Copyright © CC-BY-NC 2019, CRIBFB | AMFBR American Finance & Banking Review; Vol. 4, No. 1; 2019 ISSN 2576-1226 E-ISSN 2576-1234 Published by Centre for Research on Islamic Banking & Finance and Business, USA 22 A Small Macro-Econometric Model Bijan Bidabad B.A., M.Sc., Ph.D., Post-Doc. Professor Economics and Chief Islamic Banking Advisor Bank Melli, Iran E-mail:bijan@bidabad.com Abstract Different sizes of macro-econometric models are used for different policy purposes. In this paper, we introduce a small macro- econometric model that includes macro-aggregates variables that can be solved dynamically and be used as a sample model to be estimated for other countries. Keywords: Macro-Econometric, Econometric Model, Mathematical Model. 1. Introduction The largest-scale macro-econometric model for Iran performed by the author is a high detailed model, and working with it is more cumbersome for those who need a general forecast scheme for major macro-variables. Indeed this model is used to draw a simple working scheme to fulfill general view’s needs. In addition to its simplicity, this model substantially has a good performance. This model compromises the fiscal position of the government; a well understood transmission mechanism between monetary aggregates, price level, production, and balance of payments. 2. The Model A very simple monetary model is presented according to the monetarist's view. The following flow chart presents the relationship between the main variables of the model. As it is seen, the liquidity is decomposed to the net domestic assets and net foreign assets of the banking system. The net foreign asset component is affected by the official exchange rate and the balance of payments. The net domestic assets consist of three components: private sector debt to the banking system, government debt to the banking system, and net of other assets. The private sector debt to the banking system is affected by gross domestic product (GDP). The government debt to the banking system is influenced by the government budget deficit and foreign exchange obligations account. The price level is defined as a function of liquidity. Change in GDP is affected by the balance of payments. The estimated results are presented in the following section. The econometric model was estimated by OLS technique. The sample period covers 1960-2001. To avoid integration problem, all level variables are used in their first differences. 2.1 Variables: M2NFAE = Net foreign assets of the banking system (in billion dollars) M2NGV = Net government debt to the banking system (in billion Rials) M2LPV = Net Private sector debt to the banking system (in billion Rials) M2NW = Other assets of the banking system (in billion Rials) OBD = Government budget deficit (in billion Rials) BOP = Balance of payments (million dollars) mailto:bijan@bidabad.com Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 23 GDPV = Nominal GDP (in billion Rials) GDP = Gross Domestic Production at fixed prices of 1982 (in billion Rials) PGDP = GDP deflator (base year=1982) M2 = Liquidity (in billion Rials) E = Exchange rate D…. = Dummy variables. @Trend = Time trend 2.3 Relationship between the main variables of the monetary model 2.4 The Mathematical Model The following system of equations was built and estimated: D(M2NFAE) = C(11)*BOP/1000+C(12)*D72+C(13)*D69+C(14)*D60+C(15)*D7680 D(M2NGV) = C(20)+ C(21)*OBD +C(22)*D79 +C(23)*D80 D(M2LPV) = C(31)*D(GDPV)+C(32)*D80 D(M2NW) = C(41)*D7780+C(42)*D79+C(43)*D80+C(44)*@TREND D(PGDP) = C(51)*D(M2) +C(52)*D80 D(GDP) =C(60)+C(61)*BOP/1000+ C(62)*D(GDP(-1))+C(63)*D5659 +C(64)*D65 +C(65)*D55 M2 = M2NFAE * E + (M2NGV + M2LPV + M2NW) GDPV = GDP * PGDP Real GDP Nominal GDP Official exchange rate Liquidity M2 Price level Balance of payments Changes in other assets of the banking system Net other assets Net gov. debt to banking system Net private debt to banking system Government budget deficit Changes in previous real GDP Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 24 ====================================================== Estimation results ====================================================== System: SYS_INF Estimation Method: Least Squares Date: 12/03/03 Time: 15:57 Sample: 1339 1380 (1960-2001) Included observations: 42 Total system (unbalanced) observations 251 ====================================================== Coefficient Std. Error t-Statistic Prob. ====================================================== C(11) 0.914673 0.097201 9.410124 0.0000 C(12) -21.40064 1.346235 -15.89666 0.0000 C(13) 9.443943 1.346362 7.014414 0.0000 C(14) 5.263224 1.367823 3.847885 0.0002 C(15) -2.368778 0.621046 -3.814173 0.0002 C(20) -274.1686 167.8247 -1.633661 0.1037 C(21) 1.257852 0.055344 22.72777 0.0000 C(22) -14060.40 975.8079 -14.40899 0.0000 C(23) 11626.61 962.0447 12.08531 0.0000 C(31) 0.309446 0.012301 25.15634 0.0000 C(32) 33424.48 2846.179 11.74363 0.0000 C(41) -12933.99 598.0382 -21.62736 0.0000 C(42) 29662.57 960.1021 30.89523 0.0000 C(43) 4877.350 960.1694 5.079677 0.0000 C(44) -15.28007 5.684013 -2.688254 0.0077 C(51) 7.03E-06 2.96E-07 23.79357 0.0000 C(52) -0.294803 0.032899 -8.960742 0.0000 C(60) 6249.474 1531.646 4.080234 0.0001 C(61) 1354.759 568.7077 2.382171 0.0180 Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 25 C(62) 0.368434 0.093348 3.946897 0.0001 C(63) -23153.95 4256.940 -5.439107 0.0000 C(64) -26557.75 8121.092 -3.270219 0.0012 C(65) 23064.76 8199.437 2.812969 0.0053 ====================================================== Determinant residual covariance 5.51E+22 Equation: D(M2NFAE) = C(11)*BOP/1000+C(12)*D72+C(13)*D69 +C(14)*D60+C(15)*D7680 Observations: 42 R-squared 0.913271 Mean dependent var 0.132592 Adjusted R-squared 0.903895 S.D. dependent var 4.341973 S.E. of regression 1.346047 Sum squared resid 67.03814 Durbin-Watson stat 2.147208 Equation: D(M2NGV) = C(20)+ C(21)*OBD +C(22)*D79+C(23)*D80 Observations: 42 R-squared 0.971197 Mean dependent var 2320.165 Adjusted R-squared 0.968084 S.D. dependent var 5260.589 S.E. of regression 939.8117 Sum squared resid 32680103 Durbin-Watson stat 2.238885 Equation: D(M2LPV) = C(31)*D(GDPV)+C(32)*D80 Observations: 42 R-squared 0.960945 Mean dependent var 5773.873 Adjusted R-squared 0.959969 S.D. dependent var 13071.46 S.E. of regression 2615.321 Sum squared resid 2.74E+08 Durbin-Watson stat 1.049681 Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 26 Equation: D(M2NW) = C(41)*D7780+C(42)*D79+C(43)*D80+C(44) *@TREND Observations: 42 R-squared 0.967070 Mean dependent var -692.9867 Adjusted R-squared 0.964470 S.D. dependent var 4158.716 S.E. of regression 783.8891 Sum squared resid 23350323 Durbin-Watson stat 3.436861 Equation: D(PGDP) = C(51)*D(M2) +C(52)*D80 Observations: 42 R-squared 0.923764 Mean dependent var 0.047743 Adjusted R-squared 0.921858 S.D. dependent var 0.089887 S.E. of regression 0.025127 Sum squared resid 0.025254 Durbin-Watson stat 2.826425 Equation:D(GDP)=C(60)+C(61)*BOP/1000+C(62)*D(GDP(-1))+C(63)*D5659+C(64)*D65+C(65)* D55 Observations: 41 R-squared 0.706315 Mean dependent var 6893.122 Adjusted R-squared 0.664359 S.D. dependent var 13732.14 S.E. of regression 7955.646 Sum squared resid 2.22E+09 Durbin-Watson stat 1.521260 As it is seen in the estimated results, the net foreign assets of the banking system has a positive significant relationship with the balance of payments. The coefficient on C(21) is positive and significant, supporting a positive link between the government budget deficit and the government debt to the banking system. Equation (5) suggests that nominal GDP is positively and significantly related to the liquidity, supporting the monetarists' view. In other words, any change in the money supply will affect the nominal GDP. In addition, net private sector debt to the banking system is positively and significantly correlated with nominal GDP. Equation (6) suggests that real GDP at fixed prices is positively and significantly related to the BOP. In Iran, the interest rate does not affect the real output. Indeed, monetary transmission policy affects the general price level, leaving trivial effects on the real output. Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 27 Graph 1 Plot of residuals of estimated equations -3 -2 -1 0 1 2 3 4 40 45 50 55 60 65 70 75 80 M2NFAE Residuals -5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 40 45 50 55 60 65 70 75 80 M2NGV Residuals -12000 -8000 -4000 0 4000 8000 12000 40 45 50 55 60 65 70 75 80 M2LPV Residuals -3000 -2000 -1000 0 1000 2000 3000 40 45 50 55 60 65 70 75 80 M2NW Residuals -.12 -.08 -.04 .00 .04 .08 .12 40 45 50 55 60 65 70 75 80 PGDP Residuals -20000 -10000 0 10000 20000 40 45 50 55 60 65 70 75 80 GDP Residuals Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 28 2.5 Dynamic Simulation To evaluate the performance of the model, we solved the whole system for the whole ex-post sample period through dynamic simulation. Graph 2 plots the actual value of the endogenous variables versus their simulated values. The 8 plots of Graph 1 show the high dynamic response and credibility of the model to build simulated series as near as the actual series with a concordance of turning points. Graph 2 Simulated versus actual values of the endogenous variables in the dynamic solution -15 -10 -5 0 5 10 15 20 25 40 45 50 55 60 65 70 75 80 85 Actual M2NFAE (Scenario 1) M2NFAE -40000 -30000 -20000 -10000 0 40 45 50 55 60 65 70 75 80 85 Actual M2NW (Scenario 1) M2NW -20000 0 20000 40000 60000 80000 100000 40 45 50 55 60 65 70 75 80 85 Actual M2NGV (Scenario 1) M2NGV -50000 0 50000 100000 150000 200000 250000 40 45 50 55 60 65 70 75 80 85 Actual M2LPV (Scenario 1) M2LPV Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 29 As it is seen, the model simulation has a good performance and can be used for policy evaluation and forecasting purposes. This small model is an adaptable model that can be used for other countries as well. -50000 0 50000 100000 150000 200000 250000 300000 350000 40 45 50 55 60 65 70 75 80 85 Actual M2 (Scenario 1) M2 -0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4 40 45 50 55 60 65 70 75 80 85 Actual PGDP (Scenario 1) PGDP -100000 0 100000 200000 300000 400000 500000 600000 700000 40 45 50 55 60 65 70 75 80 85 Actual GDPV (Scenario 1) GDPV 40000 80000 120000 160000 200000 240000 280000 320000 360000 40 45 50 55 60 65 70 75 80 85 Actual GDP (Scenario 1) GDP Copyright © CC-BY-NC 2019, CRIBFB | AMFBR www.cribfb.com/journal/index.php/amfbr American Finance & Banking Review Vol. 4, No. 1; 2019 30 References Bijan Bidabad, Macroeconometric Model of Iran, version 6.1, technical document. Lap Lambert Academic Publishing, OmniScriptum GmbH & Co. KG, ISBN: 978-3-659-14252-9, Winter 2014. Bidabad, Bijan, Macro-econometric model of Iran, version 1.00, Monetary and Banking Research Academy, Central Bank of Iran, 1996. 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