An Equilibrium Model with Applications for some of the South American countries
Cătălin Angelo Ioan1 & Gina Ioan2
Abstract: The model presented in this article is an adaptation of the IS-LM model for an open economy in which we took into account the temporal variable to more accurately determine the equilibrium levels of the macroeconomic indicators. We analyzed the periods during which the values of the indicators exceeded the level of equilibrium and we identified the possible causes that led to these situations.
Keywords: equilibrium; GDP; investments; interest rate; consumption
JEL Code: E17, E27
1. The model equations ([1])
The first equation of the model is the formula of the aggregate demand:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
where
D(t) – the aggregate demand at the moment t;
C(t) – the actual final consumption of households at the moment t;
G(t) – the actual final consumption of the government at the moment t;
I(t) – the investment at the moment t;
EX(t) – the exports at the moment t;
IM(t) – the imports at the moment t
A second equation relates the actual final consumption of households according to disposable income:
C(t)=cVDI(t)+C0, C0R, cV0
where
DI(t) – the disposable income at the moment t;
cV – the marginal propensity to consume, cV= 0;
C0 – the intrinsic achieved autonomous consumption of households
G(t)=iGTI(t)+G0, iG(0,1)
where
TI(t) – the total income at the moment t;
iG – the marginal index of final consumption of the government according to total income
G0 - the intrinsic achieved autonomous consumption of government
TI(t)=TR(t)+OR(t)
where:
TR(t) – tax rate at the moment t;
OR(t) – other revenues at the moment t
OR(t)=iORY(t)+OR0, iOR(0,1), OR0R
where:
Y(t) – the output at the moment t;
iOR – the marginal index of other revenues according to the output;
OR0 – the autonomous other revenues
I(t)=iYY(t)+irr(t)+I0, iY(0,1), ir0
where:
I(t) – investments at the moment t;
r(t) – the real interest rate at the moment t;
iY – the rate of investments;
ir – a factor of influence on the investment rate
I0 - the autonomous investments
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=cTFY(t)+TF0, cTF(0,1), TF0R
where:
TF(t) – the government transfers at the moment t;
cTF – the marginal index of government transfers according to the output;
TF0 – the autonomous government transfers
TR(t)=tYY(t)+TR0, tY(0,1), TR0R
where:
tY – the marginal index of tax rate according to the output;
TR0 – the intercept of the regression
IM(t)=imYY(t)+IM0, imY0, IM0R
where:
CH(t) – the exchange rate of the national currency based on the euro at the moment t;
imY – the rate of imports;
IM0 – the autonomous imports
EX(t)=exYY(t)+EX0, exY0, EX0R
where:
exY – the rate of exports;
EX0 – the autonomous exports
D(t)=Y(t) – the equation of equilibrium at the moment t
MD(t)=mdYY(t)+mdrr(t)+MD0, mdY(0,1), mdr0
where:
MD(t) – the money demand in the economy at the moment t;
mdY – the rate of money demand in the economy;
mdr – a factor of influencing the demand for currency from the interest rate
MD0 - the autonomous money demand
MS(t)=mSt+MS0, mM,M0R
where:
MS(t) – the money supply in the economy at the moment t;
mS – the marginal index of the money supply according to time;
MS0 – the intercept of the regression
MD(t)=MS(t) – the equation of equilibrium at the moment t
2. The Equilibrium at a Fixed Moment ([1])
From (4), (5), (11) we get:
TI(t)=(tY+iOR)Y(t)+TR0+OR0
From (3), (16):
G(t)=(iGtY+iGiOR)Y(t)+iG(TR0+OR0)+G0
From (7), (8), (9) we get:
DI(t)=(1+cTF-tY)Y(t)+TF0-TR0
From (2), (18):
C(t)=(cV+cVcTF-cVtY)Y(t)+cV(TF0-TR0)+C0
Now, from (1), (6), (10), (11), (17), (19) we have:
D(t)=(cV+cVcTF-cVtY+iGtY+iGiOR+iY+exY-imY)Y(t)+irr(t)+cV(TF0-TR0)+iG(TR0+OR0)+C0+G0+ I0+EX0-IM0
From (12) and (20) we get the first equation of the equilibrium:
(cV+cVcTF-cVtY+iGtY+iGiOR+iY+exY-imY-1)Y(t)+irr(t)+cV(TF0-TR0)+iG(TR0+OR0)+C0+G0+ I0+EX0-IM0=0
and from (13), (14), (15) we get the second equation of the equilibrium
mdYY(t)+mdrr(t)-mSt+MD0-MS0=0
Let note now:
=cV+cVcTF-cVtY+iGtY+iGiOR+iY+exY-imY-1
=cV(TF0-TR0)+iG(TR0+OR0)+C0+G0+I0+EX0-IM0
=MD0-MS0
The equilibrium equations become:
The solutions of equilibrium are:
At equilibrium, replacing (27) in (1)-(16), we have:
TI*(t)=(tY+iOR)Y*(t)+TR0+OR0=
G*(t)=
DI*(t)=
C*(t)=
OR*(t)=
TR*(t)=
TF*(t)=
I*(t)=
IM*(t)=
EX*(t)=
MD*(t)=
MS*(t)=mSt+MS0
3. Analysis of the Countries
3.1. Argentina
After the analysis during 2000-2016 the model equations are:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
C(t)=0.6414DI(t)+11173531777
G(t)=0.7570TI(t)+1865841345
TI(t)=TR(t)+OR(t)
OR(t)=0.1748Y(t)-40020711292
I(t)=0.2347Y(t)-133022602r(t)-26733479563
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=0.1779Y(t)-32442728852
TR(t)=0.1557Y(t)-12366835747
IM(t)=0.2864Y(t)-52337545847
EX(t)=0.1319Y(t)+19160267718
D(t)=Y(t)
MD(t)=0.2193Y(t)+499983409r(t)+15266995172
MS(t)=2282377123t-4484930613430
MD(t)=MS(t)
Solving the equations (1)-(15) we find that at equilibrium (“t” being the year):
Y(t)=13713035325.57t-27157174288683.00
r(t)=-1.4509t+2913.0524
TI(t)=4531366163.08t-9026265155824.16
G(t)=3430391727.88t-6831310779099.59
DI(t)=14017369393.96t-27779950688352.60
C(t)=8990438690.96t-17806288253121.10
OR(t)=2396475180.87t-4785979036355.18
TR(t)=2134890982.21t-4240286119468.98
TF(t)=2439225050.60t-4863062519138.66
I(t)=3411630956.53t-6788365737935.89
IM(t)=3927845209.54t-7831007577828.75
EX(t)=1808419159.73t-3562217096355.09
MD(t)=MS(t)=2282377123.22t-4484930613429.67
From the relationships (16)-(28) we can draw the following conclusions:
The analysis of “Actual final consumption of households” emphasizes that in 2000, 2001, 2006, 2007, 2008, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2002, 2003, 2004, 2005, 2009, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Actual final consumption of households” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of households” was registered in 2000 (118.37%) and the minimum in 2002 (86.27%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 63.23-68.16%.
The analysis of “Actual final consumption of the government” emphasizes that in 2000, 2001, 2009, 2010, 2011, 2012, 2013, 2015 is above the equilibrium value and in 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2014, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2009, 2010, 2011, 2012 is above the equilibrium value and in 2008 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of the government” was registered in 2000 (139.41%) and the minimum in 2004 (79.77%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 13.55-18.52%.
The analysis of “Other revenues” emphasizes that in 2000, 2001, 2009, 2010, 2011, 2012, 2013, 2014, 2015 is above the equilibrium value and in 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2009, 2010, 2011, 2012 is above the equilibrium value and in 2008 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Other revenues” was registered in 2000 (198.13%) and the minimum in 2005 (61.93%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 4.45-9.98%.
The analysis of “Investment” emphasizes that in 2000, 2001, 2005, 2006, 2007, 2008, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2002, 2003, 2004, 2009, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Investment” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Investment” was registered in 2000 (139.03%) and the minimum in 2002 (60.54%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 14.09-19.21%.
The analysis of “Government transfers” emphasizes that in 2000, 2001, 2005, 2006, 2007, 2008, 2010, 2011, 2012 is above the equilibrium value and in 2002, 2003, 2004, 2009, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Government transfers” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Government transfers” was registered in 2000 (139.54%) and the minimum in 2002 (33.81%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 6.61-10.89%.
The analysis of “Tax revenue” emphasizes that in 2004, 2005, 2006, 2007, 2008, 2010, 2011, 2012 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2009, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Tax revenue” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Tax revenue” was registered in 2008 (116.92%) and the minimum in 2002 (75.11%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 12.45-13.32%.
The analysis of “Broad money” emphasizes that in 2000, 2001, 2005, 2006, 2007, 2012, 2013, 2015, 2016 is above the equilibrium value and in 2002, 2003, 2004, 2008, 2009, 2010, 2011, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Broad money” emphasizes that in 2012 is above the equilibrium value and in 2008, 2009, 2010, 2011 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Broad money” was registered in 2000 (120.04%) and the minimum in 2014 (78.08%).
The analysis of “Exports” emphasizes that in 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Exports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Exports” was registered in 2007 (115.94%) and the minimum in 2015 (86.48%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 17.84-20.61%.
The analysis of “Imports” emphasizes that in 2000, 2001, 2007, 2008, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2002, 2003, 2004, 2005, 2006, 2009, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Imports” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Imports” was registered in 2000 (178.28%) and the minimum in 2002 (56.45%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 13.04-18.29%.
The analysis of “Trade balance” emphasizes that in 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Trade balance” emphasizes that in 2008, 2009, 2010 is above the equilibrium value and in 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Trade balance” was registered in 2015 (282.22%) and the minimum in 2014 (-275.62%).
The analysis of “Output” emphasizes that in 2000, 2001, 2006, 2007, 2008, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2002, 2003, 2004, 2005, 2009, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Output” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Output” was registered in 2000 (112.77%) and the minimum in 2002 (87.16%).
The analysis of “Real interest rate (%)” emphasizes that in 2001, 2002, 2003, 2008, 2010, 2011, 2012, 2014 is above the equilibrium value and in 2000, 2004, 2005, 2006, 2007, 2009, 2013, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Real interest rate (%)” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Real interest rate (%)” was registered in 2008 (662.49%) and the minimum in 2007 (-339.23%).
Figure 3.1.1.
Figure 3.1.2.
Figure 3.1.3
Figure 3.1.4
Figure 3.1.5
Figure 3.1.6
Figure 3.1.7
Figure 3.1.8
Figure 3.1.9
Figure 3.1.10
Figure 3.1.11
Figure 3.1.12
Figure 3.1.13
3.2. Bolivia
After the analysis during 2000-2016 the model equations are:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
C(t)=0.5865DI(t)+1193005244
G(t)=0.2971TI(t)+1241719715
TI(t)=TR(t)+OR(t)
OR(t)=0.1132Y(t)-824767874
I(t)=0.3075Y(t)+25521306r(t)-2758792230
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=-0.2538Y(t)+5076040555
TR(t)=0.3747Y(t)-3435974522
IM(t)=0.4487Y(t)-1707166539
EX(t)=0.4405Y(t)-497159120
D(t)=Y(t)
MD(t)=1.0820Y(t)+178826194r(t)-11298914848
MS(t)=771125776t-1537829188456
MD(t)=MS(t)
Solving the equations (1)-(15) we find that at equilibrium (“t” being the year):
Y(t)=223532459.23t-433139562970.55
r(t)=2.9596t-5915.5680
TI(t)=109051030.69t-215569274220.61
G(t)=32397882.13t-62801580873.19
DI(t)=83062687.63t-152438821065.67
C(t)=48714138.72t-88208458732.74
OR(t)=25303148.03t-49854758936.27
TR(t)=83747882.66t-165714515284.34
TF(t)=-56721888.94t+114986226620.55
I(t)=144266427.58t-286916509983.67
IM(t)=100307782.44t-196073878200.08
EX(t)=98461793.24t-191286891581.03
MD(t)=MS(t)=771125775.52t-1537829188455.51
From the relationships (16)-(28) we can draw the following conclusions:
The analysis of “Actual final consumption of households” emphasizes that in 2000, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2001, 2003 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Actual final consumption of households” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of households” was registered in 2016 (163.33%) and the minimum in 2001 (99.35%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 61.03-68.93%.
The analysis of “Actual final consumption of the government” emphasizes that in 2003, 2004, 2005, 2006, 2007 is above the equilibrium value and in 2000, 2001, 2002 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of the government” was registered in 2005 (109.03%) and the minimum in 2000 (88.71%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 13.78-15.07%.
The analysis of “Other revenues” emphasizes that in 2003, 2005, 2006, 2007 is above the equilibrium value and in 2000, 2001, 2002, 2004 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Other revenues” was registered in 2005 (120.80%) and the minimum in 2001 (90.45%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 5.82-6.76%.
The analysis of “Investment” emphasizes that in 2000, 2001, 2002, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Investment” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Investment” was registered in 2000 (146.93%) and the minimum in 2004 (78.67%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 14.18-21.48%.
The analysis of “Government transfers” emphasizes that in 2002, 2003, 2004, 2005, 2006, 2007 is above the equilibrium value and in 2000, 2001, 2008, 2009, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Government transfers” emphasizes that in 2008, 2009, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Government transfers” was registered in 2007 (200.82%) and the minimum in 2013 (-187.55%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 9.58-13.46%.
The analysis of “Tax revenue” emphasizes that in 2004, 2005, 2006, 2007 is above the equilibrium value and in 2000, 2001, 2002, 2003 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Tax revenue” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Tax revenue” was registered in 2007 (123.25%) and the minimum in 2001 (86.60%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 15.02-16.96%.
The analysis of “Broad money” emphasizes that in 2000, 2001, 2002, 2003, 2015, 2016 is above the equilibrium value and in 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Broad money” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Broad money” was registered in 2000 (159.10%) and the minimum in 2010 (75.13%).
The analysis of “Exports” emphasizes that in 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Exports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Exports” was registered in 2014 (157.61%) and the minimum in 2000 (78.66%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 37.13-46.99%.
The analysis of “Imports” emphasizes that in 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Imports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Imports” was registered in 2014 (172.14%) and the minimum in 2001 (89.04%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 32.28-41.82%.
The analysis of “Trade balance” emphasizes that in 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2012, 2013 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2011, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Trade balance” emphasizes that in 2008, 2009, 2010, 2012 is above the equilibrium value and in 2011 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Trade balance” was registered in 2006 (174.23%) and the minimum in 2000 (4.12%).
The analysis of “Output” emphasizes that in 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Output” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Output” was registered in 2016 (152.89%) and the minimum in 2000 (96.81%).
The analysis of “Real interest rate (%)” emphasizes that in 2000, 2001, 2002 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Real interest rate (%)” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Real interest rate (%)” was registered in 2000 (764.70%) and the minimum in 2011 (-8.88%).
Figure 3.2.1
Figure 3.2.2
Figure 3.2.3
Figure 3.2.4
Figure 3.2.5
Figure 3.2.6
Figure 3.2.7
Figure 3.2.8
Figure 3.2.9
Figure 3.2.10
Figure 3.2.11
Figure 3.2.12
Figure 3.2.13
3.3. Brazil
After the analysis during 2000-2016 the model equations are:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
C(t)=0.6117DI(t)+26174287857
G(t)=0.4253TI(t)+156651061708
TI(t)=TR(t)+OR(t)
OR(t)=0.3489Y(t)-474707802792
I(t)=0.1442Y(t)-5030392816r(t)+294160835915
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=0.0730Y(t)+60107021706
TR(t)=0.0948Y(t)+98719652086
IM(t)=0.2211Y(t)-244116766655
EX(t)=0.1247Y(t)-33701399828
D(t)=Y(t)
MD(t)=2.2123Y(t)+28459025567r(t)-4202024141382
MS(t)=97829418266t-195169784660699
MD(t)=MS(t)
Solving the equations (1)-(15) we find that at equilibrium (“t” being the year):
Y(t)=76571818487.85t-151703118876630.00
r(t)=-2.5148t+5082.4480
TI(t)=33979984335.55t-67696703589900.70
G(t)=14451520324.88t-28634424242975.60
DI(t)=74897115283.26t-148423830687278.00
C(t)=45811669435.90t-90758943965901.50
OR(t)=26718822516.68t-53409701231663.10
TR(t)=7261161818.87t-14287002358237.60
TF(t)=5586458614.28t-11007714168885.00
I(t)=23692355508.36t-47148712199146.30
IM(t)=16932623898.64t-33790817196614.10
EX(t)=9548897117.36t-18951855665221.10
MD(t)=MS(t)=97829418266.05t-195169784660699.00
From the relationships (16)-(28) we can draw the following conclusions:
The analysis of “Actual final consumption of households” emphasizes that in 2000, 2001, 2002, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Actual final consumption of households” emphasizes that in 2010, 2011, 2012 is above the equilibrium value and in 2008, 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of households” was registered in 2000 (110.94%) and the minimum in 2016 (86.15%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 59.84-62.32%.
The analysis of “Actual final consumption of the government” emphasizes that in 2000, 2001, 2002, 2008, 2010, 2011 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2009, 2012, 2013, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2008, 2010, 2011 is above the equilibrium value and in 2009, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of the government” was registered in 2000 (103.73%) and the minimum in 2015 (91.36%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 18.11-19.15%.
The analysis of “Other revenues” emphasizes that in 2000, 2001, 2002, 2006, 2010, 2011, 2012 is above the equilibrium value and in 2003, 2004, 2005, 2007, 2008, 2009, 2013, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2010, 2011, 2012 is above the equilibrium value and in 2008, 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Other revenues” was registered in 2000 (318.26%) and the minimum in 2005 (64.77%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 5.74-15.45%.
The analysis of “Investment” emphasizes that in 2000, 2001, 2002, 2010, 2011 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Investment” emphasizes that in 2010, 2011 is above the equilibrium value and in 2008, 2009, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Investment” was registered in 2000 (124.13%) and the minimum in 2016 (64.77%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 18.39-22.34%.
The analysis of “Government transfers” emphasizes that in 2002, 2004, 2005, 2006, 2007, 2008, 2010, 2011, 2012, 2013, 2014, 2015 is above the equilibrium value and in 2000, 2001, 2003, 2009, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Government transfers” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Government transfers” was registered in 2013 (124.83%) and the minimum in 2016 (-17.70%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 10.69-12.73%.
The analysis of “Tax revenue” emphasizes that in 2002, 2004, 2005, 2006, 2007, 2008, 2011 is above the equilibrium value and in 2000, 2001, 2003, 2009, 2010, 2012, 2013, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Tax revenue” emphasizes that in 2008, 2011 is above the equilibrium value and in 2009, 2010, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Tax revenue” was registered in 2008 (108.60%) and the minimum in 2015 (86.81%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 14.22-16.53%.
The analysis of “Broad money” emphasizes that in 2000, 2001, 2002, 2011, 2012, 2013, 2016 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Broad money” emphasizes that in 2011, 2012 is above the equilibrium value and in 2008, 2009, 2010 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Broad money” was registered in 2000 (136.24%) and the minimum in 2005 (90.25%).
The analysis of “Exports” emphasizes that in 2004, 2005, 2006, 2007, 2008 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Exports” emphasizes that in 2008 is above the equilibrium value and in 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Exports” was registered in 2007 (110.89%) and the minimum in 2000 (88.28%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 11.33-12.06%.
The analysis of “Imports” emphasizes that in 2000, 2001, 2002, 2008, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2009, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Imports” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Imports” was registered in 2000 (162.11%) and the minimum in 2016 (66.00%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 6.80-12.61%.
The analysis of “Trade balance” emphasizes that in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 is above the equilibrium value and in 2000, 2001, 2002, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Trade balance” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Trade balance” was registered in 2010 (987.21%) and the minimum in 2016 (-85.47%).
The analysis of “Output” emphasizes that in 2000, 2001, 2002, 2008, 2010, 2011 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2009, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Output” emphasizes that in 2008, 2010, 2011 is above the equilibrium value and in 2009, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Output” was registered in 2000 (106.82%) and the minimum in 2016 (84.34%).
The analysis of “Real interest rate (%)” emphasizes that in 2002, 2003, 2004, 2005, 2006, 2008, 2009, 2010, 2011, 2012, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2007, 2013 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Real interest rate (%)” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Real interest rate (%)” was registered in 2016 (320.13%) and the minimum in 2001 (90.66%).
Figure 3.3.1
Figure 3.3.2
Figure 3.3.3
Figure 3.3.4
Figure 3.3.5
Figure 3.3.6
Figure 3.3.7
Figure 3.3.8
Figure 3.3.9
Figure 3.3.10
Figure 3.3.11
Figure 3.3.12
Figure 3.3.13
3.4. Colombia
After the analysis during 2000-2016 the model equations are:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
C(t)=0.5740DI(t)+20834616313
G(t)=0.2748TI(t)+32570487137
TI(t)=TR(t)+OR(t)
OR(t)=0.2085Y(t)-38633647686
I(t)=0.3996Y(t)+120267379r(t)-50450022518
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=0.1924Y(t)-38110451268
TR(t)=0.3184Y(t)-60302413716
IM(t)=0.3307Y(t)-41101512706
EX(t)=0.1607Y(t)+893121988
D(t)=Y(t)
MD(t)=0.5489Y(t)-1170590952r(t)-79684958392
MS(t)=5966120390t-11918635674739
MD(t)=MS(t)
Solving the equations (1)-(15) we find that at equilibrium (“t” being the year):
Y(t)=-9061726381.10t+18432697868418.00
r(t)=-9.3458t+18756.8638
TI(t)=-4774620880.41t+9613246852036.98
G(t)=-1311918768.96t+2673994652892.60
DI(t)=-7920059069.23t+16132594084904.10
C(t)=-4545999772.24t+9280711139271.58
OR(t)=-1889082020.34t+3803998171600.67
TR(t)=-2885538860.06t+5809248680436.30
TF(t)=-1743871548.19t+3509144896922.42
I(t)=-4744620354.90t+9570205027015.36
IM(t)=-2997160199.25t+6055501506698.28
EX(t)=-1456347684.24t+2963288555936.69
MD(t)=MS(t)=5966120390.13t-11918635674738.70
From the relationships (16)-(28) we can draw the following conclusions:
The analysis of “Actual final consumption of households” emphasizes that in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Actual final consumption of households” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of households” was registered in 2016 (195.24%) and the minimum in 2000 (67.97%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 61.30-63.62%.
The analysis of “Actual final consumption of the government” emphasizes that in 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of the government” was registered in 2015 (214.71%) and the minimum in 2000 (62.09%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 15.50-18.22%.
The analysis of “Other revenues” emphasizes that in 2003, 2008, 2009, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2000, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Other revenues” was registered in 2013 (2754.50%) and the minimum in 2014 (-4863.72%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 8.22-13.15%.
The analysis of “Investment” emphasizes that in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Investment” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Investment” was registered in 2016 (1793.43%) and the minimum in 2000 (31.34%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 21.38-26.81%.
The analysis of “Government transfers” emphasizes that in 2003, 2008, 2009, 2010, 2011, 2012 is above the equilibrium value and in 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Government transfers” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Government transfers” was registered in 2012 (6071.27%) and the minimum in 2013 (-2698.64%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 8.12-9.76%.
The analysis of “Tax revenue” emphasizes that in 2008, 2009, 2010, 2011, 2012, 2013 is above the equilibrium value and in 2000, 2003, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Tax revenue” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Tax revenue” was registered in 2013 (7139.35%) and the minimum in 2014 (-2344.75%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 12.12-14.56%.
The analysis of “Broad money” emphasizes that in 2000, 2001, 2002, 2015, 2016 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Broad money” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Broad money” was registered in 2000 (373.52%) and the minimum in 2009 (72.52%).
The analysis of “Exports” emphasizes that in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Exports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Exports” was registered in 2016 (207.13%) and the minimum in 2000 (61.16%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 15.44-17.13%.
The analysis of “Imports” emphasizes that in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Imports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Imports” was registered in 2016 (557.86%) and the minimum in 2000 (37.97%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 16.68-22.19%.
The analysis of “Trade balance” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Trade balance” emphasizes that in 2008, 2009, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Trade balance” was registered in 2009 (-25.38%) and the minimum in 2007 (-674.50%).
The analysis of “Output” emphasizes that in 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Output” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Output” was registered in 2016 (222.92%) and the minimum in 2000 (62.25%).
The analysis of “Real interest rate (%)” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Real interest rate (%)” emphasizes that in 2008, 2009, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Real interest rate (%)” was registered in 2006 (74.35%) and the minimum in 2007 (-10170.54%).
Figure 3.4.1
Figure 3.4.2
Figure 3.4.3
Figure 3.4.4
Figure 3.4.5
Figure 3.4.6
Figure 3.4.7
Figure 3.4.8
Figure 3.4.9
Figure 3.4.10
Figure 3.4.11
Figure 3.4.12
Figure 3.4.13
3.5. Ecuador
After the analysis during 2000-2016 the model equations are:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
C(t)=0.5105DI(t)+8110757589
G(t)=0.5105TI(t)+8110757589
TI(t)=TR(t)+OR(t)
OR(t)=0.5105Y(t)+8110757589
I(t)=0.3265Y(t)-61961903r(t)-5214709671
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=0.0381Y(t)-4420995371
TR(t)=0.0381Y(t)-4420995371
IM(t)=0.3615Y(t)-5169744113
EX(t)=0.2399Y(t)+3132131307
D(t)=Y(t)
MD(t)=0.2896Y(t)+31187211r(t)-5370664617
MS(t)=1628568871t-3252535654664
MD(t)=MS(t)
Solving the equations (1)-(15) we find that at equilibrium (“t” being the year):
Y(t)=5666940905.81t-11336296726806.90
r(t)=-0.4017t+1145.5526
TI(t)=3109255968.54t-6216147155935.77
G(t)=1587366387.08t-3165414726414.64
DI(t)=5666940905.81t-11336296726806.90
C(t)=2893139581.45t-5779401290351.14
OR(t)=2893139581.45t-5779401290351.14
TR(t)=216116387.09t-436745865584.64
TF(t)=216116387.09t-436745865584.64
I(t)=1875427422.20t-3778061163153.19
IM(t)=2048331550.39t-4102705722704.73
EX(t)=1359339065.48t-2716125269592.68
MD(t)=MS(t)=1628568871.11t-3252535654663.71
From the relationships (16)-(28) we can draw the following conclusions:
The analysis of “Actual final consumption of households” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015 is above the equilibrium value and in 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Actual final consumption of households” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of households” was registered in 2000 (426.53%) and the minimum in 2016 (94.06%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 62.32-65.65%.
The analysis of “Actual final consumption of the government” emphasizes that in is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of the government” was registered in (0.00%) and the minimum in (0.00%).
The analysis of “Other revenues” emphasizes that in is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Other revenues” was registered in (0.00%) and the minimum in (0.00%).
The analysis of “Investment” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Investment” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Investment” was registered in 2000 (-29.52%) and the minimum in 2006 (-93.76%).
The analysis of “Government transfers” emphasizes that in 2015, 2016 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Government transfers” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Government transfers” was registered in 2016 (148.56%) and the minimum in 2010 (44.11%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 0.00-0.00%.
The analysis of “Tax revenue” emphasizes that in is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Tax revenue” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Tax revenue” was registered in (0.00%) and the minimum in (0.00%).
The analysis of “Broad money” emphasizes that in 2000, 2001, 2002 is above the equilibrium value and in 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Broad money” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Broad money” was registered in 2000 (201.91%) and the minimum in 2006 (89.81%).
The analysis of “Exports” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015 is above the equilibrium value and in 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Exports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Exports” was registered in 2000 (541.56%) and the minimum in 2016 (98.51%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 27.03-32.35%.
The analysis of “Imports” emphasizes that in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 is above the equilibrium value and in 2000, 2001, 2002, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Imports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is above the equilibrium value. The maximum ratio between real and equilibrium value of “Imports” was registered in 2003 (12548.52%) and the minimum in 2002 (-686.01%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 24.86-29.02%.
The analysis of “Trade balance” emphasizes that in 2013, 2014 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2011, 2012, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Trade balance” emphasizes that in 2008, 2009, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Trade balance” was registered in 2013 (834.84%) and the minimum in 2012 (-590.36%).
The analysis of “Output” emphasizes that in 2001, 2002, 2003, 2004, 2005, 2006 is above the equilibrium value and in 2000 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Output” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Output” was registered in 2001 (1486.00%) and the minimum in 2000 (-1923.85%).
The analysis of “Real interest rate (%)” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Real interest rate (%)” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Real interest rate (%)” was registered in 2000 (7.77%) and the minimum in 2001 (-2.92%).
Figure 3.5.1
Figure 3.5.2
Figure 3.5.3
Figure 3.5.4
Figure 3.5.5
Figure 3.5.6
Figure 3.5.7
Figure 3.5.8
3.6. Uruguay
After the analysis during 2000-2016 the model equations are:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
C(t)=0.6565DI(t)+1632081725
G(t)=0.4428TI(t)+35525349
TI(t)=TR(t)+OR(t)
OR(t)=0.1587Y(t)-2135788351
I(t)=0.2739Y(t)-9196668r(t)-2982575242
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=0.0659Y(t)+2726840087
TR(t)=0.2214Y(t)-1469190242
IM(t)=0.3775Y(t)-4745773828
EX(t)=0.2965Y(t)-1798905638
D(t)=Y(t)
MD(t)=0.5931Y(t)+58226820r(t)-6200525589
MS(t)=776920596t-1543622406447
MD(t)=MS(t)
Solving the equations (1)-(15) we find that at equilibrium (“t” being the year):
Y(t)=13222626936.27t-26466466109219.20
r(t)=-121.3462t+243190.4344
TI(t)=5026832050.92t-10065333313940.10
G(t)=2225763369.61t-4456658067389.12
DI(t)=11165796615.77t-22345309793122.40
C(t)=7329869390.32t-14667111036761.50
OR(t)=2098814850.19t-4203132486645.82
TR(t)=2928017200.73t-5862200827294.28
TF(t)=871186880.22t-1741044511197.49
I(t)=4737786857.08t-9488947040728.75
IM(t)=4991617346.51t-9995988207599.17
EX(t)=3920824665.77t-7849738171938.97
MD(t)=MS(t)=776920595.58t-1543622406446.51
From the relationships (16)-(28) we can draw the following conclusions:
The analysis of “Actual final consumption of households” emphasizes that in 2002, 2003 is above the equilibrium value and in 2000, 2001, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Actual final consumption of households” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of households” was registered in 2002 (260.60%) and the minimum in 2001 (-49011.72%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 63.63-67.67%.
The analysis of “Actual final consumption of the government” emphasizes that in 2003 is above the equilibrium value and in 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of the government” was registered in 2003 (213.50%) and the minimum in 2002 (-470.19%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 10.94-10.94%.
The analysis of “Other revenues” emphasizes that in 2003 is above the equilibrium value and in 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Other revenues” was registered in 2003 (258.04%) and the minimum in 2002 (-182.76%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 6.79-6.79%.
The analysis of “Investment” emphasizes that in 2003 is above the equilibrium value and in 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Investment” emphasizes that in 2010, 2011, 2012, 2013, 2014 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Investment” was registered in 2003 (430.64%) and the minimum in 2002 (-93.90%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 13.54-13.54%.
The analysis of “Government transfers” emphasizes that in 2000, 2001, 2002 is above the equilibrium value and in 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Government transfers” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Government transfers” was registered in 2000 (327.41%) and the minimum in 2016 (-7.77%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 15.60-16.42%.
The analysis of “Tax revenue” emphasizes that in 2003 is above the equilibrium value and in 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Tax revenue” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Tax revenue” was registered in 2003 (175.68%) and the minimum in 2002 (-1347.69%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 15.25-15.25%.
The analysis of “Broad money” emphasizes that in 2002, 2003, 2013, 2014, 2015, 2016 is above the equilibrium value and in 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Broad money” emphasizes that in 2013, 2014 is above the equilibrium value and in 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Broad money” was registered in 2015 (119.22%) and the minimum in 2007 (83.50%).
The analysis of “Exports” emphasizes that in 2003 is above the equilibrium value and in 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Exports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Exports” was registered in 2003 (153.49%) and the minimum in 2002 (-2180.27%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 18.70-18.70%.
The analysis of “Imports” emphasizes that in 2003 is above the equilibrium value and in 2000, 2001, 2002, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Imports” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Imports” was registered in 2003 (225.91%) and the minimum in 2002 (-170.53%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 16.64-16.64%.
The analysis of “Trade balance” emphasizes that in 2004 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2005, 2006, 2007, 2008, 2009, 2011, 2012, 2013, 2014, 2015, 2016 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Trade balance” emphasizes that in 2008, 2009, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Trade balance” was registered in 2004 (241.99%) and the minimum in 2005 (-210.22%).
The analysis of “Output” emphasizes that in 2002, 2003 is above the equilibrium value and in 2000, 2001, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Output” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Output” was registered in 2002 (536.28%) and the minimum in 2001 (-334.51%).
The analysis of “Real interest rate (%)” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Real interest rate (%)” emphasizes that in 2008, 2009, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Real interest rate (%)” was registered in 2004 (20.12%) and the minimum in 2007 (-1.99%).
Figure 3.6.1
Figure 3.6.2
Figure 3.6.3
Figure 3.6.4
Figure 3.6.5
Figure 3.6.6
Figure 3.6.7
Figure 3.6.8
Figure 3.6.9
Figure 3.6.10
Figure 3.6.11
Figure 3.6.12
3.7. Venezuela, RB
After the analysis during 2000-2014 the model equations are:
D(t)=C(t)+G(t)+I(t)+EX(t)-IM(t)
C(t)=0.8927DI(t)-139683896515
G(t)=0.8927TI(t)-139683896515
TI(t)=TR(t)+OR(t)
OR(t)=0.8927Y(t)-139683896515
I(t)=0.4800Y(t)+357416436r(t)-98824798289
DI(t)=Y(t)+TF(t)-TR(t)
TF(t)=-0.0058Y(t)-3064582687
TR(t)=-0.0058Y(t)-3064582687
IM(t)=0.4032Y(t)-85917735006
EX(t)=-0.1299Y(t)+177467132719
D(t)=Y(t)
MD(t)=0.6411Y(t)-127330171r(t)-133027486972
MS(t)=9909984931t-19789208029515
MD(t)=MS(t)
Solving the equations (1)-(15) we find that at equilibrium (“t” being the year):
Y(t)=11443030956.19t-22597285546568.90
r(t)=-20.2152t+40597.9485
TI(t)=10149509427.33t-20185634281484.70
G(t)=9060658833.16t-18159781012052.00
DI(t)=11443030956.19t-22597285546568.90
C(t)=10215409942.10t-20312707662738.90
OR(t)=10215409942.10t-20312707662738.90
TR(t)=-65900514.77t+127073381254.22
TF(t)=-65900514.77t+127073381254.22
I(t)=-1732351899.81t+3564403351344.88
IM(t)=4613708224.86t-9196902629198.54
EX(t)=-1486977694.41t+3113897147678.52
MD(t)=MS(t)=9909984931.11t-19789208029514.90
From the relationships (16)-(28) we can draw the following conclusions:
The analysis of “Actual final consumption of households” emphasizes that in 2007, 2008, 2009, 2012, 2013 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2010, 2011, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Actual final consumption of households” emphasizes that in 2008, 2009, 2012 is above the equilibrium value and in 2010, 2011 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of households” was registered in 2008 (104.16%) and the minimum in 2003 (69.12%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 48.76-59.26%.
The analysis of “Actual final consumption of the government” emphasizes that in is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Actual final consumption of the government” was registered in (0.00%) and the minimum in (0.00%).
The analysis of “Other revenues” emphasizes that in is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Other revenues” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Other revenues” was registered in (0.00%) and the minimum in (0.00%).
The analysis of “Investment” emphasizes that in 2007, 2008, 2010, 2011, 2012, 2013, 2014 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2009 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Investment” emphasizes that in 2008, 2010, 2011, 2012 is above the equilibrium value and in 2009 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Investment” was registered in 2012 (154.63%) and the minimum in 2003 (21.76%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 19.73-28.20%.
The analysis of “Government transfers” emphasizes that in 2002, 2003, 2004, 2011, 2012, 2013 is above the equilibrium value and in 2000, 2001, 2005, 2006, 2007, 2008, 2009, 2010, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Government transfers” emphasizes that in 2011, 2012 is above the equilibrium value and in 2008, 2009, 2010 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Government transfers” was registered in 2013 (275.66%) and the minimum in 2007 (-147.84%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between -3.51--2.62%.
The analysis of “Tax revenue” emphasizes that in is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Tax revenue” emphasizes that in is below the equilibrium value. The maximum ratio between real and equilibrium value of “Tax revenue” was registered in (0.00%) and the minimum in (0.00%).
The analysis of “Broad money” emphasizes that in 2000, 2001, 2007, 2009, 2012, 2013 is above the equilibrium value and in 2002, 2003, 2004, 2005, 2006, 2008, 2010, 2011 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Broad money” emphasizes that in 2009, 2012 is above the equilibrium value and in 2008, 2010, 2011 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Broad money” was registered in 2000 (174.15%) and the minimum in 2005 (76.93%).
The analysis of “Exports” emphasizes that in 2000, 2001, 2004, 2005, 2006, 2007, 2008 is above the equilibrium value and in 2002, 2003, 2009, 2010, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Exports” emphasizes that in 2008 is above the equilibrium value and in 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Exports” was registered in 2006 (112.30%) and the minimum in 2010 (89.69%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 34.01-50.87%.
The analysis of “Imports” emphasizes that in 2006, 2007, 2008, 2012 is above the equilibrium value and in 2000, 2001, 2002, 2003, 2004, 2005, 2009, 2010, 2011, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Imports” emphasizes that in 2008, 2012 is above the equilibrium value and in 2009, 2010, 2011 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Imports” was registered in 2007 (128.73%) and the minimum in 2003 (44.75%). The excess of equilibrium values is due, in the corresponding periods, to the large share of GDP, between 16.48-22.70%.
The analysis of “Trade balance” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2009, 2014 is above the equilibrium value and in 2007, 2008, 2010, 2011, 2012, 2013 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Trade balance” emphasizes that in 2009 is above the equilibrium value and in 2008, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Trade balance” was registered in 2014 (142.00%) and the minimum in 2012 (54.33%).
The analysis of “Output” emphasizes that in 2000, 2006, 2007, 2008, 2009, 2012, 2013 is above the equilibrium value and in 2001, 2002, 2003, 2004, 2005, 2010, 2011, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Output” emphasizes that in 2008, 2009, 2012 is above the equilibrium value and in 2010, 2011 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Output” was registered in 2008 (108.42%) and the minimum in 2003 (77.74%).
The analysis of “Real interest rate (%)” emphasizes that in 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014 is below the equilibrium value. During the financial crisis (2008-2012), the behavior of “Real interest rate (%)” emphasizes that in 2008, 2009, 2010, 2011, 2012 is below the equilibrium value. The maximum ratio between real and equilibrium value of “Real interest rate (%)” was registered in 2010 (54.74%) and the minimum in 2008 (-101.32%).
Figure 3.7.1
Figure 3.7.2
Figure 3.7.3
Figure 3.7.4
Figure 3.7.5
Figure 3.7.6
Figure 3.7.7
Figure 3.7.8
Figure 3.7.9
Figure 3.7.10
References
Ioan C.A.; Pusca A.C.; Nuta F.M. & Ioan G. (coord.) (2019). Economic development models of emerging countries, Galati: Danubius Publishing.
Ioan C.A. & Ioan G. (2011). The Equilibrium Analysis of a Closed Economy Model with Government and Money Market Sector, Acta Universitatis Danubius, Oeconomica, nr.5, vol.7, pp.127-143.
Ioan C.A. & Ioan G. (2013). A Mathematical Model of an Open Economy with Applications in Romania, Acta Universitatis Danubius, Oeconomica, nr.5, vol.9, pp.103-170.
Ioan C.A. & Ioan G. (2016). An Equilibrium Model for the Romanian Economy, Journal of Accounting and Management, Nr.2, Vol.6, pp.41 – 75.
Romer David. (1996). Advanced Macroeconomics, McGraw-Hill.
http://databank.worldbank.org/data/home.aspx.
https://fred.stlouisfed.org/series/.
1 Associate Professor, PhD, Danubius University of Galati, Department of Economics, Romania, Address: 3 Galati Blvd., Galati 800654, Romania, Tel.: +40372361102, Corresponding author: catalin_angelo_ioan@univ-danubius.ro.
2 Senior Lecturer, PhD, Danubius University of Galati, Department of Economics, Romania, Address: 3 Galati Blvd., Galati 800654, Romania, Tel.: +40372361102, E-mail: ginaioan@univ-danubius.ro.
AUDŒ, Vol. 16, no. 1/2020, pp.141-196