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DEMAND FORECASTING: EVIDENCE-BASED METHODSForthcoming in the Oxford Handbook in Managerial EconomicsChristopher R. Thomas and William F. Shughart II (Eds.)Subject to further revisionsFile: Demandforecasting-17-August-2011-clean.docx17 August 2011J. Scott ArmstrongThe Wharton School, University of Pennsylvania747 Huntsman, Philadelphia, PA 19104, U.S.A.T: 1 610 622 6480 F: 1 215 898 2534 armstrong@wharton.upenn.eduKesten C. GreenInternational Graduate School of Business, University of South AustraliaCity West Campus, North Terrace, Adelaide, SA 5000, AustraliaT: 61 8 8302 9097 F: 61 8 8302 0709 words in body 10,053 (requested range was 6,000 to 9,000)ABSTRACTWe reviewed the evidence-based literature related to the relative accuracy of alternative methods forforecasting demand. The findings yield conclusions that differ substantially from current practice. Forproblems where there are insufficient data, where one must rely on judgment. The key with judgment is toimpose structure with methods such as surveys of intentions or expectations, judgmental bootstrapping,structured analogies, and simulated interaction. Avoid methods that lack evidence on efficacy such asintuition, unstructured meetings, and focus groups. Given ample data, use quantitative methods includingextrapolation, quantitative analogies, rule-based forecasting, and causal methods. Among causal methods,econometric methods are useful given good theory, and few key variables. Index models are useful forselection problems when there are many variables and much knowledge about the situation. Usestructured procedures to incorporate managers’ domain knowledge into forecasts from quantitativemethods where the knowledge would otherwise be overlooked, but avoid unstructured revisions. Methodsfor combining forecasts, including prediction markets and Delphi, improve accuracy. Do not use complexmethods; they do not improve accuracy and the added complexity can cause forecasters to overlook errorsand to apply methods improperly. We do not recommend complex econometric methods. Avoidquantitative methods that have not been properly validated and those that do not use domain knowledge;among these we include neural nets, stepwise regression, and data mining. Given that many organizationsuse the methods we reject and few use the methods we recommend, there are many opportunities toimprove forecasting and decision-making.Keywords: competitor behaviour, data mining, Delphi, expectations, game theory, intentions, marketshare, index models, market size, forecast accuracy, forecasting methodology, prediction markets, salesforecasting, simulated interaction, stepwise regression, structured analogies.

Demand forecasting asks “how much can be sold given the situation and the marketing program?” Thesituation includes the broader economy, infrastructure, the social environment, the legal framework, themarket, actions by the firm, actions by those offering competing and complementary products, andactions by others such as unions and lobby groups.Overview of possible methodsIn this section we provide brief descriptions of the types of forecasting methods that might be used toforecast demand and the evidence that is available on their use. The forecasting methods and therelationships among them are shown in Figure 1, the Methodology Tree for Forecasting. The primarydistinction is between methods that rely on judgement and those that estimate relationships usingquantitative data.Figure 1Methodology Tree for Forecasting [Print landscape, full page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ethods Based on JudgmentUnaided judgmentMost important demand-related forecasts in organizations are made using unaided judgment. By“unaided” we mean judgment that does not use of evidence-based procedures. Such forecasts mightinclude those for the sales of a new product, the effects of a change in design, pricing, or advertising, or2

how competitors would respond. Forecasts by experts using their unaided judgment are most likely to beaccurate when the situation is similar to others that the experts have made forecasts about, involves relationships that are simple and well understood (e.g., demand goes up whenprices go down), is unlikely to be effected by large changes, and does not involve conflict,and when the experts are unbiased, possess information that others do not, and receive accurate, timely, and well-summarized feedback about their forecasts.Regrettably, unaided judgement is often used when the above conditions do not hold. For example, theseconditions do not apply to political and economic forecasting. Tetlock’s (2005) study of more than 82,000forecasts made over 20 years by 284 experts in politics and economics found that they were little moreaccurate than those made by non-experts and that they were less accurate than forecasts from simplemodels. His findings are consistent with those from research in other fields that involve uncertainty andcomplex problems—such as is the case for many problems related to demand forecasting.Prediction marketsPrediction markets, which are also known as betting markets, information markets, and futures markets,have a long history. Between the end of the U.S. Civil War and World War II, well-organized marketsfor betting on U.S. presidential elections correctly picked the winner in every election but 1916; also, theywere successful in identifying those elections that would be close (Rhode and Strumpf 2004). Morerecently, the Iowa Electronic Markets have performed well in predicting the margin of victory for thepresidential election winners.Despite numerous attempts since the 1930s, no methods have been found to be superior tomarkets when forecasting prices. However, few people believe this as they pay handsomely forinvestment recommendations, a finding that has been labelled the ‘Seer-sucker theory.’ The theory statesthat no matter how much evidence there is that seers do not exist, suckers will continue to pay for theexistence of seers (Armstrong 1980).Software is available for creating trading platforms that allows participants to buy and sellcontracts that represent their bets on events. Markets can be used to predict such things as the percentageof U.S. households with three or more vehicles by the end of 2015. Confidential betting markets can beset up within firms to bet on such things as first year sales of a new product. Some unpublished studiessuggest that they can produce accurate sales forecasts for companies. However, there are no empiricalstudies that compare prediction market forecasts with those from traditional groups or from othermethods.DelphiThe Delphi technique was developed at RAND Corporation in the 1950s to help capture the knowledge ofdiverse experts while avoiding the disadvantages of traditional group meetings. The latter include grouppressure, high administrative expenses, and lack of structure.To forecast with Delphi, the administrator should ask between five and twenty experts who arediverse in their knowledge and opinions for their forecasts and their reasons for them. The administratorthen provides the experts with anonymous summary statistics on the forecasts, and the experts’ reasonsfor their forecasts. The process is repeated until there is little change in forecasts between rounds—two orthree rounds are usually sufficient. The Delphi forecast is the median or mode of the experts’ final-roundforecasts. Software to help administer the procedure is available at

Delphi has led to improved accuracy compared to forecasts from traditional groups in fivestudies, harmed accuracy in one, and was inconclusive in two in a meta-analysis by Rowe and Wright(2001). They found Delphi to be more accurate than one-round expert surveys for 12 of 16 studies, withtwo ties and two cases in which Delphi was less accurate. Over all of these 24 comparisons, Delphiimproved accuracy in 71% and harmed it in 12%. On the other hand, Woudenberg’s earlier (1991) reviewdid not find an improvement in accuracy from Delphi. Delphi is likely to be most effective in situationswhere the relevant knowledge is distributed among the experts, such as in decisions on where to locate aretail outlet that would benefit from forecasts obtained from real estate, traffic, retailing, and consumerexperts.Delphi is attractive to managers because it is easy to understand and supports forecasts withreasons and authority (Green, Armstrong, & Graefe 2007). It is relatively cheap to conduct: panelists donot meet so the costs of assembling a group of highly-paid individuals in one place and the time-wastingof holding meetings are avoided. Moreover it is not necessary to employ expensive consultants toimplement the method if a competent administrator can be found in-house.Green, et al. (2007) identified eight advantage of the Delphi technique over prediction markets.These are in sum (1) broader applicability, (2) ease of understanding, (3) ability to address complexquestions, (4) ability to maintain confidentiality, (5) avoidance of manipulation, (6) revelation of newknowledge, (7) avoidance of cascades, and (8) fewer participants. Points 6 and 7 refer to the fact thatwhere the Delphi process requires participants to reveal their knowledge and reasoning and to respond tothat of others, there is no such requirement on prediction market participants. As a consequence,prediction market participants might trade erroneously thinking that they have new information i.e.cascade.Structured analogiesPeople often use analogies to make forecasts, but they tend to do so in an ad hoc manner. For example,they might search for a single analogy that suits their prior beliefs. The structured-analogies method usesa formal process to overcome biased and inefficient use of information from analogous situations.To use the structured analogies method, an administrator prepares a description of the targetsituation and selects experts who are likely to know analogous situations; preferably from directexperience. The experts identify and describe analogous situations, rate their similarity to the targetsituation, and match the outcomes of their analogies with potential outcomes of the target situation. Theadministrator derives a forecast from each expert’s analysis of his most similar analogy; one forecast perexpert.The limited research to date on structured analogies has been promising. Green and Armstrong(2007) found that structured analogies were 41% more accurate than unaided judgment in the difficulttask of forecasting decisions in eight real conflicts, which included union-management disputes, a hostiletakeover initiative, and a supply channel negotiation. The structured analogies method is especiallyappropriate when demand is affected by the actions of competitors, governments, or interest groups suchas environmental and animal activists.Game theoryThe authors of textbooks and research papers recommend game theory for making forecasts aboutnegotiations and other conflicts. Game theory involves identifying the incentives that motivate parties anddeducing the decisions they will make in response to the incentives. On the face of it, this method mightbe useful for, for example, forecasting how competitors will react to a change in prices.Despite the thousands of books on game theory, two papers by Green (2002 and 2005) providethe only evidence on the accuracy of game theorists forecasts. In these studies, game theory experts wereurged to use game theory to predict the decisions that would be made in eight real conflict situations4

involving interaction. The game theorists’ forecasts were no more accurate than those of universitystudents using their unaided judgment.Judgmental DecompositionJudgemental decomposition involves dividing the forecasting problem into parts for which it is easier toderive forecast than it is for the whole problem. Different methods can be used for forecasting each part,as is appropriate to the nature of the part and the data available. The forecasts for the parts are combinedto obtain a forecast for the whole.One approach to decomposition is to break the problem down into multiplicative components. Forexample, to forecast sales for a brand, one might forecast market sales and market share separately, andthen multiply the components. Forecasts from decomposition are generally more accurate than those froma global approach. In particular, decomposition is more accurate where there is much uncertainty aboutthe aggregate forecast and where large numbers (over one million) are involved. MacGregor (2001,Exhibit 2) summarized results from three studies involving 15 tests and found that judgmentaldecomposition led to a 42% reduction in error when there was high uncertainty about the situation.Webby et al. (2005) found that a when forecasters were given help to decompose a time series forecastingtask, their forecasts were more accurate.Judgmental bootstrappingJudgmental bootstrapping is used to estimate a formal forecasting model from experts’ subjectivejudgments. Experts are asked what information they use to make predictions about a class of situations.They are then asked to make predictions for diverse cases, which can be real or hypothetical. Forexample, they might forecast first year turnover for stores using information about product range,proximity of competing stores, visibility, and traffic flows. These forecasts are used to estimate thecoefficients of a regression equation that relates the experts’ forecasts to the information they used. Thegeneral proposition seems preposterous: it is that the model of the man will be more accurate than theman. The reason is that the model applies the man’s rules more consistently.Judgemental bootstrapping models are most useful for repetitive complex forecasting problemswhere data on the dependent variable are not available (e.g. demand for a proposed sports stadium) orwhere the available data do not vary sufficiently for the estimation of an econometric model. Oncedeveloped, judgmental bootstrapping models provide a low-cost procedure for making forecasts.Goodwin et al. (2011) suggested that judgmental bootstrapping is less likely to improve accuracywhen many potential cues are available and it is not clear which ones the experts are using, where expertshave access to information that is not available for the model or knowledge that cannot be readilyincorporated into a regression model, or where cues (variables) are autocorrelated.A meta-analysis of the evidence on judgmental bootstrapping found that forecasts were moreaccurate than those from unaided judgment (the normal method for these situations) in 8 of the 11comparisons, with two tests showing no difference, and one showing a small loss (Armstrong 2001a). Thetypical error reduction was about 6%. The one failure occurred when the experts relied heavily on anerroneous variable.Expert systemsExpert systems are structured implementations of the forecasting rules used by experts. One way todiscover experts’ rules is to create protocols by recording the experts as they talk about what they aredoing while the make forecasts. Empirical estimates of relationships from structured analyses such aseconometric studies and experiments should be used when available. Expert opinions, conjoint analysis,and bootstrapping can also provide useful information on rules. An expert system should be simple, clear,and complete.5

In their review, Collopy, Adya and Armstrong (2001) found that expert systems forecasts weremore accurate than those from unaided judgement. This conclusion was, however, based on only a smallnumber of studies, and the gains in accuracy were small. Given the high cost of developing and revisingexpert systems, we expect that other methods will be more appropriate for most situations.Simulated interactionSimulated interaction is a form of role-playing that can be used to forecast decisions by people who areinteracting with others. It is especially useful when the situation involves conflict. For example, amanager might want to know how best to secure an exclusive distribution arrangement with a majorsupplier, or how a competitor would respond to a 25% price reduction.To use simulated interaction, an administrator prepares a description of the situation, describesthe main protagonists’ roles, and provides a short list of possible decisions. If necessary, secrecy can bemaintained by disguising the situation. Role players adopt a role then read about the situation. They thenengage in feasibly realistic interactions with the other role players until they reach a decision. Thesimulations usually last between 30 and 60 minutes.Green (2005) found that relative to the usual forecasting method (unaided expert judgment),simulated interaction reduced forecast errors by 57% for the eight situations tested.Simulated interaction is most useful when little or no quantitative data are available, the situationto forecast is unique or unusual, and decision makers wish to predict the effects of different policies orstrategies. Simulated interactions can be conducted inexpensively by using students to play the roles. Forexample, it was used to determine how supermarkets would respond to a plan designed to give creditbased on shopper’s purchases so they could save money on the purchase of home appliances (Armstrong2001c), and to predict the decision a company board would make over whether or not to make acontentious and substantial investment in new technology (Green 2002).If the simulated interaction method seems onerous, you might wonder whether just following thecommon advice to “put yourself in the other person’s shoes” will help you to predict the decisions theywill make. It will not. Our study (Green and Armstrong 2011) failed to find any benefit from adopting thisapproach, even in a structured way. It is too difficult to think through the interactions of parties withdivergent roles in a complex situation. Active role-playing between parties is needed to represent suchsituations with sufficient realism to derive useful forecasts.Intentions and expectations surveys, and experimentationIntentions surveys ask people how they intend to behave in specified situations. The data collected can beused, for example, to predict how people would respond to major changes in the design or price of a good.A meta-analysis covering 47 comparisons with over 10,000 subjects found that there is a strongrelationship between people’s intentions and their behavior (Kim and Hunter 1993).Surveys can also be used to ask people how they expect they would behave. Expectations differfrom intentions because people know that unintended things happen. For example, if you were askedwhether you intended to visit the dentist in the next six months you might say no. However, you realizethat a problem might arise that would necessitate a visit, so your expectation would be that visiting thedentist in the next six months had a probability greater than zero. Morwitz (2001) summarised evidenceon expectations surveys.To forecast demand using a survey of potential consumers, the administrator should prepare anaccurate and comprehensive description of the product and conditions of sale. Expectations and intentionscan be obtained using probability scales such as

Avoid methods that lack evidence on efficacy such as intuition, unstructured meetings, and focus groups. Given ample data, use quantitative methods including extrapolation, quantitative analogies, rule-based forecasting, and causal methods. Among causal methods, econometric methods are useful given good theory, and few key variables.

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