Trends in the Interest Rate – Investment – GDP Growth Relationship
1
TRENDS IN THE INTEREST RATE –
INVESTMENT – GDP GROWTH
RELATIONSHIP
Lucian-Liviu ALBU*
Abstract
In the last years it seemed that the Romanian economy leading up to access to the
EU was going to enter a new stage, evolving more and more in line with the standard
theory. Based on more accurate statistical data for the last years, we try to verify
some hypotheses used in the standard economic literature. Also, applying few simple
models derived from the standard ones in our experiment we estimated their
parameters in the case of Romania in order to obtain an image of the trends in the
next period. The two main partial models are referring to the impact of investment on
GDP growth rate and to the relation between the interest rate and investment,
respectively. Moreover, an equation including inflation dynamics was taken into
account. Beginning in 1998, the behaviour of the national economic system and the
interest rate – investment – economic growth relationship tend to converge to those
demonstrated in a normal market economy and presented in the specialised literature.
Keywords: Investment Rate, GDP Growth Rate, Interest rate, Depreciation Rate,
Contour Plot.
JEL Classification: C51, E22, E27, P24
The Model
Coming from standard literature, we used the following three basic equations:
r (α) = a*α + b
(1)
α (i) = c / (d + i)
(2)
i (p) = e*p + f
(3)
where r - GDP growth rate, α – investment rate (in GDP), i – interest rate, p – inflation,
a, b, c, d, e, and f – parameters (estimated econometrically).
The first equation tries to capture the impact of investment on GDP growth, the
second equation demonstrates an inverse relation between interest rate and
investment, while the third equation takes into account a direct relation between
*
Institute of Economic Forecasting, Romanian Academy, e-mail: [email protected].
− Romanian Journal of Economic Forecasting – 3/2006
5
Institute of Economic Forecasting
inflation and interest rate. Using some simple algebraic operations, based on the
above equations we can obtain also some other useful derivate equations, as follows:
r (i) = b + a*c / (d + i)
(4)
α (p) = c / [d + (e*p + f)]
(5)
i (α) = (c / α) – d
(6)
Moreover, we can express the empirical inflation–GDP growth rate relation in case of
the Romanian economy:
r (p) = b + a*c / (d + e*p + f)
(7)
Estimations
We tried to estimate the parameters of equations in the case of the Romanian
economy on the basis of the whole period after 1989, but the results were very poor
because of the quality of statistical data (for instance, in 1992 average inflation was
210.4% and average active interest rate was 49.6%, in 1993 they were 256.1% and
58.9%, respectively, etc.). Only since 1998 the statistical data have become more
relevant. The output of our experiment in the period 2000-2005 is shown in Figures 13, where: variables on ordinate axis and inflation are per cent; years are denoted from
1=2000 to 6=2005; E attached to the name of variable means estimated; r_L and r_U
(represented as black dashed lines) mean the lower limit and upper limit, respectively
(95% confidence intervals).
Figure 1
11
11
10
10
rE( α)
rE( α)
9
r
t
rE1( i)
rt
7
6
rE1( i)
5
3
r_U
t
r_L
t
2
1
r_U
t
0
5
3
2
1
0
2
1
2
3
4
t
6
6
1
1
2
7
rE2( p ) 4
rE2( p ) 4
r_L
t
9
8
8
5
6
8
18
28
p
38
t
Romanian Journal of Economic Forecasting – 3/2006 −
48
Trends in the Interest Rate – Investment – GDP Growth Relationship
Figure 2
24
24
αE( i)
23
αE( i)
23
αt
22
αt
22
αE1( p ) 21
αE1( p )
21
α_L t
α_Lt
20
α_U t
20
α_Ut
19
18
19
18
1
2
3
4
5
8
6
18
28
p
t
38
48
38
48
t
Figure 3
65
60
iE( p ) 55
iE( p )
i
t
i
t
45
42
iE1( α)
iE1( α)
i_Lt
i_U
t
51
35
i_L
t
i_U
t
25
15
33
24
15
1
2
3
4
5
6
8
18
t
28
p
t
Also, Annex presents some 3D graphic representations for variables and their
attached Contour Plots corresponding to real annual registered data over the period
2000-2005. Based on historical data, among other conclusions, we may see that a
GDP growth rate of about 7% could be obtained for an investment rate of around 22%
and an interest rate of about 10% (it is represented by peak 7 on the map denoted (α,
i, r). From the contour map (p, i, r) we can see the line 5 (5% GDP growth rate) that
follow very closed the diagonal line of plan p-i, which can be interpreted as a natural
rate of GDP growth rate. A similar conclusion, but for investment rate, could be
derived from contour map (p, i, α), where the trajectory of its natural rate could be
considered the top line following very close the diagonal line of plan p-i. Contour map
(p, α, r) demonstrates the negative impact of inflation on the GDP growth.
− Romanian Journal of Economic Forecasting – 3/2006
7
Institute of Economic Forecasting
Simulation
Based on relation (1) the simulation of the model demonstrated a critical value of
13.2% for investment rate (αcr1). For α<13.2% the GDP growth rate will be negative.
Moreover, in the extreme case of no investment (α=0) GDP will decrease by 8.6% per
year (estimated value of coefficient b is around -8.6%). Accepting the hypothesis of a
constant level of the so-called capital coefficient (computed as Stock of Fixed
Capital/GDP) the value 8.6% could be used as a first estimate for the annual rate of
capital depreciation in case of Romania which means in case of no investment that
the whole stock of fixed capital will be consumed in only 12 years (to note that this
shows a special situation for the capital stock in Romania: many productive capacities
are still obsolete, physically and/or morally depreciated, more of them being
underused or in conservation). Simulation of equation (2) shows a strong inverse
correlation (hyperbolic correlation) between investment and interest rate: Coefficient of
Multiple Determination R^2=0.845443; Adjusted coefficient of multiple determination
Ra^2=0.806804; Durbin-Watson statistic=2.032844; Variable c – t-ratio=4.56026,
Prob(t)=0.01034; Variable d – t-ratio=3.87819, Prob(t)=0.01787). It also allowed us to
compute the potential level of GDP growth rate of 7.62% – a theoretical level
computed as a value of GDP growth rate at the point αcr2=c/d=25.1%, corresponding
to an hypothetical interest rate tending to be equal to zero. Based on the simultaneous
simulation of the two equations we computed a more realistic maximum for GDP
growth rate, namely equal to 7.02% – also a theoretical level computed as a value of
GDP growth rate at the point α2=24.1%, corresponding to the situation in which GDP
growth rate tends to equal interest rate. To note that in this situation we could suppose
the stability of the whole economic system, like in case of studying the sustainability of
public debt and deficits (Albu and Pelinescu, 2000). Some results of the simulation of
the two partial models represented by equations (1) and (2) are shown in Figure 4.
Figure 4
60
60
αcr1
α2
αcr1 α2
40
40
rE( α)
iE( p )
iE1( α) 20
iE1( α)
20
0
iE1( α2 )
iE( 0 )
rE( αcr1 )
iE1( α2 )
0
0 4
8 12 16 20 24 28 32 36 40
α
8
0 8 16 24 32 40 48 56 64 72 80
p,α
Romanian Journal of Economic Forecasting – 3/2006 −
Trends in the Interest Rate – Investment – GDP Growth Relationship
Figure 5
26
αcr2
αcr1 α2
α2
24
10
rE( α)
αE( i)
αE1( p )
22
rE1( 0 )
rE2( 0 )
rE1( i)
rE2( p )
20
0
b
18
16
10
0
20
40
60
80
100
0
6 12 18 24 30 36 42 48 54 60
i, p
α, i, p
References
Albu, L.-L. (1997): Strain and Inflation-Unemployment Relationship in
Transitional Economies: A Theoretical and Empirical
Investigation, CEES Working Papers, December, University of
Leicester, Centre for European Economic Studies, Leicester.
Albu, L.-L. and Pelinescu, E. (2000): “Sustainability of Public Debt and Budget
Deficit”, Economic Transition in Romania – Past, Present and
Future (Eds.: Ruhl Christof, Daianu Daniel), The World Bank,
Romanian Center for Economic Policies, Bucharest,
Washington D.C., pp. 65-90.
Barro, R. (1988): “The Ricardian Approach to Budget Deficits”, NBER,
Working Paper, No. 2685.
Blanchard, O. J. and Fischer, S. (1993): Lectures on Macroeconomics, The
MIT Press, Cambridge, Massachusetts, London, England.
Carnot, N., Koen, V., and Tissot, B. (2005): Economic Forecasting, Palgrave
MacMillan.
Pindyck, R. S. and Rubinfeld, D. L. (1998): Econometric Models and Economic
Forecasting, Irvin McGraw-Hill, Boston, Massachusetts, New
York, San Francisco.
Stournaras, Y. (1990): “Public Sector Debt and Deficits in Greece: The
Experience of the 1980s and Future Prospects”, Revista di
Politica Economica, VII-VIII, Roma, July-August, pp. 405-440.
− Romanian Journal of Economic Forecasting – 3/2006
9
Institute of Economic Forecasting
Annex
6
4
2
0
30
10
20
20
10
30
0
α , i, r
60
3
4
50
2.5
3.5
3.5
5
3
4
5.5
4.5
40
2.5
3
4.5
5.5
3.5
5.5
5
4.5
4
3.5
4
30
5
4
4.5
5
20
4.5
5
6
5 5.5 6 6.5 7
10
5.5
5
4.5
0
16
18
20
22
24
α , i, r
10
Romanian Journal of Economic Forecasting – 3/2006 −
Trends in the Interest Rate – Investment – GDP Growth Relationship
20
10
0
10
30
20
10
0
10
20
30
0
p , i, r
60
10
15
20
0
5
40
10
15
5
5
0
10
20
5
0
5
0
10
20
15
10
30
40
50
p , i, r
− Romanian Journal of Economic Forecasting – 3/2006
11
Institute of Economic Forecasting
10
8
6
4
2
0
0
10
20
30
20
30
10
0
p,α ,r
24
1
1
0
4
5
2
7
6
22
3
5
1
5 5
0
5 4
20
7
8
5
6
2
5
5
18
3
4
16
8
9
0
10
7
20
6
5
30
4
3
40
2
50
p,α ,r
12
Romanian Journal of Economic Forecasting – 3/2006 −
Trends in the Interest Rate – Investment – GDP Growth Relationship
23
22
21
20
0
19
10
0
20
10
20
30
30
p , i, α
60
20.3
20.86
20.02
19.46
19.74
20.3
20.58
20.86 20.58
40
20.02
21.14
21.42
21.14
20.3
20.86
20.58
20.86
20.86
21.14
21.14
21.42
21.7
21.98
20
20.58
22.54 22.26 21.98 21.7 21.42 21.14 20.86
0
0
10
20
30
40
50
p , i, α
− Romanian Journal of Economic Forecasting – 3/2006
13