Interest rate – Investment – GDP growth relationship:
theoretical and empirical investigation
Albu Lucian-Liviu
Institute for Economic Forecasting, Bucharest
General Director
albul@ipe.ro
Ghizdeanu Ion
Institute for Economic Forecasting, Bucharest and
National Commission of Prognosis, Bucharest
President
ion.ghizdeanu@cnp.ro
Stanica Cristian
Institute for Economic Forecasting, Bucharest and
National Institute of Statistics, Bucharest
Vice-President
stanica_cris@yahoo.com
Paper prepared for the 39th Conference on Medium-Term Economic Assessment
“THE FUTURE OF EUROPE IN A WORLD OF UNCERTAINTIES”
Romania, Iaşi, September 25-27th, 2008
Abstract
In specialised literature interest and investment are among the central variables
influencing the growth rate. Due to the complexity empirically demonstrated by the
interest rate – investment – GDP growth relationship when we try to analyse or to
forecast the economic dynamics, last decades a growing concern over the modelling
this relationship has increased attention among officials, politicians, and economists.
There are several reasons why they should be concerned, as follows: under new trends
in economy caused by the impact of globalisation and expanding of the “new
economy”, macroeconomics policy could be based on inappropriate baseline
projections or benchmark values for principal indicators; a growing tendency of
foreign investment and capital and labour migration having major impact on main
macroeconomic variables; integrating process and convergence, in case of new EU
members; etc. Based on statistical data for last years, we try to build a set of partial
models in order to investigate the interest rate - investment - growth rate relationship
in case of EU members and in the same time to verify some hypotheses usually in
standard economic literature. Applying such simple models derived from standard
ones in our experiment we estimated their parameters in case of EU countries. The
main two partial models are referring to the impact of investment on GDP growth rate
and respectively to the relation between interest rate and investment. Moreover, an
equation including inflation dynamics was taken into account. Finally, the derived
global model demonstrates complex dynamics, moreover permitting to compute socalled natural rate of interest and other key-parameters for macroeconomic decisions.
JEL Classification: C51, E22, E43, E27, O52
Keywords: Investment Rate, GDP Growth Rate, Interest rate, Depreciation Rate,
Contour Plot
1
Introduction
Among macroeconomic correlations, interest rate – investment – GDP growth
relationship places a fundamental role. In the general process of economic
development and last time in the context of convergence in EU this relationship
becomes to be more studied by economists and policy makers. As illustration, based
on empirical data for 2007, a 3D representation and its attached so-called geodesic
map or contour plot for the correlation interest rate (i) – investment ratio in GDP () –
annual GDP growth rate (r), in case of EU-27, are shown in Figure 1. As general rule,
we can see that GDP growth rate is higher (red colours) for smaller values of interest
rate and respectively for higher values of investment ratio. Contrary, smaller growth
rate (blue colours) corresponds to higher values of interest rate and respectively to
smaller values of investment rate. Indeed, moreover inflation must be considered
together with other macroeconomic variables. In such way, we shall take into account
within a dynamic model an equation including inflation dynamics. Further, the model,
demonstrating complex dynamics, could supply solution to estimate natural rate of
interest and other essential parameters for macroeconomic decisions.
24
5.078
5.078
5.078
4.69 5.854
5.466
22
5.854
6.242
3.138
5.466
5.078
5.078
6
5.078
20
4.69
4.302
4
0
2
10
3.526
2.75
5.466 4.302
2.362
5.466
4.69
5.078 3.526
3.914
4.69
5.078 3.138
2.75
3.914
18
4.302
0
20
3.526
10
20
30
30
16
4.69
0
i,  , r
10
4.302
20
3.914 3.526 3.138
30
2.75 2.75
40
50
i,  , r
Figure 1.
The Model
Coming from standard literature we used the following three basic equations:
r ()
=
a* + b
(1)
 (i)
=
c / (d + i)
(2)
i (p)
=
e*p + f
(3)
2
where r is GDP growth rate,  – investment rate (in GDP), i – interest rate, p –
inflation, a, b, c, d, e, and f – parameters (estimated econometrically).
First equation tries to capture the impact of investment on GDP growth. Second
equation demonstrates an inverse relation between interest rate and investment. Third
equation takes into account a direct relation between 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)
 (p) =
c / [d + (e*p + f)]
(5)
i ()
(c / ) – d
(6)
=
Moreover, we can express the empirical inflation – GDP growth rate relation as
follows:
r (p)
=
b + a*c / (d + e*p + f)
(7)
Estimations
We tried to estimate the parameters of equations in case of the Romanian economy
after 1989. The output of our experiment on the period 2000-2005 is shown in Figures
2-4, where: variables on ordinate axis and inflation are in per cent; years are noted
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 respectively upper
limit (95% Confidence Intervals).
11
11
10
10
9
9
rE(  )
r
t
rE(  )
8
r
t
7
rE1( i )
5
5
rE2( p ) 4
rE2( p ) 4
r_L
t
r_L
t
3
r_U
t
1
1
0
0
1
1
2
3
2
2
r_U
t
2
1
2
3
4
5
6
8
18
28
p
t
Figure 2.
3
7
6
6
rE1( i )
8
t
38
48
24
24
23
23
E( i )

t
E( i )

t
22
22
E1( p ) 21
E1( p ) 21
_L
t
_L
t
_U
t
20
_U
t
19
18
20
19
1
2
3
4
5
18
6
8
18
t
28
p
38
48
38
48
t
Figure 3.
65
60
51
55
iE( p )
iE( p )
i
i
t
45
42
iE1(  )
iE1(  )
i_L
t
t
i_L
t
35
33
i_U
t
i_U
t
24
25
15
15
1
2
3
4
5
6
8
18
28
p
t
t
Figure 4.
Also, in Appendix are presented some 3D graphic representations for variables and
their attached Contour Plots corresponding to real annual registered data in period
2000-2005. Based on historical data, among other conclusions, we can 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 noted (, i, r).
From the contour map (p, i, r) we can see the line 5 (5% GDP growth rate) that
follows very close the diagonal line of plan p-i, which can be interpreted as a natural
rate of GDP growth rate. Similar conclusion, but for investment rate, could be derived
from contour map (p, i, ), where as trajectory for its natural rate could be considered
the top line following very close the diagonal line of plan p-i. Contour map (p, , r)
demonstrates the negative impact of inflation on GDP growth.
4
Simulation
Based on relation (1) the simulation of model demonstrated a critical value of 13.2%
for investment rate (cr1). For <13.2% the GDP growth rate will be negative.
Moreover, in the extreme case of no investment (=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 that in case of no investment the whole
stock of fixed capital will be consumed only in 12 years (must be noted that this
shows a special situation for the capital stock in Romania: many productive capacities
are still old, physic and/or moral 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 permitted us
to compute the potential level for GDP growth rate of about 7.6% – a theoretical level
computed as value of GDP growth rate at the point cr2=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 about 7% – also a theoretical level computed as value of
GDP growth rate at the point 2=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 whole economic system, like in case of studying the sustainability of
public debt and deficits (Albu and Pelinescu, 2000). Some results of simulation of the
two partial models represented by equations (1) and (2) are shown in Figures 5 and 6.
60
60
cr1
2
cr1 2
40
40
rE(  )
iE1(  )
iE( p )
iE1(  )
20
20
iE1( 2 )
0
0
4
8
12 16 20 24 28 32 36 40

iE1( 2 )
0
0
8 16 24 32 40 48 56 64 72 80
p, 
Figure 5.
5
iE( 0 )
rE( cr1 )
26
cr1
cr2
2
24
2
10
rE1( 0 )
rE2( 0 )
rE(  )
E( i )
22
rE1( i )
E1( p )
rE2( p )
20
0
b
18
16
0
20
40
60
80
100
10
0
6
12 18 24 30 36 42 48 54 60
, i , p
i,p
Figure 6.
Conclusions
Based on simulation model some significant macroeconomic indicators can be
estimated. Their values vary with the development stage in which countries are
located, mainly with GDP per capita level. For instance, in following Table there are
compared values of some essential parameters of the model for different EU
countries, estimated for the period 1995-2007:
Countries
a
Germany
Estonia
Austria
Portugal
Romania
6
0.221
0.574
0.233
0.406
0.702
Parameters
b
cr1
(depreciation
rate of capital)
-2.8
12.8
-9.4
16.4
-2.7
11.5
-7.3
18.0
-12.0
17.1
k=K/Y
(capital
coefficient)
4.526
1.742
4.284
2.465
1.424
Selected bibliography
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.
7
Appendix
60
2.5
3
4
3.5
3.5
2.5
3
4
5.5
4.5
40
2.5
3
5 4.5
5.5
3.5
5.5
5.5
3.5
6
4
4.5
5
4
5
4
4
4.5
5
20
2
4.5
6
0
30
5 5.5 6 6.5 7
10
20
5
5.5
20
10
5
30
0
4.5
0
16
 , i, r
18
20
22
24
 , i, r
60
10
15
20
20
0
5
40
10
10
15
5
0
0
5
10
20
10
30
20
10
5
0
30
20
10
0
p , i, r
8
0
5
15
10
0
p , i, r
10
20
30
40
50
60
20.3
20.02
20.3
20.58
20.86
19.46
19.74
20.86 20.58
40
20.02
23
21.14
20.86
20.58
20.86 21.14 20.86
21.14
22
21
20
0
21.14
21.42
20
0
20
21.98
10
20
30
21.42
21.7
19
10
20.3
20.58
22.54 22.26 21.98 21.7 21.42 21.14 20.86
30
0
0
p , i, 
10
20
30
40
50
p , i, 
24
1
5
4
0
1
2
6
3
22
5
10
8
6
4
2
0
5 5
20
7
8
6
5
1
4
0
2
5
5
3
5
0
18
4
10
20
30
20
30
10
16
8
9
7
6
5
4
3
2
0
0
p, ,r
9
p, ,r
10
20
30
40
50