Fisher-Pry Substitution Model
Also known as: Fisher-Pry Model, Technological Substitution Model, Logistic Substitution Forecasting, Fisher-Pry Curve
The Fisher-Pry Substitution Model, introduced by John Fisher and Robert Pry of General Electric in 1971, is a foundational technique for forecasting technological substitution — the process by which a new technology displaces an older one. Its empirical premise, supported by dozens of historical cases from synthetic to natural materials and from one manufacturing process to another, is that the fractional market share captured by the new technology follows a logistic (S-shaped) growth curve. The model's elegance lies in a transformation: when the takeover ratio f/(1-f), the ratio of the new technology's share to the old's, is plotted on a logarithmic scale against time, the substitution traces a straight line. This linearization makes it easy to fit, interpret, and extrapolate substitutions from sparse early data, which is why the Fisher-Pry curve remains a workhorse of technological forecasting.
Key highlights
- Reduces S-shaped substitution to a straight line, making fitting, diagnosis, and extrapolation simple and transparent.
- Requires only a fractional-share time series and yields interpretable parameters: a rate and a midpoint.
- Delivers a single intuitive summary of speed — the ten-to-ninety-percent takeover time ln(81)/alpha.
- Validated across many historical technological substitutions, giving it strong empirical pedigree.
Intuition
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How it works
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When to use it
Use the Fisher-Pry model when one technology, product, material, or process is clearly displacing another in a shared market or function, and you have a time series of the new alternative's fractional share that already shows the substitution underway. It is ideal for forecasting how quickly the takeover will complete and when key share thresholds will be crossed, especially when early data are limited but a logistic mechanism is plausible. It is poorly suited to cases where multiple technologies compete simultaneously (where multi-mode substitution models are needed), where the new technology may not go to completion, where the market itself is the thing growing rather than a share being transferred, or very early before any substitution trend is visible. It also presumes the displaced technology is not itself improving fast enough to reverse the trend.
Strengths & limitations
- Reduces S-shaped substitution to a straight line, making fitting, diagnosis, and extrapolation simple and transparent.
- Requires only a fractional-share time series and yields interpretable parameters: a rate and a midpoint.
- Delivers a single intuitive summary of speed — the ten-to-ninety-percent takeover time ln(81)/alpha.
- Validated across many historical technological substitutions, giving it strong empirical pedigree.
- Assumes substitution proceeds to completion, which fails when the incumbent survives or rebounds.
- Handles only one-to-one substitution; simultaneous multi-technology competition needs richer models.
- Forecasts are fragile in the early phase when few points constrain the slope and midpoint.
- The constant-rate logistic shape ignores shocks, policy shifts, and improvements in the old technology.
Common pitfalls
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Applications
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Frequently asked
What do the parameters alpha and t0 mean?
Alpha is the substitution rate: the slope of the straight line on the semilog plot, governing how fast the new technology takes over. The midpoint t0 is the time at which the new technology reaches fifty percent share, where ln[f/(1-f)] crosses zero. A convenient derived quantity is the ten-to-ninety-percent takeover time, ln(81)/alpha, which expresses the whole transition's speed in a single number of years. Together alpha and t0 fully specify the logistic curve and hence the entire forecast.
Why transform to f/(1-f) instead of fitting the S-curve directly?
Because the transformation linearizes the problem. Plotting the odds ratio f/(1-f) on a logarithmic axis against time turns the logistic S-curve into a straight line, so you can fit it with ordinary linear regression, judge goodness of fit by eye, and extrapolate trivially. The straightness of the transformed data is also a built-in diagnostic: if the points lie on a line, the Fisher-Pry mechanism is operating; if they curve, the simple model is suspect and a richer one may be needed.
When does the Fisher-Pry model break down?
It breaks down whenever its assumptions are violated. If the substitution does not go to completion — because the incumbent improves, regulation intervenes, or the new technology stalls — the logistic shape will mislead. If several technologies compete at once, a single two-way substitution model is inappropriate and multi-mode logistic methods are required. And in the very early phase, with only a few data points, the estimated slope and midpoint are highly uncertain, so forecasts should be treated as provisional until the trend is well established.
Sources
- 1.Fisher, J. C., & Pry, R. H. (1971). A simple substitution model of technological change. Technological Forecasting and Social Change, 3, 75-88.
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ScholarGate. (2026, June 23). Fisher-Pry Substitution Model. ScholarGate. https://scholargate.app/futures-foresight-studies/fisher-pry-substitution