MODELLING DIFFUSION OF ENERGY TECHNOLOGIES:
A SYSTEM DYNAMICS APPROACH
A.K. VIJ
Systems Engg. & Computer Services Divn
Engineers India Limited
1, Bhikaji Cama Place
New Delhi 110 066
INDIA
PREM VRAT
Asian Institute of Technology
Bangkok, THAILAND
SUSHIL
Indian Institute of Technology
Hauz Khas, New Delhi, INDIA
ABSTRACT
This paper presents an approach to model the spread of new energy technologies
in. an economy using System Dynamics methodology. Empirical studies on the
process of technology diffusion lend evidence to sigmodial diffusion curves
e.g. Gompertz's curve or logistic curve. Two major approaches reported in the
literature concerning the process of technology diffusion are: ‘epidemic
approach' and 'probit approach'. The probit approach is closer to the reality
of economic world, and has been adopted in the present model. The principle
of the model is that the firms are not alike in their expectations of return
on investment or risk perceptions. Hence the initial adoption of a new
technology is low. But various exogenous and endogenous changes, e.g. price
rise of petroleum products, brings increasing number of threshold firms into
the category of actual adopters, which generates the diffusion path for the
new technology. The model considers internal rate of return as the basis of
such an adoption. ‘ ‘
Page 636
System Dynamics '91 Page 637
2.1
INTRODUCTION
Our world is currently experiencing a major transition to the new energy
era. "Each major uprising of the long wave has had its unique
technology. In energy we have had the wood-burning cycle, the coal-
burning cycle, and the oil-burning cycle. Each of these has reached a
crest, fallen to a minor usage, and been replaced by a new energy source
and new technology. We are now nearing the end of the oil cycle"
(Forrester 1979). Recent uncertainties in the oil supplies and
fluctuating oil prices in the world market and persistent dependence of
developing countries like India on oil imports for meeting their energy
requirements underline the need for new energy supply technologies that
are commercially viable alternatives to oil. Paradoxically, the spread
of mew energy technologies has not been fast enough. Inspite of
numerous energy options available today through R & D efforts the world
over, and massive organisational efforts in India like establishment of
a separate Department of Non-conventional Energy Sources in the Ministry
of Energy, dependence on oil has not reduced significantly. Oil demand,
which had slowed down for.a few years due to energy crisis of seventies,
picked up again in 1976-77 and increased substantially during the end of
the sixth plan-period (Government of India, Planning Commission 1985).
Hence, there is a need to study the factors which influence the
acceptance and usage of new technologies.
This paper presents an approach to model the spread of new energy
technologies in an economy using System Dynamics methodology. Some
basic concepts regarding the process of technology diffusion, as
described in literature are presented. Later, based on these concepts,
a system dynamics model for the diffusion of new technologies is
formulated and illustrated with an example.
TECHNOLOGY DIFFUSION
The term "technology diffusion" signifies the spread of new technology.
There are three phases in the process of technological change:
invention, innovation and diffusion. Using Freeman's . (1974)
definitions, invention is an idea, a sketch or a model for a’ new
improved device, product, process or system; innovation is associated
with their first commercial transaction. The theory of diffusion starts
at the point where the user has already innovated; it relates to the
process by which the innovation spreads across the market. Empirical
studies on the process of technology diffusion lend evidence to
sigmodial (S-shaped) diffusion curves, e.g. Gompertz's curve or logistic
curve. The well known Bass model of product life cycle also shows a S-
shaped curve.
The study of the diffusion of new technologies can be categorised into
three parts :
a) Intra-firm diffusion;
b) Inter-firm diffusion;
ec) Economy-wide diffusion.
Intra-Firm Diffusion
Intra-firm diffusion relates to the study of time-path of use of the new
technology within a firm from the introduction stage to a point where
the diffusion is complete. It is a micro-level approach. Some
Page 638 System Dynamics '91
2.2
2.3
important models of the intra-firm diffusion are: Mansfield's model
(1968), Stoneman's Bayesian learning model (1981), and empirical
studies, e.g. Mansfield's (1968) work on the spread of diesel
locomotives in US railroads, Romeo's (1975) work on the intra-firm
diffusion of numerically controlled (NC) machine tools, and Dixon's
(1980) work on Hybrid corn.
Inter-Firm Diffusion
The inter-firm diffusion relates to the diffusion of technology in
different firms constituting a sector. Two important approaches to the
study of inter-firm or intra-sectoral diffusion are described as
follows:
2.2.1 The Mansfield's Approach
The Mansfield's (1968) approach, has been labelled as
‘psychological approach' or as ‘epidemic approach'. This defines
diffusion in terms of the number of firms using the new
technology, rather than the intensity of use. This approach is
based on the assumption that the use of new technology will spread
as individuals make contact with one another. The diffusion curve
generated is logistic. However, the model assumes that the
profitability and the investment requirements remain unchanged
over time. These are not valid assumptions in real life.
2.2.2 The Probit Approach
Probit models are based on the assumption that the returns to an
innovation change over time. At each moment in time, firms hold
the stock of new technology which is appropriate to their
estimates of the returns from the use of the new technology, i.e.
the firms adopt a new technology if the expected returns from its
use exceed a critical value. However, all the firms are not alike
and their critical level of expected returns is described by a
distribution of values. There are two important models based on
probit approach. David's (1969) model considers firm size as the
critical parameter affecting the diffusion of new technology.
Davies's (1979) model considers expected pay-off period from the
use of the new technology as a critical factor for its adoption.
Probit approach is closer to the reality of the economic world,
and hence adopted for modelling the technology diffusion in the
present paper.
Economy-wide and International Diffusion
This category of technology diffusion covers the entire national and
international economy. This analysis related to major innovations that
have economy-wide applications. The epidemic and probit models as
discussed earlier, may be used for study of diffusion at the economy-
wide level. Some additional approaches are - the Schumpeter's approach
(1934); the vintage approach, (e.g. Salter 1966); and the stock
adjustment approach (e.g. Chow 1967; Nickell 1978).
System Dynamics '91 Page 639
3.
4.1
METHODOLOGICAL FRAMEWORK
The methodology proposed in the study consists of the following steps:
a. Qualitative assessment of the future technologies based on the
innovations which have already taken place or which are likely to
occur in the near future using the standard techniques of
technological forecasting, e.g. opinion survey,’ DELPHI, cross—
impact analysis, etc. Such a forecast may cover the inhouse R&D
efforts as well as the possibilities of technology transfer from
other advanced countries. The outcome of the forecast is a kit of
technologies which are the candidates of future adoption.
b. Detailed study of the cost structure, capital and labour
requirements and the commercial viability of each of. these
technologies.
Cc. Study of the structural details of the economy in terms of the
firm sizes, their expected rates of return, marginal cost of
capital, risk perceptions and ability to raise financial resources
for investment.
d. Assessment of the demand for each of these technologies based on
their expected diffusion rates. It is based on the implicit
assumption that a kit of all the new technologies is available for
adoption, but their diffusion depends on various exogenous and
endogenous factors which influence either the "stimulus variate"
or the "critical level" required to elicit their adoption.
e. Modern inter-dependent production heavily relies on the flow of
intermediate goods and services. Much of the technological change
that occurs in one sector, leads to new methods and specifications
in others. The authors have earlier developed an integrated
energy model combining Leontief's input-output approach with
System Dynamics (Vij et. al. 1989). The methodology proposed here
for modelling technology.diffusion may be used for updation of
technological coefficients in input-output tables. Revised
technological coefficients can be derived by augmenting the
existing input-output table using the cost data of new
technologies and their estimated final demand (Vij 1990).
MODEL DETAILS
The choice of a new technology may depend on a combination of factors
e.g. relative factor prices, capital requirements, foreign exchange
requirements, economic risk, environmental pollution, physical hazards,
etc. However, many of the decision criteria which enter into the choice
of a technology can be represented in terms of profitability, which is
measured in terms of the risk adjusted internal rate of return (IROR).
The proposed model is based on a single factor, i.e. the risk adjusted
TROR, which simplifies the modelling process.
Flow Diagram
The flow diagram of the proposed model is shown in the Figure 1. There
are two level variables in the model, i.e. User Fraction (UF) and
Financial Risk (RISK). UF is the exponentially smoothed average of the
Page 640 System Dynamics '91
User Fraction Increase Rate (UFIR). UFIR at any point of time depends
on two auxiliary variables, i.e. Risk Adjusted Rate of Return (AROR) and
firms Distribution as per Cost of Capital (DCK). AROR depends on
Internal Rate of Return (IROR) of the new technology adjusted for the
Financial Risk (RISK). When the technology is introduced for the first
time, uncertainty associated with it is high and so is the risk.
However, with the passage of time, as more and more firms adopt the new
technology, the risk is reduced. Risk Change Rate (RCR) is represented
by an exponentially decreasing curve with a time constant LEMDA. IROR
depends on the Annual Cash Flow from the new technology (ACF), Initial
Capital required (IK) and Capital Life (KL). ACF is affected by the
SAVING per unit of output and the Quantum of Production (OUTPUT). The
new energy technologies result in savings in the energy consumer
sectors. SAVING depends on the difference in production cost between
the new and the old technology. It is hypothesised that the prices: of
non-replenishable energy resources such as the fossil fuels are likely
to increase with the passage of time due to their scarcity and growing
demand.
The model is driven by the energy price changes, which in turn influence
the potential savings through the new energy conservation technologies.
These savings influence the expected cash flow from the introduction of
the new technology and the resulting IROR. The perceived risk
associated with the new technology decreases with the passage of time.
Hence, the firms which are initially less inclined to adopt the new
technology later accept it.
RATE OF
RETURN
INTERNAL
RATE OF
RETURN
WME
CONSTANT
FIGURE 1 FLOW DIAGRAM OF TECHNOLOGY
DIFFUSION MODEL BASED ON
PROBIT APPROACH
System Dynamics '91 Page 641
4.2
System Equations
Based on the flow diagram shown in the previous section, system
equations for the model are given below:
L UF.K
N UF
R UFIR.KL
A AROR.K
A ARORC.K
A DCK.K
= UF.J + DIE (UFIR.JK) (1)
= 0.0 (2)
= (ARORC.K/AROR.K)* DCK.K (3)
= SROR.K - RISK.K (4)
= AROR.K — AROR.J (5)
= 0.398862 * (EXP ( -Z.K * Z.K)/2) (6)
= (CCOK.K-MEAN) /SD (7)
= AROR.K (8)
= Constant (9)
= Constant (10)
User fraction (Dimensionless)
User fraction increase rate (Fraction per year)
Sectoral rate of return from the new technology (Fraction per
year)
Financial risk (Fraction per year)
Risk adjusted rate of return (Fraction per year)
Change rate of risk adjusted rate of return (Fraction per year
per year)
Distribution of firms as per cost of capital (Dimensionless)
Normal frequency distribution variate (Dimensionless)
Critical cost of capital (Fraction per year)
Mean of the normal frequency distribution of firms (Fraction
per year)
Standard deviation of the normal frequency distribution of
firms (Fraction per year).
Sectoral rate of return is calculated as a function based on the annual
cash flow, initial capital and capital life.
A SROR.K
A ACE.K
Cc OUTPUT
where
SROR
ACF
IKAP
= TROR (ACF.K, IKAP, KL) (11)
= SAVING.K * OUTPUT (12)
= Constant (13)
= Sectoral rate of return (Fraction per year)
-— Annual cash flow (Monetary units per year)
_- Initial capital (Monetary units)
Page 642 System Dynamics '91
KL - Capital Life (years)
SAVING _ Saving per unit of output (Fraction)
OUTPUT -— Rated output from new technology (Monetary units per
year)
Savings per unit depend on the reduction of cost of inputs per unit from
the new technology as compared to the old technology.
A SAVING.K = (CSTEO.K - CSTEN.K) (14)
A CSTEO.K = (KPEO*PIPE.K) + (KNPEO*PINPE.K) (15)
A CSTEN.K = (KPEN*PIPE.K) + (KNPEN*PINPE.K) (16)
where
CSTEN _ Cost of energy per unit output based on new technology
(Fraction)
CSTEO -_ Cost of energy per unit output based on old technology
(Fraction)
KPEO _ Technological coefficient of petroleum energy input
based on old technology (Dimensionless)
KPEN _ Technological coefficient of petroleum energy input
based on new technology (Dimensionless)
KNPEO a Technological coefficient of non-petroleum energy input
based on old technology (Dimensionless)
KNPEN - Technological coefficient of non-petroleum energy input
based on new technology (Dimensionless)
PIPE — Price index of petroleum energy (Dimensionless)
PINPE _ Price index of non-petroleum energy (Dimensionless)
L RISK.K = RISK.J + DT (RCR.JK) (17)
R RCR.K = RISK.K * LEMDA (18)
C LEMDA = Constant (negative) (19)
where
RISK -- Financial risk (Fraction per year)
RCR -—- Risk change rate (Fraction per year per year)
LEMDA -- Time Constant
ILLUSTRATIVE EXAMPLE
In the following paragraphs, the methodology has been explained through
an illustrative example based on hypothetical data of a new technology
for the industrial sector which leads to substitution of petroleum
energy with power.
The new technology is initially dormant, i.e. the entire final output
from the industrial sector comes from the old technology, and the user
fraction (UF) of new technology is initially zero. Final demand for the
new technology depends on its diffusion process. The following techno-
economic parameters are assumed for the new technology:
System. Dynamics '91 Page 643
USER FRACTION
Initial Capital (IKAP)
2000 (monetary units)
Capital Life (KL)
10 (years)
Rated Output (OUTPUT) 50000 (monetary units)
Technological coefficients of energy inputs for unit output of industry
in monetary terms are as follows:
Old Technology New Technology
Petroleum 0.010623 0.0
Power 0.019654 0.030277
Firms in the industrial sector are assumed to follow a_ normal
distribution pattern in terms of the cost of capital with MEAN 0.10
and standard deviation 0.06.
The dynamics in the model is generated through an exponential rise in
the petroleum prices, which makes the dormant technology attractive by
leading to savings in the relative cost of energy inputs. The time
constant of exponential increase in the petroleum sector prices is
assumed to be 0.10. >
a7
0.24
3 10 "
FIGURE 2 DIFFUSION CURVE OF NEW TECHNOLGOY
Page 644 System Dynamics '91
The diffusion curve generated with these parameters is shown in Figure
2. It shows that the new technology remains dormant for six years,
after which it picks up because its IROR becomes high enough for the
firms to adopt it. As IROR increases, more and more firms, even with
higher cost of capital start adopting it. The demand reaches a near
saturation level in the tenth year.
INTEGRATION WITH MULTISECTOR MODEL
The technology diffusion model described in the earlier sections is a
submodel of an integrated multisector energy model. The integrated
model combines Leontief's input-output approach in a physical systems
theory framework with System Dynamics (Vij 1990). In the integrated
model, the technological coefficients are updated every year depending
on the. absorption of new technology. Further, the savings are
considered on the basis of. difference in sectorial output costs with the
new and the old technologies. These modifications result in
establishing a feedback relationship between user fraction (UF) and
sectorial internal rate of return (SROR).
CONCLUDING REMARKS
In this paper, the issues related to the representation of technological
change in a multisector energy model have been discussed. Details of
the flow diagrams and system equations for the technology diffusion
model based on the probit approach have been explained. The technology
diffusion model is based on the criteria of risk adjusted rate of return
(IROR) . S
An illustrative example based on the hypothetical data of a new inter-
fuel substitution technology for the industrial sector has been
described. The approach can be incorporated with multisector models for
updation of technological coefficients.
System Dynamics '91 Page 645
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Davies, S., 1979, The Diffusion of Process Innovations, Cambridge University
Press.
Dixon, R., 1980, Hybrid Corn Revisited, Econometrica, 48, 1451-62.
Freeman, C., 1974, The Economics of Industrial Innovation, Penguin,
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Forrester, J.W., 1979, An Alternative Approach to Economic Policy:
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