رشد جمعیت در مدل رشد اقتصادی با انباشت سرمایه انسانی و R & D افقی

This paper reconsiders the effects of population growth on per-capita income growth within a Romerian (1990)-type endogenous growth model with human capital accumulation. One important novelty of our contribution is that in the human capital supply equation we explicitly consider the possibility that agents’ investment in skill acquisition might be positively, negatively or not influenced at all by technological progress. We find that both the growth rate and the level of real per-capita income are independent of population size. Moreover, the population growth may affect or not real per-capita income growth depending on the size of the degree of altruism of agents towards future generations and on the nature of technical progress, for given agents’ degree of altruism.

Today it is well known that most of the world population growth is concentrated in poorer countries (United Nations, 2001) and that such trend will persist even in the long run. The latter fact is especially evident if one looks at the evolution over one century of the share of the world population living in three different sub-samples of countries (more developed, less developed and least developed, according to the repartition adopted by the United Nations): in the period 1950–2050 the share of world population residing in the more developed regions is expected to decrease (from 32% to 13%), whereas it is expected to increase in the less developed and, in particular, in the least developed regions (respectively, from 60% to 67% and from 8% to 20%).1 Thus, a natural concern arising from these data pertains to the long-run effects of population change on the economic performance of a country (the growth rate of real per-capita income of its inhabitants). Until now, the literature has proposed three broad approaches to the analysis of this deep-rooted issue (see Bloom et al., 2003, pp. 1–20). According to the Pessimistic View, population growth unambiguously hinders economic growth through two different channels: (a) in a world where economic resources are fixed and technological progress is low or totally absent, the food production activity is overwhelmed by the pressures of a rapidly growing population. The available diet would then fall below the subsistence level and so would the productivity growth rate also do (Malthus, 1798); (b) when population growth is rapid, a large part of investment (typically in physical capital) is used to satisfy the needs of the growing population (“investment-diversion effect” – Kelley, 1988, p. 1699), rather than to increase the level of per-capita capital endowments. As a consequence, per-capita economic growth would be lower in the presence of a higher population growth rate. As per the Optimistic View, the population growth fuels economic growth. This is the main message coming from Kuznets, 1960, Kuznets, 1967, Simon, 1981, Boserup, 1989 and Kremer, 1993, according to whom larger economies can more easily build on, exploit and disseminate the flow of knowledge they produce. In other words, population growth by raising the returns to innovation induces technological change, one of the main engines of economic development. More recent contributions in the optimistic view also include Jones, 2001a, Tamura, 2002 and Tamura, 2006. Jones, 2001a and Tamura, 2006 extend the Kremer’s (1993) model by introducing mortality. In both models, fertility depends positively on the level of mortality. However, they differ in two important respects. While in Jones (2001a) mortality, and hence fertility, falls because of rising levels of consumption in the population, in Tamura (2006) what makes the mortality risk decline is the increase in the average level of human capital in the population.2 Moreover, in Jones (2001a) acceleration of economic growth comes not only from rising population (as in Kremer, 1993) but also from an exogenous increase in the productivity of population in producing ideas, whereas in Tamura (2006) higher economic growth is ultimately driven by the larger level of human capital accumulation due to falling fertility. Tamura (2002), instead, presents a model of economic and population growth able to generate endogenously a transition from a classical (agricultural) to an industrial mode of production. The first method of production employs labor and a fixed factor (land), while the second one combines labor and intermediate services acquired through trade. For low human capital, the classical method dominates the industrial one, but for high human capital the opposite is true. The switch to the industrial mode of production is made possible by human capital accumulation,3 which eventually raises the productivity of the industrial technology above the classical one. Once the transition to industry has occurred, the growth rate of per-capita income is positively related to the growth rate of population. Many papers that have analyzed the statistical correlation between population change and economic growth have found that, once other factors (such as country size, openness to trade, educational attainment of the population, and the quality of existing institutions) are taken into account, there exists little cross-country evidence that population growth might either slow down or encourage economic growth (Bloom et al., 2003, p. 17). Accordingly, a third view on the relationship between population growth and economic growth is the so-called Population Neutralism View. Our paper considers all of these three views as reasonable4 and combines them within the same analytical framework. Thus, the two main questions of the present contribution are the following: In an economy where human capital is not fixed and represents an indispensable input to firms’ research and development (R&D) activity producing endogenous technological change, under which conditions can we account for the existence of a positive/negative/no relation at all between population change and economic growth? In a situation in which aggregate income growth is explained by technological progress (horizontal R&D activity), but ultimately driven by human capital investment, is economic growth sustainable in the long run even in the absence of any population change? We try to answer these two questions by developing a theoretical, dynamic, general-equilibrium growth model with human capital accumulation and R&D activity. In more detail, we consider a multi-sector economy where an undifferentiated consumption good is produced by using human capital, the existing stock of ideas and intermediate goods. These goods are available in different varieties and produced under monopolistic competition conditions. Purposive R&D activity, which combines human capital and ideas, is the source of technical progress. Population grows at an exogenous rate and each individual in the population is endowed with a certain amount of skills that may grow over time through formal investment in human capital. We also assume that human capital is fully employed and used to produce consumption goods, intermediates, ideas and new human capital. The most important novelty of our model consists in the fact that in the human capital accumulation equation we explicitly take into account the possibility that the investment in skill acquisition by agents might be positively, negatively or not influenced at all by technological progress (the invention of new varieties of intermediate goods). In the first case, it is postulated that a faster technological progress, by increasing the demand for skills, induces agents to accumulate more human capital (skill-biased technical change hypothesis). In the second case, instead, the model captures all those situations where technological progress exerts a sort of “erosion effect” on human capital investment (“eroding” technical change hypothesis). Finally, the last case corresponds to the specific circumstance in which individual incentives to invest in schooling are totally independent of the nature and the direction of technical change (neutral technical change hypothesis). The main result of the paper is that, along the balanced growth path (BGP, henceforth) equilibrium, population growth may affect (positively or negatively) or not real per-capita income growth depending on: (1) the sign of the relation between some of the technological and preference parameters of the model (in particular, an important role is played by the size of agents’ degree of altruism towards future generations as compared to the parameter reflecting the impact of technological progress on human capital investment); (2) the nature of technical change (whether it is skill-biased, “eroding” or neutral), for given agents’ degree of altruism. While the first conclusion (the link between population growth and economic growth is a function of the relationship between preference and technological parameters) is not new (see, among others, Dalgaard and Kreiner, 2001 and Strulik, 2005), we believe that tying the effect of population growth on economic growth to the direction of technical change is of particular interest. Intuitively, an increase in the population growth rate implies two possible consequences as far as per-capita income growth is concerned: on the one hand, it is likely to lead to a fall of per-capita income growth (the reason being that, ceteris paribus, when the population grows the given, available, aggregate income has to be divided among a larger number of people). At the same time, however, the increase in the population growth rate also leads to a major number of innovations (technological progress).5 If, as an example, such technical change is skill-biased in nature (meaning that it spurs the demand and, thus, the consequent supply of human capital), then per-capita income growth (driven by skill investment in the model) rises. Accordingly, the final effect on economic growth of an increase in population growth can well be positive or negative or else exactly equal to zero. On the other hand, if technical change is of the “eroding” type (meaning that it lowers further human capital investment by agents and, hence, economic growth), the effect of population growth on per-capita income growth is unambiguously negative. Finally, we show that in the case of neutral technical change (technological progress does not influence at all the agents’ incentive to invest in schooling), population growth is more likely to bear an adverse effect on per-capita income growth (such effect can be, at most, equal to zero). However, even with respect to the above-mentioned works by Dalgaard and Kreiner, 2001 and Strulik, 2005, our paper presents some major differences. Unlike Dalgaard and Kreiner (2001), who use a one-sector growth model with human and technological capital accumulation (patents and education are generated by the same production function), we build a two-sector growth model reflecting the fact that the production of human capital is relatively intensive in human capital. Instead, unlike Strulik (2005), who uses a two-R&D-sector growth model (innovation expands the variety and quality of intermediate goods), we show that two further results of our paper (namely that economic growth is no longer semiendogenous, i.e., driven solely by exogenous population growth, but fully endogenous, i.e., ultimately driven by private incentives to invest in human capital, and that in the long run economic growth is sustainable even in the absence of population growth) can be obtained using a much simpler and more tractable model with only one R&D dimension (the horizontal one). Furthermore, while Strulik considers a purely Lucas (1988)-type per-capita human capital accumulation equation where, besides population growth, an exogenous depreciation rate of skills operates, in our model the presence of the growth rate of ideas in the law of motion of per-capita human capital acts as an endogenous mechanism of depreciation/appreciation of (embodied) knowledge. The remainder of the paper is structured as follows. In Section 2 we set the basic model, whose BGP properties are analyzed in Section 3. In Section 4 we discuss the main results concerning the long-run relationship between population growth, the direction of technical change and economic growth. Finally, Section 5 concludes.

Since the early 18th century world population has considerably increased to over 6 billion people and is expected to reach 9 billion people by 2050. More importantly, “…Past and projected additions to world population have been, and will increasingly be, distributed unevenly across the world. The disparities reflect the existence of considerable heterogeneity in birth, death, and migration processes, both over time and across national populations …” (Bloom and Canning, 2004, p. 3). In this regard, it is well-known that most of the explosive population growth is mainly concentrated in developing countries, with the developed regions of the world succeeding in maintaining roughly constant the number of their inhabitants especially thanks to the migration dynamics from abroad. By taking the population growth rate as exogenous, in this paper we built an endogenous Romerian (1990)-type growth model with human accumulation, the objective being to analyze the long-run effects of population change on real per-capita income growth. One peculiarity of our contribution is that technological progress (the growth of the number of ideas) is explicitly recognized as (potentially) able to influence agents’ decision to invest in skill acquisition, the engine of economic growth in our model. Thus, and depending on whether technical change is postulated to affect positively, negatively or not affect at all human capital accumulation, we may have, respectively, “skill-biased”, “eroding” or else “neutral” technical change. Unlike the standard approach (in which population growth adds to the exogenous depreciation rate of per-capita skills), the presence of the growth rate of ideas in the law of motion of human capital acts in our model as an endogenous mechanism of depreciation or appreciation of (embodied) knowledge. This is important because it allows us in tying the effects of the population growth on the per-capita income growth to the nature and the direction of technical change. We find that, for the given type of technical progress, such effects may also significantly depend on the size of the agents’ degree of altruism towards future generations (the intuition being that this preference parameter influences households propension to save and, thus, to invest in human and R&D capital). Furthermore, we also find that, even in a framework where economic growth is explained by horizontal R&D (even though it is ultimately driven by human capital accumulation), population growth is neither necessary nor conducive to long-run growth in per-capita real income. Clearly, more work (both theoretical and empirical) is needed to resolve the ambiguities concerning the effect of population change on economic growth and to come to more definitive conclusions on this topic. As an example, from a purely theoretical point of view, it would be interesting to study how the results of this paper might change in the presence of an endogenous population growth (i.e., endogenous fertility and migration decisions). Moreover, it is well-recognized that population growth is only one (yet very partial) facet of global demographic change and that the shifting age structure of the world population is another aspect that certainly needs to be considered in the analysis. We leave these and other possible paths of study to future research.