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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


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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 



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====================================================== 

                                                      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           



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      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                                          

 

 

 



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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. 

 

 

 

 

 



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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



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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



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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



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30 
                         
 

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Copyright for this article is retained by the author(s), with first publication rights granted to the journal. This is an open-access 
article distributed under the terms and conditions of the Creative Commons Attribution license 
(http://creativecommons.org/licenses/by/4.0/). 

 
 

 

 

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