Returns to specialization, competition, population, and growth

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Abstract

Using an expanding-variety endogenous growth model with purposive human capital accumulation, this paper provides an alternative explanation of why we may observe an ambiguous correlation between product market competition (PMC) and economic growth, and between population and economic growth rates. Our explanation is based on the notion of ‘returns to specialization’. Under the model's assumptions, PMC and economic growth are ambiguously correlated when returns to specialization are decreasing, whereas population growth and productivity growth are ambiguously correlated when returns to specialization are increasing. From a theoretical point of view, these results are explained by the presence or absence of an ‘increasing production-complexity’ effect associated to the use of a larger number of intermediate-input varieties in the same production process.

Introduction

Does product market competition (PMC, hereafter) promote or deter economic growth in the long run? What is the sign of the impact of population growth on productivity growth? Although economists have been studying for a long time the effects of an increase in the intensity of PMC and in the population growth rate on R&D incentives, the pace of innovation and productivity growth, these questions still remain to a large extent unsettled.

Given its intrinsically nonrival nature, the presence of technological progress (in the form of creation of new ideas) leads to non-convexities in an otherwise standard neoclassical production function with constant returns to scale to rival inputs and, therefore, a decentralized equilibrium with price-taking competition cannot be sustained. Schumpeter (1942) was among the first to recognize that more market power,1 by increasing the rents that can be appropriated by the successful innovator, definitely spurs R&D incentives and, hence, stimulates economic growth in the long run. Contrary to this view, more recent theoretical research (both IO and macro-based)2 finds mixed results in the correlation between PMC and innovation/growth, and the existing empirical evidence confirms the ambiguity of this correlation.3 In order to account for this varied evidence, the basic Schumpeterian-growth paradigm (Aghion and Howitt, 1992) has been recently re-formulated and extended4 to include consideration of agency problems, a more gradualist (“step-by-step”) view of technological progress, and the decomposition of R&D activities into research and development. As a whole, it is a fair conclusion that there now exist many different and persuasive (theoretical and/or empirical) arguments showing that the sign of the relationship between PMC, innovation and economic growth may be either always positive, or always negative, or ambiguous.

Though, it is well known that R&D activity and growth in real per-capita incomes are influenced not only by the degree of PMC but also by demographic change. Kuznets (1960), Simon (1981) and Boserup (1981) have been among the main and early advocates of the so called “population-push hypothesis”, according to which: “…Population growth…produces an absolutely larger number of geniuses, talented men, and generally gifted contributors to new knowledge whose native ability would be permitted to mature to effective levels when they join the labor force…” (Kuznets, 1960, p. 328). Similarly to the relationship between PMC, innovation and productivity growth, so far a complete agreement about the sign of the long run correlation between population and economic growth rates has not emerged yet, both empirically and theoretically (Ehrlich and Lui, 1997, Kelley and Schmidt, 1995, Kelley and Schmidt, 2001, Tournemaine, 2007).5 Proponents of the view that population growth is detrimental to economic growth (for example, Solow, 1956, Barro, 1991, Mankiw et al., 1992) found their argument on the belief that an increase in population leads to a dilution of reproducible resources. Conversely, proponents of the optimistic view (population growth is beneficial to economic growth) emphasize the positive effect that a larger population can exert on innovation and the rate of technological progress (R&D-based growth theories).

Using an expanding-variety endogenous growth model with purposeful human capital accumulation, the first aim of the present paper is to provide an alternative explanation of why we may observe an ambiguous correlation between PMC and economic growth, and between population growth and economic growth. Our explanation is based on the notion of “returns to specialization”, that is the extent “…To which society benefits fromspecializingproduction between a larger number of intermediates” (Benassy, 1998, p. 63). In our model the markup ratio is related (although in a contradictory manner) to the returns to specialization. The sign of such correlation depends, in fact, on the magnitude of a key parameter that indicates (when compared to one) which of the two opposing forces (specialization vs. increasing production-complexity) associated to the simultaneous use of a larger number of intermediate-input varieties prevails over the other. This trait of our model represents a departure not only from the first generation growth models with endogenous technological change—such as Grossman and Helpman (1991, Chapter 3), in which there exists a one-to-one relationship between the monopolistic markup and the degree of returns to specialization—but also from Benassy, 1996a, Benassy, 1996b, Benassy, 1998, where the degree of returns to specialization is set to a level completely independent of the markup rate. Along the balanced growth path (BGP, henceforth), human capital and ideas grow at constant rates and the growth rate of real per-capita income depends on population growth, the degree of returns to specialization and the rates at which individuals and firms accumulate, respectively, human capital and ideas. Moreover, the returns to specialization are also ambiguously correlated to the growth rate of ideas and human capital, with the sign of these correlations ultimately depending on whether agents’ intertemporal elasticity of substitution in consumption is higher, lower, or equal to one. In the light of all this, an exogenous increase in the markup ratio affects the economy’s growth rate in two fundamental ways: directly, through the effect it has on the degree of returns to specialization (‘returns to specialization’ effect) and indirectly, via the impact that the changed degree of returns to specialization has, in turn, on factor accumulation (i.e., the accumulation of ideas and human capital, this is the ‘accumulation’ effect). Although it exhibits an ambiguous sign, we see that along the BGP the indirect ‘accumulation’ effect does not alter the sign of the whole impact of a change in the markup on economic growth, which is therefore uniquely determined by that of the direct ‘returns to specialization’ effect. Likewise, an increase in population influences real per-capita income growth both directly (‘dilution’ effect) and indirectly (‘ideas’ effect). The direct dilution effect measures the impact of a more sizable population on the per-capita endowment of the reproducible resources, and is always negative. On the other hand, the indirect ‘ideas’ effect describes the influence that an exogenous change of population size may have on the economy’s growth rate of ideas and is positive if, for given intertemporal elasticity of substitution in consumption, the degree of agents’ altruism towards future generations is sufficiently high (the more altruistic agents are, the more patient they become, and the more willing they are to invest for the future). When the ‘ideas’ effect is positive, the total impact of a rise of population size on real per-capita income growth is then a priori ambiguous, and we find that it is again crucially associated to the degree of the returns to specialization.

Another objective of the model is to explain not only why in some (typically OECD) countries the correlation between PMC and economic growth may be ambiguous, but also why in other (notably, less-developed but fast growing, non-OECD) countries the same correlation seems definitely negative. Our analysis reveals that an important role in this regard is played by whether a rise of the number of available input-varieties being combined within the same production process can result (as it is more likely to occur in OECD, as opposed to non-OECD, countries) in a simultaneous escalation of production-complexity.

The main conclusion of the article is that in theory the ambiguity in the signs of the correlations between PMC and economic growth and between population and economic growth rates can ultimately be explained by the presence or absence of an ‘increasing production-complexity’ effect induced by variety-expansion. We suggest a possible way by which the theory proposed in the paper can be corroborated/falsified through data. Indeed, the effort to yield an empirically plausible and testable model may itself be viewed as part of this paper’s contribution.

The present work is closely related to Dalgaard and Kreiner (2001), Strulik (2005), Bucci (2008), and Boucekkine et al. (in press). The first paper, using a horizontal innovation-driven growth model with human capital accumulation, develops a theory of scale-invariant endogenous growth according to which population growth may only have a non-positive effect on the long run growth rate of income per-capita. Strulik (2005), instead, by analyzing an endogenous growth model with skill acquisition and both vertical and horizontal product innovation, finds that the correlation between population and economic growth rates is ambiguous and reliant on the size of the degree of agents’ altruism towards future generations. Moreover, in his model the long run growth rate of the economy is always decreasing in the markup. Contrary to Dalgaard and Kreiner (2001) and Strulik (2005), in our paper we stress the importance of the returns to specialization in determining the sign of the correlation between economic and population growth rates. Furthermore, while the role of PMC in economic growth is not analyzed in Dalgaard and Kreiner (2001), unlike Strulik (2005) we can also explain the existence of a negative or no correlation at all between PMC and economic growth. Bucci (2008, Table 1, p. 1141), in a model in which individuals can purposefully accumulate human capital and innovation is solely horizontal, demonstrates that the relationship between population growth and the growth rate of real per-capita income is influenced not only by the degree of agents’ altruism but also (for given altruism) by the nature (skill-biased, “eroding”, or neutral) of technical change. Differently from Bucci (2008), the present paper is to our knowledge the first one that, simultaneously and within the same setting, can account for the correlation between population and per-capita income growth rates, as well as between PMC and economic growth. Finally, with respect to Boucekkine et al. (in press), who consider a traditional framework where growth is generated by human capital accumulation in line with the Lucas's (1988) and Uzawa's (1965) two sector model without endogenous R&D activities, we do not look at the effects of population on the long run levels of human capital and income per-capita, and focus on the population impact on the growth rates of these two variables.

The article proceeds as follows. In Section 2, we set the model and analyze its predictions along the BGP. In Section 3, we present the findings concerning the long run relationship between PMC and economic growth. Section 4 is devoted to the analysis of the long run correlation between population and productivity growth rates. In the same section, we also study how this relationship would change under three different specifications of household’s preferences (Millian, Benthamite, and an intermediate case between the two). Section 5 assesses and discusses all together the main results of the model, whereas Section 6 concludes and provides hints for possible future extensions.

Section snippets

The model

Imagine an economy where three sectors of activity are vertically integrated. In the research sector firms use skilled labor (human capital) and, eventually, the existing stock of ideas (knowledge capital) to engage in innovative activity. Innovation consists in discovering new designs for firms producing intermediate inputs (capital goods, or durables). The intermediate sector is composed of monopolistically competitive firms, each manufacturing a differentiated variety of durables and endowed

PMC and economic growth

The following theorem analyzes the interplay between PMC and economic growth in the model developed in the previous section.

Theorem 1

In this model economy, PMC and economic growth can be either positively correlated, or negatively correlated, or else non-correlated at all. In particular,

  • (γy/m)<0 when ε>1. In this case the correlation between competition and growth is positive;

  • (γy/m)=0 when ε=1. In this case there exists no correlation between competition and growth;

  • (γy/m)>0 when ε<1. In this case

Population growth and economic growth

In this section we analyze the link between population growth and economic growth, and how the sign of this relationship relates to the degree of returns to specialization, to the size of ε and to ω.

Theorem 2

In this model economy, population growth and economic growth can be either positively correlated, or negatively correlated, or else non-correlated at all depending on the degree of returns to specialization. In particular, under the requirements of Assumption A and with ω(0;1), we observe that:

  • (γy/

Discussion: Returns to specialization, PMC, population, and economic growth

The results of the paper may be summarized by the following:

Proposition 5

Assume m<(1+(1/α)), ω(0;(1/1+Δ)), and (1αΔ)>0. These restrictions, together with α(0;1), m>1 and Δ>0, ensure that the inequality (ω[α(m1)Δ+1]1/αmωΔ)<(α(m1)1/αm)<0<1<(α(m1)Δ+1/αmΔ) is checked. Then, the relationship among the size of ε, the degree of returns to specialization (R), and the sign of the effect of an increase in the level of monopoly power (m) and in the population growth rate (n) on real per-capita income growth (γy

Conclusions

Economic theory has long ago made clear that PMC and population, by affecting respectively the path of future profits accruing to successful innovators and the availability of researchers in an economy, have a significant impact on productivity growth. Using an expanding-variety growth model with purposive human capital investment, the main objective of this paper was to account simultaneously for the ambiguous correlations between PMC and economic growth and between population growth and

Acknowledgments

I am grateful to seminar participants at the University of Barcelona (May 2010) for comments and remarks on a very preliminary version of this paper. K. Prettner and S. Boikos provided useful suggestions on the first draft of the article. The final version of the paper was conceived in one of my visits at the Economics Department of the Université catholique de Louvain (Louvain-la-Neuve, Belgium). I thank this institution for kind hospitality. I revised this article while visiting the Durham

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