CROSS IMPACT MATRIX METHOD OF FORECASTING
Definition and Historical Background
A basic limitation of many forecasting methods and the Delphi method is that they produce only isolated forecasts; that is, events and trends are projected one by one, without explicit reference to their possible influence on each other. Most events and developments however, are in some way connected to each other. Interdependencies between these events and developments can be taken into consideration for more consistent and accurate forecasts. Cross-impact analysis addresses Delphi's lack of a mechanism for discovering mutually exclusive or conflicting outcomes. Thus, some outcomes forecasted by Delphi could be impossible to obtain simultaneously (Patton and Sawicki, 1993): for example full employment and a low rate of inflation. Cross-impact analysis addresses this problem directly by analyzing conditional probabilities -for example, the likelihood that inflation will be low if full employment is achieved. It examines the interactions of forecasted items (Gordon and Hayward, 1968).
The cross-impact concept originated with Olaf Helmer and Theodore Gordon in conjunction with the design of a forecasting game for Kaiser-Aluminum (Helmer, 1977). It represented an effort to extend the forecasting techniques of the Delphi method. In 1968 at UCLA, Gordon and Hayward developed a computer-based approach to cross-impact analysis and they published their findings in the paper titled "initial experiments with the cross-impact matrix method of forecasting" (Gordon and Hayward, 1968). In this approach, events were recorded on an orthogonal matrix and at each matrix intersection the question was asked: If the event in the row were to occur, how would it affect the probability of occurrence of the event in the column? The judgements were entered in the matrix cells. Allen (1977) states that most forecasting methods may not consider many reactions between forecasted events. Cross-impact analysis, however, attempts to reveal the conditional probability of an event given that various events have or have not occurred.
Alter and Enzer (1978) claim that cross-impact analysis differs from both probability theory and mathematical statistics; a cross-impact analysis is concerned with the identification of possible outcomes rather than with an understanding of what is or what was. They define cross-impact analysis as a systematic way to examine possible future developments and their interactions.
Helmer (1977) developed the causal cross-impact approach. Duperrin and Godet (1975) have considered the rather different notion of correlational cross-impacts, The main problem associated with this was stated by Helmer (1977) as being the difficulty of obtaining consistent estimates of the conditional probabilities of A given B and of B given A. Later Enzer and Alter (1978) illustrated two versions of conditional probability as used in a cross-impact analysis, one based on correlation and one based on causation, and showed that the latter is much better suited to the study of alternative futures. A sequential approach to cross-impact analysis was developed by Sarin (1978). The proposed approach sequentially solicits information from the expert and checks it for consistency.
The Basics of the Cross Impact Analysis Method
Technology forecasting does not follow a fixed methodological pattern. However, the way in which the study is approached and the choice of methods depend on the individual researcher (Wissema, 1982). Several versions of cross-impact analysis have been developed by researchers (Gordon and Hayward, 1968; Fontela, 1976; Helmer, 1977; Sarin, 1978; Novak and Lorant; 1978; Wissema and Benes, 1980; Hanson and Ramani, 1988). The evaluation of the technique has not followed a single path but has produced a variety of different methods for constructing, utilizing, and evaluating cross-impact matrices.
Helmer (1977) claims that causal relations cannot be handled without explicitly introducing a time dimension. He describes the planning interval (which extends from the present to some planning horizon) is split up into subintervals, to be called "scenes", and the occurrence of an event in some scene has repercussions in the form of cross-impacts in subsequent scenes. In addition to events the model also contains trends, whose fluctuations from expected values in one scene affect trend levels and event probabilities in subsequent scenes.
In applying cross-impact analysis to a particular area, it is important to select for inclusion those developments (events and trends) whose expected impact on the future of that area is judged to be relatively greatest. Helmer (1977) asserts that in practice it will be found that it is rarely possible to do justice to the planning process in a given area by selecting fewer than 20 or 30 developments, and often quite a few more are required. Fowles (1978) also underlines the importance of the definition of events to be included in the study. The major steps in the use of cross-impact analysis for evaluating future situations are described by Helmer (1977) and Fowles (1978) as:
- Define the events and trends to be included in the analysis
- Define the planning interval and subintervals, "scenes".
- Develop cross-impact matrices to define the interdependencies between events and trends.
- Estimate the entries in the cross-impact matrix, i.e., information on how the occurrence of an event
or how the deviation of a trend Tj
from its expected value in a given scene would affect other event probabilities and trend values in later scenes.
- Estimate the initial occurrence probabilities of each event in each scene.
- Estimate the value of each trend at the beginning of each scene.
- Perform a calibration run
- Define the policies, actions, or sensitivity tests to be run with the matrix.
- Perform the cross-impact calculations.
- Evaluate results
The initial occurrence probabilities of events, values of trends, and the magnitude of impacts between the variables may be estimated by individual experts but more commonly estimated by groups containing experts from the various disciplines covered by the events (Fowles, 1978). Delphi questionnaires or interviews also can be used to collect these judgements.
Once a cross-impact model has been put together, it should be run a number of times in order to test the computer program's performance. Helmer (1977) described a single run as follows:
- In scene 1, decide which of the events occur (by a standard Monte Carlo drawing of random numbers); adjust the event probabilities and trend values for scene 2 according to cross-impact matrix;
- Proceed to scene 2, having adjusted the trend values further by adding random deviates to them that were drawn from the appropriate exogenous-uncertainty distributions. Again decide which further events are now occurring, and adjust event probabilities and trend values for scene 3 according to the prescribed event cross impacts; observe the deviations
of trend values in scene 2 from their predicted values, and adjust event probabilities and trend values for scene 3 further in accordance with the prescribed trend cross impacts; apply carryovers where appropriate.
- Repeat the procedure for scenes 3, 4 and so on.
The result will be a "scenario", that is, a sequence of event occurrences, by scenes, and of adjustments in trend values. Several runs will produce different scenarios because of the random elements that are present.
The ability to add information (e.g., policy changes) that was not part of the prior information makes an interactive cross-impact model an open-ended technique for exploratory analysis (Enzer and Alter, 1978). By evaluating the forecast interactively, one could asses not only the occurrences that would affect the nominal forecast, but one could also explore the effect of various policies and the impact of timing.
There are several methodologies for different applications. Gordon and Hayward (1968) define three modes of connection between variables. Assume event
occurs. A second event, E2, may be completely unaffected by
E1; it may be enhanced by the occurrence of
E1; or it may be inhibited by the occurrence of
may affect E2
Enhancing and inhibiting modes of connection may be further clarified by explaining some mechanisms that may occur. Enhancing linkages, those where the probability of the second event is improved by the occurrence of the first, result from several mechanisms, including:
- The occurrence of
makes occurrence of E2
feasible or practical. This kind of relationship is designated "enabling".
- The occurrence of
obligates occurrence of E2
for the efficient use of E1. This type of enhancing relationship is designated "provoking".
Inhibiting linkages, those in which the probability of the second event is diminished by the occurrence of the first, also result from several mechanisms, including:
- The occurrence of
unfeasible or impractical. This type of inhibiting relationship is designated "denigrated".
- The occurrence of
obligates non-occurrence of E2
for the efficient use of E1. This kind of inhibiting relationship is designated "antagonistic".