# Growth and Cycles

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**DOI:**https://doi.org/10.1057/978-1-349-95121-5_1234-2

## Abstract

There is a long tradition in macroeconomics of treating growth and cycles as distinct phenomena. However, various economists have also recognized the virtue of incorporating the two forces into a single framework and to study the way they are related. This article reviews this literature, with emphasis on attempts not only to integrate growth and cycles into a single framework but also to endogenize growth, cycles, or both.

## Keywords

Capital accumulation Endogenous growth Growth and cycles Innovation Kydland, F. Prescott, E. Ramsey model Research and development Risk Technical change Precautionary savings## JEL Classifications

O4Growth and cycles are two key features that characterize real output per capita in most industrialized countries. Real output per capita grows systematically over time; and the rate at which it grows tends to fluctuate over time.

A long tradition in macroeconomics treats these two features as distinct. On the one hand, economists who study why output per capita consistently grew in most countries during the 20th century often ignore the fact that growth in any given country was uneven over time. Underlying this approach is the assumption that temporary fluctuations in economic growth are transitory and have no consequences for long-run growth. On the other hand, economists interested in cyclical fluctuations often abstract from long-run economic growth. In particular, various business cycle models have been devised in which output fluctuates around a constant level of output rather than a path that grows over time. This approach again reflects the view that long-run growth is driven by forces that are independent of the factors that drive booms and busts in economic activity. On this assumption, we can analyse why output deviates from its long-run trend without bothering to model the trend itself.

While this dichotomy has proven useful for exploring certain questions, economists have become increasingly critical of this approach. Various attempts at integrating these two phenomena can be found in work on growth and business cycles from the late 1960s and early 1970s. Richard Goodwin’s entry for growth and cycles in the first edition of this dictionary surveys some of this work (Goodwin 1987, pp. 574–6).

Arguably, however, the article that contributed most to advancing the view that growth and business cycles should be analysed within a single model is Kydland and Prescott (1982). They argued that business cycles were driven not by short-run variations in aggregate demand, as most previous work had assumed, but by fluctuations in the same force that drives long-run growth, namely, technological progress. They started with the Ramsey (1928) growth model in which long-run growth is due to labour-augmenting technical change. But rather than assuming a constant rate of technical change, they allowed it to vary over time. This captures the notion that new ideas arrive sporadically, so productivity growth is inherently random. Households react to these shocks by varying their capital accumulation and labour supply.

Kydland and Prescott went on to argue that technology shocks could account for most of the volatility in US output during the post-war period. This claim remains controversial. However, even those who were sceptical of the claim that productivity shocks were responsible for business cycles were forced to acknowledge that temporary shocks could affect decisions relevant for long-run growth, such as capital accumulation, and conversely that the forces which shape long-run growth could have important short-run consequences. This implies that treating growth and cycles as distinct processes might overlook important connections between the two phenomena.

While Kydland and Prescott’s paper was influential in promoting the view that growth and cycles should be modelled jointly, their model offered only limited insight into the connection between the two. This is because they modelled both long-run growth and fluctuations as exogenous: output per capita in their model grows because the economy is assumed to undergo technical change, and it grows in cycles because technical change is assumed to occur in cycles. As such, their model does not explain what drives technical change, why it should be inherently volatile, or whether growth and cycles might affect one another.

For example, Kydland and Prescott’s model cannot tell us whether business cycles affect the rate of long-run growth. Are entrepreneurs more reluctant to undertake activities that lead to technical change in the face of macroeconomic volatility? Addressing this question requires us to model growth as an endogenous process rather than as the outcome of exogenous technical change. As another example, Kydland and Prescott asserted that technical change is inherently volatile. While this is undoubtedly true for any individual sector, it is not obvious why this volatility does not cancel out in the aggregate, resulting in a constant rate of technical change for the economy as a whole. Addressing this question requires us to model the underlying fluctuations in the rate of technical change as an endogenous outcome rather than as the result of an exogenous process. Fortunately, economists have since developed models in which either long-run growth or fluctuations, or both, are endogenous.

One line of research endogenizes growth while maintaining exogenous fluctuations. This approach allows us to study the effects of cyclical fluctuations on long-run growth. One of the first papers to tackle this question was Leland (1974), who built on previous work by Levhari and Srinivasan (1969). The latter studied the problem of a household deciding between consumption and saving given uncertain returns on its savings. Leland showed that this model could be reinterpreted as a representative household economy with a linear technology for producing output from capital. Growth in this model was driven by capital accumulation, so shocks to productivity – the analogue of uncertain returns – affected growth by affecting average investment.

Leland showed that the effect of cycles on growth depended on household attitudes towards risk. If the coefficient of relative risk aversion among households exceeded one, they would engage in more precautionary savings in the face of macroeconomic volatility, accumulating capital more rapidly. When relative risk aversion is below unity, macroeconomic volatility would induce households to accumulate less capital, leading to a slower rate of growth. Thus, whether cycles encourage or discourage long-run growth is ambiguous from a theoretical standpoint.

Ramey and Ramey (1995) provided empirical evidence on the relationship between growth and cycles using cross-country evidence. They found that volatility is associated with slower growth. At the same time, they found that more volatile countries do not have lower investment rates, contradicting Leland’s analysis on how volatility ought to affect growth. This contradiction was resolved by Ramey and Ramey (1991) and Barlevy (2004), who argued that volatility affects growth not by changing average investment but by making investment less volatile; more volatile investment lowers long-run growth because growth is concave in investment. Barlevy (2004) in particular argued that this channel implies that exogenous cyclical fluctuations would be associated with very large welfare costs.

A separate line of research proceeded in the opposite direction: it assumed long-run growth was exogenous, and examined whether fluctuations in the economy-wide rate of technical change could arise endogenously. For example, Shleifer (1986) developed a multi-sector model where in each period innovators in a fixed fraction of sectors develop more productive technologies. They could use these to earn profits for a limited period, after which rivals in their sector could copy the technology and drive profits to zero. If innovators implemented their ideas as soon as they came up with them, the rate of aggregate technical change would be constant. But Shleifer allowed firms to delay implementation, and showed that there exist equilibria where technical change occurs in spurts: innovators wait until there is enough innovation in other sectors before they implement their own ideas, so growth would be concentrated rather than spread out evenly over time.

Shleifer’s result emerges because in his model implementing new technologies exhibits strategic complementarities: when one firm implements a new technology, its owners earn excess profits which they use to purchase goods in other sectors. Firms that come up with a new technology might therefore prefer to wait until others come up with new ideas. Even though the economy arrives at new ideas at a constant rate, growth proceeds at an uneven rate in equilibrium.

A third line of research has sought to endogenize both long-run growth and fluctuations. For example, Francois and Lloyd-Ellis (2003) consider a modification of the Shleifer model where innovators choose how much research to undertake, rather than assuming the rate at which new ideas arrive is fixed exogenously. This allows them to examine whether implementation cycles can affect long-run growth. Since implementation cycles emerge endogenously, the connection between cycles and growth may be different from the way growth responds to exogenous shocks as in Leland’s analysis.

Francois and Lloyd-Ellis find that the equilibrium with cycles involves unambiguously higher average growth than the equilibrium in which innovators implement their new ideas immediately. This is because innovators earn higher profits when they coordinate implementation, providing them with more incentive to engage in research. However, welfare turns out to be lower in the presence of cycles, so faster but more uneven growth is less desirable. Lastly, Francois and Lloyd-Ellis show that, if countries differ in research productivity, we would observe a negative correlation between growth and cycles across countries; countries that are less productive in research will grow more slowly and exhibit longer and larger deviations from average growth. This helps to reconcile their results with Ramey and Ramey’s evidence, and points out an important caveat for interpreting the cross-country evidence on growth and cycles.

Other authors have used models where both growth and cycles arise endogenously to explore whether technical change occurs in spurts not because of implementation delays but because of fluctuations in innovation. That is, even if innovators implement their new ideas immediately, they might still choose to concentrate their research activity in particular periods. Examples include Bental and Peled (1996), Walde (2002), and Matsuyama (1999). All three describe models in which the economy alternates between capital accumulation and innovation. In the first two papers, successful innovation raises the marginal product of capital, inducing a shift towards capital accumulation until the return to capital is low enough for innovation to turn profitable again. Matsuyama develops a model in which the economy grows as the variety of goods produced increases. Profits depend on the ratio of capital to the number of goods, so successful innovation reduces the profitability of innovation rather than increase the returns to physical capital. But all three models imply that the amount of innovation, and thus the rate of technical change, fluctuates along the equilibrium path.

A central feature of these models is that the economy fluctuates between innovation and capital accumulation. However, empirical evidence suggests research and development activity is high when capital accumulation is high. Recent work by Comin and Gertler (2006) and Barlevy (2005) examines why research activity might vary positively with capital accumulation. However, both assume cycles are due to exogenous shocks rather than that they arise endogenously in equilibrium. It remains a question for future research whether innovation might fluctuate endogenously but still co-vary with capital accumulation.

## See Also

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