In many growth models, economic growth arises from people creating ideas, and the long-run growth rate is the product of two terms: the effective number of researchers and their research productivity. We present a wide range of evidence from various industries, products, and firms showing that research effort is rising substantially while research productivity is declining sharply. A good example is Moore's Law. The number of researchers required today to achieve the famous doubling every two years of the density of computer chips is more than 18 times larger than the number required in the early 1970s. Across a broad range of case studies at various levels of (dis)aggregation, we find that ideas — and in particular the exponential growth they imply — are getting harder and harder to find. Exponential growth results from the large increases in research effort that offset its declining productivity.

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想法越来越难找到吗？

在许多增长模型中，经济增长源于人们的创造力，长期增长率是两个术语的乘积：研究人员的有效人数及其研究生产率。我们提供了来自各行各业，产品和公司的大量证据，这些证据表明，研究工作量正在大幅增加，而研究效率却急剧下降。摩尔定律就是一个很好的例子。如今，要使计算机芯片的密度每两年提高一倍，所需的研究人员数量是1970年代初期所需数量的18倍以上。在（分解）聚合的各个级别的大量案例研究中，我们发现想法（尤其是它们所暗示的指数增长）越来越难找到。