Chapter 5 Theories of Endogenous Growth

Economics 314 Coursebook, 2010 Jeffrey Parker 5 THEORIES OF ENDOGENOUS GROWTH Chapter 5 Contents A. Topics and Tools ............................................................................. 1 B. The Microeconomics of Innovation and Human Capital Investment ........... 3 Returns to research and development .............................................................................. 4 Human capital vs. knowledge capital ............................................................................. 6 Returns to education ..................................................................................................... 6 C. Understanding Romer=s Chapter 3, Part A ............................................. 9 Introduction .................................................................................................................9 Romer’s modeling strategy and the research literature ...................................................... 9 The basic setup of the R&D model ............................................................................... 10 The knowledge production function .............................................................................. 11 Analysis of the model without capital ........................................................................... 12 The R&D model with capital ...................................................................................... 16 Returns to scale and endogenous growth ....................................................................... 17 Scale effects in the R&D model .................................................................................... 18 D. Understanding Romer’s Chapter 3, Part B ........................................... 20 The specification of the human-capital model ................................................................ 20 Analysis with the human-capital model ........................................................................ 20 Output per person vs. output per worker ........................................................................ 21 The specification of Romer’s predation model ................................................................ 24 Agents’ decisions in the predation model ....................................................................... 25 E. Suggestions for Further Reading ........................................................ 28 General texts on modern growth theory ......................................................................... 28 Selected seminal papers in modern growth theory .......................................................... 28 F. Works Cited in Text ........................................................................ 29 A. Topics and Tools The neoclassical growth theory that we studied in Chapters 3 and 4 largely evolved in the 1950s. There was considerable filling-in of details in the 1960s, but by the 1970s growth theory had largely become moribund. A tremendous revitalization has occurred since the 1980s, spurred by several shortcomings of the previous theories. First, because growth rates are exogenous in the Solow and Ramsey models, these theories are unable to explain why growth rates (and, in particular, the rate of technological progress) might change from one time period to another. This became an important research topic in the 1980s when emerging data began to convince ma- croeconomists that productivity growth in the United States and other advanced countries had declined significantly beginning about 1974. A second failing of neoclassical growth theory is that it cannot explain the large and lasting differentials in per-capita income that we observe across countries and regions. Solow’s growth model implies more rapid convergence of incomes than seems actually to have occurred, particularly between developed and developing countries. International differences in technological capability can help explain this gap, but beg for an economic explanation that cannot be provided by models in which technology is exogenous. Another feature of neoclassical growth models that some economists and poli- cymakers find troublesome is that they provide no mechanism by which the saving and investment rate (or government policies directed at influencing it) can affect the steady-state growth rate. While this conclusion of neoclassical models is not obviously counterfactual, many find it counterintuitive and have explored models in which saving plays a more central role. The pioneer of “endogenous growth theory” is Paul Romer, a former colleague 1 but not a relative of our textbook author. His 1986 paper in the Journal of Political Economy is a seminal work in the modern revitalization of growth theory. The prin- cipal engine behind endogenous growth is the elimination of the assumption of de- 2 creasing returns to “capital.” In order to justify this radical departure from a long- 1 In the early 1990s, there were three famous young Romers teaching macroeconomics at the University of California at Berkeley. Paul, who focuses on growth theory and is now at the Stanford Business School, David (our author), who is a prominent neo-Keynesian, and Da- vid’s wife Christina, who is a macroeconomic historian and now chair of the Council of Eco- nomic Advisors in the Obama Administration. 2 This is a good time to clarify two closely related concepts: “diminishing marginal returns” and “decreasing returns to scale.” The former is usually applied to changes in only a single factor of production holding all other factors constant. Thus, diminishing returns to capital means that when more capital is added to production with all other factors held constant, the ensuing increase in output becomes smaller as more and more capital is added. Returns to scale usually apply to the effect on output of simultaneous changes in many or all factors of production. “Constant returns to scale” by itself means that increases of an equal percentage in all factors leads to an increase of the same percentage in output. In this chapter, we will extend the idea of returns to scale to situations where a subset of factors changes. 5 – 2 established assumption of microeconomic theory, Romer and his followers have broadened the definition of capital to include human capital and/or knowledge capital. As we shall see, once this broader view of capital is adopted it is no longer ob- vious that there are decreasing returns. This leads to radical changes in the conclu- sions that we derive from models that are otherwise similar to those of Solow and Ramsey. There are three basic models developed in the chapter: the R&D model of 3.2 and 3.3, the human-capital model of 3.8, and the production-protection-predation model of section 3.11. We will give attention to all three. The mathematical tools used here are largely familiar ones. To keep the analysis simple, Romer reverts to the simple Solow assumptions about saving (and other stat- ic resource allocation decisions). The original literature on these models bases decisions on utility and profit maximization, which is more satisfactory, but the dynamic properties of the model are similar with constant growth rates, so Chapter 3 will teach you the essential features of the model without all the complicated mathemat- 3 ics that we saw in Romer’s Chapter 2. As in previous chapters, we will be searching for steady-state balanced growth paths. To find these, we will usually look for situations in which the growth rates of the key state variables are constant. In most of the models of this chapter, there will be two state variables, either physical capital and knowledge capital or physical capital and human capital. We will use a two-dimensional phase plane that looks on the surface like the one in the Ramsey model, but is fundamentally different because in these models both variables are state variables that cannot jump, whereas in the Ramsey model c was a control variable that could jump vertically to adjust to changes in economic conditions. B. The Microeconomics of Innovation and Human Capital Investment Romer’s Chapter 3 examines the macroeconomic implications of investment in research and development (innovation) and human capital. However, some of the most important theoretical issues in modeling these concepts are microeconomic in nature. The seminal papers in the modern growth literature vary a lot in how careful- 3 Barro and Sala-i-Martin (2004) is a more advanced textbook that looks at more sophisticated versions of these models. Acemoglu (2009) is a more recent, and more mathematical, treat- ment. For those interested in learning about them, Econ 454 develops the more complete models. 5 – 3 ly they model these microeconomic issues, but Romer’s simplified presentation of the models largely ignores the microeconomics. In this section, we briefly consider some of the basic microeconomic issues involved. (Romer discusses some of these topics in Section 3.4.) The models of Chapter 3 attempt to make endogenous the “production” of technology. In the R&D model, an R&D sector produces additions to society’s stock of technical knowledge. In the second, individuals add to their human capital by spend- ing time in education rather than producing output. A key microeconomic issue that underlies this analysis is the question of what incentive people have to make investments in knowledge or in human capital. Unless people get utility directly from the process of research or education (which cannot be ruled out—consider the case of the “professional

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