A procedure for adapting technological forecasting models

TECHNOLOGICAL

FORECASTING

AND SOCIAL

CHANGE

7,99-106

99

(1975)

A Procedure for Adapting Technological Forecasting Models M. NAWAZ SHARIF and GHAZI ANWAR UDDIN

ABSTRACT A simple procedure is presented for adapting available mathematical models for forecasting technological substitution. The procedure takes into consideration the strengths and weaknesses of the available models and the environmental interactions to identify a set of feasible alternative forecasts, from which a selection is to be made by the decision-maker based on judgement.

Introduction Many forecasting techniques have been developed in recent years to deal with the increasing variety and complexity of technological forecasting problems [2, 4, 81. Each has its special use. For example, Blackman [3] , Fisher and Pry [.5] , and Floyd [6] have presented some mathematical models to describe the rate at which market substitution occurs as a result of technological change. All of them have shown remarkable success of their models when applied to specific cases. However, as expected, none of these models can be used universally. Therefore, an analyst faced with the problem of forecasting the market share of a product, not covered in one of those studies, will normally have to select a model suitable for his particular application. The selection, quite obviously, will depend on many factors--the context of the forecast, the assumptions underlying each available model, the relevance and availability of data, etc. Unfortunately, in very rare cases an available model can readily meet the requirements of the analyst. The purpose of this paper is to show how some of the available mathematical models for forecasting technological substitution can be adapted in determining the prospect of jute fiber against its synthetic substitutes in the world market. Available Models For forecasting the market share of synthetic mathematical models can be used: 1. Blackman’s Model [3] The model equation is given by

f

lnF_/

substitutes

against jute, the following

= C, f C,t,

M. NAWAZ SHARIF is a faculty member in the Industrial Development and Management Division of the Asian Institute of Technology, Bangkok, Thailand. GHAZI ANWAR UDDIN is a graduate student in the Industrial Development and Management Division of the Asian Institute of Technology, Bangkok, Thailand. 0 American

Elsevier Publishing

Company,

Inc., 1975

M. NAWAZ SHARIF and GHAZI ANWAR UDDIN

100

where F = maximum synthetic substitutes 2. Fisher’s Model The model equation

possible market share of synthetic substitutes; over time; t = time; and, Cr , C, = constants. [S] is given by

f = market share of

6 =exp [2a(t-to)] where f = market share of synthetic substitutes over time; t = time; to = time at which substitution is half complete; and, 2a = slope of the regression line. 3. Floyd’s Model [6] The model equation is given by F+ln

F-f

f -=c, F-f

+c2t,

where F = maximum possible market share of the synthetic substitutes; f = market share of synthetic substitutes over time; t = time; and, Cr , C2 = constants. The basic difference between Blackman’s and Floyd’s models on one side and the Fisher’s model on the other is that the Fisher’s model assumes “if a substitution has progressed as far as a few percent, it will proceed to completion”, whereas the other models assume that there is a maximum limit upto which substitution is possible. However, it can be observed that the Fisher’s model is a very special case of Blackman’s model where the value of F = 1 .O. Another observation could be made about these substitution models. Blackman’s and Fisher’s models are essentially Pearl curve [8b] which is expressed as Y=L/[l

+A exp(-Bt)]

where L = the upper limit of the growth curve; A = the position of the mid-point of the curve along the time axis; B = the steepness of the curve; and, t = time. Martin0 [8b] has found out that the error in either A or B is directly proportional to the error in the estimate of L; and the error in either A or B or in both could be substantial for a small change in L. This means that an error in the estimation of L could lead to either over-estimated or under-estimated forecast. Forecasting Market Share The two major synthetics which compete directly with jute fiber products are Polypropylene (PP) and high density Polyethylene (PE). Whereas PP competes with jute backing materials and jute bags, PE is used to manufacture jute cloth [l] . The use of PE is much less (approximately 2% to 3% [7] ) m . comparison to the use of PP as synthetic substitutes. Because of the smaller percentage and also due to the lack of availability of data, PE is not considered for the analysis presented in this paper. PP appeared in the world market about 1960. Its production since then increased at a rate of 46.73% whereas world jute production increased at a rate of only 2.23% [l] . The world production figures for PP and Jute are shown in Table 1. In order to apply the three models presented above to the data given in Table 1, one must determine the value ofF. A study made by F.A.O. has indicated that total substitution of jute by synthetics is not possible, though the synthetic substitutes have threatened the jute products to a great

ADAFWNG

FORECASTING

101

MODELS TABLE World Production Production

Year 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970

:) 25 55 95 155 220 305 460 625 860b 1,1126 1,370b

1

of PP and Jute”

(in 1000 metric

tons)

JUTE

TOTAL

Fraction of PP

(B)

(A +B)

AI(A+B)

2,563 2,961 3,214 3,137 3,317 3,782 3,548 3,569 3,591 3,124 3,543

2,588 3,022 3,369 3,292 3,537 4,087 4,008 4,194 4,451 4,236 4,913

0.0096 0.0182 0.0282 0.0471 0.0622 0.0746 0.1141 0.1490 0.1932 0.2625 0.2788

‘Source: Ref. [7,9, lo]. bEstimated values see Ref.

[1]

extent [7]. For example, synthetics have threatened the jute bags and the primary carpet backing markets. But due to some superior and advantageous quality of jute, the secondary carpet backing market has been least threatened by the synthetic substitutes. Also, the study made by the F.A.O. indicated a future increase in the consumption of secondary carpet backings whose market could be captured by jute easily. Though the complete substitution of jute is not possible, as it appears, it is difficult to predict the future maximum market share of synthetics. Hence, with the help of Blackman’s model a set of curves Al, Bl , C 1, Dl, El are drawn, as shown in Fig. 1, with the values of F, the maximum possible market share of synthetic substitutes, as 1.0,0.9, 0.8, 0.7 and 0.6, respectively. The values of the constants Cr and C, for different values of F, determined by the method of least square, are shown in Table 2. From the curves in Fig. 1, the following observations are made: (1) Curve Bl shows that it takes about 24 years from 1960 to capture 89% of the market in 1984. (2) Curve Cl shows that it takes about 22 years from 1960 to capture 79% of the market in 1982. (3) Curve Dl shows that it takes about 21 years from 1960 to capture 69% of the market in 1981. (4) Curve El shows that it takes about 20 years from 1960 to capture 59% of the market in 1980. Based on the above observations, the time scale for the forecasts made by the Blackman’s model for different values of F appears to be less sensitive to the value of F chosen. If the value of F is changed from 0.6 to 0.7, it takes only about one year to capture the additional 10% of the market share. Similar is the case when F is changed from 0.7 to 0.8, and so on. Because of this lack of very significant difference and due to the fact that it is next to impossible to predict the most likely value of F (without which there could be substantial error in the forecast), one may be inclined to take the value of F= 1.0.

102

M. NAWAZ SHARIF TABLE

c,

1.0 0.9 0.8 0.7 0.6

UDDIN

F

Correlation coefficient

C2

-4.6823 4.5871 A.4827 -4.3681 -4.2424

ANWAR

2

Values of Constants for Different using Blackman’s Model

F

and GHAZI

0.3619 0.3663 0.3719 0.3796 0.3909

0.9912 0.9918 0.9924 0.9933 0.9943

Fisher’s model is a special case of Blackman’s model with the value of F = 1.O. This is represented in Fig. 2 as curve A2, which is congruent to curve Al in Fig. 1. The model equation with data from Table 1 has been determined as

f

1

[ 1-f

= exp [0.3619(t-t,,)]

It can be observed from the Fisher’s model forecast curve that the “take-over” time (the time betweenf= 0.1 andf= 0.9) is 12 years, from 1966 to 1978. It is quite unlikely, as it appears, that 90% of the market share will be captured by the synthetic substitutes by 1978. This is supported by the fact that the recent sharp increase in crude oil price will increase the cost of synthetic substitutes as crude oil is the basic raw material for such products. The increase in price of crude oil may, thus, reduce the growth rate of synthetic substitutes significantly. Therefore, Fisher’s model forecast needs some modification. Furthermore, it has been observed that with small quantity of data Fisher’s model gives an over-estimated forecast [I]. For our case, we have less data which is likely to give an over-estimated forecast. The Floyd’s model equation, with data in Table 1, comes out as LOO

70

-

60

-

10

01960

I 1968

I 1976

I

I

I I I

1

1 1984

I 1992

Years

FIG. 1. Blackman’s model forecast.

I 2000

2[

ADAPTING FORECASTING

1960

103

MODELS

1984

1976

1968

1992

2000

Yea-s

FIG. 2. Fisher’s and Floyd’s model forecasts.

L

t In f

1-f

= -3.7704

1-f

+ 0.4t

taking F = 1 .O. This equation when plotted gives a curve F2 as shown in Fig. 2. The curve shows that 90% of the market share of the synthetic substitutes will be attained by 1999, apparently a more reasonable result than obtained by Fisher’s model forecait. However, Blackman pointed out that Floyd’s model predictation of technological development is slower than would be predicted by a logistic curve [3]. In the earlier period of development of a technology, Floyd’s model gives a reasonable result, but the model predicts a slower rate of development as the upper performance limit is reached. Based on the suggestion of Blackman, though Floyd’s model forecast may not be acceptable to us, it gives a strong support for the need for modification of Fisher’s model forecast. Improving the Forecast The fact that small number of data in Fisher’s model gives an over-estimated forecast in the upper range whereas Floyd’s model gives an underestimation for the same range suggests that the actual forecast will lie in between these two extremes. Thus, an improvement over Fisher’s model forecast may be achieved by assuming that the rate of growth of substitution in the Fisher’s model will decrease after a certain point. Now the question is at what rate and from which point it will decrease? Since the historical data is available up to 1970 and Fisher’s model fits these data very well, we can observe from Fig. 2 that the change in the growth rate can be after the 35% point. As we do not know the deereased growth rate, a set of curves with different slopes and break off points are drawn as shown in Fig. 3. Curve A3 is the original Fisher’s model forecast (with slope 0 = 0.3619). Curves B3 and C3 have a slope of 0.50 and 0.30, respectively and are brzmching off from the curve A3 after PP has captured 60% of the market share. Curves l3 md E3 are similar curves but branching off from the 40% point mstead of the 60% point. The curve F3 corresponds to Floyd’s model forecast. It may be noted here that many other

104

M. NAWAZ SHARIF and GHAZI ANWAR UDDIN

90

-

2m

80

-

:: g E "

70

-

60

-

50

-

40

-

: u 0 fz R

A3: E3: C3: D3: E3: F3:

Fisher's model with Curve with slope = Curve with slope = Curve with slope = Curve with slope = Floyd's model

slope 0.55; 0.36; 0.56; 0.36;

I

I

I

I

I

I

1968

1976

1984

1992

2000

2008

5 : z

0 1960

B = 0.3619 break at 60% break at 60% break at 40% break at 40%

Years

FIG. 3. Curves with different

slopes at different

break points.

curves with different slopes at different break points can be extreme curves A3 and F3, depending upon the judgement of the Considering the curves shown in Figs. 1,2, and 3 the problem most likely forecast. In order to do that one can use the following

plotted within the two analyst. now is to determine the reasoning:

(1) Although many curves shown in Fig. 3 fall within the two extremes as identified in Fig. 2, one may decide to pick the one which is close to midway between the two extremes. (2) When we compare the two sets of curves with 0.50 and 0.30 as slopes, curves with slope 0.30 appear to give moderate results. (3) The environmental conditions may dictate the likely location of the breaking point of the original rate of growth of PP’s market share. The sudden increase in the crude oil price in 1973 may be considered as one such condition. This year corresponds to the 60% point. Based on the foregoing, our selection is that curve which has a slope of 0.30 after 60% of the market share has been reached. This curve is shown as B4 in Fig. 4. The 95% confidence interval is also shown in Fig. 4. Our forecasted line B4 shows that by 1989 the synthetic substitute will capture 90% of the world jute market. Summary of the Procedure The procedure used in this paper for adapting the available mathematical forecasting technological substitution can be summarized as follows:

models for

(1) Use Blackman’s model to forecast the market share if the value of maximum possible market share can be reasonably ascertained. Otherwise, go to step 2. If Blackman’s model is used, plot a set of curves by taking a range of values instead of just one value for the anticipated maximum possible market share. Go to step 4. (2) Use Fisher’s model and Floyd’s model (with F = 1.O) to obtain a range of feasible forecasts. (3) Plot a set of curves, within the region obtained in step 2, using Fisher’s curve as

105

ADAPTING FORECASTING MODELS

80 t

60 t 50 40 30 20 10

/9S%

1

ConfidenceYIntervalLine ! I

I

0

1960

1968

,

I

1992

2000

1

1976

1984

-I

2008

Years

.

FIG. 4. Adapted model forecast with confidence interval. the stem and branching of substitution. (4) Identify the environmental

off at different

the most factors

likely

points

forecast

With decreased

based

that may influence

values of the rate of growth

on judgement

the rate of growth

With due consideration of substitution

to

to change

over time. References 1. Anwar Uddin, Ghazi, An Investigation into the Prospect of Jute Manufacturing Industry of Bangladesh, Master of Engineering Thesis, Industrial Development and Management Division, Asian Institute of Technology, Bangkok, 1974. 2. Ayres, R. V., Technological Forecasting, McGraw-Hill, New York, 1969. 3a. Blackman, A. Wade, A Mathematical Model for Trend Forecast, Technol. Forecast. Sot. Change 3,441-452 (1972). 3b. Blackman, A. Wade, New Market Dynamics of Technological Substitutions, Technol. Forecast. Sot. Change 6,41-63 (1974). 4. Cetron, M. J., Technological Forecasting, Gordon and Breach, New York, 1969. 5. Fisher, J. C., and Pry, R. H., A Simple Substitution Model of Technological Change, Technol. Forecast. Sot. Change 3,75-88 (1971). 6. Floyd, A., Trend Forecasting: A Methodology for Figure of Merit, in First Annual Technology and Management Conference (J. Bright, Ed.), Prentice-Hall, New Jersey, 1968. 7. Impact of Synthetics on Jute and Allied Fibres, Commodity Bulletin Series, No. 46, F.A.O., UN, Rome, 1969. 8a. Martino, J. P., Technological Forecasting for Decisionmaking, American Elsevier Publishing Co., New York, 1972. 8b. Martino, J. P., The Effect of Errors in Estimating the Upper Limit of a Growth Curve, Technol. Forecast. Sot. Change 4,77-84 (1972). 9. Monthly Bulletin of Economics and Statistics 22 (March, 1973), F.A.O., Rome. 10. Statistical Year Book of Asia and the Far East (I 9 71), ECAFE, Bangkok, 197 1. Received April 29, I9 74; revised June 19, I9 74