Empirical Laws Of Progress

Technological progress (as distinguished from knowledge) is normally understood, as above, in terms of the performance of some activity or function, however generic (for example, transportation, communications, life expectancy). Functional capability typically grows according to a different 'covering law', namely the 'law of constrained growth'. The idea of such a law was originally suggested by the biologist Raymond Pearl, who applied it (for example) to the growth of a colony of fruit flies in a bottle or yeast cells in a dish (Pearl 1925; Lotka 1956 [1924]). Growth is constrained by natural limits.

It is worth mentioning here that two important empirical regularities have been put forward, by different authors, as quasi-general laws. The first pseudo-law is the so-called 'experience curve' - or 'progress function' - which treats direct labor input, or costs, as a characteristic function of cumulative production experience, where the parameters of the curve vary from technology to technology. This regularity was first noted in aircraft manufacturing (Wright 1936) and subsequently observed in a variety of other cases (namely, Hirsch 1956; Conway and Schultz 1959; Rapping 1965; Argote and Epple 1990; David 1970).

The good news is that once a trajectory as characterized by a rate of progress in relation to experience has been established, it is likely to continue for some time, perhaps as in the case of microelectronics even for many doublings of cumulative production experience (see Table 1.1). Unfortunately, however, the progress function or learning curve has never become a reliable basis for forecasting a priori. There have been many efforts to 'explain' the observed regularity in terms of economic theory, but so far the results are mixed. One of the crucial difficulties is that empirical progress functions may change direction unexpectedly (Ayres and Martinas 1990). In many cases, it appears that there are limits to learning, in any given situation. The earliest and most noteworthy effort to explain

Table 1.1 Examples ofproductivity improvements from experience

Example Improving Parameter Cumulative Parameter Learn. Curve Time Frame No of vol.

Slope doublings

Model-T Ford

Production

Price

Units produced

86%

1910-

-1926

10

Aircraft Assembly

Direct man-hrs per unit

Units produced

80%

1925-

-1957

3

Catalytic cracking units

Days needed per

Million bbls run

90%

1946-

-1958

10

for petroleum

100 million bbls

Cost of fluid cracking

Cost per bbl of capacity

Installed design

94%

1942-

-1958

5

units

capacity of plants

80%*

Equipment maintenance

Avg. time to replace a

No of replacements

76%

circa 1957

4

in electric plant

group of parts during a shutdown

Man-hrs per barrel in

Avg. direct man-hrs per

Millions of bbls refined

84%

1860-

-1962

15

petroleum industry

bbl refined

in US

Electric-power

generation

Mils per kW-hour

Millions of kW-hrs

95%*

1910-

-1955

5

Steel production

Production worker man-hrs per unit produced

Units produced

79%

1920-

-1955

3

Integrated circuit prices

Avg. price per unit

Units produced

72%*

1964-

-1972

10

MOS/LSI prices

Avg. price per unit

Units produced

80%

1970-

-1976

10

Electronic digital watch

prices

Avg. factory selling price

Units produced

74%

1975-

-1978

4

Hand-held calculator

prices

Avg. factory selling price

Units produced

74%

1975-

-1978

2

MOS dynamic RAM

Avg. factory selling price

No of bits

68%

1973-

-1978

6

prices

per bit

Example Improving Parameter Cumulative Parameter Learn. Curve Time Frame No of vol.

Slope doublings

Disk memory drives Avg. price per bit No of bits 76% 1975-1978 3

Price of minimum active Price of minimum No of functions 60% 1960-1977 13

electronic function in semiconductor function produced by (early semiconductor products semiconductor industry products)

Note: * Constant Dollars. Source: Cunningham (1980).

the phenomenon was by Arrow (Arrow 1962). Other efforts include Oyi (1967), Preston and Keachie (1964), Sahal (1979, 1981). The subject has not been discussed intensively in recent years, however.

The second pseudo-law is the 'logistic', or S-shaped, curve, often modeled on a simple biological process such as yeast cells reproducing in a constrained medium (Pearl 1925).12 The logistic function takes values between zero and unity. It increases slowly at first, then more rapidly until the slope reaches an inflection point, after which the slope gradually falls again to zero as the function approaches unity. The simplest form of this function is the solution to a differential equation df i 5 f 1 2f) O.D

where f is symmetric about the origin on the time axis and symmetric, with an inflection point, at f = 0.5 on the vertical axis.

Quite a number of adoption or diffusion phenomena seem to have fit this pattern, or a closely related one. One of the early economic studies invoking this law was on the adoption of hybrid corn (Griliches 1957). Edwin Mansfield used the logistic function to describe the rate of adoption of an innovation in a firm (Mansfield 1961, 1963). Others have applied it to a variety of adoption and diffusion phenomena (for example, Fisher and Pry 1971).13 Early applications to technological change were noted especially by Ayres (1969) and later by Linstone and Sahal (1976). Market researchers, such as Mahajan and colleagues have also adopted the logistic form and simple variants to explain market penetration (Easingwood et al. 1983; Mahajan and Schoeman 1977; Mahajan and Peterson 1985).

The form of the function can be varied by modifying the above differential equation, mainly by adjusting parameters or adding terms on the right-hand side. For instance, the inflection point can be in the lower-left quadrant, or in the upper-right quadrant, depending on parameters (for example, Blackman 1972; Skiadas 1985). In recent years double logistics and other complexities have been suggested (Meyer and Ausubel 1999; Meyer et al. 1999).

Why is the pattern of acceleration followed by deceleration so general? Recall Schumpeter's description of a radical innovation as the implementation of 'new combinations' such as new goods (or services), new methods of production, new markets, new sources of supply and new forms of organization (Schumpeter 1934, p. 66). Schumpeter was not only referring to innovations in the realm of products or processes. Examples of important social inventions with economic implications include laws and courts-of-law, taxes, professional armies, insurance, public schools, universities, churches, and various forms of governance, both corporate and political.

But notwithstanding Marchetti's many examples, and others, the S-curve tool has proven to be unreliable as a 'law', for quantitative forecasting. There are too many exceptions and alternative shapes for the S-shaped diffusion curve. Historical examples developed for various biological and epidemiological cases include those of Gompertz (1832), Pearl (1925), Bailey (1957) and von Bertalanffy (1957). But the bottom line is that the range of possible variations is extremely large and there is no way to predict a priori which shape the curve will take in any given case.

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