Kalman filtering
Do Firms Forecast Well?

The mathematical technique known as 'Kalman filtering' has been widely applied to engineering problems such as that of tracking the trajectory of a projectile. There is a clear analogy between this problem and that facing an economic agent who wishes to predict an economic variable. In both cases some theory of the underlying process will be available, and this theoretical information can be combined with the relevant data in order to generate the desired predictions.

In Discussion Paper No. 62, Matthias Mors and Research Fellow Colin Mayer use the Kalman filter as a framework within which to examine how economic agents form expectations. Kalman filtering allows the economist to examine the way in which agents utilize available information and the extent to which such information is combined with the structure of the model that agents appear to employ.

Mayer and Mors apply this approach to data on UK companies' expectations of their future activity levels, derived from the Confederation of British Industry (CBI) survey of manufacturing industry. Although the data require some transformation, they are well suited to a Kalman filter analysis, since they provide information not only on firms' expectations of their future levels of activity, but also the levels of activity which subsequently occurred - the 'outturns'.

Mayer and Mors also compare the performance of relatively straightforward forecasting rules with the firms' own forecasts or 'expectations' as they are revealed in the survey. Mayer and Mors consider an autoregressive moving average (ARMA) model as well as a model which incorporates a random walk and a random trend. In general these basic models do not provide an adequate description of how companies form short-term predictions of variables, such as changes in new orders and employment. Either a simple adaptation of the random walk or the autoregressive models, however, do track recorded expectations quite well. More strikingly, even the most basic random walk representation yields predictions for new orders which are superior to companies' own predictions. Mayer and Mors argue that this throws serious doubt on whether managers employ even the simplest forecasting rules in appropriate ways.

The authors find that a much better description of company expectations can be obtained by combining different Kalman filters to produce an average forecast. This suggests that companies may employ different descriptions of the processes governing the variables and that the aggregate forecast is therefore a combination of different individual predictions. Mayer and Mors find evidence that the forecasting models used by companies have varied over time. There appears to have been a significant change in forecasting procedures during the early 1970s. During the 1960s firms appear to have shown a greater willingness to revise estimates of trend growth than they did during the 1970s and 1980s.

Mayer and Mors conclude that it is remarkably easy to outperform firms' own predictions, especially for those variables for which companies form true predictions rather than formulate plans. For such variables even straightforward models offer more accurate predictions of the outturn than the firm's own expectations. The Kalman filter analysis used by Mayer and Mors suggests that firms tend to discount new information too heavily and place too much reliance on their underlying beliefs about the system's dynamics. They argue that this provides a powerful refutation of the view that agents employ even simple forecasting rules in an optimal manner.


Company Expectations and New Information: an Application of Kalman Filtering
Colin Mayer and Matthias Mors

Discussion Paper No. 62, April 1985 (ATE)