model coefficients:

#Estimate model coefficients
S_model=ESTIMATE(S_model
                 ,TSRANGE = c(1998,1,2019,1)          #Choose time range for estimations
                 ,forceTSRANGE = TRUE                 #If TRUE, the TSRANGE above takes precedence over individual equations TSRANGEs  
                 ,CHOWTEST = FALSE                    #If TRUE, performs Chow test: stability analysis (reject H0 of "no structural break")
                 ,CHOWPAR = NULL                      #If NULL, use last periods
                 )

Now, we can execute the entire code, enabling the creation of the model and the estimation of the associated coefficients. Information on the estimations is displayed in the Console. For instance, the following details pertain to the estimation of the risk premium for government securities ($\mu_b$), which was the last variable defined in the txt chunk. This risk premium is considered a positive function of the debt-to-GDP ratio and a negative function of both the share of debt held by the ECB and the policy rate level. The rationale here is that when the policy rate increases, the interest rate on Italian securities increases less than proportionally.

BEHAVIORAL EQUATION: mub
Estimation Technique: OLS

mub                 =   0.03222813  TSLAG(deb/y,1)
                        T-stat. 12.05956    ***

                    -   0.07942629  bcb/bs
                        T-stat. -3.732844   **

                    -   0.4223384   rstar
                        T-stat. -6.374726   ***


STATs:
R-Squared                      : 0.9773436   
Adjusted R-Squared             : 0.9737663   
Durbin-Watson Statistic        : 0.9611077   
Sum of squares of residuals    : 0.0002797596
Standard Error of Regression   : 0.003837208 
Log of the Likelihood Function : 92.7822     
F-statistic                    : 273.2053    
F-probability                  : 8.881784e-16
Akaike's IC                    : -177.5644   
Schwarz's IC                   : -173.2002   
Mean of Dependent Variable     : 0.02246469  
Number of Observations         : 22
Number of Degrees of Freedom   : 19
Current Sample (year-period)   : 1998-1 / 2019-1


Signif. codes:   *** 0.001  ** 0.01  * 0.05  


...ESTIMATE OK

The details of the other estimations can be visualised by scrolling up through the Console information. The complete list of estimated coefficients is provided below:

Name Description Value
$δ$ Depreciation rate (average 1996-2019) 0.046
$θ$ Share of undistributed profits 0.265
$ϕ$ Elasticity of personal loans to consumption 0.058
$μ_{b1}^h$ Premium on gov. bills held by households: coefficient 1 0.793
$μ_{b2}^h$ Premium on gov. bills held by households: coefficient 2 0.804
$μ_{l1}$ Markup on loans to firms: coefficient 1 -0.014
$μ_{l2}$ Markup on loans to firms: coefficient 2 0.49
$μ_{h1}$ Markup on personal loans: coefficient 1 0.029
$μ_{h2}$ Markup on personal loans: coefficient 2 0.23
$λ_{h0}^{oa}$ Other financial assets of households: coefficient 1 134828.967
$λ_{h1}^{oa}$ Other financial assets of households: coefficient 2 0.908
$λ_b^b$ Stock of bills held by banks: coefficient 1 0.918
$τ_1^T$ Average tax rate on labour incomes 0.514
$τ_2^T$ Average tax rate on non-labour incomes 0.061
$τ_3^T$ Average tax rate on wealth 0.042
$τ_1^{TR}$ Transfers and benefits: auto-regressive component 1.043
$τ_2^{TR}$ Transfers and benefits: elasticity to unemployment rate 374169.858
$λ_B$ Holdings of government bills: coefficient 1 0.903
$λ_E$ Holdings of shares as a ratio to total wealth 0.925
$λ_c$ Elasticity of cash holdings to real consumption 0.006
$ρ$ Reserve ratio 1.004
$g_y^{row}$ Foreign growth rate 0.037
$exr$ Exchange rate coefficient 1
$r^*$ Policy rate 0.019
$μ_{b1}$ Premium on government bills held by banks: coefficient 1 0.924
$μ_{b2}$ Premium on government bills held by banks: coefficient 2 0.248
$μ_{b1}^{row}$ Premium on government bills held by RoW: coefficient 1 0.554
$μ_{b2}^{row}$ Premium on government bills held by RoW: coefficient 2 0.916
$ν_0$ Labour productivity: autonomous component -0.004
$ν_1$ Labour productivity: elasticity to real wage rate 0.397
$ν_2$ Labour productivity: elasticity to real output 0.183
$ν_{s1}$ Labour force: auto-regressive component 1.001
$ν_{s2}$ Labour force: elasticity to labour demand gap 0.031
$ω_1$ Wage growth rate: elasticity to inflation 0.009
$ω_2$ Wage growth rate: elasticity to unemployment rate -0.786
$p_{row}^0$ Foreign price level: coefficient 1 0.207
$p_{row}$ Foreign price level: coefficient 2 0.959
$ϵ_2^{en}$ Share of energy prod. to tot. import: elasticity to energy inflation -0.002
$ϵ_1^{en}$ Share of energy prod. to tot. import: elasticity to real output 0.013
$p_{en}$ Energy price coefficient 1.006
$λ_{f0}^{oa}$ Other financial assets/liabilities of firms: coefficient 1 16702.341
$λ_{f1}^{oa}$ Other financial assets/liabilities of firms: coefficient 2 0.897
$λ_{g0}^{oa}$ Other financial assets/liabilities of government: coefficient 1 86022.616
$λ_{g1}^{oa}$ Other financial assets/liabilities of government: coefficient 2 0.583
$λ_{b0}^{oa}$ Other financial assets held by banks: coefficient 1 -431517.076
$λ_{b1}^{oa}$ Other financial assets held by banks: coefficient 2 0.745
$λ_{cb0}^{oa}$ Other financial assets held by ECB: coefficient 1 -4533.844
$λ_{cb1}^{oa}$ Other financial assets held by ECB: coefficient 2 1.141
$α_1$ Marginal propensity to consume out of real income 0.906
$α_2$ Marginal propensity to consume out of real wealth 0.055
$σ_1$ Real government spending: auto-regressive coefficient 1.01
$γ_0$ Real net investment: autonomous component -117.512
$γ_1$ Real net investment: elasticity to output to capital ratio 138.616
$ε_0$ Real export: autonomous component 7.879
$ε_1$ Real export: elasticity to foreign income 0.512
$ε_2$ Real export: elasticity to relative price of export 0.08
$μ_0$ Real import: autonomous component 4.092
$μ_1$ Real import: elasticity to domestic income 0.633
$μ_2$ Real import: elasticity to relative price of import -0.106
$π_y^2$ GDP deflator: elasticity to energy price level 0.058
$π_y^1$ GDP deflator: elasticity to foreign price level 0.619
$π_y^3$ GDP deflator: elasticity to real output 0.104
$π_c^2$ Consumer price index: elasticity to energy price level 0.182
$π_c^1$ Consumer price index: elasticity to foreign price level 0.505
$π_c^3$ Consumer price index: elasticity to real output 0.101
$μ_{b1}$ Av. premium on gov. bills: elasticity to debt to GDP ratio 0.032
$μ_{b2}$ Av. premium on gov. bills: elasticity to ECB’s holdings -0.079
$μ_{b3}$ Av. premium on gov. bills: elasticity to policy rate -0.422

Note: Simple OLS estimations have been employed. Additionally, log levels (instead of first differences) have been considered. In principle, this may raise concerns, as most variables are non-stationary, thus possibly leading to spurious correlations. The rationale for our choice is that observed annual time series are quite short and affected by structural breaks (such as the launch of the euro, the COVID-19 crisis, etc.). This makes the use of more sophisticated estimation techniques challenging. Furthermore, while the stationarity issue could be addressed by taking first differences, abandoning levels would imply a further loss of information. Lastly, note that the aim of the model is not to outpredict other methods, but to provide a theoretical tool to develop and assess alternative policy scenarios.

2_Accouting_tables

As mentioned earlier, the first step in defining the level of aggregation for the model and reclassifying available data is to create the balance sheet and the transactions-flow matrix of the economy. This process can also be used to double-check ex-post model consistency. The following code chunk facilitates the creation of the balance sheet using observed series (in both HTML and LaTeX format):

#Balance-sheet for Italy SFC model

#Observed series

################################################################################
#Choose a year (26=2020)
yr = 27

#Create row names for BS matrix
rownames<-c( "Cash and reserves",
             "Deposits",
             "Securities",
             "Loans",
             "Shares",
             "Other net FA",
             "Net financial wealth",
             "Column total")

################################################################################

#Create firms aggregates
Firms        <-c( 0,                                                                    
                  0,                                                                    
                  0,                                                                    
                  round(-S_modelData$lf[yr], digits = 0),                                                                    
                  round(-S_modelData$es[yr], digits = 0),                                                                     
                  round(S_modelData$oaf[yr], digits = 0),                                                                     
                  round(S_modelData$vf[yr], digits = 0),
                  round(-S_modelData$lf[yr]-S_modelData$es[yr]+S_modelData$oaf[yr]-S_modelData$vf[yr], digits = 0)
)                                                                    

#Create table of results
FirmDataBS<-as.data.frame(Firms,row.names=rownames)

#Print firms column
kable(FirmDataBS)

################################################################################

#Create banks aggregates
Banks        <-c( round(S_modelData$hbd[yr], digits = 0),                                                                    
                  -round(S_modelData$ms[yr], digits = 0),                                                                    
                  round(S_modelData$bb[yr], digits = 0),                                                                    
                  round(S_modelData$ls[yr], digits = 0),                                                                    
                  0,                                                                     
                  round(S_modelData$oab[yr], digits = 0),                                                                     
                  round(S_modelData$vb[yr], digits = 0),
                  round(S_modelData$hbd[yr]-S_modelData$ms[yr]+S_modelData$bb[yr]+S_modelData$ls[yr]+S_modelData$oab[yr]-S_modelData$vb[yr], digits = 0)
)                                                                    

#Create table of results
BankDataBS<-as.data.frame(Banks,row.names=rownames)

#Print banks column
kable(BankDataBS)

################################################################################

#Create ECB aggregates
ECB          <-c( -round(S_modelData$hs[yr], digits = 0),                                                                    
                  0,                                                                    
                  round(S_modelData$bcb[yr], digits = 0),                                                                    
                  0,                                                                    
                  0,                                                                     
                  round(S_modelData$oacb[yr], digits = 0),                                                                     
                  round(S_modelData$vcb[yr], digits = 0),
                  round(-S_modelData$hs[yr]+S_modelData$bcb[yr]+S_modelData$oacb[yr]-S_modelData$vcb[yr], digits = 0)
)                                                                    

#Create table of results
ECBDataBS<-as.data.frame(ECB,row.names=rownames)

#Print ECB column
kable(ECBDataBS)

################################################################################

#Create government aggregates
Government    <-c(0,                                                                    
                  0,                                                                    
                  round(-S_modelData$bs[yr], digits = 0),
                  0,                                                                    
                  0,                                                                     
                  round(S_modelData$oag[yr], digits = 0), 
                  round(S_modelData$vg[yr], digits = 0),
                  round(-S_modelData$bs[yr]+S_modelData$oag[yr]-S_modelData$vg[yr], digits = 0)
)                                                                    

#Create table of results
GovDataBS<-as.data.frame(Government,row.names=rownames)

#Print government column
kable(GovDataBS)

################################################################################

#Create household aggregates
Households    <-c(round(S_modelData$hh[yr], digits = 0),                                                                    
                  round(S_modelData$mh[yr], digits = 0),                                                                    
                  round(S_modelData$bh[yr], digits = 0),                                                                    
                  round(-S_modelData$lh[yr], digits = 0),                                                                    
                  round(S_modelData$eh[yr], digits = 0),                                                                     
                  round(S_modelData$oah[yr], digits = 0),
                  round(S_modelData$vh[yr], digits = 0),
                  round(S_modelData$hh[yr]+S_modelData$mh[yr]+S_modelData$bh[yr]-S_modelData$lh[yr]+S_modelData$eh[yr]+S_modelData$oah[yr]-S_modelData$vh[yr], digits = 0)
)                                                                    

#Create table of results
HouseDataBS<-as.data.frame(Households,row.names=rownames)

#Print households column
kable(HouseDataBS)

################################################################################

#Create foreign sector aggregates
Foreign      <-c( 0,                                                                    
                  0,                                                                    
                  round(S_modelData$brow[yr], digits = 0),                                                                    
                  0,                                                                    
                  0,                                                                     
                  round(S_modelData$oarow[yr], digits = 0),                                                                     
                  round(S_modelData$vrow[yr], digits = 0),
                  round(S_modelData$brow[yr]+S_modelData$oarow[yr]-S_modelData$vrow[yr], digits = 0)
)                                                                    

#Create table of results
ROWDataBS<-as.data.frame(Foreign,row.names=rownames)

#Print foreign sector column
kable(ROWDataBS)

################################################################################

#Create row total (when entries > 2)
Total        <-c( round(S_modelData$hh[yr]+S_modelData$hbd[yr]-S_modelData$hs[yr], digits = 0),                                                                    
                  round(S_modelData$mh[yr]-S_modelData$ms[yr], digits = 0),                                                                    
                  round(S_modelData$bh[yr]+S_modelData$bb[yr]+S_modelData$bcb[yr]+S_modelData$brow[yr]-S_modelData$bs[yr], digits = 0), 
                  round(-S_modelData$lf[yr]-S_modelData$lh[yr]+S_modelData$ls[yr], digits = 0),                                                                    
                  round(S_modelData$eh[yr]-S_modelData$es[yr], digits = 0),                                                                       
                  round(S_modelData$oaf[yr]+S_modelData$oab[yr]+S_modelData$oacb[yr]+S_modelData$oag[yr]+S_modelData$oah[yr]+S_modelData$oarow[yr], digits = 0),                                                                     
                  round(-(S_modelData$vf[yr]+S_modelData$vb[yr]+S_modelData$vcb[yr]+S_modelData$vg[yr]+S_modelData$vh[yr]+S_modelData$vrow[yr]), digits = 0),
                  round(S_modelData$hh[yr]+S_modelData$hbd[yr]-S_modelData$hs[yr] +
                          S_modelData$mh[yr]-S_modelData$ms[yr] +  
                          S_modelData$bh[yr]+S_modelData$bb[yr]+S_modelData$bcb[yr]+S_modelData$brow[yr]-S_modelData$bs[yr] +
                          -S_modelData$lf[yr]-S_modelData$lh[yr]+S_modelData$ls[yr] + 
                          S_modelData$eh[yr]-S_modelData$es[yr]+ 
                          S_modelData$oaf[yr]+S_modelData$oab[yr]+S_modelData$oacb[yr]+S_modelData$oag[yr]+S_modelData$oah[yr]+S_modelData$oarow[yr], digits = 0) )                                                                    

#Create table of results
TotalDataBS<-as.data.frame(Total,row.names=rownames)

#Print foreign sector column
kable(TotalDataBS)

################################################################################

#Create BS matrix
Italy_BS_Matrix<-cbind(HouseDataBS,FirmDataBS,GovDataBS,BankDataBS,ECBDataBS,ROWDataBS,TotalDataBS)
kable(Italy_BS_Matrix)

################################################################################

#Upload libraries
library(knitr)
library(kableExtra)

#Create caption
captionBS <- paste("Table 1. Balance sheet in period", yr+1994)

#Create html table for BS
Italy_BS_Matrix %>%
  kbl(caption=captionBS,
      format= "html",
      #format= "latex",
      col.names = c("Households","Firms","Government","Banks","ECB","Foreign","Total"),
      align="r") %>%
  kable_classic(full_width = F, html_font = "helvetica")

Similarly, the code chunk for the transactions-flow matrix is:

#TFM matrix for Italy SFC model

#Observed series

################################################################################
#Choose a year (26=2020)
yr=27

#Create row names for TFM matrix
rownames<-c( "Consumption",
             "Total investment",
             "Government spending",
             "Export",
             "Import",
             "[GDP]",
             "Taxes",
             "Transfers",
             "Wages",
             "Interest payments",
             "Corporate profit",
             "Bank profit",
             "CB seigniorage",
             "Other payments",
             "Change in cash and reserves",
             "Change in deposits",
             "Change in securities",
             "Change in loans",
             "Change in shares",
             "Change in other net FA",
             "Change in net wealth",
             "Column total")

################################################################################

#Create firms (current) aggregates
Firms_c      <-c( round(S_modelData$cons[yr], digits = 0),                                                                    
                  round(S_modelData$id[yr], digits = 0), 
                  round(S_modelData$gov[yr], digits = 0),                                                                    
                  round(S_modelData$x[yr], digits = 0),                                                                    
                  round(-S_modelData$im[yr], digits = 0),                                                                    
                  paste("[",round(S_modelData$cons[yr]+S_modelData$id[yr]+S_modelData$gov[yr]+S_modelData$x[yr]-S_modelData$im[yr], digits = 0),"]"),                                                                 
                  0,                                                                    
                  0,                                                                  
                  round(-S_modelData$wb[yr], digits = 0),                                                                     
                  round(-S_modelData$intf[yr], digits = 0),                                                                     
                  round(-S_modelData$ff[yr], digits = 0),                                                                    
                  0,
                  0,
                  round(S_modelData$opf[yr], digits = 0),
                  0,
                  0,
                  0,
                  0,
                  0,
                  0,
                  0,
                  paste(round(S_modelData$y[yr]-S_modelData$wb[yr]-S_modelData$intf[yr]-S_modelData$ff[yr]+S_modelData$opf[yr] , digits = 0)))    

#Create table of results
FirmData_c<-as.data.frame(Firms_c,row.names=rownames)

#Print firms column
kable(FirmData_c)


################################################################################

#Create firms (capital) aggregates
Firms_k      <-c( 0,                                                                    
                  round(-S_modelData$id[yr], digits = 0),                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                 
                  0,
                  0,
                  0,                                                                    
                  0,                                                                     
                  0,                                                                    
                  round(S_modelData$fu[yr], digits = 0),                                                                      
                  0,
                  0,
                  0,
                  0,
                  0,
                  0,
                  round(S_modelData$lf[yr-1]-S_modelData$lf[yr], digits = 0),
                  round(S_modelData$es[yr-1]-S_modelData$es[yr], digits = 0),
                  round(-(S_modelData$oaf[yr-1]-S_modelData$oaf[yr]), digits = 0),
                  round(S_modelData$vf[yr]-S_modelData$vf[yr-1], digits = 0),
                  round(-S_modelData$id[yr] + S_modelData$fu[yr]-
                          -(S_modelData$vf[yr-1]-S_modelData$vf[yr]), digits = 0)
)                                                                    


#Create table of results
FirmData_k<-as.data.frame(Firms_k,row.names=rownames)

#Print firms column
kable(FirmData_k)

################################################################################

#Create banks aggregates
Banks        <-c( 0,                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                 
                  0,                                                                    
                  0,                                                                    
                  0,
                  round(S_modelData$intb[yr], digits = 0), #^^
                  0,                                                                    
                  round(-S_modelData$fb[yr], digits = 0),                                                                    
                  0,
                  round(S_modelData$opb[yr], digits = 0),
                  round(S_modelData$hbd[yr]-S_modelData$hbd[yr-1], digits = 0),
                  round(-(S_modelData$ms[yr]-S_modelData$ms[yr-1]), digits = 0),
                  round(S_modelData$bb[yr]-S_modelData$bb[yr-1], digits = 0),
                  round(S_modelData$ls[yr]-S_modelData$ls[yr-1], digits = 0),
                  0,
                  round(S_modelData$oab[yr]-S_modelData$oab[yr-1], digits = 0),
                  round(S_modelData$vb[yr]-S_modelData$vb[yr-1], digits = 0),
                  paste(round(S_modelData$opb[yr]-(S_modelData$vb[yr]-S_modelData$vb[yr-1])+S_modelData$intb[yr]-S_modelData$fb[yr], digits = 0)))                                                                    

#Create table of results
BankData<-as.data.frame(Banks,row.names=rownames)

#Print banks column
kable(BankData)

################################################################################

#Create ECB aggregates
ECB          <-c( 0,                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                 
                  0,                                                                    
                  0,                                                                    
                  0, 
                  round(S_modelData$fcb[yr], digits = 0),     #                                                              
                  0,                                    
                  0,                                                          
                  round(-S_modelData$fcb[yr], digits = 0), # 
                  round(S_modelData$opcb[yr], digits = 0),
                  round(-(S_modelData$hs[yr]-S_modelData$hs[yr-1]), digits = 0),
                  0,
                  round((S_modelData$bcb[yr]-S_modelData$bcb[yr-1]), digit = 0),
                  0,
                  0,
                  round(S_modelData$oacb[yr]-S_modelData$oacb[yr-1], digits = 0),
                  round(S_modelData$vcb[yr]-S_modelData$vcb[yr-1], digits = 0),
                  paste(round(S_modelData$opcb[yr]-(S_modelData$vcb[yr]-S_modelData$vcb[yr-1]), digits = 0)))                                                                    

#Create table of results
CBData<-as.data.frame(ECB,row.names=rownames)

#Print ECB column
kable(CBData)

################################################################################

#Create government aggregates
Government   <-c( 0,                                                                    
                  0,
                  round(-S_modelData$gov[yr], digits = 0),                                                                    
                  0,                                                                    
                  0,                                                                    
                  0,                                                                 
                  round(S_modelData$tax[yr], digits = 0),                                                                    
                  round(-S_modelData$tr[yr], digits = 0),                                                                    
                  0,                                                                     
                  round(-(S_modelData$intg[yr]), digits = 0),                                                                   
                  0,
                  0,                                                          
                  round(S_modelData$fcb[yr], digits = 0), 
                  round(S_modelData$opg[yr], digits = 0),
                  0,
                  0,
                  round(-(S_modelData$bs[yr]-S_modelData$bs[yr-1]), digits = 0),
                  0,
                  0,
                  round(S_modelData$oag[yr]-S_modelData$oag[yr-1], digits = 0),
                  round(S_modelData$vg[yr]-S_modelData$vg[yr-1], digits = 0),
                  paste(round(-S_modelData$gov[yr]+S_modelData$tax[yr]-S_modelData$tr[yr]-(S_modelData$intg[yr])+S_modelData$fcb[yr]+S_modelData$opg[yr]-(S_modelData$vg[yr]-S_modelData$vg[yr-1]), digits = 0)))                 

#Create table of results
GovData<-as.data.frame(Government,row.names=rownames)

#Print government column
kable(GovData)

################################################################################

#Create households aggregates
Households   <-c( round(-S_modelData$cons[yr], digits = 0),                                                                    
                  0,                                                                    
                  0,
                  0,                                                                    
                  0,                                                                    
                  0,                                                                 
                  round(-S_modelData$tax[yr], digits = 0),                                                                    
                  round(S_modelData$tr[yr], digits = 0),                                                                    
                  round(S_modelData$wb[yr], digits = 0),                                                                     
                  round(S_modelData$inth[yr], digits = 0), 
                  round(S_modelData$fdf[yr], digits = 0),                                                                    
                  round(S_modelData$fb[yr], digits = 0),                                                          
                  0,
                  round(S_modelData$oph[yr], digits = 0),
                  round(S_modelData$hh[yr]-S_modelData$hh[yr-1], digits = 0),
                  round(S_modelData$mh[yr]-S_modelData$mh[yr-1], digits = 0),
                  round(S_modelData$bh[yr]-S_modelData$bh[yr-1], digits = 0),
                  round(-(S_modelData$lh[yr]-S_modelData$lh[yr-1]), digits = 0),
                  round(S_modelData$eh[yr]-S_modelData$eh[yr-1], digits = 0),
                  round(S_modelData$oah[yr]-S_modelData$oah[yr-1], digits = 0),
                  round(S_modelData$vh[yr]-S_modelData$vh[yr-1], digits = 0),
                  paste(round(-S_modelData$cons[yr]-S_modelData$tax[yr]+S_modelData$tr[yr]+S_modelData$wb[yr]+S_modelData$inth[yr]+S_modelData$fdf[yr]+S_modelData$fb[yr]+S_modelData$oph[yr]-(S_modelData$vh[yr]-S_modelData$vh[yr-1]), digits = 0)))                                                                    

#Create table of results
HouseData<-as.data.frame(Households,row.names=rownames)

#Print households column
kable(HouseData)

################################################################################

#Create Foreign sector aggregates
Foreign      <-c( 0,                                                                    
                  0,                                                                    
                  0,     
                  round(-S_modelData$x[yr], digits = 0),                                                                    
                  round(S_modelData$im[yr], digits = 0),                                                                       
                  0,                                                                 
                  0,                                                                    
                  0,  
                  0,
                  round(S_modelData$introw[yr], digits = 0),                                                                     
                  0,                                                                    
                  0,                                                          
                  0,
                  round(S_modelData$oprow[yr], digits = 0),
                  0,
                  0,
                  round(S_modelData$brow[yr]-S_modelData$brow[yr-1], digits = 0),
                  0,
                  0,
                  round(S_modelData$oarow[yr]-S_modelData$oarow[yr-1], digits = 0),
                  round(S_modelData$vrow[yr]-S_modelData$vrow[yr-1], digits = 0),
                  paste(round(-S_modelData$x[yr]+S_modelData$im[yr]+S_modelData$introw[yr]+S_modelData$oprow[yr]-(S_modelData$vrow[yr]-S_modelData$vrow[yr-1]), digits = 0)))                                                                    
#Create table of results
ROWData<-as.data.frame(Foreign,row.names=rownames)

#Print foreign sector column
kable(ROWData)

################################################################################

#Create row total
Total        <-c( 0,                                                                    
                  0,
                  0,                                                                    
                  0,                                                                    
                  0,                                                                       
                  round(S_modelData$y[yr]-(S_modelData$cons[yr]+S_modelData$id[yr]+S_modelData$gov[yr]+S_modelData$x[yr]-S_modelData$im[yr]), digits = 0),                                                                 
                  0,                                                                    
                  0,                                                                    
                  0,                                                                     
                  round(-S_modelData$intf[yr]+S_modelData$fcb[yr]-S_modelData$intg[yr]+S_modelData$inth[yr]+S_modelData$introw[yr]+S_modelData$intb[yr], digits = 0),                                                                     
                  0,                                                                    
                  0,                                                          
                  0,
                  round(S_modelData$oph[yr]+S_modelData$opf[yr]+S_modelData$opg[yr]+S_modelData$opb[yr]+
                          +S_modelData$opcb[yr]+S_modelData$oprow[yr], digits = 0),
                  round((S_modelData$hh[yr]-S_modelData$hh[yr-1])+(S_modelData$hbd[yr]-S_modelData$hbd[yr-1])-(S_modelData$hs[yr]-S_modelData$hs[yr-1]), digits = 0),              
                  round((S_modelData$mh[yr]-S_modelData$mh[yr-1])-(S_modelData$ms[yr]-S_modelData$ms[yr-1]), digits = 0),
                  round((S_modelData$bh[yr]-S_modelData$bh[yr-1])-(S_modelData$bs[yr]-S_modelData$bs[yr-1])+
                          (S_modelData$bb[yr]-S_modelData$bb[yr-1])+((S_modelData$bcb[yr])-(S_modelData$bcb[yr-1]))+
                          (S_modelData$brow[yr]-S_modelData$brow[yr-1]), digits = 0),
                  round(-(S_modelData$lh[yr]-S_modelData$lh[yr-1])-(S_modelData$lf[yr]-S_modelData$lf[yr-1])+(S_modelData$ls[yr]-S_modelData$ls[yr-1]), digit = 0),
                  round((S_modelData$es[yr]-S_modelData$es[yr-1])-(S_modelData$eh[yr]-S_modelData$eh[yr-1]), digits = 0),
                  round((S_modelData$oah[yr]-S_modelData$oah[yr-1])+(S_modelData$oaf[yr]-S_modelData$oaf[yr-1])+(S_modelData$oag[yr]-S_modelData$oag[yr-1])+
                          +(S_modelData$oab[yr]-S_modelData$oab[yr-1])+(S_modelData$oacb[yr]-S_modelData$oacb[yr-1])+(S_modelData$oarow[yr]-S_modelData$oarow[yr-1]), digits = 0),
                  round((S_modelData$vh[yr]-S_modelData$vh[yr-1])+(S_modelData$vf[yr]-S_modelData$vf[yr-1])+(S_modelData$vg[yr]-S_modelData$vg[yr-1])+
                          +(S_modelData$vb[yr]-S_modelData$vb[yr-1])+(S_modelData$vcb[yr]-S_modelData$vcb[yr-1])+(S_modelData$vrow[yr]-S_modelData$vrow[yr-1]), digits = 0),
                  0)                                                                    

#Create table of results
TotalData<-as.data.frame(Total,row.names=rownames)

#Print banks column
kable(TotalData)

################################################################################

#Create TFM matrix
Italy_TFM_Matrix<-cbind(HouseData,FirmData_c,FirmData_k,GovData,BankData,CBData,ROWData,TotalData)
kable(Italy_TFM_Matrix)

################################################################################

#Upload libraries
library(knitr)
library(kableExtra)

#Create caption
captionTFM <- paste("Table 2. Transactions-flow matrix in period", yr+1994)

#Create html table for TFM
Italy_TFM_Matrix %>%
  kbl(caption=captionTFM,
      format= "html",
      #format= "latex",
      col.names = c("Households","Firms (current)","Firms (capital)","Government","Banks","ECB","Foreign","Total"),
      align="r") %>%
  kable_classic(full_width = F, html_font = "helvetica")

The associated tables are those displayed in Section 1.

3_In_sample_predictions

The model is now ready to perform simulations. In fact, we can use in-sample simulations of model variables to verify how well the model replicates observed data for the past years. The first step is to define the exogenization list, which comprises the variables kept exogenous in the simulations. In this regard, we have chosen the variables named 'Other payments', 'Other financial assets', the policy rate, the foreign price level, and the energy price level. The associated code chunk is:

# Define exogenization list to 2021
  exogenizeList <- list(
    
    #Adjusted endogenous variables in 1998-2021
    oph = TRUE,                                 #Other payments associated with households
    opf = TRUE,                                 #Other payments associated with firms
    opb = TRUE,                                 #Other payments associated with banks
    opcb = TRUE,                                #Other payments associated with ECB
    oacb = TRUE,                                #Other financial assets of ECB
    oaf = TRUE,                                 #Other financial assets held by firms
    oab = TRUE,                                 #Other financial assets held by banks
    oag = TRUE,                                 #Other financial assets held by government
    oah = TRUE,                                 #Other financial assets held by households
    rstar = TRUE,                               #ECB refinancing rate
    Lp_row = TRUE,                              #Log of foreign price level
    Lp_en = TRUE                                #Log of price of energy 
  )

In-sample unadjusted simulations can be generated simply by running the following additional code:

# In-sample prediction (no add factors)
  S_model <- SIMULATE(S_model
                      ,simType='STATIC'
                      ,TSRANGE=c(1998,1,2021,1)
                      ,simConvergence=0.00001
                      ,simIterLimit=100
                      ,Exogenize=exogenizeList,
                      verbose = FALSE )

Since we are conducting an in-sample simulation, we use a static prediction approach. This means that historical values for the lagged endogenous variables are utilised in the solutions of subsequent periods.

Note: A dynamic prediction can also be performed. All it takes is to replace STATIC with DYNAMIC (or FORECAST) in the code chunk above. However, the presence of several structural breaks in the period considered (e.g., the launch of the euro, three financial crises, and the Covid-19 crisis) is likely to worsen the model fit even beyond its shortcomings. In principle, this problem can be partly addressed by exogenising variables reflecting the shocks or using dummy variables.

Having clarified this, we can now plot the observed series against the simulated one for each variable.

#Define layout
layout(matrix(c(1,2,3,4,5,6,7,8,9), 3, 3, byrow = TRUE))

#Define colour of simulated series
color <- "red1"

# Show predicted Nominal GDP
plot(S_model$simulation$y,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(a) Nominal GDP (constant prices)",ylab = 'Million Euro',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(min(S_modelData$y),max(S_model$simulation$y)))
lines(S_modelData$y,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)
abline(h=1795100,col=4)

# Show predicted Nominal consumption
plot(S_model$simulation$consR,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(b) Nominal consumption (constant prices)",ylab = 'Million Euro',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(min(S_modelData$cons),max(S_model$simulation$cons)))
lines(S_modelData$consR,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

# Show predicted Nominal investment
plot(S_model$simulation$id,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(c) Nominal investment (constant prices)",ylab = 'Million Euro',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(min(S_modelData$id),max(S_model$simulation$id)))
lines(S_modelData$id,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

# Show predicted import
plot(S_model$simulation$im,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(d) Nominal import (constant prices)",ylab = 'Million Euro',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(min(S_modelData$im),max(S_model$simulation$im)))
lines(S_modelData$im,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

# Show predicted export
plot(S_model$simulation$x,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(e) Nominal export (constant prices)",ylab = 'Million Euro',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(min(S_modelData$x),max(S_model$simulation$x)))
lines(S_modelData$x,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

# Show predicted employment
plot(S_model$simulation$nd,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(f) Employment",ylab = 'Number of employees',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(20000,24000))
lines(S_modelData$nd,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

# Return rate on bonds
plot(100*S_model$simulation$rb,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(g) Average yield on gov. securities",ylab = '%',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(0,9))
lines(100*S_modelData$rb,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

# Debt to GDP ratio
plot(100*S_model$simulation$deb/S_model$simulation$y,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(h) Government debt to GDP ratio",ylab = '%',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(95,160))
lines(100*S_modelData$deb/S_modelData$y,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

# GDP deflator
plot(S_model$simulation$p,col=color,lty=1,lwd=1,font.main=1,cex.main=1,main="(i) Price level (GDP deflator)",ylab = 'Index (2015=100)',xlab = '', cex.axis=1,cex.lab=1,xlim=range(1998,2020),ylim=range(70,110))
lines(S_modelData$p,col="darkorchid4",lty=3,lwd=3)
legend("bottom",c("Observed","Simulated"),  bty = "n", cex=1, lty=c(3,1), lwd=c(3,1), col = c("darkorchid4",color), box.lty=0)

The figure below shows selected flow variables and ratios over the period 1998-2021.

fig 1 ITA

While the primary goal of our model is not to outperform existing prediction models (but rather to provide a new tool for creating and comparing alternative scenarios), it tracks past data reasonably well. The main issue appears to be the inclusion of annual lags, causing model predictions to lag when the static simulation is performed. Arguably, this drawback can be overcome by using quarterly data, although seasonality and data availability issues may arise in this case.

After checking the model's fit, in-sample predictions can be adjusted to the observed series using prediction errors. This is done by exogenizing the endogenous variables of the model.

# Define exogenization list to 2021
  exogenizeList <- list(
    
    #Adjusted endogenous variables in 1998-2021
    Lpc = c(1998,1,2021,1),                     #Log of consumer price index
    Lp_en = c(1998,1,2021,1),                   #Log of price of energy 
    mul = c(1998,1,2021,1),                     #Markup on loans to firms 
    mulh = c(1998,1,2021,1),                    #Markup on personal loans    
    mubb = c(1998,1,2021,1),                    #Average premium on bills held by banks 
    mubrow = c(1998,1,2021,1),                  #Average premium on bills held by foreign sector 
    mubh = c(1998,1,2021,1),                    #Average premium on bills held by households 
    fuf = c(1998,1,2021,1),                     #Firms undistributed profit
    lh = c(1998,1,2021,1),                      #Personal loans to households
    gov = c(1998,1,2021,1),                     #Government spending
    tr = c(1998,1,2021,1),                      #Transfers
    Leh = c(1998,1,2021,1),                     #Log of household demand for shares 
    Lbh = c(1998,1,2021,1),                     #Log of household demand for government bills
    Lhh = c(1998,1,2021,1),                     #Log of household demand for cash
    Lbb = c(1998,1,2021,1),                     #Log of bank demand for bills
    prod = c(1998,1,2021,1),                    #Labour productivity
    Lns = c(1998,1,2021,1),                     #Log of labour force
    gw = c(1998,1,2021,1),                      #Growth rate of wages
    Lp = c(1998,1,2021,1),                      #Log of price level
    LidR = c(1998,1,2021,1),                    #Log of real investment
    LimR = c(1998,1,2021,1),                    #Log of real import
    LconsR = c(1998,1,2021,1),                  #Log of real consumption 
    intmh = c(1998,1,2021,1),                   #Interests received by households on bank deposits
    rstar = c(1998,1,2021,1),                   #ECB refinancing rate
    tax = c(1998,1,2021,1),                     #Tax revenue
    LxR = c(1998,1,2021,1),                     #Log of real export
    Lp_im = c(1998,1,2021,1),                   #Log of price of import
    Lp_row = c(1998,1,2021,1),                  #Log of foreign price level
    oph = TRUE,                                 #Other payments associated with households
    oacb = TRUE,                                #Other financial assets of ECB
    oaf = TRUE,                                 #Other financial assets held by firms
    oab = TRUE,                                 #Other financial assets of banks
    oag = TRUE,                                 #Other financial assets of government
    oah = TRUE,                                 #Other financial assets of households
    mub = TRUE,                                 #Average premium paid by the government 
    perc_en = TRUE,                             #Percentage of energy import to total import 
    lambdarow = TRUE,                           #Share of government bills held by foreign sector
    yf = TRUE,                                  #Foreign income  
    rho = TRUE                                  #Reserve ratio   
  )
  
  # Simulate again model
  S_model <- SIMULATE(S_model
                      ,simType='STATIC'
                      ,TSRANGE=c(1998,1,2021,1)
                      ,simConvergence=0.00001
                      ,simIterLimit=100
                      ,Exogenize=exogenizeList
                      ,quietly=TRUE)

The figure below shows the adjusted values of selected flow variables and ratios over the period 1998-2021.

fig 1 ITA adj

4_Out_of_sample_predictions

The model allows performing out-of-sample predictions, which can be used as the baseline scenario.

The first step is to extend exogenous variables up to the end of the forecasting period, which, in this exercise, is 2028.

# Extend exogenous and conditionally evaluated variables up to 2028
S_model$modelData <- within(S_model$modelData,{ 
                     dum = TSEXTEND(dum,  UPTO=c(2028,1))       #Dummy for Bb
})

Note: the only exogenous variable to be extended is the dummy variable named $dum$.

Similar to what we did for adjusted in-sample predictions, the second step is to create an 'exogenization list', encompassing all the endogenous variables of the model. These variables are adjusted up to 2021 and then set free to follow the dynamics implied by the model equations.

# Define exogenization list to 2021
exogenizeList <- list(
  
  Lpc = c(1998,1,2021,1),                     #Log of consumer price index
  Lp_en = c(1998,1,2021,1),                   #Log of price of energy 
  mul = c(1998,1,2021,1),                     #Markup on loans to firms 
  mulh = c(1998,1,2021,1),                    #Markup on personal loans    
  mubb = c(1998,1,2021,1),                    #Average premium on bills held by banks 
  mubrow = c(1998,1,2021,1),                  #Average premium on bills held by foreign sector 
  mubh = c(1998,1,2021,1),                    #Average premium on bills held by households 
  fuf = c(1998,1,2021,1),                     #Firms undistributed profit
  lh = c(1998,1,2021,1),                      #Personal loans to households
  gov = c(1998,1,2021,1),                     #Government spending
  tr = c(1998,1,2021,1),                      #Transfers
  prod = c(1998,1,2021,1),                    #Labour productivity
  Lns = c(1998,1,2021,1),                     #Log of labour force
  gw = c(1998,1,2021,1),                      #Growth rate of wages
  Lp = c(1998,1,2021,1),                      #Log of price level
  LidR = c(1998,1,2021,1),                    #Log of real investment
  intmh = c(1998,1,2021,1),                   #Interests received by households on bank deposits
  rstar = c(1998,1,2021,1),                   #ECB refinancing rate
  LimR = c(1998,1,2021,1),                    #Log of real import
  LxR = c(1998,1,2021,1),                     #Log of real export 
  tax = c(1998,1,2021,1),                     #Tax revenue
  Leh = c(1998,1,2021,1),                     #Log of household demand for shares
  Lhh = c(1998,1,2021,1),                     #Log of household demand for cash
  Lbh = c(1998,1,2021,1),                     #Log of household demand for government bills
  Lbb = c(1998,1,2021,1),                     #Log of bank demand for bills
  LconsR = c(1998,1,2021,1),                  #Log of real consumption 
  yf = c(1998,1,2021,1),                      #Foreign income
  perc_en = c(1998,1,2021,1),                 #Percentage of energy import to total import 
  lambdarow = c(1998,1,2021,1),               #Share of government bills held by foreign agents   
  mub = c(1998,1,2021,1),                     #Average premium paid by the government
  Lp_im = c(1998,1,2021,1),                   #Log of price of import
  Lp_row = c(1998,1,2021,1),                  #Log of foreign price level
  oph = TRUE,                                 #Other payments associated with households
  oacb = TRUE,                                #Other financial assets of ECB
  oaf = TRUE,                                 #Other financial assets held by firms
  oab = TRUE,                                 #Other financial assets of banks
  oag = TRUE,                                 #Other financial assets of government
  oah = TRUE,                                 #Other financial assets of households
  rho = TRUE,                                 #Reserve ratio
  exr = TRUE                                  #Exchange rate
)

The next step is to create the list of 'add factors', encompassing both the necessary adjustments to align with the 2022 series as predicted by the Italian government and other major institutions (for which we did not have all the series from Eurostat) and the expected shocks and institutional changes.

# Define add-factor list (defining exogenous adjustments: policy + available predictions)
constantAdjList <- list(
  
  #Adjustments for 2022
  Lp = TIMESERIES(0,-0.017,-0.01,0.006,0.018,0.03, 0.04,0.045,START=c(2021,1), FREQ='A'),  #GDP deflator correction
  LimR = TIMESERIES(0,0.156,0.156-0.031,0.156-0.045,0.156-0.045,0.156-0.045,0.156-0.045,0.156-0.045,START=c(2021,1), FREQ='A'),  
  LxR = TIMESERIES(0,0.075,0.075-0.012,0.075-0.01,0.075-0.01,0.075-0.01,0.075-0.01,0.075-0.01,START=c(2021,1), FREQ='A'),  
  LconsR = TIMESERIES(0,0,0.01,0.05,0.05,0.05,0.045,0.045, START=c(2021,1), FREQ='A'), 
  deltak = TIMESERIES(0,0.0126,0.0069,0.0011,-0.0016,-0.0033,-0.0033,-0.0033,START=c(2021,1), FREQ='A'),
   
  #Shocks and institutional changes
  Lp_en = TIMESERIES(0,0.38,0.055,0.06,0,0,0,0, START=c(2021,1), FREQ='A'),  #Shock to energy price log-level
  rstar = TIMESERIES(-0.01858333+0,-0.01858333+0.0156,-0.01858333+0.038,-0.01858333+0.03,-0.01858333+0.025,-0.01858333+0.025,-0.01858333+0.025,-0.01858333+0.025 ,START=c(2021,1), FREQ='A'),  
  mub = TIMESERIES(0,-0.004,-0.02,-0.014,-0.010,-0.008,-0.008,-0.008 ,START=c(2021,1), FREQ='A') )

Afterward, we simulate the model out of sample using the function DYNAMIC, which employs simulated values for the lagged endogenous variables in the solutions of subsequent periods.

# Simulate model
S_model <- SIMULATE(S_model
                    ,simType='DYNAMIC' #'FORECAST'
                    ,TSRANGE=c(1998,1,2028,1)
                    ,simConvergence=0.00001
                    ,simIterLimit=1000
                    ,Exogenize=exogenizeList
                    ,ConstantAdjustment=constantAdjList
                    ,quietly=TRUE)

A few amendments to the plotting chunk used in Section 3 allow extending the chart of the selected variables (here expressed in real terms) until 2028.

fig 2 ITA

The definition of the model baseline is complete. Before we move to alternative scenarios, additional diagrams and tables can be created.

5_Model_watertightness

One may want to double-check whether the model remains consistent when it is simulated out of sample. This can be done in two ways. The first is to modify slightly the code used in Section 2 to create the accounting matrices. All it takes is to replace S_modelData with S_model$simulation as a preamble for each model variable. The reference year must be adjusted as well. For instance, the predicted balance sheet and transactions-flow matrix for Italy in 2025 are, respectively:

$$ \begin{array}{lccccccc} \hline & Households & Firms & Government & Banks & ECB & Foreign & Total\\ \hline Cash ~ and ~ reserves & 282986 & 0 & 0 & 13129 & -296115 & 0 & 0\\ Deposits & 1733715 & 0 & 0 & -1733715 & 0 & 0 & 0\\ Securities & 460261 & 0 & -3349829 & 1736563 & 823832 & 329174 & 0\\ Loans & -1062515 & -1634042 & 0 & 2696557 & 0 & 0 & 0\\ Shares & 1380728 & -1380728 & 0 & 0 & 0 & 0 & 0\\ Other ~ net ~ financial ~ assets & 1583746 & 284629 & 323282 & -1563895 & -783662 & 155900 & 0\\ \hline Net ~ financial ~ wealth & 4378921 & -2730141 & -3026546 & 1148638 & -255945 & 485073 & 0\\ \hline Column total & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \hline \end{array} $$

$$ \begin{array}{lcccccccc} \hline & Households & Firms ~ (current) & Firms ~ (capital) & Government & Banks & ECB & Foreign & Total\\ \hline Consumption & -1352755 & 1352755 & 0 & 0 & 0 & 0 & 0 & 0\\ Total ~ investment & 0 & 467972 & -467972 & 0 & 0 & 0 & 0 & 0\\ Government ~ spending & 0 & 444072 & 0 & -444072 & 0 & 0 & 0 & 0\\ Export & 0 & 830971 & 0 & 0 & 0 & 0 & -830971 & 0\\ Import & 0 & -799597 & 0 & 0 & 0 & 0 & 799597 & 0\\ [GDP] & 0 & [ 2296174 ] & 0 & 0 & 0 & 0 & 0 & 0\\ Taxes & -647708 & 0 & 0 & 647708 & 0 & 0 & 0 & 0\\ Transfers & 232271 & 0 & 0 & -232271 & 0 & 0 & 0 & 0\\ Wages & 874860 & -874860 & 0 & 0 & 0 & 0 & 0 & 0\\ Interest ~ payments & -6777 & -24812 & 0 & -107594 & 121903 & 4118 & 13163 & 0\\ Corporate ~ profit & 839820 & -1141970 & 302150 & 0 & 0 & 0 & 0 & 0\\ Bank ~ profit & 121903 & 0 & 0 & 0 & -121903 & 0 & 0 & 0\\ CB ~ seigniorage & 0 & 0 & 0 & 4118 & 0 & -4118 & 0 & 0\\ Other ~ payments & -60675 & -254531 & 0 & 0 & 299391 & -6552 & 22367 & 0\\ \hline \Delta ~ in ~ cash ~ and ~ res. & 15812 & 0 & 0 & 0 & 309 & -16121 & 0 & 0\\ \Delta ~ in ~ deposits & 40803 & 0 & 0 & 0 & -40803 & 0 & 0 & 0\\ \Delta ~ in ~ securities & 991 & 0 & 0 & -132111 & 117395 & 9569 & 4156 & 0\\ \Delta ~ in ~ loans & -59712 & 0 & -162778 & 0 & 222490 & 0 & 0 & 0\\ \Delta ~ in ~ shares & 3044 & 0 & -3044 & 0 & 0 & 0 & 0 & 0\\ \Delta ~ in ~ other ~ net ~ f.a. & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \hline \Delta ~ in ~ net ~ wealth & 939 & 0 & -165822 & -132111 & 299391 & -6552 & 4156 & 0\\ \hline Column ~ total & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \hline \end{array} $$

An alternative method to verify model consistency is to create a checking mechanism based on the redundant equation of the model ($H_d = H_s$). Specifically, one can either plot the difference between $H_s$ and $H_d$ or create a consistency statement like the following:

#Create consistency statement
error=0
for (i in 1:31){  error = error + (S_model$simulation$hs[i]-S_model$simulation$hd[i])^2    }
if ( error<0.1 ){cat(" *************************************************************** \n Good news! The model is watertight!. Error =", error, "< 0.1 \n ***************************************************************")} else{
  if ( error<1 ){cat(" ******************************************************** \n Double-check model consistency. Error =", error, "> 0.1 \n ********************************************************")}
  else{cat(" *************************************************************** \n Warning: the model is not fully consistent! Error =", error, "> 1 \n ***************************************************************")} }

which, in this case, yields:

*************************************************************** 
 Good news! The model is watertight!. Error = 0.04068899 < 0.1 
 ***************************************************************

Note that a small error is always likely to be present due to rounding.

Lastly, note that a more sophisticated representation of the transactions-flow matrix for a specific year (here 2021) can be obtained using a Sankey diagram:

fig 3 ITA

This diagram illustrates that each flow (and change in stock) originates from somewhere and goes to somewhere. The related code is:

#Choose a year. Note: 1 = 1998, 26 = 2021
yr=26

#Upload libraries for Sankey diagram
library(networkD3)
library(htmlwidgets)
library(htmltools)

#Create nodes: source, target and flows
nodes = data.frame("name" = 
                     c("Firms outflow", # Node 0
                       "Banks outflow", # Node 1
                       "ECB outflow", # Node 2
                       "Government outflow", # Node 3
                       "Households outflow", # Node 4
                       "Foreign outflow", # Node 5
                       
                       "Firms inflow", # Node 6
                       "Banks inflow", # Node 7
                       "ECB inflow", # Node 8
                       "Government inflow", # Node 9
                       "Households inflow", # Node 10
                       "Foreign inflow", # Node 11
                       
                       "Consumption", # Node 12
                       "Investment", # Node 13
                       "Government spending", # Node 14
                       "Export", # Node 15
                       "Other import", # Node 16
                       
                       "Taxes", # Node 17
                       "Transfers", # Node 18
                       "Wages", # Node 19
                       "Interest payments", # Node 20
                       "Corporate profit", # Node 21
                       "Bank profit", # Node 22
                       "CB seigniorage", # Node 23
                       "Other payments", # Node 24
                       
                       "Change in net wealth", # Node 25
                       "Gross energy import" #Node 26
                       )) 

#Create the flows
links = as.data.frame(matrix(c(
  
  4, 12, S_model$simulation$cons[yr],
  12, 6, S_model$simulation$cons[yr],
  
  0, 13, S_model$simulation$id[yr],
  13, 6, S_model$simulation$id[yr],
  
  3, 14, S_model$simulation$gov[yr],
  14, 6, S_model$simulation$gov[yr],
  
  5, 15, S_model$simulation$x[yr],
  15, 6, S_model$simulation$x[yr],
  
  0, 16, S_model$simulation$im[yr]-S_model$simulation$im_en[yr],
  16, 11, S_model$simulation$im[yr]-S_model$simulation$im_en[yr],
  
  0, 26, S_model$simulation$im_en[yr],
  26, 11, S_model$simulation$im_en[yr],
  
  4, 17, S_model$simulation$tax[yr],
  17, 9, S_model$simulation$tax[yr],
  
  3, 18, S_model$simulation$tr[yr],
  18, 10, S_model$simulation$tr[yr],
  
  0, 19, S_model$simulation$wb[yr],
  19, 10, S_model$simulation$wb[yr],
  
  0, 20, S_model$simulation$intf[yr],
  3, 20, S_model$simulation$intg[yr],
  20, 7, S_model$simulation$fb[yr],
  20, 8, S_model$simulation$fcb[yr],
  20, 10, S_model$simulation$inth[yr],
  
  0, 21, S_model$simulation$fdf[yr],  
  21, 10, S_model$simulation$fdf[yr],
  
  1, 22, S_model$simulation$fb[yr],  
  22, 10, S_model$simulation$fb[yr],
  
  2, 23, S_model$simulation$fcb[yr],  
  23, 9, S_model$simulation$fcb[yr],
  
  0, 24, if (S_model$simulation$opf[yr]<0){-S_model$simulation$opf[yr]}else{0},  
  1, 24, if (S_model$simulation$opb[yr]<0){-S_model$simulation$opb[yr]}else{0},
  2, 24, if (S_model$simulation$opcb[yr]<0){-S_model$simulation$opcb[yr]}else{0},
  3, 24, if (S_model$simulation$opg[yr]<0){-S_model$simulation$opg[yr]}else{0},
  4, 24, if (S_model$simulation$oph[yr]<0){-S_model$simulation$oph[yr]}else{0},
  5, 24, if (S_model$simulation$oprow[yr]<0){-S_model$simulation$oprow[yr]}else{0},
  
  24, 6, if (S_model$simulation$opf[yr]>=0){S_model$simulation$opf[yr]}else{0},
  24, 7, if (S_model$simulation$opb[yr]>=0){S_model$simulation$opb[yr]}else{0},
  24, 8, if (S_model$simulation$opcb[yr]>=0){S_model$simulation$opcb[yr]}else{0},
  24, 9, if (S_model$simulation$opg[yr]>=0){S_model$simulation$opg[yr]}else{0},
  24, 10, if (S_model$simulation$oph[yr]>=0){S_model$simulation$oph[yr]}else{0},
  24, 11, if (S_model$simulation$oprow[yr]>=0){S_model$simulation$oprow[yr]}else{0},
  
  0, 25, if (S_model$simulation$vf[yr]-S_model$simulation$vf[yr-1]<0){-S_model$simulation$vf[yr]+S_model$simulation$vf[yr-1]}else{0},  
  1, 25, if (S_model$simulation$vb[yr]-S_model$simulation$vb[yr-1]<0){-S_model$simulation$vb[yr]+S_model$simulation$vb[yr-1]}else{0},
  2, 25, if (S_model$simulation$vcb[yr]-S_model$simulation$vcb[yr-1]<0){-S_model$simulation$vcb[yr]+S_model$simulation$vcb[yr-1]}else{0},  
  3, 25, if (S_model$simulation$vg[yr]-S_model$simulation$vg[yr-1]<0){-S_model$simulation$vg[yr]+S_model$simulation$vg[yr-1]}else{0},  
  4, 25, if (S_model$simulation$vh[yr]-S_model$simulation$vh[yr-1]<0){-S_model$simulation$vh[yr]+S_model$simulation$vh[yr-1]}else{0},
  5, 25, if (S_model$simulation$vrow[yr]-S_model$simulation$vrow[yr-1]<0){-S_model$simulation$vrow[yr]+S_model$simulation$vrow[yr-1]}else{0},  
  
  25, 6, if (S_model$simulation$vf[yr]-S_model$simulation$vf[yr-1]>=0){S_model$simulation$vf[yr]-S_model$simulation$vf[yr-1]}else{0},  
  25, 7, if (S_model$simulation$vb[yr]-S_model$simulation$vb[yr-1]>=0){S_model$simulation$vb[yr]-S_model$simulation$vb[yr-1]}else{0},
  25, 8, if (S_model$simulation$vcb[yr]-S_model$simulation$vcb[yr-1]>=0){S_model$simulation$vcb[yr]-S_model$simulation$vcb[yr-1]}else{0},  
  25, 9, if (S_model$simulation$vg[yr]-S_model$simulation$vg[yr-1]>=0){S_model$simulation$vg[yr]-S_model$simulation$vg[yr-1]}else{0},  
  25, 10, if (S_model$simulation$vh[yr]-S_model$simulation$vh[yr-1]>=0){S_model$simulation$vh[yr]-S_model$simulation$vh[yr-1]}else{0},
  25, 11, if (S_model$simulation$vrow[yr]-S_model$simulation$vrow[yr-1]>=0){S_model$simulation$vrow[yr]-S_model$simulation$vrow[yr-1]}else{0}  
  ), 

  byrow = TRUE, ncol = 3))
names(links) = c("source", "target", "value")
my_color <- 'd3.scaleOrdinal() .domain([]) .range(["chartreuse","red","green","yellow","dodgerblue","darkorchid","khaki","peru","violet","cyan","pink","orange","beige","gray","blue","black","darkorchid4","goldenrod4"])'

#Create and plot the network
sankeyNetwork(Links = links, Nodes = nodes,
              Source = "source", Target = "target",
              Value = "value", NodeID = "name", colourScale=my_color,
              fontSize= 20, nodeWidth = 30)

6_Experiments

Three additional scenarios are considered and compared with the baseline scenario.

Alternative Scenario 1: The energy-led price shock has a more persistent effect on inflation, with the inflation rate (CPI) still projected to be around 5% for the foreseeable years.

Alternative Scenario 2: The economy is affected by two shocks, namely, a persistent inflation rate and a robust policy response by the ECB, which maintains the policy rate at 4.5% over the 2024-2026 period.

Alternative Scenario 3: Effects of policy austerity measures that, in accordance with the Maastricht Treaty, bring the government deficit to GDP ratio to 3% in 2024 (and subsequent years).

The scenarios are created by adding shocks to model variables in the constantAdjList. Therefore, the first scenario is obtained by exogenously increasing the (log) series of the energy price:

 Lp_en = TIMESERIES(0,0.38,0.2,0.2,0.2,0.2,0.2,0.1, START=c(2021,1), FREQ='A')

Similarly, the second scenario is obtained by exogenously increasing the policy rate set by the ECB, in addition to the change in the energy price index

rstar = TIMESERIES(-0.01858333+0,-0.01858333+0.0156,-0.01858333+0.038,-0.01858333+0.045,-0.01858333+0.045,-0.01858333+0.045,-0.01858333+0.045,-0.01858333+0.045 ,START=c(2021,1), FREQ='A')

Moreover, the real consumption volume is adjusted downward to account for its elasticity to the policy rate, which we estimate to be 0.58. Therefore:

LconsR = TIMESERIES(0,0,0.01,0.05-0.07*(0.58/2),0.05-0.07*(0.58/2),0.05-0.07*(0.58/2),0.045-0.07*(0.58/2),0.045-0.07*(0.58/2), START=c(2021,1), FREQ='A')

Finally, the third scenario is derived by cutting government spending in comparison to the baseline scenario:

gov = TIMESERIES(0,0,0,-47000,-15000,-33000,-39000,-40000, START=c(2021,1), FREQ='A')

Once again, a visual representation of the experiments can be obtained by introducing a few amendments to the plotting chunk used in Section 3.

fig 3 ITA

Summing up, in Alternative Scenario 1, a persistent inflation rate of around 5% leads Italy into a recession with rising unemployment, accompanied by a deterioration of public finance. By 2028, economic growth is projected to drop to -2.5%, unemployment to exceed 10%, and government debt and deficit ratios to reach 159% and 8.4%, respectively.

Alternative Scenario 2 explores similar effects of persistent inflation but with a robust ECB response, resulting in an immediate and prolonged economic recession and higher government debt and deficit ratios of 173% and 10.1% by 2028.

Lastly, Alternative Scenario 3 depicts the impact of austerity measures to comply with the 3% Maastricht rule, causing a severe recession, an annual drop of around 3% in economic growth, and an unemployment rate exceeding 15% by 2028.

7_Quick_execution

This approach is recommended for experienced users. Simply execute the numbered files in sequence. We recommend executing the R code paragraph by paragraph for better clarity and control.

About

These R codes replicate the models and the experiments discussed in Canelli, Fontana, Realfonzo and Veronese Passarella (2021, 2022, 2024).

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