Technological Complexity, R&D and Education: Some Pleasant Arithmetic

Persistent trends in R&D intensity and educational attainment, in conjunction with the absence of any trend in per capita income growth, are inconsistent with the predictions of most growth models. Jones (2002) has made a strong point that the data are consistent with out-of-steady state predictions of his semi-endogenous growth model. He concludes that when secular increases in R&D intensity and educational attainment will come to an end, income growth can be expected to decline dramatically. In this paper we suggest an alternative explanation that predicts no such collapse. We assume that increases in productivity can result from formal R&D effort and from learning by doing. However, during the latter half of the 20th century, increased technological complexity has made passive learning more difficult. We argue that firms have consequently substituted R&D for learning and, because skilled workers can overcome the challenges of learning in a more complex environment more readily than can unskilled workers, the relative demand for skill has risen. The consequent increase in the returns to skill in turn has induced an increase in educational attainment. Our theory explains how increases in R&D intensity and educational attainment can be equilibrium responses to changing conditions that make growth more difficult. Despite greater complexity, R&D and educational attainment must, as in Jones (2002), eventually cease to grow. But, in stark contrast to Jones, our theory does not imply that income and productivity growth will collapse once the new steady state is reached. We formalize these ideas with a general equilibrium model of R&D and learning in the spirit of earlier work by Young (1991, 1993), Lucas (1993), and Parente (1994). For simplicity we assume that R&D is not necessary to develop new product generations, which arrive to each firm randomly according to an exogenous Poisson process. Instead, R&D is assumed to influence the productivity of a new product at the time it is launched, and the more R&D that is conducted, the less there is left to learn. Skilled labor is a necessary input into R&D, and it also enhances a firm’s ability to learn in production. We further assume that the value of skilled labor in learning increases the more difficult learning is. Thus, we show that an increase in the difficulty of learning raises the demand for skilled workers in R&D and in production. The immediate effect is to increase the price of skill. The initial increase in wages of skilled workers is offset over time by an induced rise in the supply of skills. To sustain an increased supply of skills in the long run wage inequality must remain higher than before the increase in the difficulty of learning. These dynamic responses are obtained in a setting in which the aggregate rate of growth is constant. Thus, a reversal in the difficulty of learning would induce a decline in R&D and in the returns to skill, but no decline in economic growth.