An Equilibrium Model for an Open Economy. Romania’s Case
Catalin 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 both the static aspects and dynamic ones are approached. Also, based on the model built, it is determined the level of potential GDP and the natural unemployment rate. The determination of marginal main indicators of GDP and interest rates, allow to identify problems and the directions of action to achieve economic equilibrium.
Keywords: equilibrium; GDP; investments; interest rate; consumption JEL Code: E17; E27
1. Introduction
The economic equilibrium problem, whose origins and manifestations are lost in the mists of time, it is always new. After a number of approaches more or less rigorous, that have benchmarks the largest economic thinkers from different current and ideologies (François Quesnay, Léon Walras, Vilfredo Pareto, Alfred Marshall) John Maynard Keynes formulated a first economic equilibrium model for a closed economy without governmental sector.
The controversies on economic equilibrium get to the maturation and development of further researches, today being analyzed the fluctuations that accompany this process. Within theory of economic equilibrium, a synthetic analysis it is the IS- LM model consisting of simultaneous equilibrium in two markets, money market and the goods and services in an autarkic economy.
Based on Keynesian macroeconomic equilibrium, in 1937, Roy Harrod, James Meade and John Hicks tried to express mathematical majors relations of Keynes'
1 Associate Professor, PhD, Danubius University of Galati, Faculty of Economic Sciences, Romania, Address: 3 Galati Blvd, Galati, Romania, Tel.: +40372 361 102, fax: +40372 361 290, Corresponding author: [email protected].
2 Assistant Professor, PhD in progress, Danubius University of Galati, Faculty of Economic Sciences, Romania, Address: 3 Galati Blvd, Galati, Romania, Tel.: +40372 361 102, fax: +40372 361 290, e-
theory, finally to elucidate the interrelationships between theory effective demand and liquidity preference theory. (Hahn, 1977)
John Hicks' IS-LL scheme (Hicks, 1937) is the predecessor IS-LM model, the author also trying to capture the real opposition between classical and Keynesian theory, much criticized by J.M. Keynes.
Subsequent developments of Alvin Hansen (based on LL-IS schema) of 1949 and 1953 play an important role in systematizing known IS-LM model and, also, its popularization. In his book (Hansen, 1959) in order to get the curve IS, Hansen calls the investment demand function of Keynes and the neoclassical paradigm and for the LL curve is the curve of points where supply and demand. (Beaud &
Dostaler, 1996)
The IS-LM model (King, 1993; Lawn, 2003a; Lawn, 2003b; Romer, 1996; Romer, 2000; Smith & Zoega, 2009; Weerapana, 2003) was the basis for further researches and we refer both the theoretical and the empirical, the major aim being the theoretical reconstruction and development of the model and practical solutions to complex problems arising in the context of globalization. (Gali, 2000) Thus, Samuleson and Solow include the original model the Phillips curve (1960), Fleming Mundell and Fleming include balance of payments (1960 and 1962), Modigliani and Friedman use the consumption function (1954 and 1957), Tobin includes the demand for money (1958).
Until the mid 1990’s, the most researches were focused on modeling a closed economy, then economic literature approached, with studies undertaken by Maurice Obstfeld and Kenneth Rogoff (1995), static and dynamic equilibrium in open economies.
Although economic literature that explores New Open Economy Macroeconomics (NOEM models) is not as rich as that of the closed economy model, it is a significant theoretical edifice for the current macroeconomic modeling: Bergin (2004), Schmitt-Grohe and Uribe (2002) Justiniano and Preston (2008 & 2010), Martínez-García and Vilán (2012). The new approach enables researchers to explain the new changes that have occurred in the international macroeconomic environment based on introspection but rather on empirical causal observations, and theory is empirically validated in these cases.
In this article we propose, based on ideological vision and studies of the most important researchers in the field to determine a model for an open economy, with applications on the Romanian case, with empirical arguments, meaning for each variable used in the model it is specified degree of influence.
2. The Model Equations
The first equation of the model is the formula of the aggregate demand:
(1) D=C+G+I+NX where
D – the aggregate demand;
C – the actual final consumption of households;
G – the actual final consumption of the government;
I – the investments;
NX – the net export.
A second equation relates the actual final consumption of households according to available income V:
(2) C=cVV+C0, C00, cY(0,1)
where cV – the marginal propensity to consume, cV= dV
dC(0,1) and C0 is the intrinsic achieved autonomous consumption of households.
We will assume below that G and NX are proportional to the GDP, denoted by Y, given that in the absence of GDP can not engage any government spending (excluding in this analysis foreign loans) and also can not conduct foreign trade.
(3) G=gYY, gY(0,1) (4) NX=YY, Y(0,1) where:
gY – the marginal government consumption;
Y – the marginal net exports
Relative to investments, we will consider a direct linear dependence of the GDP level and inverse from the interest rate:
(5) I=inYY+irr, inY(0,1), ir0, I00
inY –the rate of investments, inY(0,1);
ir – a factor of influence on the investment rate, ir0;
The following equations express the dependence of the net income GDP, the
(6) V=Y+TR-TI, TR0 (7) TR=YY, Y(0,1)
(8) TI=riYY+T0, riY(0,1), T00
In equation (7) we assumed the linear dependence of transfers of GDP, assuming in the case of the fees an affine dependence, T0 being the independent taxes from the income (property taxes and so on). Let note that: Y – the marginal government transfers and riY – the tax rate, riY(0,1).
The static equilibrium equation is:
(9) D=Y
The following set of equations refers to monetary issues. We assume so:
(10) MD=mdYY+mrr, mdY0, mr0 where:
MD – the money demand in the economy;
mdY – the rate of money demand in the economy;
mr – a factor of influencing the demand for currency from the interest rate, mr0;
r – the real interest rate.
The equilibrium equation being:
(11) MD=M
where M represents the money supply.
The dynamic equations of the model are:
(12) dt
dY=(D-Y), 0
(13) dt
dr=(MD-M), 0
3. The Static Equilibrium From (1)-(8) we get:
(14) D=cVV+C0+gYY+inYY+irr+YY=Y(cV+cVY-cVriY+gY+inY+Y)-cVT0+C0+irr
(15) E=C0cVT0 (16) =1YriY
(17) =1cV
1Y riY
gYinYY=1cVgY inYY let note first that from (2), (6)-(8): V=Y(1+Y-riY)-T0=Y-T0, and:(18) C=cV(Y-T0)+C0=cVY+E
As in the absence of GDP (Y=0) the consumption must be positive, follows that E0.
From the fact that riY(0,1), Y(0,1) we get that: =1YriY(0,2).
With the notations (15)-(17), equation (14) becomes:
(19) D=Y(1-)+irr+E
The equilibrium condition D=Y in (9) implies: Y(1-)+irr+E=Y therefore:
(20) Y=
r E ir
The natural condition that at the increase of r, Y must decrease required:
ir 0 so
0.
From the fact that cV,gY,inY,Y,Y,riY(0,1) we get that 0 if and only if:
(21)
Y Y
Y Y Y
V 1 ri
in g c 1
Similarly, from equations (10),(11): MD=mdYY+mrr=M therefore:
(22) Y=
Y Y
r
md r M md
m
The condition of equilibrium on the two markets (goods & services and monetary):
(23)
Y Y
r r
md r M md Y m
r E Y i
After solving the system we have:
(24)
r Y r
Y r Y r
r r
m md i
Emd r M
m md i
Em Y Mi
The equations (24) give the static equilibrium model.
Noting now, for simplicity:
(25) =
r
Y
rmd m
i
1 0
(26) =
MirmrE
20 follows:(27) 2
r Y 2
r
Y m
M md i
M E E
md
(28)
r Y
r m
md M i
r E Y
From formulas (24) we have therefore:
(29)
0 r
V
T c m
Y ,
r Y Y
Y
in m Y Y g
Y ,
V r Y Y
c ri m
Y
Y ,
Y r
md i M
Y ,
r Y
md i
Y ,
r Y r
r m
md i M
m
Y
,
ir
M Y
(30)
0 Y
V
T c md
r ,
Y Y
Y Y
in md r r g
r ,
V Y Y
Y
c ri md
r
r ,
r Y Y
r m
md md M
i
r
,
mdY
r ,
r Y
r m
md M m
r
,
M
r
(31)
2
r 2 0
V 2
m T c 2
Y ,
2
2 r Y 2 2 Y 2 2 Y 2
m in 2
Y Y g
Y ,
2
r 2 V
Y 2 2
Y 2
m c ri 2
Y
Y ,
Y 2 Y
r 2
md md M i 2
Y ,
2
2 r Y 2
i md 2
Y ,
r Y 2 r
r 2
m md i M
m 2
Y
, 0
M Y
2
2
(32)
r Y 2 0
V 2
m md T
c 2
r ,
Y 2 r
Y 2 2 Y 2 2 Y 2
md m in 2
r r g
r ,
Y r 2 V
Y 2 2
Y 2
md m c ri 2
r
r ,
Y r
2 Y 2
r 2
md m M
2md i
r ,
2 r Y 2
i md 2
r
,
r 2 Y
2 r 2
m md 2 M
m
r
, 0
M r
2
2
To analyze the monotony of Y and of r, it is imperative to study the signs of
T0 and MmdY. Noting:
(33) 1=
0 r
r Y r 0 r 2 0 r V
T m
m md i T Mi T m c
, 2=
Y 0 Y V
md T md c M
we get that 1>2 if and only if
M T0 mdY
.
On the other hand, since E=C0 cVT00 i.e. C0 cVT0 results:
2-cVT0= 0 md
M
Y
therefore: 2cVT00, 1-cVT0= 0 T
m
m md i T Mi
0 r
r Y r 0
r
.
In conclusion, we get that:
1cVT0 if
r r Y
0 Mi
m M
T md and 1cVT0 if
r r Y
0 Mi
m M T md After these considerations, there are three main cases:
1. M
T0 mdY
1>2cVT00
2. M T md Mi
m M
md Y
0 r r Y
21cVT00
3.
r r Y
0 Mi
m M
T md 2cVT01.
On the other hand, the condition that T00 lead to C0 1, and
mdY
M 0 lead to C02. Regardless of the above, we have:
Y is strictly increasing and strictly convex with respect to marginal government consumption gY, with respect to marginal net exports Y, with the rate of investments inY and the marginal government transfers Y. Y is strictly decreasing and strictly concave with respect to the tax rate riY. Y is strictly decreasing and strictly convex in relation to the rate of money demand in the economy mdY. Y is strictly increasing and affine in relation to the money supply M.
r is strictly increasing and strictly convex with respect to the marginal government consumption gY, with respect to the marginal net exports Y, with the rate of Investments inY and the marginal government transfers Y. r is strictly decreasing and strictly concave with respect to the tax rate riY. r is strictly increasing and strictly concave in relation to the rate of money demand in the economy mdY. r is strictly decreasing and affine in relation to the money supply M.
We now have the following cases:
Case 1
M T0 mdY
and C0(cVT0,2) implies: T00, MmdY0. In this case:
Y is strictly increasing and strictly convex in relation to the marginal propensity to consume cV and the factor of influencing the demand for currency from the interest rate mr. Y is strictly decreasing and strictly convex in relation to the factor of influence on the investment rate ir.
r is strictly increasing and strictly convex in relation to the marginal propensity to consume cV. r is strictly decreasing and strictly concave in relation to the factor of influence on the investment rate ir and the factor of influencing the demand for currency from the interest rate mr.
Case 2
M T0 mdY
and C0[2,1] implies: T00, MmdY0.
Y is strictly increasing and strictly convex in relation to the marginal propensity to consume cV and in relation to the factor of influence on the investment rate ir. Y is strictly decreasing and strictly convex in relation to the factor of influencing the demand for currency from the interest rate mr.
r is strictly increasing and strictly convex in relation to the marginal propensity to consume cV and the factor of influence on the investment rate ir. r is strictly decreasing and strictly concave in relation to the factor of Influencing the demand for currency from the interest rate mr.
Case 3
M T0 mdY
and C0(1,) implies: T00, MmdY0.
Y is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV. Y is strictly decreasing and strictly convex in relation to the factor of influencing the demand for currency from the interest rate mr. Y is strictly increasing and strictly convex in relation to the factor of Influence on the investment rate ir.
r is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV. r is strictly increasing and strictly convex in relation to the factor of influence on the investment rate ir. r is strictly increasing and strictly concave in relation to the factor of influencing the demand for currency from the interest rate mr.
Case 4
M T md Mi
m M
md Y
0 r r Y
and C0(cVT0,1) implies: T00,
mdY
M 0.
Y is strictly increasing and strictly convex in relation to the marginal propensity to consume cV and the factor of influencing the demand for currency from the interest rate mr. Y is strictly decreasing and strictly concave in relation to the factor of Influence on the investment rate ir.
r is strictly increasing and strictly convex in relation to the marginal propensity to consume cV. r is strictly decreasing and strictly concave in relation to the factor of influence on the investment rate ir and the factor of influencing the demand for currency from the interest rate mr.
Case 5
M T md Mi
m M
md Y
0 r r Y
and C0[1,2] implies: T00,
mdY
M 0.
Y is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV and the factor of influence on the investment rate ir. Y is strictly increasing and strictly convex with respect to mr.
r is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV, the factor of influence on the investment rate ir and the factor of influencing the demand for currency from the interest rate mr.
Case 6
M T md Mi
m M
md Y
0 r r Y
and C0(2,) implies: T00,
mdY
M 0.
Y is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV. Y is strictly increasing and strictly convex in relation to the factor of influence on the investment rate ir. Y is strictly decreasing and strictly convex in relation to the factor of influencing the demand for currency from the interest rate mr.
r is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV. r is strictly increasing and strictly convex in relation to the factor of influence on the investment rate ir. r is strictly increasing and strictly concave in relation to the factor of influencing the demand for currency from the interest rate mr.
Case 7
r r Y
0 Mi
m M
T md and C0(cVT0,2) implies: T00, MmdY
0.
Y is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV and the factor of Influence on the investment rate ir. Y is strictly increasing and strictly convex in relation to the factor of Influencing the demand for currency from the interest rate mr.
r is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV, with the factor of influence on the investment rate ir and the factor of influencing the demand for currency from the interest rate mr.
Case 8
r r Y
0 Mi
m M
T md and C0[2,) implies: T00, MmdY0.
Y is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV. Y is strictly increasing and strictly convex in relation to the factor of influence on the investment rate ir. Y is strictly decreasing and strictly
r is strictly decreasing and strictly concave in relation to the marginal propensity to consume cV. r is strictly increasing and strictly convex in relation to the factor of influence on the investment rate ir. r is strictly increasing and strictly concave in relation to the factor of influencing the demand for currency from the interest rate mr.
4. The Determination of the Potential GDP. Okun's Law
Considering the money supply constant in time, we can consider as potential GDP value, the static equilibrium value:
(34) Y =*
r Y r
r r
m md i
Em Mi
Once determined the potential level of GDP, we naturally put the problem of determining the natural rate of unemployment. The known expression of Okun's law is:
(35) * * c
u u*
Y Y
Y
where:
Y – the actual GDP;
Y* – the potential GDP;
u – the unemployment rate;
u* – the natural rate of unemployment;
c – a factor of proportionality.
Due to the difficulties in the appliance of Okun's law (consisting in the impossibility to determine the potential GDP - made in conditions of full employment of labor) and also the natural rate of unemployment, is used in practice, a modified form of it, as follows:
(36) a c u
Y
Y
The advantage of this is to eliminate the explicit expressions of the potential GDP and the natural unemployment. On the other hand, in our analysis, we will determine the value of the constant c using the relation (36) and then inserting it into (35) which allows the determination of the natural rate of unemployment at a
Being so determined the constant c, we have from (34), (35):
(37)
*
*
*
cY Y u Y
u =
Mi Em
Yc
m md i c u 1
r r
r Y r
From equation (37) it is observed that u increases with Y with the factor *
r r
r Y r
Em Mi c
m md i
.
5. The Dynamic Equilibrium
The equations (12) and (13) is constituted as laws of dynamic equilibrium. Let so the system of first order differential equations:
(38)
) M MD dt (
dr
) Y D dt (
dY
, ,0
From (10),(19) we can write (38) as:
(39)
M r m Y dt md
dr
E r i dt Y
dY
r Y
r
Using the lemma from appendix A.1, it follows that: Y~ ) t ( Y limt
, limr(t) ~r
t
,
r~
,
Y~ R+ if and only if:
1. =(+mr)2+4irmdY=0 then:
(40)
Y r r t Y 2
m
r r r
r r
0 r 0 r
2 t m 2
r Y 0
Y r r
r t r
2 m 2
r r r 0
2 t m
r r r
0 r 0 r
md i m
E md te M
i 2
m m
) m ( E M i r 2 i 2 Y
m
m e E md 4 M
r r
md i m
E m M e i
) m (
M i E 4 m Y
m te ) m ( E M i r 2 i 2 Y
Y m
r r
r
r
and:
Y r r
Y Y r r
r r
md i m
E md r~ M
md i m
M i E Y~ m
2. =(+mr)2+4irmdY0 and 12 are roots of the equation: 2+(-mr)-
(mr+irmdY)=0 then:
(41)
Y r r t Y 2 r t 2
1 r 1
Y r r
r t r
2 t 1
md i m
M E e md
i k e
i k r
md i m
M i E e m
k e k Y
2 1
2 1
where:
1 2
Y r r
r r 1
0 1
Y r r
Y r 0 r 2
1 2
Y r r
Y r 0 r Y r r
r r 2
0 2
1
md i m
M i E Y m
md i m
M E i md r
i k
md i m
M E i md r
md i i m
M i E Y m
k
and:
Y r r
Y Y r r
r r
md i m
E md r~ M
md i m
M i E Y~ m
3. =(+mr)2+4irmdY0 and 1=+i, 2=-i, 0 are roots of the equation: 2+(-mr)-(mr+irmdY)=0 then:
(42)
Y r r
Y
t Y
r r
r r Y Y
r 0 r 0 Y
t Y r r
Y 0
Y r r
r r
t Y
r r
Y r
r r r 0 r 0 r
t Y r r
r r 0
md i m
E md M
t sin ) e
md i m ( 2
) M i E m ( md 2 ) E md M )(
m r ( 2 Y m 1 md
t cos md e
i m
E md r M
r
md i m
E m M i
t sin ) e
md i m ( 2
) E md M ( i 2 ) E m M i )(
m Y ( 2 r m 1 i
t cos md e
i m
M i E Y m Y
and:
Y r r
Y Y r r
r r
md i m
E md r~ M
md i m
M i E Y~ m
We will call Y~
- the limit of the output and ~r - the interest rate limit.
6. The Analysis of the Romanian Economy
Using the data table A.1 and the results of analyzes from the appendix A.2 there are obtained the corresponding regression equations for Romania during 2001- 2011.
Table 1 The regression equation The regression’s coefficients C=0.59526V+18527.39699 cV=0.59526 C0=18527.39699
G=0.07703Y gY=0.07703
I=0.28077Y-79168.78775r inY=0.28077 ir=79168.78775
NX=-0.08858Y Y=-0.08858
TR=0.09727Y Y=0.09727
TI=0.06905Y+5117.37477 riY=0.06905 T0=5117.37477 MD=0.08850Y-59560.45339r md =0.08850 m=-59560.45339
Substituting in relations (24) we obtain the values of static equilibrium are, for 2011 (expressed in 2000-national currency) and M=11603.05: Y=130753.8 and r=- 0.00053=-0.053%.
Considering the inflation rate from 2011 as i=5.79% we obtain using the formula:
rn=r
i1 i where rn is the nominal interest rate: rn=5.73%.On the other hand, the potential level of GDP calculated by formula (32) in the period was:
Table 2
It can therefore be seen that in 2011, the Romanian economy was close to the potential output level, the only disturbing factor being the rate averaged 6.25%
higher than those of equilibrium.
Relative to Okun's law, the data in table A.2, gives us a value for c=1.707.
From formula (35) follows, for Romania:
(43) u =* Y
1573970536 M
121 . 135141
351 . 14077 5858
. 0
u
Considering the monetary base for the reference period, we get:
Anul Y Y* Y-Y* *
*
Y Y Y 2001 85841.1936 88910.28844 -3069.094844 -3.45%
2002 89658.25153 89721.72265 -63.47112168 -0.07%
2003 93904.04246 90443.68138 3460.361078 3.83%
2004 102310.9459 94351.2625 7959.683385 8.44%
2005 106421.2703 101420.1072 5001.163027 4.93%
2006 114561.3451 112366.9512 2194.393982 1.95%
2007 122371.7164 123753.4116 -1381.695222 -1.12%
2008 135665.8673 134831.2139 834.6533952 0.62%
2009 124029.6072 129248.2296 -5218.622443 -4.04%
2010 124837.2351 128197.8657 -3360.630587 -2.62%
2011 129050.5671 130753.8278 -1703.26069 -1.30%
Table 3
Year
The real unemployment rate
(u)
The natural unemployment
rate (u*)
Difference u-u*
2001 8.60% 6.59% 2.01%
2002 8.10% 8.06% 0.04%
2003 7.20% 9.42% -2.22%
2004 6.20% 11.10% -4.90%
2005 5.90% 8.77% -2.87%
2006 5.20% 6.34% -1.14%
2007 4.10% 3.45% 0.65%
2008 4.40% 4.76% -0.36%
2009 7.80% 5.45% 2.35%
2010 6.87% 5.35% 1.52%
2011 5.12% 4.36% 0.76%
The corresponding data from the tables 2 and 3 show that in 2003-2006 and in 2008 the Romanian economy was overheated, Romania's GDP being in excess in comparison to the potential level. Thus, in 2004, the relative difference was 8.44%
being explained and justified by an ill-founded relative increase in the monetary base of 15.67% from the previous period when the increase was ranging between 2.98% and 3.47%. Since 2009 the situation has changed radically, its level being 4.04% less than the potential, the difference becoming smaller over time.
Relative to the unemployment rate, the phenomenon has evolved almost identical.
If in 2003-2006 and in 2008 was an over-hiring (with a maximum difference of - 4.90% in the same year 2004), since 2009, the economic crisis set, the appropriate values over 1% (with a peak in 2009 of 2.35% above the natural level).
Relative to the rate evolution, we have:
Table 4
Year The nominal interest rate (rn)
The equilibrium nominal interest
rate (r) rn-r
2001 38.80% 42.87% -4.07%
2002 28.47% 29.97% -1.50%
2004 20.27% 17.95% 2.32%
2005 9.59% 13.74% -4.15%
2006 8.44% 9.38% -0.94%
2007 7.46% 5.89% 1.57%
2008 9.46% 7.13% 2.33%
2009 9.33% 5.77% 3.56%
2010 6.67% 6.44% 0.23%
2011 6.25% 5.73% 0.52%
It is noted that in the periods 2001-2003 and 2005-2006, the NBR’s (the National Bank of Romania) interest rate was below the equilibrium level. During the crisis, since 2009, it has overwhelmed the equilibrium (even with 3.56% in 2009) which led to the deepening crisis by discouraging investments.
Considering now the dynamic evolution of GDP and the money demand are obtained average values =3.183904003 and =7.5723610-6 where 0.
The graphs of progression to equilibrium values are:
Figure 1. The evolution of GDP for <0 (2000 national currency)
Considering now perturbed values =3 and =7,5723610-6 for which =0, we obtain graphs of evolution towards equilibrium values:
Figure 2. The evolution of GDP for =0 (2000 national currency)
Finally, considering now new perturbed values =3 and =10-6 for which 0, we obtain graphs of evolution towards equilibrium values:
Figure 3. The evolution of GDP for 0 (2000 national currency)
From the graphs above, it appears that the most favorable situation to achieve potential output in terms of a minimum interest is the corresponding value of 0 in which approximately seven years to obtain optimum.
Otherwise there is a very weak decrease of the real interest rate which is kept at high enough levels, accompanied by a reduction in GDP over a period of about three years, which is unacceptable. Therefore the condition that 0 (+m 2+4i 0 is the most convenient.
Considering: 222
mr2irmdY
m2r20 we find that:
2
Y r r Y r Y r r 2
Y r r Y r Y r
r m 2imd 2 imd m imd
md , i m md i 2 md i 2 m
Computing the partial derivatives of Y for the existing monetary basis in 2011, we get to a 0.01 variation of parameters:
5472 Y c 0,01
V
, Y g 0,01 Y 0,01 Y in 0,01 5532
Y Y
Y
,
3293 Y
Y 0,01 ri 0,01
Y
Y
,
7353 Y md 0,01
Y
.
In relation to the above indicators, it is noted that in the case of IS variables, the largest GDP's growth is due to the rate of investments, net exports and marginal government consumption. A similar increase can be achieved also by an increasing in the marginal propensity to consume.
7. Conclusions
The model presented above shows a more flexibility in macroeconomic modeling, because it removes the common assumptions of constancy of variables. Thus, net exports, government consumption and transfers are approached by their econometric dependence of GDP. After the analysis of static equilibrium there are obtained the value of potential GDP and the interest rate.
The dynamic analysis revealed three cases of economic development in which both GDP and interest rates converge to limit values, clearly identical with those in the static equilibrium. The three cases which are dependent on statistical parameters, push faster or slower the economy to the equilibrium. From predicted equilibrium values, we have defined the potential GDP, based on which we determined (with Okun's law) the natural rate of unemployment.
Romania's situation, presented in the case study, reveals a contradictory economic policy.
Thus, although econometric indicators leading to optimal convergence (0) of GDP to the potential, this is due to compensation data period. In fact, in 2003-2006 and 2008, the Romanian economy was overheated, with an overemployment of labor and a positive output gap. In the period of economic crisis, the unemployment has returned to a relatively normal situation, in turn the interest rate has increased unjustified (2008,2009) led to discouraging investments. Recent years (2010, 2011) approached the interest rate from equilibrium, which was reflected in an dynamic increased of investments. For Romania, the analysis of marginal indicators proposes as directions for growth, the increase of investments, net exports, government consumption marginal, but also the marginal
8. References
Beaud, Michel & Dostaler, Gilles (1996). La pensée économique depuis Keynes/The Economic thought since Keynes. Paris: Édition du Seuil.
Bergin, Paul R. (2004). How well can the new open economy macroeconomics explain the exchange rate and current account? NBER Working Paper, No. 10356.
Gali, Jordi (2000). The return of the Phillips curve and other recent developments in business cycle theory. Spanish Economic Review. Springer-Verlag.
Hahn, Frank Horace (1977). Keynesian Economics and General Equilibrium Theory: Reflections on Some Current Debates. Microeconomic Foundations of Macroeconomics edited by Harcourt, London, pp. 25-40.
Hansen, A.H. (1959). A Guide to Keynes. UK: Mc Graw-Hill.
Hicks, J.R. (1937). Mr. Keynes and the “Classics”; A Suggested Interpretation. Econometrica, Vol. 5, No. 2, pp. 147-159.
Justiniano, Alejandro & Preston, Bruce (2008). Can Structural Small Open Economy Models Account for the Influence of Foreign Disturbances? NBER, Working Paper, No. 14547, December.
Justiniano, Alejandro & Preston, Bruce (2010). Monetary policy and uncertainty in an empirical small open-economy model. Journal of Applied Econometrics, Volume 25, Issue 1, January, pp. 93-128.
King, Robert G. (1993). Will the New Keynesian Macroeconomics Resurrect the IS-LM Model?
Journal of Economic Perspectives, Vol. 7, No 1, Winter, pp. 67-82.
Lawn, Philip A. (2003a). Environmental Macroeconomics: Extending the IS-LM Model to Include an 'Environmental Equilibrium' Curve. Australian Economic Papers, Vol. 42, issue 1, pp. 118-134.
Lawn, Philip A. (2003b). On Heyes’ IS–LM–EE proposal to establish an environmental macroeconomics. Environment and Development Economics, Vol. 8, pp. 31–56, Cambridge University Press.
Martínez-García, Enrique & Vilán, Diego (2012). Bayesian Estimation of NOEM Models:
Identification and Inference in Small Samples. Federal Reserve Bank of Dallas, Globalization and Monetary Policy Institute, Working Paper, No. 105, March.
Romer, David (1996). Advanced Macroeconomics. UK: McGraw-Hill.
Romer, David (2000). Keynesian Macroeconomics without the LM Curve. Journal of Economic Perspectives, Vol. 14, No 2 (Spring), pp. 149–169.
Schmitt-Grohe, Stephanie & Uribe, Martin (2002). Closing small open economy models. Journal of International Economics 61, March, pp. 163–185.
Smith, R.P. & Zoega, G. (2009). Keynes, investment, unemployment and expectations. International Review of Applied Economics, 23(4), pp. 427-444.
Weerapana, Akila (2003). Intermediate macroeconomics without the IS-LM model. Journal of Economic Education, 34, 3, Summer, pp. 241-262.
Appendix A.1 A result on the stability of solutions of a system of differential equations of first order, linear, with constant coefficients satisfying some conditions
Lemma
Let the system of differential equations:
f e Y X d c
b a dt dYdt dX
, a,b,c,d,e,fR, a,b,d0, c,e,f0, X(0)=X0, Y(0)=Y0.
Then X~
) t ( X limt
, Y~
) t ( Y limt
, Y~
,
X~ R if and only if:
1. =(a-d)2+4bc=0 with the solution:
2 t
2 d a 0
0 t
2 d a 0 2
2 t
2 d a 0 2
t 2
d a 0
0
) d a (
af 4 ce b te
2 d a d a
) d a ( e bf bY 2 2 X
d e a
d a
ce 4 af Y Y
) d a (
de 4 bf ) e
d a (
bf 4 de X d te
a
) d a ( e bf bY 2 2 X
d X a
2. =(a-d)2+4bc0 and 12 are roots of the equation: 2-(a+d)+(ad-bc)=0: e,fR with the solution:
bc ad
af e ce
b k e a
b k Y a
bc ad
bf e de
k e k X
t 2 t 2
1 1
t 2 t 1
2 1
2 1
where:
1 2
0 1
0 1 2
1 2
0 2
0 2 1
bc ad
af bce bc bY
ad bf a de X
a k
bc ad
af bce bc bY
ad bf a de X
a k
3. =(a-d)2+4bc0 and 1=+i, 2=-i, 0 are the roots of the equation: 2- (a+d)+(ad-bc)=0: e,fR with the solution:
