The futility of forecasting

0024+301/84 $3.00 + .OO Pergamon Press Ltd.

Long Range Planning, Vol. 17, No. 1, pp. 65 to 72, 1984 Printed

in Great

Britain

The Futility Reed Moyer,

University

of Forecasting

of California,

is an integral part of planning,

Berkeley

but

te forecasts.

Samuel Goldwyn allegedly said : ‘Never prophesy, particularly about the future’. A review of long-run forecasters’ performance records shows that he may have had a point. Evidence of forecast performance, analysis of factors contributing to forecast errors, and suggestions for coping with forecast uncertainty form the agenda for this article. Assume that you, as a forecaster, the following : In 1845, the 1855 California

Forecasting population.

In 1945, the demand

in 1950 for pleasure

In 1955, the demand 1970.

for hotel accommodation capacity

(e.g. 1855 Calif ornia population) the possibility of large error is obvious. Some of these forecasts suffered from the intervention of unforeseen events such as the discovery of gold in California. Others fell victim to the effects of depression and inflation, both outside the forecaster’s control (outside his ken?). A combination of social and political forces and myopia might have contributed to errors in the other forecasts. One common element exists in the first seven cases: it was easier to look back and see where events had led than to accurately forecast the future. (I include the eighth as an example of a current forecast likely to be off the mark.) No reasonable observer expects completely accurate long-range forecasts. But their importance in sound business planning requires far better results than many have shown.

had had to predict

In mid-1929, the 1932 level of common stock prices on the New York Stock Exchange.

In 1955, the installed plants in 1965.

of nuclear

aircraft. in

power

for U.S. crude

oil

Performance

Obtaining a representative sample of long-range forecasts to test their accuracy is difficult. However, as an alternative, we have available William Ascher’s compilation of results of over 165 forecasts in six subject areas. Table 1 summarizes his findings. Let’s study them in detail, starting first with population and economic forecasts that form the basis for many other detailed long-range forecasts. Poylrlatiou

In 1972, the price per barrel imports in 1975.

65

Forecasts

some instances, wildly inaccurate forecasts of the foregoing phenomena exist; where none is available

Population forecasts assume special importance since a number of other projections arc cast in per capita terms. The data in Table 1 on population forecasts reveal an apparently high level of accuracy that is misleading. Median forecast errors for the thirty one 5-, lo- and ‘O-year forecasts were 2.5,6*2 and 8.7 per cent respectively.’ Since over 80 per cent of the population forecasted 10 years hence are alive when a forecast is made, an 11.5 per cent forecast error (see Table 1, IO-year results) is substantial.

Professor Reed Moyer is at the Graduate School of Business Administration, University of California, 350 Barrows Hall, Berkeley, CA 94720, U.S.A. There he teaches marketing and international business. Prior to teaching he was Vice President and a Dlrector of a coal mining company.

Accuracy of population forecasts depending on the year when completed. A gloomy forecast at Great Depression (1930) predicted

In December, 1978 the world price per ounce for gold in January, 1980. On the latter date, the gold price in mid-1982. In 1982, the demand facilities.

in 1995 for retail banking

has varied greatly the forecast was the depths of the a decline in U.S.

66 Table

Long

Range

1. Long-run

Planning

forecasting

Object of forecast Nuclear power installed Nuclear power installed Nuclear power installed Electricity consumption Electricity consumption Electricity consumption General aviation aircraft General aviation aircraft General aviation aircraft General aviation aircraft General aviation aircraft General aviation aircraft Commercial airline travel passenger miles) Commercial airline travel Commercial airline travel Commercial airline travel Commercial airline travel Commercial airline travel Computer capability Population Population Population

capacity capacity capacity

sales sales sales sales sales sales (revenue

Vol. 17

February

1984

performance No. of forecasts

Date of forecast

Period of forecast

Margin of error (arithmetic mean)

22 13 11 28 23 16 3 3 2 1 IO 3 n.a.

1954-I 970 Pre-1960 Post- 1960 1953-l 970 1952-l 965 1952-l 960 1944 1945 1947 1947 1960-l 970 1960-l 970 Post-l 953

5 years 10 years 10 years 5 years 10 years 15 years 5 years 10 years 8 years 13 years 5 years 10 years 5 years

n.a. 4 4 2 5 5 9 12 10

Post-l 1972 1973 1974 1975 1966-l 1928-l 1928-l 1928-I

10 years 8 years 7 years 6 years 5 years 7-9 years 5 years 10 years 20 years

’ Median. 2Factor of error. Source: William Ascher. Forecasting: An Appraisal for Policy-Makers

population to 100m by the end of the 20th century.2 a world A U.N. report in 1970 predicted population in the year 2000 of 7.5bn; 5 years later the estimate was reduced to 5.6bn!3 Forecasts including the period of the post-World War II baby boom were especially flawed. A 20-year forecast in 1938 erred by 17 per cent. One made 13 years earlier, however, that did not have to deal with that baby surge was only 3.4 per cent off target.

Success rates for forecasts of GNP depend, as with population forecasts, partly on the date made and the effect of unforeseen intervening events. Ascher studied real GNP forecasts made by five private and governmental bodies between 1952 and 196H.4 Predictions for 1965 erred by less than 5 per cent. The 1970 error rate ran from 5 to 10 per cent. GNP forecasts for 1975 made after 1965 had error rates of 15-20 per cent. Predictions of 1975 GNP made in the early part of the 1952-1968 period were no worse on average than those made in later years, and many were superior, despite the forecasts’ longer time horizons. One problem with economic forecasts is the transitory character of some of the forecasts’ key elements. Constituents of a GNP forecast are the size of the work force, the uncmploymcnt level, the average number of hours worked per worker, and productivity growth. A GNP forecast for a particular year may badly miss the mark because of a temporary economic slowdown accompanied by

953

968 955 955 955

50% 4.0 x ‘.z 1.4x ‘.z 3.5% 6% 15% 224% 394% 369-381% 1310% l-18% 19-23% -15% -40% 4.8% 4.0% 19.0% 25.6% 1 ,6-20.1 x z 0.46.1% 0.2-l 1.5% 0.420.9%

and Planners, The Johns Hopkins Press, Baltimore (1978).

high unemployment and a reduced average work week. This fact should, therefore, condition evaluations ofeconomic (and some other) forecasts. Analysts evaluating the reliability of long term economic forecasts might consider another factor. Ascher’s review of 25 long-term forecasts made from 1952 to 1970 found 21 to be overly optimistic.5 To deal with this condition may require that planners scale back all long-range economic forecasts before building their results into business plans. A final note on economic and population forecasting: attention to the gross numbers for these and other forecasts (e.g. federal budget deficits) may obscure more important forecasting considerations. For example, a 10 per cent shortfall in an estimate of federal revenue receipts might trigger an enormous percentage error in the estimated budget deficit. Alan Reynolds, writing in 1983 during the debate over President Reagan’s projected S200bn deficit reinforces this point. He concludes that ‘The federal budget deficits arc wrong’. That can be said with certainty, because estimated dcficlts are always wrong. The Office of Management and Budget was able to get within 25 per cent of estimating the following year’s deficit in only three of 11 years. Ikficitx were underestimated before recessions, but olvrcstimated m four other years by 44 to 141 per cent.”

These

represent

short-

rather

than

long-range

The Futility forecasts. Longer-term forecasts increase the size of the error.

would

of Forecasting

67

presumably in an erratic pattern. Five-year a median error of around 15 to 1959 nearly of the 5year forecasts were to 1966 nearly 4 years most forecasts 10 years, were almost

Table 1

nuclear

power

twenty-two

in forecasted installed capacity plants are similar to what we often of the in Table 1 A year Atomic Energy as late as 1970 by almost 50

forecasters In retrospect, estimates of technological

relied

too

heavily

on

of such short-run factors pricing policies, economic and cost conditions and competitive considerations. The forecasts covered the median of 25.6 in Table 1 all represent underestiin air travel

result ofsharply

higher to account

feasible

saturation

an inability rate for

to gauge

a component

approach

Estimates the latter nuclear costs relative

of that total. on such factors as alternative fuels

to different projected nuclear in different parts of the country. of long-term

forecasts

into

By late 1982, to

halt. Electricity

18-26 5 per cent for

determine

have

to

of the forecasts by Table 2 new products and services where one might 2 presents data

to expect

It compares levels of demand in 1972 with those by the Paley 20 years earlier. Comparisons are made both for

a shorter time horizon. as late as 197G1973 by 12-18 by roughly

for total energy on

through the 1950s substantial overestimates

thereafter.

both superior

actual

as late as 7-11 to 1974 that Ascher in all) overestimated consumpto two common an unwillingness or to recognize long-term trend a failure to anticipate and even react oncefor-all trend-shattering 42 per cent to 4.6 of the reduction of the 1973 oil crisis. Forecasts

travellers

consumption by

1974

to to which substitute

a

1975

forecasts by

of the forecasts cases, although to those of the

less than commendable the U.S. forecasts are eighteen

20 per cent the of the By including other minerals by the commission, is only 16

to iron

an error factor

of 5.6. Earlier I noted the importance of economic and population variables in determining values for phenomena covered by other forecasts. One would expect an especially close correlation between growth of these basic variables and growth in the demand for minerals which are the building blocks of manufactured output. Table 3, in conjunction with Table 2, allows us to check whether such a correlation exists. This table compares forecasted and actual performance for a number of economic and demographic variables. Forecasted values for these variables buttressed the Paley Commission’s minerals forecasts.

68

Long Range

Planning

Table 2. Paley Commission: economies (thousand tons)

Vol. 17

forecasted

February

1984

vs actual demands

for non-ferrous

U.S.

Mineral Iron ore Crude steel products Bismuth

metals,

Other

U.S. and other

market

economies

1970s

Actual

Forecast/ actual

1970s’

Actual

Forecast/ actual

forecast

1972

%

forecast

1972

%

100,000 150,000

81,900 124,500 1.75

122 138 120

1.46

61,000 124,000 -

404,800 280,900

Chromium Cobalt Manganese

1960 20 1242

558 19.5 1366

351 103 91

1230 13 -

3500 39’ -

Molybdenum Nickel Tungsten Aluminum Antimony Cadmium Copper Lead Magnesium Mercury

35 200 7.5 3600 28 12.5 1800 1200 500 2.4

25.8 246 7.1 4701 19.9 6.3 1951 954 1109 2.0

136 81 106 77 141 198 92 126 45 118

13.5 64 27.5 2400 50 6 2050 1500 -

360: 35.32 5600 29 12.4’ 4024 2201 -

Tin Zinc

94 1500

49 1206

192 124

122 1700

199 3289

’ 1974. ‘Non-communist world production less U.S. consumption. Source:William Cageand Howard Rush,Theaccuracyof long-termforecastsfor Forecasting, p. 207, The Macmillan Press, London (1979).

Table 3. Paley Commission: growth in selected economic 1970s’ (percentage increases)

Variable Population Labor force Phones in use Dwelling units in use Gross national product Residential construction Private non-residential construction Demand for new producer durable equipment New passenger cars New railroad equipment Demand for new agricultural machinery Demand for new consumer durables Shipbuilding

market

forecasted variables,

vs actual 1950 to

Forecast for 1970s

Actual 1972

(%)

(%)

27 27 50-85 50 100

38 39 156 60 123

Reasons

50

150

15 100 0

39 33 52

Many errors

40

285’

‘The Paley Report forecasted values for the mid-l 970s. 1972 was selected as the last year in the early 1970s that was free from boom or recession. 2Personal consumer expenditure on durable goods. Source: William Page and Howard Rush, ibid., p. 210.

The first thing to note about Table 3 is the generally record for these variables. weak forecasting

21 21 78 43 170 48 51 68 61 52

However, unlike the U.S. minerals forecasts which were predominantly optimistic, forecasts for the economic and demographic variables were mostly trnderestimates. Had the latter projections been more accurate (i.e. higher) the minerals forecasts presumably would have been even more inaccurate than they were. In the case of the OME, on the other hand, the commission underestimated economic growth. Improvement in predicting the economic variables doubtless would have improved minerals forecasts for the OME as well.

3;:

-12

35 33

non-ferrousmetals, inTom Whiston (ed.), TheUsesandAbusesof

;:

0

15 44 -

for Errors

forces contribute to long-range forecast in general. They include the following:

(1) Forecasters may analyse and measure only surface factors and ignore important underlying forces. For example, population projections consider such things as the number of fertile-age women and trend values for numbers of children per family. Equally important and often overlooked are the effects of birth rates on general economic conditions, the growing incidence of dual career families, and the changing social status of child-rearing. Coal demand forecasts have consistently overshot actual consumption. Such ‘obvious’ measures as long-run reserve availability and favorable cost comparisons vis ;1 vi_
The Futility fuels generate optimistic coal demand forecasts. Analysts fail adequately to consider the negative drag on coal demand from the fuel’s undesirable characteristics. Mining it creates safety and environmental hazards; burning it under certain conditions pollutes the atmosphere. In the long run its consumption could create a ‘greenhouse’ effect with enormously harmful consequences. These adverse characteristics breed political pressure to reduce its use. Failure of coal demand forecasts to factor in this political dimension leads to a continual upward bias. (2) Long-range predictions pay too little attention to substitution effects. In addition to the factors mentioned above that might confound population forecasts, couples might decide to substitute travel and other leisure-time activities for expenditures related to child-rearing. There is an infinite variety of expenditure-substitution possibilities. Some involve the exchange of one product for another in a particular product class, e.g. coal for oil as a fuel, or electric-driven cars vs those powered by internal combustion engines. Substitution may also occur across product and activity classes-for example, leisure vs babies, or vacation homes vs educational expenditures. Some are hybrids: home video purchases (a capital expenditure for entertainment purposes) vs theater movies (services), or the purchase of personal computers plus assorted peripherals substituting for several products and services. The more advanced a society economically, technologically and in educational attainment, the greater are substitution possibilities. These developments increase the number of branches in each person’s lifetime decision tree. Since time is fixed for each individual, consumption patterns come close to being zero-sum games. Increased consumption of x may reduce the consumption of y. (This is not completely true since one can, for example, ‘consume’ both television and the electricity needed to power it as a leisure time substitute for book reading that, during the day at least, may entail no electricity consumption.) Also much increased consumption expenditure represents a move toward higher value added purchases rather than the consumption of more goods. One may acquire a Mercedes-Benz to replace a Chevrolet, or Gucci shoes for sandals. Nonetheless, increased affluence and an enlarged product and service menu fostered by technological developments continually enlarge consumption options. Thus they add to forecasting difficulty. The substitution effect and the influence of technological developments on product substitution could have accounted for some of the Paley Commission’s errors in forecasting minerals demand. For example, overestimates of demand in the United States for iron ore and steel products coupled with underestimates in demand for

of Forecasting

69

aluminum could be related if manufacturers substituted one metal product for the other. Moreover, the rapid technological progress that accompanied high economic growth rates in the period covered by Tables 2 and 3 may also have stimulated changes in production processes and the introduction of new products that, together, created unforeseen demand patterns for many minerals.” (3) Assumption problems confound forecasting results. They may take several forms. C. W. Beck, Planning Director for Shell U.K. Ltd., points out one problem-the absence of independent forecasts among rival forecasters of the same phenomenon. Concerned about the use of inaccurate forecasts in Shell’s planning process, Beck found that there were few ‘uncorrelated estimates’ in the work done by so-called independent forecasters whose output Shell tracked. The reason was that they tended to use the same assumptions, figures and theories.” Another problem is what Ascher calls ‘assumption drag’, that is, the use of outmoded assumptions even when current data counter their validity.” This may occur for several reasons: Reluctance

to question

received

doctrine.

Doubt that the data, in fact, negate the assumptions-a feeling that the data represent merely a temporary ‘blip’. Delay

in getting

the ‘true’ data.

Delay also in constructing the forecast may render assumptions obsolete.

which

factors may contribute to (4) Other time forecasting problems. Beck cites the failure of some forecasters to realize the time lags involved with certain developments.‘3 Witness the delays associated with attempts in the United States to develop coal slurry pipelines and synthetic fuel plants. Even when technology has been perfected, political, social and economic forces may intervene to delay construction start-up. Also inauguration of other forecasted developments often depends upon phasing out existing facilities, and that may take more time than forecasters have predicted. Another temporal variable is the forecast’s time horizon. The longer the period between the time a forecast is made and its target date, the more opportunity there is for change in the major trenddetermining factors. Ironically, in some cases longer time horizons lead to improved forecast results as two or more unforeseen developments cancel each other. This condition obtained with a 20 year population forecast made in 1928 that was more accurate than a 10 year forecast completed in the same year. This is an unusual occurrence. The length of forecasts and their degree of error are almost always directly related.

70

Long Range

Planning

Vol. 17

February

It also appears that some periods of time offer more hazards for forecasters. A cataclysmic event such as World War II and its aftermath changed a lot of trend lines. Even if the war had been predicted, its social and economic consequences probably could not have been. The manifold increase in crude oil prices is another event with potential for disrupting many forecasts. (5) Forecasts may err because oferrors in forecasts of its components. Many forecasts are summations of predicted values for several constituents of the phenomenon being forecasted. For example steel demand forecasts may result from adding up separate forecasts for major end-use categories. Forecast components may take different forms in other cases. Example: population forecasts based on fertility, mortality and net migration rates. Forecast results may vary because forecasters choose different components. Thus components of an energy demand prediction may be end-user categories (industrial, commercial, residential), or a combination of such things as population and energy use per capita. Forecast accuracy depends, therefore, not only on the choice of appropriate components but on the accurate prediction of the components’ future values. The forecaster must contend with exogenous social, cultural and political events that may upset trend values for those components. Often, hard-to-predict technological developments may also alter forecasts. Consider the potential effect, for example, of development of a low cost, implantable artifical heart on population forecasts. (6) Bias may cause forecast error. Critics of the Club of Rome’s doomsday scenario attribute their gloomy resource forecasts to a predisposition to limit growth. Forecasts issued by political units are notoriously error-prone since political expediency often substitutes for objectivity.

How to Cope with an Uncertain Future The inaccuracy of so many long-range forecasts leads one to question their value. It is unlikely that planners will dispense with them so it remains to consider how to improve them or at least adjust planning to their inaccuracy. A corrective measure that one might take is to allow for the bias mentioned above. Bias may be self-generated-the planner or forecasters on his staff may naturally incline to optimism or pessimism. Recognizing the bias allows one to adjust to it. More likely is the existence of bias in forecasts issued by government agencies or industry groups either because they are too close to the trees to see the forest or because the forecast is used to further a policy aim. Example: exaggerated Defense

1984

Department forecasts of a Soviet military build-up to prod Congress into enlarging the defense budget. Here it pays to recognize the potential for selfinterest in the forecast and to monitor the performance of those making the forecasts. Evidence of bias should show up fairly quickly. Bias may account for a familiar forecasting phenomenon-the ‘hockey stick’ forecast. Here the forecaster says, in effect, ‘sales (or whatever else is being forecasted) are declining now, but we foresee them leveling off and then increasing in the future’. A graph depicting this sales pattern resembles the configuration of a hockey stick. The Reagan Administration’s economic forecasts throughout 1982 fell into the hockey stick category. Whether the optimistic bias was politically motivated, the result of inherent optimism, or the product of inept forecasting is hard to determine. Government officials are not alone in the use of hockey stick forecasting. The phenomenon also prevails in business, perhaps for the same reasons that motivate its use by government agencies. A hockey stick forecast may reduce pressure on business managers from stockholders and other interested parties when a company’s sales and profits decline. The 1981-1983 recession has spawned a surfeit of hockey stick forecasts in business. These forecasts are no better than the assumptions relating to general economic recovery that undergird them. Checking the validity of forecasts’ assumptions may reduce errors associated with them. Every forecast is premised on one or more assumptions covering external factors that affect either the phenomenon being forecast or directly related forces. The first requirement is to recognize and make explicit the assumptions that are built into the forecast. If y depends upon x, the manager should ask what outcome the absence of x implies. If x then does not occur, plans involving the occurrence of y need to be adjusted as quickly as possible. Consider how this approach might have worked when Congress in 1981 enacted tax legislation designed in part to foster increased savings that were expected to finance increased investment. Legislators might have asked: ‘If this train of events does fret occur, can we consider the legislation to have been a mistake, and therefore correct it?’ Having accounted for key assumptions underlying a forecast, continually monitoring them is the next requirement. Do values for the variables underlying the assumptions match one’s expectations for them? Some variation is bound to exist. Significant deviation from expected values, however, should trigger an objective evaluation of the assumptions. The analyst should try to determine whether the ‘surprises’ represent temporary ‘blips’ or significant changes in trend lines. The latter calls for changes in the forecasts.

The Futility Ascher reaches a similar conclusion. Looking ahead, he foresees three developments designed to sensitize long-range forecasts to ‘surprise’ outcomes. First is the need, as I suggest, to account for deviations from previous patterns. He recommends establishing trend lines from the most current data. The is to eliminate plausibility second suggestion checks. This forecasting technique requires the forecaster to determine whether the forecast’s outcome is implausible. If so, it is presumed to be incorrect. But it is in the nature of surprise events to create ‘implausible’ outcomes. By eliminating these checks, the forecaster is freer to consider a forecast model’s outcome that his intuition, based on conformity, might incorrectly reject. Third, Ascher recommends rejecting consensus forecasts since they tend to average high and low ‘surprise’ forecasts; hence they probably miss the actual surprise outcomes. The above techniques may sensitize the forecaster to surprises, but they obviously cannot prevent their occurrence. Basing plans on scenarios rather than forecasts is one way to deal with the uncertainty of political, economic and social systems. P. W. Beck, who advocates using scenarios to overcome the uncertainty that hampers the use of ‘the greatest difference’ forecasts, says that [between forecasts and scenarios] is in the basic philosophies: forecasts are based on the belief that the future can be measured and controlled. Scenarios are based on the belief that it can not.‘14 They have been defined as ‘hypothetical sequences of events constructed for the purpose of focusing attention on causal processes and decision points’.15 Starting from the premise that business faces an uncertain future, Shell planners argue that their role is not to provide a ‘single-line’ numerical forecast but to ‘promote conceptual understanding’.16 The scenario says ‘here are some of the key factors you have to take into account, and this is the way these factors could affect your line of business’.” Unlike the forecast which attempts to quantify the future, a scenario serves as a tool to aid the decision-making process. In practice planners construct multiple scenarios (since one would constitute a single-line forecast). Built into the scenario may be competitive, technical, social, political and economic factors that are woven into an internally consistent pattern. There are obvious problems lvith reliance upon scenarios for business planning. One is the difficulty ofencapsulating a number ofunknowns into t\vo or three tracks down which the firm may travel. Another is ensuring that the variables are internally consistent. Consistency based on past relationships may not apply to a future in Lvhich new de\relopments break traditional patterns. How does one account for changes in expectations resulting from unique events that failed to influence previous

of Forecasting

71

relationships? For example, recent experience with high inflation rates and uncertainty about future rates of inflation may, for the time being at least, have altered the level of real interest rates. Thus a scenario based upon a low level of demand, a low inflation rate and correspondingly low level of interest rates would miss the mark. A firm whose success depended in large part on low interest rates might as a result base its plans on deceptively inaccurate scenarios.

Several management techniques can reduce the risks associated with potential forecasting error. The first is-to the extent possible-to implement plans on a with step-by-step basis. This is true especially involving capital expenditures and decisions product line expansion and market development. Expanding in small modules rather than through large-scale additions to capacity provides the flexibility necessary to respond to faulty forecasts. Avoiding vertical integration also contributes to flexibility. Managements inclined to its use might want to reconsider this policy. Recent research points to some of vertical integration’s drawbacks.ls Not the least of its shortcomings is the increased financial commitment necessary to support plant expansions based on what might turn out to be erroneous forecasts.

This cautious approach obviously copes with overly optimistic forecasts-the usual event-but penalizes the firm when demand levels outpace projections. To allow for this possibility management can contract for a part ofits output rather than produce it all itself. Being, say, 80 per cent selfsufficient in production provides a comfortable ‘fudge’ factor in case demand lags forecasted levels, but may also create quick expansion opportunities when the reverse is true. The key here is to negotiate contracted-production arrangements that assure flexible output with acceptable quality control.

Long-range forecasters’ ultimate asset may be an apparently ineluctable tendency of phenomena to move toward equilibrium. Force meets counterforce. A phenomenon moving in one direction sets in motion forces that will modify its course. Malthus’ population theory recognizes this fact. Nature abounds with examples of the tendency tolvard homeostasis. Erosion in the demand for oil and in the crude oil price level in early 1983 is a dramatic business world example. There are countless other examples-business cycles, the ebb and flow of interest rates, pendulum swir-gs of social mores and political orientations. Recognizing the existence of a tendency toward homeostasis may reduce forecast error. Still it will remain. Reducing error is a laudable goal but ~~3pir1,~ with it may be more important to the firm’s welfare.

Long Range

72

Planning

Vol. 17

February

1984

Re$wtres

Howard Rush, The accuracy of long-term forecasts for nonferrous metals, in Tom Wiston (ed.), The Uses and Abuses of Forecasting, DD. 204-126. The Macmillan Press. London (1979).

(1) There were ten, 20-year forecasts, The 8.7% median referred to averages the two middle forecast even percentages of 5.8 and 11.5. (2) Julian L. Simon, The Ultimate Resource, University Press, Princeton (1981). (3)

p. 7. Princeton

Range

Ibid., p. 91

(6) Alan Reynolds, The OMB’s questionable budget estimates, The Wall Street Journal, 18 January, p. 26 (1983). (7)

United States Atomic Energy Commission, Forecast of Growth Power, January (1971) in National Petroleum Council, U.S. Energy Outlook: An InitialAppraisal, 1971-1985. Vol. 1, July (1971). of Nuclear

(8) Ascher, op. cit., p. 106 (9) The material in this section

for a review of attempts to account for errors in the Paley Commission’s forecasts.

(11) C. W. Beck, Corporate planning for an uncertain future,

Ibid.

(4) William Ascher, Forecasting: An Appraisal for Policy-Makers and Planners, The Johns Hopkins Press, Baltimore (1978). (5)

(10) See Page and Rush, pp. 209-211,

Planning,

from William

Page and

August

Long

(1982).

(12) Ascher, op. cit., p. 53 (13)

Beck, op. cit., p. 15

(14)

Beck, op. cit., p. 18.

(15)

Herman Kahn and Anthony J. Wiener, The Year 2000, The Macmillan Co.. New York (1967); Beck, p. 17.

(1’3) Beck, op. cit., p. 17. (17)

Beck, op. cit., p. 18

(18)

Robert Business

is drawn

15 (4).

D. Buzzell, Review,

Is vertical integration January-February

83 (l),

possible?, (1983).

Harvard