I am provoked by this. The benchmark of constant research productivity" defined as the same *real dollar* expenditure on research produces the same *proportional* increase in output? I have heard people say that the benchmark should be that the same share of national product spent on R&D should produce the same proportional increase in output. I have heard people say that the benchmark should be that the natural growth in the share of national product spent on R&D should be such as to produce the same proportional increase in output. I have never heard anybody say that the benchmark is that the same *real dollar* expenditure on research produces the same *proportional* increase in output: **Nicholas Bloom, John Van Reenen, Charles I. Jones, and Michael Webb**: *Are Ideas Getting Harder to Find?*: "One of the key drivers of economic growth during the last half century is Moore’s Law: the empirical regularity that the number of transistors packed onto an integrated circuit serving as the central processing unit for a computer doubles approximately every two years...

...Figure 3 shows this regularity back to 1971. The log scale of this figure indicates the overall stability of the relationship, dating back nearly fifty years, as well as the tremendous rate of growth that is implied. Related formulations of Moore’s Law involving computing performance per watt of electricity or the cost of information technology could also be considered, but the transistor count on an integrated circuit is the original and most famous version of the law, so we use that one here.

A doubling time of two years is equivalent to a constant exponential growth rate of 35 percent per year. While there is some discussion of Moore’s Law slowing down in recent years (there always seems to be such discussion!), we will take the constant exponential growth rate as corresponding to a constant flow of new ideas back to 1971. That is, we assume the output of the idea production for Moore’s Law is a stable 35 percent per year. Other alternatives are possible. For example, we could use decadal growth rates or other averages, and some of these approaches will be employed later in the paper. However, from the standpoint of understanding steady, rapid exponential growth for nearly half a century, the stability implied by the straight line in Figure 3 is a good place to start. And any slowing of Moore’s Law would only reinforce the finding we are about to document.

If the output side of Moore’s Law is constant exponential growth, what is happening on the input side? Many commentators note that Moore’s Law is not a law of nature but instead results from intense research effort: doubling the transistor density is of- ten viewed as a goal or target for research programs. We measure research effort by deflating the nominal semiconductor R&D expenditures of all the main firms by the nominal wage of high-skilled workers, as discussed above. Our semiconductor R&D series includes research spending by Intel, Fairchild, National Semiconductor, Motorola, Texas Instruments, Samsung, and more than two dozen other semiconductor firms and equipment manufacturers. More details are provided in the notes to Table 1 below and in the online data appendix.

The striking fact, shown in Figure 4, is that research effort has risen by a factor of 18 since 1971. This increase occurs while the growth rate of chip density is more or less stable: the constant exponential growth implied by Moore’s Law has been achieved only by a massive increase in the amount of resources devoted to pushing the frontier forward. Assuming a constant growth rate for Moore’s Law, the implication is that research productivity has fallen by this same factor of 18, an average rate of 6.8 percent per year. If the null hypothesis of constant research productivity were correct, the growth rate underlying Moore’s Law should have increased by a factor of 18 as well. Instead, it was remarkably stable. Put differently, because of declining research productivity, it is around 18 times harder today to generate the exponential growth behind Moore’s Law than it was in 1971...

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