# Logit forecasting of high tech products.

One approach to the problem of new product forecasting is the economic use of Logit or Gompertz curves. Gompertz or market penetration curves have been used to forecast the sales of a relatively new specialty plastic. Starting with sales data reported at the close of the third quarter of 1986. A forecast can be made and the results compared to actual sales as they developed through 1989. Finally, the results of this approach contrasted to a trend extrapolation method as a verification of the results.

The problem

Sales of the new plastic products grew rapidly for the period starting with the fourth quarter of 1982 and ending with the third quarter of 1986. However, the industry in which this product was competing also experienced substantial growth during that time. A plot of industry sales versus new product sales shows that the growth of the new product was not caused only by the expansion of the industry. Instead, the new plastic's market share was increasing. The new product was displacing older materials used for the same purposes. Market share is defined here as 100 times new product sales divided by industry sales, putting share on a percentage basis.

This market share was itself growing explosively up to the third quarter of 1986. Clearly, market share could not continue to grow indefinitely at this rate, and the growth of sales eventually would have to parallel the growth of the industry. The questions to be answered by a forecast are:

* When would market penetration level off?

* At what level would market share stabilize?

* What path would the remaining market share growth follow?

Gompertz curve method

The approach here is to fit a Gompertz curve to market share using an economic variable to modify market penetration. The curve was used to forecast market share, and this forecast was extended by an econometric forecast of the industry to project the new product line's sales.

The concept behind the application of a Gompertz curve is to impose a particular shape on the growth path of a time series. Econometrics is used to estimate the parameters associated with that shape. That is, a Gompertz curve is an S-shaped curve, but there is a wide range to that shape.
``` PRODUCT SALES (000)
Time Fitted Actual Error
1987 30.2 33.4 11%
1988 43.8 45.0 3%
1989 43.2 43.7 1%
```

Estimation of the model

The Gompertz curve equation fitted was as follows:

|Mathematical Expression Omitted~

Where D is the Gompertz curve parameter, expected to lie between 0 and 1, measuring the speed of market penetration; SHARE is the target market share the new product is expected to reach; A is a coefficient; ZB371/SC371 is the ratio of corporate profits to corporate sales in the automotive industry; MKTSHARE is 100 times the ratio of new product sales to industry sales. D, SHARE, and A are the unknown values to be estimated.

The profit/sales variable is included to reflect the fact that product users shift to new materials and production processes more quickly when profitability is high. This modification means that the stable market share will actually be equal to SHARE plus X, where X equals the exponent of |Mathematical Expression Omitted~ the average of |ZB371/SC371~). The regression yielded the following curve (fitted from 1983 to the third quarter of 1986);

|Mathematical Expression Omitted~

Forecast

Market share was forecast by solving the Gompertz curve equation for the years beyond the estimation period. The equation was solved by using the values of D, SHARE, and A that were estimated, and plugging in estimates ZB371 (corporate profits) and SC371 (corporate sales) from a macro-econometric model. In this case, of course, we have actual historical values for profits and sales to use. The market share forecast from the fourth quarter of 1986 to the same quarter in 1989, plus the equations fitted values from the fourth quarter of 1982 to the third quarter of 1986, are shown in Figure 1. We see that market share flattens out by 1989. The curve differs from the pure Gompertz curves because of the fluctuations in the profit ratios to the auto industry, which modify the smooth adoption of the new material as a substitute for the old.

Sales are forecast by multiplying the market share forecast by an econometric forecast of the industry. The industry sales estimates come from a regression equation relating the industry to constant-dollar consumption of autos and parts, constant-dollar inventory change and capacity utilization. The industry equation tracks well, increasing the accuracy of the product line sales forecast.

As the new product market penetration reached completion, sales must increasingly follow industry sales and cycles. This fact is reflected in the forecasts generated by the econometric use of Gompertz curves. The forecast showed the peak in market share growth occurring in the third quarter of 1985; the inflection point was already past at the time of the analysis, the third quarter of 1986, and share growth was projected to drop steadily from there on out.

Performance

Historically, the econometric Gompertz curve forecast has performed quite well. Figure 1 shows actual product sales compared to the forecast made only with data through the third quarter of 1986. The forecast picked up the leveling off of sales growth and the effect of the target industry's irregularities on the product's sales. The model's projection that market penetration was nearing completion and that sales soon would closely follow industry sales proved accurate.

Using this approach, we can forecast the later stages of a new products life given only data from the early stages. This technique can be applied to any new product whose market share or sales growth path is likely to be S-shaped. It is a useful way of separating the impact of the economy and of market penetration on new product sales, and of forecasting their combined effect on the future pattern of that product's sales.

If a regression of sales on a time trend was made in the third quarter of 1986, and that regression was used to project sales through 1989, projected sales would have far exceeded actual sales soon after the forecast was made. A straight time trend could not pick up the decline in growth in market share, nor could it track the influence of the economy on the industry and in turn on the new product's sales.

Croxton, Frederick E., and Cowden, Dudley J., Applied General Statistics, Prentice Hall Inc., 1956.

Prescott, Raymond D., "Law of Growth in Forecasting Demand," Journal of the American Statistical Association, December 1922.

Conway L. Lackman is currently associate professor at the Palumbo School of Business at Duquesne University. Prior to his current position, he served the international telecommunications industry as marketing consultant for AT&T, GTE and CBIS in product development. He completed his Ph.D. studies in econometrics and market research from the University of Cincinnati.
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