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