Endogenous Technological Change

This 1990 Journal of Political Economy paper by Paul Romer models long-run growth as driven by technological change that arises from intentional research investment by profit-maximizing firms, treating technology – specifically, a design for a new producer durable – as a nonrival but only partially excludable good: once created, a design can be used in production without limit, but because it cannot be perfectly kept secret its benefit to future researchers is nonexcludable even though its use in manufacturing the specific patented good is legally protected. Because a nonrival input makes the aggregate production function nonconvex, Romer shows that ordinary price-taking competition cannot be supported and instead builds an equilibrium with monopolistic competition, in which firms that have purchased a patented design earn a markup over marginal cost that is bid away, in present-value terms, by free entry into the market for designs. Solving for a balanced-growth-path equilibrium, the paper’s central result is a growth equation that depends on the interest rate and on the total stock of human capital devoted to research, but not on the size of the labor force or on the unit cost of manufacturing new capital goods, implying that a country’s raw population is not the relevant scale variable for growth and that, if the total stock of human capital is too low, the model can generate no growth at all. Two distinct externalities – spillovers from a new design onto future researchers’ productivity, which are entirely nonexcludable, and the wedge introduced by monopoly markup pricing in the market for durables – cause equilibrium research investment to fall short of the socially optimal level. Romer argues that, in contrast to his own earlier (1986) model or Arrow’s (1962) learning-by-doing model, in which knowledge accumulation was forced by assumption to move in step with physical capital accumulation, a subsidy to physical capital is here a poor and possibly counterproductive substitute for a direct subsidy to research, and that integration into world markets speeds growth for any country – including a populous one such as China or India – by pooling the effective supply of human capital available for research, a claim supported with historical evidence from Sokoloff (1988) on U.S. counties gaining access to navigable waterways.

Increasing Returns and Long-Run Growth

This 1986 Journal of Political Economy paper by Paul Romer builds a fully specified competitive-equilibrium model of long-run growth in which knowledge is an input to production with increasing marginal productivity, in contrast to the diminishing-returns assumption underlying the standard Ramsey-Cass-Koopmans growth model. Growth is driven by profit-maximizing firms that invest forgone consumption in a research technology exhibiting diminishing returns (so the proportional growth rate of a firm’s own knowledge is bounded above by a constant), while the resulting stock of knowledge generates a positive externality across firms because it cannot be perfectly patented or kept secret; production of the consumption good is globally convex, not concave, in the aggregate stock of knowledge. Romer proves that a finite-valued social optimum exists despite the global increasing returns, because diminishing returns in research bound the feasible growth rate of knowledge, and that – under an additional asymptotic-growth condition – a suboptimal competitive equilibrium with externalities also exists, in which private agents underinvest in research relative to the social optimum because they do not internalize the externality. Historical productivity data for the three successive “leader” countries since 1700 (the Netherlands, the United Kingdom, and the United States), decade-by-decade U.S. per capita growth since 1800, a nonparametric test for trend across eleven countries’ growth rates, and the repeated failure of growth-accounting exercises to explain measured output growth from measured input growth are all offered as evidence consistent with, though the paper is careful to say not decisive proof of, increasing rather than diminishing returns. Under linear or sufficiently weakly curved utility, per capita consumption and output can grow at a rate that is monotonically increasing over time toward an asymptotic upper bound, small current or anticipated future disturbances can have permanently amplified aggregate effects, and – in a multicountry extension with imperfectly mobile knowledge – countries starting from identical initial conditions can diverge permanently, with the composite knowledge/capital good flowing toward the initially more developed country. Romer is explicit that these unbounded-growth and instability results depend on the specific functional forms and utility restrictions used in the worked examples (e.g., logarithmic versus linear utility) and that the model is deliberately restricted to a single state variable (knowledge), holding population and physical capital fixed, for analytical tractability.

Paul M. Romer | Macro Paper Warehouse

Endogenous Technological Change

Increasing Returns and Long-Run Growth