تغییرات ساختاری، چرخه های مصرف انگل و حقایق Kaldor از رشد اقتصادی

Non-linear Engel-curves for consumer goods cause continuous structural change. Goods are sequentially introduced starting out as a luxury with high income elasticity and ending up as a necessity with low income elasticity. Although this leads to rising and falling sectoral employment shares, the model exhibits a steady growth path along which the Kaldor facts are satisfied. Extending the basic model to the case of endogenous product innovations shows that complementarities between aggregate and sectoral growth may give rise to multiple equilibria.

The process of economic development is characterized by fundamental changes in the structure of production and employment. In historical perspective, the emergence of new and the decline of old industries has led to a dramatic reallocation of resources between sectors of production.2 Despite these huge structural changes, the long-term growth process has been remarkably stable in the aggregate. As mentioned by Kaldor (1961) in his famous stylized facts, a situation where the growth rate, interest rate, capital output ratio, and labor share are constant over time is a reasonable approximation of the long-run growth experience of a modern economy. Changes in the structure of production and employment result either from sectoral differences in productivity growth or from sectoral differences in income elasticities of demand. This paper focuses on the demand side. In this case, the structural transformation is driven by changes in consumer demand as households get richer. In a poor society, the overwhelming part of income is spent on basic goods, predominantly food. Consequently, the larger part of the population is working in the agricultural sector. As the society gets richer, consumers devote their expenditures to cover less basic needs which is associated with the creation of employment opportunities in the manufacturing sector. In the mature society consumers direct their expenditures increasingly towards the satisfaction of more advanced wants covered predominantly (though not exclusively) by services. The importance of the demand-based approach to structural change lies in the close relationship between the dynamics of sectoral employment and the composition of aggregate consumer demand. A strong case for such a relationship can be made for the agricultural sector. Historically, increasing per-capita incomes were not only associated with a strong decline in the employment share in agriculture but also with a strongly declining budget share for food, the latter relationship being known as “Engel's law”. According to Houthakker (1987), “of all the empirical regularities observed in economic data, Engel's law is probably the best established.”3 In the U.S., for instance, the budget share for food has been strongly decreasing from 28% in 1950 to 14% in 2000 whereas service expenditures have been steadily increasing during the same period, from 21.8% in 1950 to 43.9% in 2000. Over the same period, the budget share for non-food manufactures (clothing, durables, other non-durables) decreased from 38.9 to 27.8. Moreover, the familiar sectoral trichotomy—agriculture, manufacturing, services—obscures a lot of heterogeneity within these sectors. For instance, further disaggregation shows that within the service sector, purchases of medical services rose disproportionately, similarly, purchases of clothing among non-food manufactures declined very strongly. This suggests that there is substantial structural change not only between but also within broad sectors which underlines the relevance to allow for heterogeneity in industries within these broad sectors. Modern growth theory has been surprisingly silent on the issue of how to reconcile the huge structural changes with the Kaldor facts of economic growth. The first paper that has explicitly addressed the issue is Kongsamut et al. (2001). They study a three-sector model where consumers have Stone–Geary preferences over an agricultural good (a necessity), a manufactured good (with an income elasticity near unity), and services (a luxury). They find that a “generalized balanced growth path” along which the Kaldor facts are satisfied is only possible if preference and technology parameters jointly satisfy a knife-edge condition. Just like in Kongsamut et al. (2001), in our model structural change is driven by sectoral differences in income elasticities. Unlike Kongsamut et al. (2001), however, our model studies a situation where new goods are continuously introduced, leading to the expansion of new and the decline of old industries. This creates a non-linear relationship between manufacturing employment and the level of development that does not show up in the Kongsamut et al. (2001) model. To the best of our knowledge, other papers rationalizing structural change and steady growth in a unified framework have focused exclusively on technological differences across sectors. In Ngai and Pissarides (2007) sectors experience different total factor productivity growth rates (but have identical capital intensities). They show that the aggregate growth process satisfies the Kaldor facts if the intertemporal utility function is logarithmic in the consumption composite; and the consumption composite is non-logarithmic (yet homothetic) across goods. Another recent paper by Acemoglu and Guerrieri (2008) does not only allow for different rates of technical progress but also for differences in capital intensities across sectors. In a two-sector growth model with constant elasticity of substitution preferences and Cobb–Douglas production technologies they show that, provided the elasticity of substitution is less than one, convergence to the limiting equilibrium may be slow and along the transition path (when the sectoral structure changes) the capital share and the interest rate vary only by relatively small amounts hence reconciling structural change with the Kaldor facts.4 In contrast to these technology-based approaches, our model is based on the assumption of hierarchic preferences. New goods are continuously introduced and each of these new goods starts out as a luxury with a high income elasticity and ends up as a necessity with a low income elasticity. These non-linearities in Engel-curves generate consumption cycles that account for structural change. To highlight the demand-channel and to keep things as simple as possible the analysis abstracts from technological differences across sectors. However, a separate section discusses how various dimensions of technological heterogeneity can be incorporated in our model without substantially changing our main message. Our analysis leads to the following results. First, non-linear Engel-curves for the various products can be consistently embedded into a growth model that features Kaldor's facts of economic growth. While previous papers have studied models featuring Engel's consumption cycles (e.g. Matsuyama, 2002), a main contribution of the present paper is to show that this framework is consistent with balanced growth.5 Prima facie reconciling non-linear Engel-curves and the Kaldor facts seems to be non-trivial. However, just as a constant elasticity of intertemporal substitution is required for steady growth in a one-good economy, a constant intertemporal substitution elasticity of total consumption expenditures is required in our framework where there are many goods. Along the balanced growth path total consumption expenditures grow at the same rate as total output. However, along this path the level of demand for a particular product does not grow at the economy-wide growth rate. New goods experience a higher increase in demand than old goods involving a transfer of labor resources from old to new industries. By featuring a steady growth path our analysis provides a natural extension of the one-sector growth model to a multi-sector set-up in which preferences over the various goods have a hierarchical structure. Second, while the main purpose of the paper is theoretical, an illustrative numerical exercise makes the qualitative features of our model transparent. Our model may be interpreted in the context of the sectoral trichotomy (agriculture, manufacturing, services) by assuming that the most urgent wants are satisfied by agricultural goods, the less urgent ones by manufactures and the most luxurious ones by services. The model leads to monotonically decreasing (increasing) employment sharesin the agricultural (service) sector whereas employment in the manufacturing sector increases in early stages of development and decreases in later stages. Hence our model generates quite naturally the hump-shaped evolution of the manufacturing employment share observed in the data. This feature is hard to generate in supply-based approaches. Third, when consumption evolves along a hierarchy of wants consumers get increasingly satiated with existing products, new goods have to be continuously introduced to ensure that demand keeps pace with technical progress. To highlight the importance of product innovations for sustaining growth our basic growth model is extended to endogenous product innovations. In that case an interesting two-way causality between growth and structural change arises. On the one hand, innovation activities depend on the speed of structural change as innovation incentives are determined by the expansion of demand in new industries. On the other hand, the speed of structural change is itself determined by the aggregate growth rate. To highlight this interdependence our model is presented as a standard endogenous growth framework à la Romer (1990) and Grossman and Helpman (1992). The complementarities between sectoral and aggregate growth may give rise to multiple equilibria: when innovators expect a disproportionate increase in demand for new products, incentives to innovate are strong and vice versa. Expectations are self-fulfilling as high sectoral growth requires high aggregate growth which can only be sustained in an innovative environment. The paper is organized as follows. Section 2 discusses our assumptions on hierarchic preferences and characterizes the equilibrium allocation of consumption expenditures. In Section 3 the implications of hierarchic preferences in an otherwise standard neoclassical growth model are explored. In particular, it is shown that a balanced growth path exists along which the sectoral composition changes continuously. Section 4 extends our model to the case of endogenous growth due to product innovations. Section 5 discusses the robustness of our main results with respect to several crucial assumptions. Section 6 concludes.

Two dominant features of the long-run growth process were reconciled in this paper: the dramatic changes in the structure of production and employment; and the Kaldor facts of economic growth. Our model has focused on the demand-explanation of structural change which is based on the idea that households expand their consumption along a hierarchy of needs. In such a context structural change results from differences in income elasticities across sectors. The paper proposed a specification of hierarchic preferences featuring realistic patterns of structural change while also generating an equilibrium growth path that is consistent with the Kaldor facts. Furthermore, a simple numerical example showed that our model can capture realistic patterns of structural change. In particular, the model predicts not only monotonically decreasing (increasing) employment in agriculture (services) but also a manufacturing share that first increases and then decreases in the course of economic development. In contrast to previous approaches that try to explain the Kaldor facts together with changes in the structural composition of output, our approach has studied the non-homothetic nature of preferences together with a situation where new goods are sequentially introduced. In our model, new goods start out as luxuries with a high income elasticity and finally become necessities with a low income elasticity. In this sense, our paper presents a model of rising and stagnating products and highlights the importance of structural changes also within broadly defined sectors. While our basic model was presented in the context of exogenous technical progress where new goods are introduced without any costs, our analysis was extended to study endogenous growth. In such a framework, it was shown that hierarchic preferences highlight interesting interactions between structural change and long-run growth. On the one hand, the aggregate growth rate depends on structural change because innovation incentives are crucially determined by the growth rates in the new industries. On the other hand, the speed of structural change is itself determined by aggregate growth. The resulting complementarities between sectoral and aggregate growth open up the possibility for multiple equilibria. Hence our model is not only capable of yielding insights into the process of growth and structural change, but sheds also light on the question why some countries experience high long-term growth and many industries take off, while in other countries there is neither a change in the production structure nor increases in aggregate productivity. Our model can be extended in several directions. Two extensions are most promising. First, while our analysis has focused on a representative consumer, the introduction of consumer heterogeneity is potentially interesting. As preferences are non-homothetic, rich and poor households will consume different consumption bundles which opens up a new channel by which income inequality could affect growth and structural change (Foellmi and Zweimüller, 2006). Second, hierarchic preferences in a world economy with rich and poor countries would imply interesting patterns of growth and the international division of labor. Our model provides a natural way of modelling the Linder-hypothesis (Linder, 1961) and/or the product-cycle hypothesis (Vernon, 1966). A rich country faces high home-demand and hence will innovate early. The poor country will first import new goods, but later on start to imitate. Hence rich countries will produce new goods with a high income elasticity and poor countries will produce old goods with a low elasticity. Our set-up may also be useful to understand the mixed empirical evidence concerning the Prebisch/Singer-hypothesis (Prebisch, 1950 and Singer, 1950) according to which the terms of trade for the poor countries deteriorate as their exports are concentrated on goods with low income elasticities.20