Modern Growth Theory

Citation

Olivier Cardi (2013), "Modern Growth Theory", Indian Growth and Development Review, Vol. 6 No. 2, pp. 306-311. https://doi.org/10.1108/IGDR-08-2013-0033

Introduction

This book presents the foundations of modern economic growth, offering a detailed analysis of the technical tools used to solve growth models in a pedagogical way. While there are excellent books on economic growth, such as Introduction to Modern Economic Growth by Acemoglu (2009), The Economics of Growth by Aghion and Howitt (2008), Economic Growth by Barro and Sala-i-Martin (2003), Introduction to Economic Growth by Jones (1998), the first three chapters of Romer ' s (2006) Advanced Macroeconomics, and Economic Growth by Weil (2005) among others, Dipankar Dasgupta ' s book is essential reading for economists. The reason is threefold. First, each chapter contains an intuitive interpretation of the mathematical tools applied to growth models. In this regard, the first chapter is remarkable as it presents dynamic optimization in an intuitive manner. Economists equipped with differential calculus should be able to grasp the book ' s content with comfort. Second, Dasgupta ' s book explains how to solve growth models without skipping technical difficulties. Chapter 4 is essential and strongly recommended to anyone wishing to learn the necessary background before reading recent articles on economic growth. Third, the literature on economic growth is vast and diverse and a non expert may feel lost tackling this subject; using a unified theoretical framework, the book carefully and progressively highlights how modern economic growth has been built from Solow to Grossman and Helpman. While Jones (1998), Romer (2006) and Weil (2005) concentrate on economics issues and most of the chapters of Acemoglu (2009) or Aghion and Howitt ' s (2008) books skip details of derivation, Modern Growth Theory is just the right book for graduate students and economists who are willing to go deeper into the new growth theory. As well as Barro and Sala-i-Martin ' s (2003) Economic Growth, Modern Growth Theory is another best reference that should be used by every graduate student.

Outline of the book

To review and summarize the material of this book, I will confine myself to the essential points. The book is divided into two parts. The first is a quick, essential refresher of the mathematical tools used in the literature of economic growth and introduces the standard neoclassical models with exogenous technical change. The second part explores the determinants of technical progress. While in earlier models assuming perfectly competitive markets, technical change is the result of an externality, in models at the end of the 1980s and the beginning of the 1990s it is a conscious outcome of investment in R & D activities or education. In this second part, all the major articles which have founded the new growth theory are dissected.

Chapter 1 briefly presents the Solow (1956) model in a rigorous yet intuitive way. Since the dynamics of the neoclassical model of economic growth have been thoroughly analyzed by a large number of excellent books, the author instead sheds light on an issue which is usually not addressed by existing manuals. This issue is related to the assumption of reversible investment which is often viewed by students as a strong assumption and thus deserves comment.

While Chapter 1 considers a private economy, Chapter 2 compares planned and private decisions. The planner maximizes intertemporal welfare over an infinite horizon. The technical treatment of the optimal allocation of resources between consumption per capita and capital accumulation (per unit of effective labor) is illuminating in many respects. It sheds light on the economic interpretation of Hamiltonian. It graphically illustrates the optimal choice by the planner in a very intuitive way by using the transformation locus between per capita consumption and capital accumulation. Using simple words, the author moves progressively towards the transversality condition and the concept of no-arbitrage condition to interpret the co-state variable. All this essential material is contained in just ten pages! Then the author tackles a tricky issue related to golden rule and its associated concept of modified golden rule, providing the opportunity to discuss the intertemporal trade-off in the Ramsey-Cass-Koopmans model: because agents value present consumption more than future consumption, the short-term sacrifice is too high compared with the long-term gain which implies that the per unit of effective labor capital stock is smaller than the one associated with golden rule. In my view this point perhaps deserves more explanation in the book and could fill the missing link between the Solow model with exogenous savings and the Ramsey-Cass-Koopmans model.

One major conclusion of the first part is that long run growth of standard of living is not possible without technical change as technical progress circumvents the law of diminishing returns in physical capital accumulation. However, technical progress is exogenous and therefore arises from unexplained causes. The second part of Dasgupta ' s book introduces the reader to the different pathways taken by economic theory to provide an explanation for the technical change. If the reader wants a quick overview of the theory of economic growth I would urge her/him to read pages 50-52 of Dasgupta ' s book as they are remarkably clear.

The first pathway followed by the theory to circumvent the force of diminishing returns is to assume that investment undertaken by an individual firm benefits other existing firms. Put differently, a product or process innovation can be disseminated across other firms, which then experience an increase in their productivity. Hence, the overall return on investment becomes higher than its private return due to improvements in other firms ' productivity. As a result, there is room for public intervention since firms underinvest with respect to the socially optimal level of investment. While the literature modelling technical progress as an externality is diverse, the different classes of models share a common result: the existence of spillovers circumvents the law of diminishing returns in capital accumulation. Chapter 3 of Dasgupta ' s book provides an excellent review of this literature.

Spillovers could be seen as the result of learning by doing. More precisely, production activity induces workers to improve the production process, and further induces greater investment in capital goods. Put differently, as assumed by Arrow (1962), the exposure to physical capital produces improved labor skills by “inducing workers to learn”. Hence, one additional unit of physical capital increases output as in the Solow model, but also contributes to the development of new ideas and therefore raises the level of technology. However, entrepreneurs are not aware of the effect of capital accumulation on technical progress as reflected by a private marginal product of capital below its social return. Dasgupta provides a mathematical treatment of the comparison of the planner ' s and private economy ' s decisions. In my view, this part is essential reading for an in-depth understanding of the concept of externality. The author ends Chapter 3 by investigating sustained endogenous economic growth in the neoclassical model. The AK model assumes that the production function displays constant returns to scale with respect to capital. In this case, the law of diminishing returns vanishes and the economy grows at a long run rate equal to the saving rate. Hence, capital accumulation could act as the engine of sustained economic growth.

In the Arrow (1962) model, accumulation of skills is not the result of a deliberate effort but rather the outcome of learning in the production process. In this regard, this theory is not entirely satisfactory. So economic growth theory has developed models of human capital formation where the acquisition of skills is the result of a conscious decision. In Chapter 4, the author solves different versions of the two-sector model of growth. Before presenting the model of Lucas (1988) which is, together with Romer ' s (1990) model, the cornerstone of the theory of endogenous growth, Dasgupta introduces the reader to two-sector growth models by considering a two-sector AK model originally proposed by Rebelo (1991). In this simplest possible endogenous growth model, the consumption sector features decreasing returns to capital while the investment sector is described by an AK technology with constant returns to capital. As noted by Felbermayr and Licandro (2005, p. 2), the two-sector AK model, which is almost ignored by today ' s major growth textbooks, predicts that the relative price of investment trends downward in line with the evidence. More precisely, as the economy accumulates capital, the Rybczynski effect implies that the production of the more capital intensive sector increases so that the price of capital relative to consumption falls. As emphasized by Dasgupta, the decline in the relative price circumvents the depressing effects of diminishing returns in capital accumulation.

Chapter 4 presents the two-sector model of Lucas (1988) where the investment sector is replaced by a human capital sector. A major feature of this model is the presence of an externality which affects the production of the final good. More precisely, the more skilled workers are, the better resources are used. Since this effect is not internalized by workers when they make their decision on the acquisition of skills, there is an externality. While it is not necessary to produce endogenous growth, the existence of positive externalities leads to higher rates of growth for consumption and capital. Since the level of skills is not socially optimal in the private economy, the government must subsidize education. At this stage it is necessary to mention that while each model of endogenous growth emphasizes a peculiar element of growth, only the combination of these elements can explain the comparative advantage of advanced economies in the production of complex goods. In this regard, Costinot (2009) sheds light theoretically and empirically on the specialization of countries following trade liberalization: economies which specialize in the more complex goods are those where the product of institutional quality and workers ' productivity is larger. Institutions of better quality imply a higher degree of labor contract enforcement while workers ' productivity depends on the level of human capital.

As well as the degree of contract enforcement and the maintenance of law and order, economic growth would be impossible without public infrastructure. Chapter 5 of Dasgupta ' s book tackles a major issue related to the development of infrastructure and economic growth. This chapter starts with the presentation of the works by Barro (1990) and Barro and Sala-i-Martin (1992) who introduce infrastructure as a flow. In this model, the production function depends on capital, labor and government spending on infrastructure. This model is attractive in three respects. First, as infrastructure is supplied by the state and considered as an input, there is room for policy intervention. More precisely, government spending on infrastructure raises the marginal productivity of capital and therefore has a positive effect on the growth rate. Second, as public investment must be financed by taxes for the budget constraint to be balanced, there exists an optimal level of tax: higher taxes raise the growth rate as higher infrastructure increases the marginal product of capital but exerts a negative impact by reducing consumption. Interestingly, as proved by Dasgupta, the growth maximizing tax rate is also welfare maximizing. Third, while the social planner internalizes the social marginal productivity of capital, the firm does not. So the author compares the planner with the private economy, assuming congestion or not. In what follows, Dasgupta develops an interesting two-sector model with two key features: infrastructure is a stock instead of a flow and the government sector providing public capital is not a profit maximizer but rather employs public capital to capacity. Contrasting the planner solution with the mixed economy solution, it is found that the former yields higher welfare while the latter leads to a higher rate of growth, and thereby more employment growth, thus raising a policy question.

Since knowledge appears to be a prime driver of economic growth over time and new technologies are created by profit-seeking individuals, we must understand how factor endowments, expenditure on research and development and market structures interact to determine technological change. Romer (1990) and Grossman and Helpman (1991a) develop alternative conceptual frameworks with a research sector to formalize the growth process through the creation of new ideas. While in Romer ' s framework, expanding varieties of inputs raise the productivity of the final good sector, Grossman and Helpman formulate a model where greater variety of products raises households ' utility. These models presented in Chapter 6 share the feature of imperfectly considering competitive markets. Because prices are higher than marginal cost, there is a reward for innovation. Beyond the existence of endogenous growth, these models are a crucial move towards capturing the mechanism of the creation of new ideas by specifying the costs and benefits of investing in new technologies. Dasgupta emphasizes the role of knowledge spillovers in driving economic growth and highlights the inefficiencies of a private economy. Interestingly, in these models, greater competition lowers long-run growth by reducing markups and thereby the incentives to produce new varieties of inputs.

As Jones (1995) argues, these expanding variety models feature a scale effect in the sense that a larger population translates into a higher growth rate which does not accommodate the evidence. This observation caused Jones (1995) to suggest a modified version of Romer ' s (1990) model by reducing the impact of knowledge spillovers. The Jones critique is presented in Chapter 8 of Dasgupta ' s book, which also discuses inequality issues.

While Chapter 6 presents models where technical change is based on expanding inputs or product varieties, Chapter 7 presents “Schumpeterian growth models” proposed by Aghion and Howitt (1992) and Grossman and Helpman (1991a, b). In these models, new varieties of products replace old ones. In this regard, the creative destruction process captures a major aspect of innovation dynamics. While these Schumpeterian models are more complicated, Dasgupta present them in a pedagogical way, taking care to discuss analytical results without skipping details of derivation. The author draws a distinction between drastic and non-drastic innovations and compares the planner economy with the private economy. Unlike expanding varieties models, the growth rate may be lower in the centralized economy in Schumpeterian growth models.

Conclusion

Modern growth theory is a difficult subject and students can sometimes feel lost due to the complexity and the variety of approaches. Dasgupta ' s book aims to provide an overall picture of the determinants of economic growth, dealing with most of the major topics, giving the current state of the discipline, and covering the essential technical material remarkably. Dasgupta has made a lot of efforts to make growth theory more accessible to graduate students or economists inexperienced in this topic. From a pedagogical point of view, one could perhaps regret the book ' s lack of emphasis on empirical verification or discussion of factual evidence related to economic growth. However, his aim is to provide a well-grounded comprehension of modern economic growth and to teach its basic modelling tricks. In this regard, Dasgupta ' s book succeeds in providing many basic tools for delving into the analysis of recent economic growth issues.

My only quibble is the absence of open-economy growth models and the discussion of the effects of competition on growth. While Dasgupta ' s book contains the prerequisites for an understanding of current research in economic growth and covers a wide range of topics, in my view, the book would benefit from addressing these two issues more fully. As stressed by Aghion and Griffith (2005), expanding variety models and Schumpeterian growth models predict that greater competition and weaker patent protection result in lower economic growth. However, empirical evidence documented by Aghion et al. (2005) reveal that product market competition can stimulate growth and thus suggests the need to formulate growth models that could produce this positive relationship. A discussion of these issues in Chapters 6 and 7 of the book would give the opportunity to address competition-oriented policies. Finally, an additional chapter reviewing growth issues in an open economy framework could shed light on the dynamics of growth in emerging economies. In particular, the analysis of the growth implications of international trade by Ventura (1997) and Acemoglu and Ventura (2002) deserves attention as the former rationalizes “growth miracles” by the countries with high savings ratios and the latter illuminates the role of terms of trade in world income distribution.