*The Harvard Journal of Law & Technology recently released its Fall 2010 issue, now available online. John M. Golden, author of “Innovation Dynamics, Patents, and Dynamic-Elasticity Tests for the Promotion of Progress” has written an abstract of his article for the Digest, presented below.*

*- The Digest Staff*

**JOLT Print Preview: Innovation Dynamics, Patents, and Dynamic-Elasticity Tests for the Promotion of Progress
**John M. Golden

This article develops a model for innovation dynamics and studies its implications for technological development and policies to promote innovation. The model generates a diverse array of trajectories for technological progress as a function of time. Among the forms of possible trajectories, trajectories featuring linear or exponential growth are only special cases. The model suggests that growth according to a supralinear power law might be more common: i.e., the cumulative amount of innovation might frequently be expected to grow like the quantity *t ^{z}*, where

*t*is a measure of time and

*z*is a positive exponent.

The model also suggests that, under a variety of circumstances, whether a given incremental policy change accelerates or decelerates technological progress will be determined by a “dynamic-elasticity” or “double-ratio” test involving comparison of percentage changes in model parameters. The existence of such double-ratio tests might suggest that patents’ effects on innovation are even more sensitive to technologic and industrial circumstance than has commonly been appreciated.

The model’s mathematical form is that of a differential equation. This equation resembles a Newtonian equation of motion for a physical object moving in the presence of air resistance. The displacement *x* represents the cumulative amount of technological progress at a given time *t*, and the velocity *v* represents the rate at which new progress occurs. Within the model, such progress is accelerated by “push” terms, such as a constant push term *α*, and decelerated by “drag” terms, such as a linear air-resistance-like term –*γv*. Significantly, the model features among its push terms a positive-feedback term *βx ^{ε}*, which reflects the tendency of past technological progress to generate enhanced demand, opportunities, and capacities for further technological progress.

The interaction between push and drag terms generates the diverse array of potential trajectories mentioned above. Further, the time-dependent nature of the model’s *x* and *v* inputs means that the basic functional behavior of a trajectory for technological progress can change with time. Different parameter regimes (e.g., a small-*v* and small-*x* regime versus a large-*v* and large-*x* regime) frequently yield different combinations of push and drag terms that dominate the time-dependent behavior of *x*(*t*). Many forms of such behavior feature growth according to a supralinear power law *t ^{z}*

^{ }with

*z*> 1.

Numbers of issued patents are sometimes taken as a crude measure of technological progress. Thus, it might be viewed as significant that growth in the cumulative number of U.S. patents appears commonly to correspond to a supralinear power law, a form of behavior that this article’s model often predicts. More precisely, growth in the cumulative number of U.S. patents can be plausibly described as having experienced three different historical phases: (1) a first phase from about 1793 through 1856, in which the cumulative number of U.S. patents grew roughly as *t*^{2.5}, where *t* represents the time elapsed since 1790: (2) a second phase of extraordinarily robust growth from about 1856 through 1894, in which the cumulative number of patents grew roughly as *t*^{7.3}; and (3) a third phase of intermediate-level growth from about 1894 through 2009, in which the cumulative number of patents grew roughly as *t*^{3.4}. Further work might provide better ways of characterizing U.S. patent growth and its historical phases. In the meantime, the present study might be viewed as corroborating a suggestion from this article’s theoretical model that supralinear power-law behavior might be a commonly occurring pattern of such growth.

Another potentially significant implication of the model is the existence of dynamic-elasticity or double-ratio tests for whether a policy change will promote progress. A double-ratio test commonly takes a form such as (*ΔB*/*B*)/(*ΔC*/*C*) > 1, where *ΔB* represents the policy-induced increase in a parameter *B* associated with progress acceleration (e.g., the coefficient *β* in the positive-feedback term *βx ^{ε}*), and where

*ΔC*represents the policy-induced increase in a parameter

*C*associated with progress deceleration (e.g., the coefficient

*γ*in the negative-feedback term –

*γv*). Such a double-ratio test contrasts with classic single-ratio tests that commonly take the form

*ΔB*/

*ΔC*> 1.

If a double-ratio test applies, the success or failure of a policy in promoting progress might be more sensitive to the nature of an industry and its technology than has been commonly realized. This follows from the fact that double-ratio tests are sensitive not only to the magnitudes of policy-induced changes such as *ΔB* and *ΔC*, but also to the preexisting magnitudes of *B* and *C* themselves. All four of these magnitudes can vary by industry or technology. Thus, a double-ratio test provides four ways, rather than merely two, by which industry or technology differences can have an effect.

For policymakers looking to increase the rate of invention, double-ratio tests can suggest potentially useful rules of thumb. For example, when technological development is characterized by enormous non-patent-related drag—perhaps due to high regulatory, educational, or disruption costs for introducing new technologies—there might be particularly good reason to expect that a patent-related policy change will have a net positive effect even if the policy change is expected to increase both drag parameters and push parameters. On the other hand, for technological situations in which preexisting drag parameters are comparatively small, such a policy change might be properly expected to be much more likely to act as a net impediment, rather than a net stimulant. Such rules of thumb might thereby help explain the common perception that strong patent rights are more likely to help promote progress in pharmaceuticals than in software.

In sum, this article’s theoretical model provides insights into (1) the potential for different behavioral regimes for innovative progress, (2) the vulnerability of such behavioral regimes to change, (3) the ways in which a particular innovation-related policy can contribute to push and drag, and (4) the existence of dynamic-elasticity or double-ratio tests that turn on percentage effects on push and drag parameters. In the embryonic study of innovation dynamics, these contributions appear to constitute a step forward.