The Ricardian Law of Diminishing Returns. A ew Interpretation . Leveraging productivity to drive globalization.
Lucy Badalian — Victor Krivorotov
11501 Maple Ridge Rd Reston VA 20190 Millennium Workshop, USA [email protected]
Abstract . The 2009 IMF report found notable differences between the pre and post 1985 busts in their ratios of capital/labor. According to historical trends it cited, the recent extreme financialization may cloud our mid term recovery prospects. The Market Pendulum Model (further MPM) stresses the importance and fluidity of interrelationship between traditional factors of production: land, labor, capital and entrepreneurship. MPM shows the difference between productivity factors during demand shocks, such as today, and supply shocks (the 1970s 80s). It traces the causal roots of the financialization in market’s compensation for failing fundamentals, the direct result of the Ricardian Law of Diminishing Returns (further RLDR).
Keywords : Ricardian Law of Diminishing Returns, financialization, financial crisis, demand shocks/demand shortages, supply shocks/supply shortages, ratio of capital/labor.
JEL codes: E1, E20. E5, E6.
1. Introduction. The Interrelationship between Various Factors of Production as a Potential Predictive Tool.
The October 2009 report of the IMF showcased the importance of the hitherto under researched area of the inter relationship between factors of production, which, in its opinion, holds significant predictive power as to the length and severity of the unfolding recession. It found that the growth in productivity since 1985 was accompanied by a rapid rise in the ratios of capital to labor. Earlier research noted other specific patterns of labor productivity. Among them, the wavelike behavior of multifactor productivity growth, which peaked in 1928 50 and slowed gradually, both when moving back to 1870 91 and forth to 1972 96 (Gordon 2004). The countercyclical rise of productivity was noted during the 1929 Great Depression (Bernanke, Parkinson 1992, Bordo, Evans 1995). It may be conjectured that the latter contributed to the final exit out of the lengthy depression and led to the follow up strong growth in the 1950s 70s. Meanwhile, despite a long history of studying productivity and its input into economic growth both for the US (Fabricant 1942) and in the economic practice of other countries (Kendrick 1961 and 1982, Kennedy 1971, Salter 1960, Wragg and Robertson 1978), the fluidity of the interrelationship between different factors of production didn’t get its due attention. Its causal roots remain unclear and under researched, despite the intriguing findings cited above (IMF 2009 report, Bernanke, Parkinson 1992, Bordo, Evans 1995). The ongoing crisis further underscores the importance of the underlying causality, if, as the cited research hints, the changing ratios between diverse factors of production may indeed influence such parameters as the length of the related depression and its severity, importance of which was stressed again recently by Pisani Ferry and van Pottelsberghe (2009). In this paper, we research the effects of productivity shifts on the economy of the leading country of its time, such as the US today or Britain of the 19 th century. Our main analytical tool is the Market Pendulum Model, further MPM, first presented in (Badalian, Krivorotov 2009). It is used here to shed new light at the rhythmic causality of fluid interrelationships between diverse factors of production. While the topic is extremely complex and our hypotheses need substantial future research, their initial conjectures, provided below, can hardly be ignored and invite further discussion and more testing and input, especially from other researchers.
In a nutshell, as it would be shown below, MPM turns from shortages of demand to shortage of supply and back (Badalian Krivorotov 2009) as market shifts from one leading factor of production to another. This suggests that the traditional factors of production, such as land, labor, capital and entrepreneurship may star in leading roles not all at once, but sequentially, in turns. A new factor of production comes to the top as soon as the other supporting factors get exhausted due to the Ricardian Law of Diminishing Returns, further RLDR. Meanwhile, the latter’s influence grows as the economy matures. This would explain the recent growing ratios of capital/labor as an attempt to compensate through extra capital infusions for the negative influence of RLDR exerted on the labor productivity in a mature economy. This explanation finds additional, though indirect, support in the well known fact that mature industries gradually turn more capital intensive and heavily depend on economies of scale while their margins fall. (Grant 2005: 367)
It should be noted that, while RLDR is commonly accepted in the economic practice, its validity as a physical law, able to apply force, still remains unclear. As it was often noticed, starting from Ricardo himself, its influence in practice is often compensated by other factors, such as economies of scale at the root of the comparative advantage. The latter suggests the existence of extensive trade routes, whose support and maintenance, by definition, is extremely capital extensive, thus bridging together three factors of production: faraway land, global labor and capital.
Below, MPM provides a first glimpse at the causal chains, where the exhaustion of a given factor productivity is compensated through the additional input from another. A shift from one leading factor to its successor is usually accompanied by an MPM turn from shortages of supply to shortages of demand and back. For example, from the 1929 Great Depression, the US economy resolved shortages of demand through the rise in productivity of its labor (Bernanke, Parkinson 1992). The shortages of supply, which became evident in the 1970s 80s, were resolved in an altogether different way, through capital inputs (2009 IMF report). In its turn, as soon as the follow up deleveraging causes growing shortages of demand, the solution may come through the rising importance of entrepreneurship, which produces a rising tide of technological innovations – innovation heavy resolution of a similar situation at the start of the 20 th century was noted by many including (Gordon 2004).
As it was expressed through Fabricant’s Law (Fabricant 1942), the decade before WWI notably differed from the depressive conditions at the end of the 19 th century. Not only there was a tendency for a speeding productivity growth to accompany faster output growth, but, due to technological progress, both were correlated with savings in wage costs and materials costs per unit of output and with slower rates of growth in prices. Thus, a rapid technological change and introduction of new business and production models, based on mass production, such as Swift’s meat packing and conveyor, still in its infancy, contributed, even at this early stage, to the substantial rise in production volume accompanied by lower costs. This increased demand on labor, while greatly boosting the value of land, needed to feed and house labor. Below, we summarize the periodical MPM related shifts during the 20 th century in the US, the leading country of the era. The model, with intentional oversimplification, stresses the causal relationship between factors of production, where the next leading factor comes to the top as soon as its counterpart is exhausted. This is interpreted as the lifecycle of a specific economy of the era.
The 20 th Century: the lifecycle of the economy of mass production, US style.
• Entrepreneurship and industrial revolution . From the depression at the end of the 19 th century and up to the 1913 inflationary peak and WWI – shortage of demand was gradually turning into shortage of supplies. The leading factor of production seems entrepreneurship , which boosts the value of land and labor through a major technological shift, with a surge in revolutionary innovations, birth of new industries and the introduction of new models of mass production (Gordon 2004). As Solomon Fabricant (1942) noted, the cost of production drops drastically, while its volume goes up. The higher productivity margins easily support increases in employment.
• Land and agrarian revolution in the situation of immature domestic markets . From 1914 and throughout the Great Depression up to the 1940s– the wartime global shortage of supplies gradually morphs into dire shortages of demand in 1919. Land becomes the leading factor of production, when its value starts growing accompanied by surging land prices during WWI. The US industries are still export driven, thus resource dependent, and domestic demand remains rather limited. WWI led to huge increases in acreage, leading to extreme agrarian oversupply and drop in prices in 1919 (Olson 2001 : 2). In the course of WWI, the US grew into the main agricultural supplier to the world. The rural debt expanded dramatically as land prices shot up. In 1917 there were more than 24 million draft animals and, from 1917 to 1925, 500,000 Fordson tractors were sold. The productivity of land grows notably, helped by better transport and the early effects of the mass car. Due to huge investments into the rural infrastructure (especially, rural electricity and rural roads) starting from the administrations of Hoover and further intensified during Roosevelt’s New Deal, the US is able to singlehandedly shoulder the great burden of supplying the WWII allies.
• Labor and consumption: the rise of domestic markets. The 1950s 70s – the earlier shortage of demand at the time of the Great Depression gradually ends with its opposite, the shortage of supplies manifested by the Oil Shocks. During this period, the US economy is in the surging growth mode and thrives on the expansion of its reach domestic markets. The main driver of the expansion is the labor , the basis of its surging consumer society. By creating huge demand for both industrial and agricultural products it links production to consumption in huge revolving flows.
• Capital and financialization. From the Oil Shocks and up to the 2009 Financial Crisis – the earlier shortage of supplies, especially oil, gradually morphs into shortage of demand. With the help of new global markets created during the globalization, the resource/labor shortages of the 1980s turn into oversupply. Capital turns into the leading factor of production – huge expansion of the role of financial institutions drives the surging global trade and compensates for the loss in domestic productivity by pulling in more global resources and labor. As modeled below, the surging rate of expenditures of capital/labor noted by the IMF can only be sustained through self generating issuance of financial instruments. As this process gradually gets out of control, it ends causing the global financial crisis. Severe deleveraging brings in shortages of demand due to insolvability of customers, who lost tremendous amounts of wealth, both real and imagined.
Below, we provide initial data to support this model by considering similar trends in the past. Then we develop a mathematical model of the process, which demonstrates the possible ways of compensating for the influence of RLDR. It shows that attempts to boost the sagging labor productivity through capital infusions may start a self generating process of financialization. This model, in its turn, is supported both by IMF findings and statistical charts presented below. Again, we stress the very preliminary character of our findings. Significantly more research and extended discussion are needed for supporting or rejecting our model. If accepted, however, it may provide a new predictive tool for forming right policy responses.
2. Market Pendulum and its oscillations in the 19 th and the 20 th centuries. Such cycles, which reflect MPM oscillations from supply shortages to demand shortages and back, seem to be fairly regular. As it was demonstrated in detail in (Badalian, Krivorotov, 2009), they were repeatedly played out in the past, revealing thus the inner logic of the related lifecycle. It marked the regular passage of the successive evolutionary stages of the known historic economies, such as the economy of the early industrial era of coal in the 19 th century or the economy of mass production based on oil in the 20 th century.
Among appropriate historic examples, the crises of the 20 th century USA had their nearly exact homologues in the 19 th century Britain. Spurred by the Great Depression of the 1830s, the 1840s reformist British government under Robert Peel actively protected labor rights. Post Great Depression of the 1830s, the suddenly important domestic demand was switched on by boosting salaries and increasing leisure time. This was the time when labor ruled. Of course, this period closely foreshadowed the New Deal and the similar boost to demand generated during the 1940s, when labor productivity shot up. Simultaneously, the Corn Laws, established from 1815, which, in Ricardo’s opinion “posed a barrier to the expansion of manufacturing” (Grabowski et al 2007: 47) were abolished, creating better conditions for labor and freeing up discretionary spending on new industrial goods. As predicted, this led to the huge expansion of domestic manufacturing in the 1840s 60s. After the economy reached its inflationary peak, shortages of supply were reversed to the deflation of the 1870s, much resembling the precipitous drop in oil prices in the late 1980s.
Foreman Peck argues that such extreme price movements have real causes. Among examples he cites is “ the opening of the Suez Canal in 1869 and the spread of railways. These caused large and unexpected declines in agricultural and raw material prices as a result of easier and cheaper transport ”. (Foreman Peck 1995: 85). Obviously, the related rise of the international trade in the 1870s 1890s resembled the current globalization. The latter was similarly enabled by the modern infrastructure of the global trade built in the 1990s (the Internet, the robust container/tanker traffic etc), which led to a sharp drop in the costs of communications and transport. Foreshadowing the recent financialization, when in 2007 financial companies earned one third or more of all profits of the US multinationals, in 1914 the British foreign investments amounted to over two fifths of the world total – Britain was drawing a tenth of its national income from its FDI. This was the time of financialization when capital ruled as the chief factor of production, helped by the rise of new forms of capital accumulation. I.e., the large joint stock corporation appeared in the 1860s, while multinationals came out in force in the 1980s. Of course, both now and a century ago, the switch from domestic to international mode of production fully conformed to the old prediction made by David Ricardo. He famously noted that a temporary antidote to his Law of Diminishing Returns would be provided by a shift to the international trade, so resources can be drawn in from afar. This activates the comparative advantages of different countries, realized by achieving economies of scale. In full concordance with his prediction, in both the 19 th and the 20 th centuries, Britain and the US, respectively, ended with visible U turns from domestic (IN) to international mode of production (OUT).
Summarizing the lifecycle of the 19 th century below, we underscore the similarities with the 20 th century.
The 19 th Century: the lifecycle of the industrial economy, British style.
• Entrepreneurship and industrial revolution . From the depression at the end of the 18th century and up to the Napoleonic Wars – the revolutionary era shortage of demand was gradually turning into shortage of supplies. This is the time of Industrial Revolution, where the leading factor of production seems entrepreneurship . Innovation boosts the value of land and labor through the major technological shift of the Industrial Revolution, with the birth of new industries and the introduction of labor division based modes of industrial production, described by Adam Smith as much more productive. The cost of production drops drastically, while its volume goes up, turning Britain into the global workshop. The higher productivity margins easily support the increase in employment.
• Land and agrarian revolution in the situation of immature domestic markets. In essence, this was caused by the earlier industrial pick up. From 1815 and, throughout the Great Depression, up to the end of the 1830s– the wartime global shortage of supplies gradually morphs into dire shortages of demand in the 1830s. Land becomes the leading factor of production, as the British industries are still export driven and domestic demand remains rather limited. In the course of the Napoleonic Wars, Britain grew into the main industrial supplier to the world. Industrial development was accompanied by an agricultural boom serving the fast growing cities. This period earned the name of the “second agricultural revolution” (c. 1820 60) – “farmers took advantage of artificial grasses and manures, clay drainage and farm mechanization” (Thompson 1968 cited in Floud and McCloskey 1994 : 145). From 1815 to 1846, the domestic agricultural interests are protected by the Corn Law, which led to rural poverty and discontent in the first half of the 19 th century, contributing also to the distress in Ireland. Deane and Cole (1962 : 170, cited in Floud and McCloskey 1994 : 145) note that “though firm estimates are unavailable, agricultural output may have doubled from 1820 to 1860”. The productivity of land grows notably, helped by better transport and the early effects from introducing the railroad, which notably boosts the horse based transport to stations (Aldcroft and Freeman 1983). This expansion is supported by the railroad boom of the 1830s, which opens access to the inner regions. The rural markets for industrial products start growing.
• Labor and consumption: the rise of domestic markets. The 1840s 60s – the earlier shortage of demand at the time of the Great Depression gradually ends with its opposite, the shortage of supplies manifested by the inflationary peak of the 1860s. The British economy is in the surging growth mode and thrives on the expansion of its domestic markets. The main driver of the expansion is the labor , the basis of its surging consumption, protected by new legislation. Its new power is reflected in the chartist movement, more equitable voting rights, Factory Acts, which gradually restricted first child and then female labor, especially in mines and difficult conditions, and expanding consumption. Supply demand chains are finally joined through surging consumer demand supported by rising employment.
• Capital and financialization. During the prolonged and painful global recession from the 1870s and up to the end of the century – the earlier shortage of supplies, especially coal, grain and iron (from the 1880s replaced with mass steel (Carnegie)), gradually morphs into shortage of demand. Colonial expansion creates new global markets for industrial production and helps to bring new resources from the abroad, mostly from the US, Argentina, Australia etc. This drive to globalization, the 19 th century style, resolves the resource/labor shortages of the 1870s reverting them into oversupply. Capital turns into the leading factor of production – huge expansion of the FDI was at the root of colonization, driving the surging global trade and compensating for the loss in domestic productivity by pulling in more global resources and labor. This foreshadows by a century the surging rate of expenditures of capital/labor noted by the IMF for the similar period after 1985. As this process gradually gets out of control, it ends in the global financial crisis at the end of the 19 th century. Severe deleveraging during the global switch to the universal gold system, which was backed by the pound of sterling, evolves amidst the sharp devaluation of silver (the 1894 6 “Gold Cross” in the US). This leads to shortages of demand due to insolvability of customers, who lost tremendous amounts of wealth, both real and imagined. This period is excellently described by Eric Hobsbawm, a noted British historian. He named it the “hollow” economy, since expansion of the British FDI abroad was accompanied by the loss of industrial power at home (Hobsbawm 1999).
These drastic MPM about face turns of the 19 th and 20 th centuries, which accompanied shifts between the leading factors of production presented above, are easily seen through market conditions, moving from supply to demand shortages and back.
The Supply-Demand Pendulum
capital land capital 7 1 2020? 5 1980s 3 1913-22 1860s 1880s 1930s 1990s 4 entrepreneurship 2 6 labor entrepreneurship
Supply shortages Demand shortages
Pic. 1. The Market Pendulum.
1. Supply shortages of the 1860s, with peak prices on coal and food, pushed Britain, which was the dominant country at that moment, OUT to the far periphery, in its search for coal and other inelastic resources. This started the globalization of 1860 1914s which was accompanied with the rise of colonialism. With intentional simplification, this period can be seen as devoted to the production of steel.
2. While steel was badly needed, especially for armaments, it could be obtained at a reasonable cost only if mass produced. This caused shortages of demand and deflation of the 1880 90s. 3. Low steel prices stimulated a technological shift, centered at the rising industry of precise machining. New technologies of machining thin uniform steel walls enabled such novel applications as the internal combustion engine, along with the mass production of steel rails/steamship. The latter greatly reduced the cost and increased the volume of the global trade, reversing shortages of demand into shortages of supply . The second peak of coal prices was reached in 1913.
4. WWI started within a year, replacing globalization with fragmentation. The older forms of capital accumulation and production showed their limitations, being pushed aside by an alternative rising form, the Fordism
AE, traditionally dated from 1908, with the “true” conveyor and the mass tractor arriving after WWI. It can be argued that shortages of demand on mass produced machinery contributed to the Great Depression, resolved only after the great boost to demand during WWII.
5. After WWII, the expansion of the Fordism AE to Europe and Japan in the 1950 60s brought in the happy equilibrium of balanced growth, with economy boosted by the rise of the consumer society, which linked the causal chains of production and consumption. Then, the exhaustion of domestic oil supplies caused another shortage of supply during the Oil Shock of the 1970 80s. The need to reach OUT for resources/labor of the far periphery started the current globalization.
6. From the mid 1980s to the 1990s, oil resources of the far periphery, including the former USSR, provided two decades of low-priced oil . Just as the global trade networks a century ago were enabled by the easy access to cheap mass steel, the current globalization became possible due to the affordable mass chip.
7. Today, in the depressed post crisis economy, whose monetary resources were sharply deleveraged, the awakened periphery is on the verge of its own surge in demand , to satisfy domestic needs. First and foremost, it
comes from China, India and other emerging countries. The recent demand for resources from China led to a swift
doubling of oil prices despite otherwise sluggish demand on the backgrounds of the evolving global crisis. The new production, however, should produce much more at a much reduced cost, as it was indeed the case at the start of the
20 th century (Fabricant 1942). This implies a need in a major technological shift.
Summarizing:
… 1860s = progressive shortage of supply = progressive inflation – Labor (Peel’s government, labor friendly legislation). 1880s 1895 = progressive shortage of demand = progressive deflation – Capital (colonialism, expansion of
British FDI).
1895 1913 = progressive shortage of supply = progressive inflation – Entrepreneurship (the II Industrial
Revolution).
1925 1945 = progressive shortage of demand = progressive deflation – Land (major projects of infrastructure –
Hoover dam, TVA, rural roads etc).
1945 1980 = progressive shortage of supply = progressive inflation – Labor (the rise of the US consumer
society).
1990 2000 = progressive shortage of demand = progressive deflation – Capital (globalization, financialization).
2011s … = progressive shortage of supply = progressive inflation – Entrepreneurship (the III Technological
Revolution – chip?).
the Lifecycle of the Smithian MA the Lifecycle of the Fordism MA
Coal-IN Coal-OUT Oil-IN Oil-OUT
entrepreneurship
labor capital land labor capital
1830s 1860s 1880s 1914-19221930s 1980s 1990s
Pic. 2 The Lifecycle of an Economy . (MA stands for the preferred Mechanism of Accumulation of its time, such as the joint stock company for the US and the charter company for Britain of the 19 th century, see (Badalian, Krivorotov, 2009))
3. The Inner Logic of the Lifecycle of an Economy. Sequencing the Leading Factors of Production: Land, Labor, Capital, and Entrepreneurship. MPM implies the existence of a strong causal interrelationship between 4 traditional factors of production: land, labor, capital and entrepreneurship. It divides the factors of production into two separate groups. The first unites land and labor, which are less elastic, since they are limited by physical boundaries of a given leading country, such as the US in the 20 th century or Britain in the 19 th century. Within this pair, labor is less inelastic than land, since its shortages can be compensated through migration, typical during globalization, when capital rules, and increased birth rates, typical for the initial stages of land acculturation, when land rules. The second group of factors of production is composed of the remaining pair: capital and entrepreneurship, which are much more elastic, since they are created through human activity – entrepreneurship in our case serves as the proxy for innovation, both in business organization and technologies. However, this elastic pair also helps in mitigating resource shortages by pulling in resources and labor of the faraway periphery, when technologies and institutions are refined to such a degree that they are universally accepted. Needless to say, this also starts major changes, when new technologies and business practices are adjusted to fit the specifics of faraway regions. Neither steel, nor the car nor methods of mass production were invented in the US. however, coming from Europe, they could truly shine only in the US, starting a new cycle of development on its vast territory.
Summarizing, land serves as the object to deal with, and the remaining three factors of production become the subjects, which actively stretch land’s productive power. In this sense, land remains the only immediate source of wealth, as Physiocrats once believed. All the other factors of production are no more than indispensable tools for unveiling its wealth, since without the right tools it remains latent and unobtainable.
MPM implies that the growing exhaustion of any of the production factors is perhaps inevitable due to the relentless work of the RLDR and produces notable market imbalances – alternating from supply to demand shortages. Equilibrium is thus achievable only in the midmovement from shortages of one type to shortages of the opposing type.
Historically, the exhaustion of the marginal utility of domestic resources (encompassing both natural resources and labor) of the original leading country was compensated through globalization (Badalian, Krivorotov 2009). This was typically accomplished by increasing the input from the factors of production belonging to the second pair, capital and entrepreneurship, which are significantly more elastic and territory insensitive (capital or entrepreneurship). The latter quality becomes paramount for the global expansion of capital as the leading factor of production. This explains many recent effects: the extreme levels of standardization from the 1980s, the global spread of the neo liberal model, universalism and international acceptance of the leading business practices and technologies, which became widespread at the farthest edges of the globe. To the faraway periphery, first there comes capital, made available through the financial institutions and instruments of the leading country, then the innovations, which also initially come from the center.
Working in tandem, capital and entrepreneurship help to awaken new territories. This results in an initial boost to the productivity of new global land. At this point, it is mostly export driven, bringing the wealth of the new area into the reach of the leading economy of the time. Simultaneously, its resources of global labor, torn out of their traditional habitats, also become available. This brings additional territories from the far periphery into the economic area of the dominant, while also adding previously underrepresented groups to the global labor force. This both alleviates the then extant shortages up to the point of oversupply and awakens the faraway periphery. If new suitable technologies for using its abundant virgin resources can be developed, the new land may enter an intensive mode of production, by finding innovative suitable tools for boosting its productivity to support and employ a denser population. The level of productivity would thus advance to a higher level. Eventually, RLDR will start its work anew, but from a much higher vantage point, providing the next leading country/region an ample room for economic development, based on innovative functionality of its virginal resources/plentiful labor.
This scenario presumes a dramatic shift. Due to the well known phenomenon of asset inertia (Roberts 2004), it thus would unfold only after a major crisis, the very start of which we may be experiencing today. This has a deep reason. As a rule, the conditions of new global territories on the periphery substantially differ from those of the initial zone of development – both their land and labor are far from matching the best possible levels of productivity of the leading country, in our case the US. In fact, the introduction of the periphery is a forced step. It becomes the last frontier of the falling productivity of the older technologies, which is compensated through extreme economies of scale, noted by Krugman as the root of global trade flows (Krugman 1994). Historically, this kind of size eventually became unwieldy. As demonstrated by the mathematical model below, infusions of capital of this scale are destined to self generate monetary flow and self destroy as soon as they uncontrollable growth. Deflation, due to the lower earning power of newer places and the sharp deleveraging at the collapse of excessive financialization, becomes inevitable sooner or later. In its turn, it opens the gate for Schumpeterian creative destruction, which means radical innovation, thus entrepreneurship. For example, the technologies of the 20 th century would be unthinkable before the extreme fall in steel prices during the deflation at the end of the century. The cheap steel might have not made major profits, but this dramatic fall in costs made it available for the use in the new applications: the bicycle, the mass car, the tractor etc. These cheap means of transportation, with a huge market among the masses, came in addition to the earlier and much more expensive projects of steel bridges, skyscrapers etc, which could be used in more affluent places.
Modeling a Lifecycle – the Sequence of Leading Factors of Production
1. Typically, entrepreneurship is spurred on by an effort to survive during deflation. In parallel, innovation opens up access to new places and ignites new types of demand – for affordable products for less wealthy masses. Today, we see similar processes in the third world, whose residents eagerly purchase any mobile means of communication, from the cheap motorcycle to the phone. However, as the Economist notes in its leader in the September 24 th , 2009 issue, this development still waits for its last frontier, the truly mass internet, which may reawaken the growth of productivity, passing the impulse from the west to the developing world. If this indeed happens in the 21 st century, it would match similar developments at the start of the 19 th and the 20 th centuries (such as the availability of cheap pig iron and cheap steel and the widespread light bulb etc, respectively). Such falls in prices open the door for smaller players, whose survival depends on adjusting the existing technologies to the territory – example, the passage from Carnegie to Ford. The former was a large player, able to bring steel prices down. However, the true awakening of the US territory is owed to Ford, a bit sized player, who introduced both the new method of production on the conveyer belt and the mass car, the crucial invention, which shaped the 20 th century.
2. Land. The necessity of an Agrarian revolution, which ends with massive projects of land improvement and transport/communication infrastructure, follows from the need to feed the growing cities, which, in turn, need markets for their production. Markets, at this point, are mostly export driven. However, this new demand starts large land improvement projects on the scale of tilling the Great Plains etc, perhaps, causing an environmental disaster of the Dust Bowl in its wake, since the technology is still untested. Thus, a thorough reworking of land’s geometry through construction of interrelated networks of roads/communication along with a dramatic improvement in the agriculture must follow, which indeed happened during the New Deal. This period starts with the problem of supplying the cities and ends with the opposite problem of demand shortages due to the immaturity of domestic markets.
3. Labor . At this stage, industrial and agrarian products can finally be united through labor, creating ample domestic markets. The rising employment creates demand for agrarian staples, whose production, in turn, depends on inflows of industrial goods. Huge revolving flows of demand circle through cities and rural areas, contributing to the growth in wellbeing, and contributing to the growing shortages of supply.
4. Capital . This was shown above and would be modeled below. Most recently, the 2008 crisis vividly demonstrated that, by increasing the ratios of capital per labor from 1985, domestic labor limitations could be successfully mitigated, up to a point, as it can be shown by juxtaposing the IMF 2009 report and the labor productivity data. The domestic debt issued by financial institutions was used as collateral underlying issuance of easy foreign credits. Serving as the proxy to hard cash, these dollar denominated credits, often backed by various derivatives, were also helped by the global popularity of US Treasuries. Acting together, the array of financial tools was quite successful in supporting the immense flows of dollar denominated trade, which brought real goods back home from abroad.
4. Capital – Modeling the Financial Leveraging of Falling Productivity.
The end stage in the lifecycle, when capital comes to the top as the leading factor of production, is modeled below. Capital is presented through its proxy, the global flow of dollar denominated credits at the heart of globalization and outsourcing. As it is well known now, they were based on the issuance of new financial instruments – derivatives (CDSs, CDOs etc). Within the aforementioned scheme of the lifecycle passing through logically related sequential stages this characterizes a mature economy, at the advanced stage of RLDR. This applies to the US after 1985, a watershed year of the aforementioned IMF report. According to our hypothesis, capital becomes the last leading factor of production, when the other three factors already exhausted their potential for growth due to the relentless work of RLDR. Among those are: entrepreneurship (as a proxy for radical technological changes at the start of a lifecycle), land (the greatest source of wealth on the condition of developing suitable technologies for harnessing it) and labor (the main justification for starting a lifecycle and the most active force in dealing with land).
The labor productivity data below seems contradicting our assumption of RLDR as a physical law, able to exert force. After a fall in the 1970s, it starts growing back in 1985. However, the equation (1) below shows that the effects of falling labor productivity, just as any other physical force, can be, up to a point, compensated by applying a counterforce, in this case, by expanding economies of scale. During globalization, this becomes an outside source of increases in productivity, totally unrelated to manufacturing of goods in the leading economy, such as the US today.
Pic. 3 Growth of Productivity 1947-2008.
Source: The US Bureau of Labor Statistics. http://www.bls.gov/lpc/prodybar.htm
Huge flows of dollar denominated credit funded the global economy of scale and brought in steady supply of outside resources and goods. As a side effect, up to the 2008 crisis, these two counter forces (RLDR versus expansion of the global economy of scale), while they were still mutually balanced, also supported a stable growth of the US GDP. This is presented below by introducing the target rate of returns per invested dollar (per unit of time), as represented by the US GDP. Supporting this target rate on the more or less stable level made the US economy viable. If, meanwhile, RLDR was indeed falling, as our hypothesis suggests, then the real return per transaction per dollar would be small and diminishing. As a result, the balance between these two counter forces would be fluid and in the need of constant adjustments. Compensation for falling returns per transaction would, evidently, come from
increases in the frequency of transactions – with each transaction producing smaller returns, the increase in their numbers would, up to a point, more than compensate for the fall, producing, as the end result, the target rate. The frequency or speed of return is thus defined by the implicit self preservation of the market, which strives to preserve its current . thus is the ratio of the observable target rate to the real rate , which remains unobservable.
(1)
Eq.1 describes the coefficient of self generation for cash flows, in this case dollar denominated credits. In its most generic form, cash credit flow generation is expressed through a d simple equation of self generation (2), which estimates the resulting increase of the flow , if dt
is the observable frequency or speed of self generation per monetary unit .
(2)
where: • – target rate of productivity (return) per monetary unit, which is sufficient for the survival of the system. We assume it fixed (constant) for a given and measure it in dollars/(per second*per unit) • –– real rate of productivity per transaction, further, a quantum of productivity. A transaction/cycle of return refers to any activity aiming to produce returns – from production and sales to investments. Real rates of return for various cycles of production are measured uniformly, in dollars/(per cycle*per unit). This measures the producing capacity of the land under consideration, for all its uses, agricultural to industrial.
From (1) and (2) we obtain the generic equation of money flow, in this case dollar denominated credits, used to produce returns for the globally outsourced US economy (3)
Eq.3 describes a self generated growth process. This model describes the process of leveraging the real productivity for obtaining the target rate , which was running up to the 2008 crisis. When the process is slow, the market has time to adjust to it and remains controllable. After reaching its critical mass, the leveraged monetary flow becomes uncontrollable and its expansion acquires the character of a chain reaction style explosion. This is demonstrated below.
The limits of economic expansion marked by RLDR.
Historically, the 1970s (73 79) experienced an unprecedented fall of productivity, interrupting its steady growth after WWII (see pic.3). This was compensated by an expansion of monetary leverage, which fueled outsourcing/globalization by issuing affordable dollar denominated credits.
Below we assume that RLDR is expressed as an inverse dependency of the quantum of capital productivity to the total number of monetary units – the more capital is generated the less productive it becomes.
(4) , where .
Eq.4 is further called the Ricardian curve. The interpretation is obvious. Due to RLDR each additional unit of a factor of production, in this case capital expressed through credit money, would have a lower real rate of productivity, since the best sources of collateral would be used first, leaving those of decreasing quality, such as subprime, for later additions.
As told above, we obtain the target rate by approximating statistics on labor productivity available from the BLS. Meanwhile, the utility is measured through the real rate, which can’t be measured directly through any official data. However, it can be measured indirectly through Eq.3, since we have the data on the extant monetary flow.
Corollary.
If any given factor productivity, such as capital, obeys a Ricardian Curve (4), then its detrimental effects can, for a while, be compensated, by leveraging its productivity through d increase in its flows as follows: dt
(5) , where – the constant target rate, and parameters k, l are
constant
Theorem 1. If the target rate of productivity is fixed at , while RLDR (4) remains valid, then the overall size of any given factor productivity in (5), such as leveraged capital, grows hyperbolically with an asymptote at the moment of time t= as defined by (6) below.
(6) where are constants, and t0 depends on the
initial conditions of the system.
Proof .
Combination of (4) and (5) produces (6) for the factor of productivity , with parameters . The hyperbolic curve (6), which measures leveraged , is the solution of the differential equation (5) with constant parameters . Hyperbolic self generation follows from (5), since
each added unit of generates growth .
The existence of asymptotes at follows from (6).
The possible asymptotic hyperbolic solutions (6) of the equation (5) are shown on Pic.4 below. 5 l=10 l=5 l=4 l=3 4 l=2 l=1 l=1/2 l=1/3 3 l=1/4 l=1/5 l=1/10
2
1
0 -10 -8 -6 -4 -2 0 2
Pic. 4. A series of hyperbolic solutions (9) of equation (8) for different values of parameters k and l. when
The sharply accelerating curves on Pic. 4 mean that, generally, due to the lower productivity of each consecutive added unit of capital, the scale of its leveraging would gradually acquire self generating hyperbolic character leading to the explosive growth in its units at some moment
t0 . The latter can be calculated using the known initial conditions init (tinit ) . According Eq.6
k 1 (t ) = ( ) l ) at some earlier moment t . As the system moves towards t , init init − init 0 H 0 (tl 0 tinit ) entering its close environs produces telltale signs, described below.
Theorem 2. If the target rate of productivity is fixed at , while RLDR expressed in (4) remains valid, then the function (t) has a singularity at the point t0 . In the terms of standard calculus this means that, for any arbitrary small period of time and any arbitrary large growth > δ in the size of as the leading factor of production, namely capital, in the close vicinity to the asymptotic point , there exists a moment such that the additional growth in the size of would exceed δ within an arbitrary small period of time .
Proof . It is obvious from the fact that the hyperbolic function (6) grows to ∞ asymptotically at the point of singularity .
In practical terms, reaching the close environs of the singularity would mean that, starting < from some moment t1 t0 , cash flow outgrows any given limits. This theorem shows that, as we approach closer to the asymptotic singularity even infinitesimally small changes in the initial conditions may cause huge swings in vital economic parameters. This is the main feature of the condition of deterministic chaos (Lorenz 2005) 1. In the close vicinity to the asymptotic singularity, the rapid growth in the size of the factor productivity produces “sunspot equilibrium” (Cass 1983). In this case, even infinitesimally small random changes in the initial conditions or even some random, seemingly unrelated variables may produce unexpectedly strong results.
In the case of a rapid and uncontrollable growth of capital as the factor of production through a run off issuance of credit the system enters into the condition of deterministic chaos/sunspot equilibrium.
Among other historical situations, its main features closely match the recent pre crisis conditions, when the excessive monetization and hyperbolically growing leveraged monetary flows caused a surge in risk levels taken on by banks etc. This analysis shows that, in such cases, a 3S style catastrophic event (Calvo et al 2008) would happen sooner or later, with nearly a 100% probability. The only remaining question would be not whether, but when.
The reason for the hyperbolic acceleration described in theorems above is quite simple – obviously enough, the best territories with the most productive workers and the best endowment factors would be among the first entering globalization. The second, third etc tiers by definition would have lower natural endowment and productivity factors and, thus, decreasing levels of productivity. The step by step spread of globalization abroad would thus produce a hyperbolic curve of self generating and accelerating monetary flows, in an attempt to compensate for the falling productivity by increases in capital inflows. In the process, after using all the better producing territories, the crucial factors of natural endowment and productivity would be sped up to their natural limits of leveraging. For example, in order to compensate for the falling
1The research by Edward Lorenz was well predated by Jules Henri Poincaré (1890) cited from Torretti, 1984).working on the famous problem of three bodies, Jacques Hadamard (1898) on geodesic lines on a surface, George Birkhoff (1927) (cited from Aubin 2005) on dynamical systems and Andrey Kolmogorov (1941) on turbulences in incompressible fluids. All these seemingly diverse topics described the same phenomenon. productivity per employee ever more workers would be involved at the each next step of this iteration. Thus, labor saving at home translates into labor spending abroad, until this becomes too cumbersome and unsustainable even with the help of leveraging and capital infusions.
The validity of this theorem and the underlying RLDR is supported by a simple observation. Reaching for the workforce of the developing world is costly, implies investments into a major dedicated infrastructure and carries considerable risks. Such pricey undertakings would have been impossible if target rates could be indeed achieved at home.
It is a well known fact that both workers in developing countries and migrant laborers from developing countries are often relegated to the least expensive and menial jobs which cannot be performed cost efficiently by the workers of developed countries. The latter get assigned to more lucrative jobs either in logistics or finishing. Conservative estimates put one worker in a developed country at the top of a pyramid of 250+ workers toiling afar in developing countries. This lends empirical support for our hypothesis that the falling productivity in the developed countries is the chief reason behind globalization, which, in turn, ignites leveraging.
In this way, as the 2009 IMF report found, capital becomes the chief factor of production helping to use the less efficient land and labor of the faraway periphery without starting a fall in the rates of return and supporting the growth in GDP.
Reaching the Technological Horizon.
Corollary 2 . The excessive leverage and financialization expressed through runaway growth in is the market’s response to conditions of money hunger and undercapitalization caused by the effects of RLDR in a mature economy within the stage of globalization.
This is obvious from (6), with capital as the factor productivity under consideration , when is small and falling, while H is fixed.
Large monetary flows servicing the needs of globalization along with the resulting explosive growth in global trade were observed in reality, and caused a similarly explosive issuance of “financial instruments”. Though their sum total remains unknown, some estimate it as approaching a quadrillion.
Definition 3. The time horizon of a given economy.
We define
(7) T as the temporal horizon for a given factor productivity , where T measures the
average time of return on an investment, which apparently changes during the lifetime of a given economy.
Eq.7 is a tautology, since by definition. It explains the preference of mature economies for shorter transactions, with faster returns, since an excessive economy of scale, with small rates of return, increasingly depends on credit. During the crisis the time horizon reaches its temporal limit at the singularity , where, according to (6), the overall money supply (M3, M4++ etc) becomes virtually unlimited as it speeds up the asymptote.
Theorem 3. A dramatic shortening of temporal horizons T produces inverted or flat yield curves. In contrast, a significant lengthening of temporal horizons produces humped yield curves.
Proof.
According to Eq.2 generation of monetary flows is proportional to , which measures the frequency of returns. The accelerating capital market prefers short term credits over long term credits, since only the former generate sufficiently large monetary flows due to much faster returns. This preference of the market for short term credits over long term credits produces, in practice, an inverted yield curve, since the short term credits, as more desirable, become more valuable and command higher prices than the long term ones, which are delegated to serve in the quality of collateral.
In plain English, the mechanics of this are as follows: 1. Production of affordable collateral through long term loans . If is excessively large – the market favors short term investments over long term ones. The market, represented through its plethora of willing players, from government (which forcefully promotes home ownership) to government backed entities (Fannie Mae etc) to any ordinary investment company (banks to private equity), desperately needs more collateral. In our case, the latter was found mostly in housing funded through long term debt, which was deemed extremely safe due to its fast appreciation. Its presumed safety was increased even further through the use of insurance and rating agencies for the products of its securitization. The latter converted the initial illiquid collateral (housing) into market coveted liquidity. 2. The two factors of the rise in the rates for short term loans . The first one was mentioned above, namely, the market’s preference for the short term loans as the only available vehicle for generating sufficient credit flow. The second one is related to the riskier nature of short term loans lacking suitable collateral and thus unfit for securitization, reserved for the long term debt backed by collateral.
These two factors taken together would produce an inverted or flat yield curve, which indeed was observed repeatedly before the 2008 crisis, as shown below. This is a telltale sign of the unsupportable shortening of the investment time horizons.
Meanwhile, long term loans become valuable to their issuers as the source of collateral backing securitization. Their interest rates drop, since the profit is obtained through securitization and leveraging them as collateral. In this case, short term investments would be even used for refinancing payments on long term debts, which can’t be repaid on their own due to the falling productivity. Assets chase money, leading to the situation of severe undercapitalization in a shallow low margin economy of overblown scale. Since, in this case, short term investments become riskier than the long term ones, which are both backed by collateral and used in the quality of collateral underlying the short term loans, thus, the short term rates race up. This favors consumption over production due to the faster returns for the former and slower for the latter.
Meanwhile, the collapse of the bubble would lead to abrupt deleveraging, revealing thus the underlying situation of undercapitalization and igniting deflation – i.e. the Great Depression of the 1930s. Kindleberger (2006) noted that severe financial crises at the end of both the 18 th and 19 th centuries, started from the prickling of real estate bubbles, a final event of periods of increased consumption.
Corollary 3. External boundaries to globalization are of two sorts: temporal and spatial .
Proof . Follows from (6) and Theorem 2.
The theorem 2 above states the existence of a vertical asymptote for the factor productivity curve (6) at the point of singularity . At the same time, for technical reasons, each factor productivity cannot exceed the value , which differs per economy reflecting its size. This twin wall like boundary binds together the phenomena of temporal and spatial leverage – as a result, we get both ever shorter credits and ever bigger territory to use as a source of collateral.
Hyperbolic solutions (6) of the equation (5) for generic factors productivity show that the hyperbolic spatial leveraging ends by hitting the rigid boundary of the vertical temporal asymptote. For the case of leveraging the money supply:
1. Spatial leveraging is achieved by using collateral from one locality to fund a loan in another. This creates a vital problem of trust, as those who accept this collateral must be sure of its value, despite having no immediate access to it. As we know now, this problem arose in the reality and was resolved by the rise of a vast industry of rating agencies and risk insurers, from Moody’s to AIG. In this case, spatial limits were reached within a few years due to the necessity to constantly increase the size total of the underlying collateral. This shows the interrelationship of spatial and temporal boundaries. For an observer, the spatial leveraging would produce a series of bubbles or swift price increases in anything that can be used as collateral. Usually, such price increases would appear as a series – as soon as valuations for the collateral of one type stop growing for one or another reason, there would be an attempt to replace it with any acceptable substitute. 2. Temporal leveraging appears upon reaching extremes of spatial leveraging. The latter leads to increasingly short term borrowing, which would gradually substitute all the functionality of mid and long term debt other than as collateral. Gradually, as temporal leveraging acquires extreme forms, nearly all real credits would become short term, and even long term investment needs, which cannot be in fact repaid by the borrower due to insufficient productivity/returns, would be covered by additional tiers of refinancing, increasingly short term 2. As told above, for an outside observer, this would produce the inverted yield curve. In fact, an inverted yield curve steadily appeared not only in 2006 7, but also in 1927 1929 3.
5. The Data: Revealing the Hidden Force Exerted by RLDR .
The considerations presented above are strongly supported by empirical data. The three graphs below support the thesis that the counterforce to RLDR unfolds through the compensatory mechanisms, where the expansion of the monetary flow accelerates as the real rate falls down. Technically, this means inclusion of ever new types of assets to serve as collateral for securitization. This produced a series of bubbles of pic.5 below. As housing peaked, there was a series of sharp price appreciations in other assets, first in banking, then in the stock market and natural resources forming a serial pattern of bursting bubbles mentioned above.
Pic. 5. The Bubble Bursts . Source: Taylor, John B (2008).
2 This resembles the shell game, where a coin is placed underneath one shell (cup, thimble etc) out of three and the player must choose the right one. In the case of extreme temporal leveraging, a single coin will be found under all of the three (or thousands) objects simultaneously, which is achieved by raising the speed of movement between them to the limit of perception. Of course, instead of shells we had loans. 3 Among many others, John Waggoner of USA Today happily reported on 2/13/2007 that “Inverted yield curve may no longer be sign of recession”. Asset price acceleration is followed then by commodity bubbles. According to the graph below from (Taylor 2008), oil prices shot up in 2007 or as soon, as the rapid appreciation of the US based real estate first slowed down, then completely stopped and even reversed. At that moment, there was also a notable rise in automobile loans, also used as (secondary) collateral for tranches of financial instruments. However, after reaching the limits of appreciation for the US based housing, which was the most massive and easy to use collateral, a global credit squeeze became quite pronounced. The bursting of the bubble coincided with the bankruptcy filing of Lehman Brothers on September 15 th , 2009. This revealed that the firm was in fact the wellspring of affordable dollar denominated credits funding globalization.
Pic. 6. The Rise in Oil Prices and the Federal funds Rate . Source: (Taylor 2008).
A third graph from the same source puts to rest the popular claim that the surge of global investments was financed by the increase in global savings. It shows that, contrary to popular beliefs, the global savings rate was in fact falling from the 1970s and indeed, during most years of this period, it was below the investment rate. Apparently, its size was dwarfed by securitization.
This conclusion is strengthened by the fact that even this curve may be greatly overestimating the size of global savings, some of which also were kept in “financial instruments”, the product of the non linear price acceleration through leveraging.
Pic. 7. Savings versus Investments . Source: Taylor 2008.
The pictures 8 and 9 below present the growth of derivatives and labor productivity respectively. They demonstrate amazing synchronicity, showcasing the hidden force exerted by RLDR through its counterforce, namely, the surging monetary flows, which compensate for the falling real rates of productivity. The growth of derivatives serves as the proxy for global, dollar denominated credit flows, which counterbalanced the falling real productivity and produced the more or less stable target productivity rate H ( ) up to 2004 2005, well before the point of its failure during the 2008 crisis. Between 2004 and 2005 there was a steep drop in the target rate of productivity, to about the third of its former size (see pic.8 9). This inability to support the target rate H ( ) despite the continuing growth in derivatives might have been the real reason for the collapse that followed. From 2005 to the mid 2007, productivity stayed low despite the feverish spike in the pace of derivatives (pic.8). In 2007, it starts growing again, to its previous level, no doubt, helped by the last, short term sharp spike in derivatives. After the 2007 credit freeze, signaling the unsustainability of derivative growth, the drop in productivity wasn’t reversed.
We model the force exerted by RLDR as follows:
1. From Eq.2, we derive
d H ( ) (7) =ν ( ) = and, finally dt h( ) 1 (8) h( ) = H ( ) ν ( )
The left side of Eq.7 measures the rate of growth in dollar denominated credits, as the counterforce, the main source of money servicing the needs of the global market. Thus, ν ( ) can be obtained indirectly from official data through its proxy of derivatives, see Pic. 8, 10. Since target rate H ( ) is approximated by labor productivity, we can directly calculate h( ) using Eq.8. Pic. 10 below shows three well defined periods:
• up to 2001, the target rate is elastic and closely follows the monetary input of the derivative growth rate • 2001 2005, its elasticity is lost and the target rate barely responds the accelerating monetary input. The real rate fell nearly six to ten fold. • 2005 2008, the target rate stops responding to torrentially accelerating monetary inputs. The elasticity is restored, for a short time, at the start of 2007, and then it is completely lost in the 2008 crash. After the crash, trends become volatile and most variables go down.
This shows the predictive power of the suggested tool – the real rate taken in conjunction with the target rate it strives to support, in this case, by increasing the capital flow, until it becomes insupportable.
Pic. 8. Growth rate as compared to derivative volume. Self prepared. Source: Bank of International Statements (BIS). Quarterly reviews. June 2009. P. A 103. www.bis.org/statistics/otcder/dt1920s.pdf
Pic. 9. Productivity index versus growth rate, including smoothed growth rate using moving averages. Self prepared. Source: Bureau of Labor Statistics.
Pic. 10. Target rate versus real rate on the backgrounds of derivative self generation and labor productivity growth. Self prepared. Source: Bureau of Labor Statistics and BIS.
Conclusions.
Above, we formulated a hypothesis about a hidden force exerted by RLDR in a mature economy. Then, we built a model to find its observable effects, aiming to reveal the hidden force through real observable data available on its counterforce, the surge in capital, in this case through the growth of derivatives.
Subject to further empirical testing, the model demonstrated that RLDR is a real physical law, able to exert force, which, up to a point, is mitigated by a counterforce, such as recent financialization. In this paper, we offered means of detecting this force indirectly, through the surge in financial instruments, measuring input of capital per labor.
The model is supported by its ability to explain a range of phenomena, which, up to this date, remained unexplained. Among them:
• Explanation of the recent bubble through the surging rise in the working capital as the leading factor of production for a mature economy, counterbalancing the negative influence of RLDR. The financialization synchronized the entire economy – under the pressure of the expanding market, in the need for more collateral, everything that could be securitized, including real estate, oil, private debt and other such entities, which normally are incompatible since they service different market segments, were synchronized and turned into collateral backing derivatives. • Explanation of the mysterious phenomenon of the inverted yield curve, whose appearance also predated the 1929 crisis. • Placement of the initial trigger event, which eventually led to the 2008 crisis, at a much earlier date around 2005. The fall in productivity (target rate) to the one third of its former size was the telltale moment, which can be used for diagnosing and predicting similar future events. It triggered a compensational spike in derivatives, as a counterforce aiming to counterbalance the pressure exerted by RLDR. The real rate didn’t respond and fell up to ten times. This created the preconditions for the 2008 Systemic Sudden Stop (Calvo et al 2008). • Introduction of a new analytical tool – the real rate of productivity h( ) . Even though it can’t be observed directly, it can be estimated through the volume of the monetary flow and the statistics on labor productivity (the target rate H ( ) ). The sharp movements in h( ) , which can’t be compensated despite visible spikes in ν ( ) , such as the one observed in 2004 5, present an advance warning of an overextended economy in a danger of collapse.
Again, we stress that the model presented in this paper remains a hypothesis in need for vigorous empirical testing. Meanwhile, its serious implications can neither be accepted at their face value nor rejected without a thorough additional research.
Select Bibliography.
Aldcroft, Derek H. and Michael J. Freeman. 1983. Transport in the industrial revolution . Manchester University Press.
Arestis, Philip; and Glickman, Murray. “Financial crisis in Southeast Asia: dispelling
illusion the Minskyan way”. Cambridge Journal of Economics 26:237 260 (2002)
Aubin, David, 2005, "Dynamical systems" in Grattan Guinness, L. ed., Landmark Writings in Western Mathematics . Elsevier: 871–81.
Badalian, Lucy; and Krivorotov, Victor. “Technological Shift and the Rise of a New Finance System: the Market Pendulum Model”. The European Journal of Economic and Social Systems . Summer 2009. Vol. 21 – No. 2/2008. 233 267.
Bernanke, B. and M. Parkinson, 1992, Procyclical Labor Productivity and Competing Theories of the Business Cycle: Some Evidence from Interwar U.S. Manufacturing Industries, Journal of Political Economy 99, 439 459.
Bordo, Michael D. and Evans, Charles L. (April 1995) Labor Productivity During the Great Depression. NBER Working Paper No. W4415. http://www.nber.org/papers/w4415.pdf
Calvo, Guillermo et al. “Systemic Sudden Stops: the Relevance of Balance Sheet Effects and Financial Integration”. 2008. BER Working Paper o. 14026 . Cass, David; and Shell, Karl. "Do Sunspots Matter?" Journal of Political Economy. 1983. 91 (21), 193–228.
Hadamard, Jacques. "Les surfaces à courbures opposées et leurs lignes géodésiques". J. Math. Pures et Appl. 4 (1898) pp. 27 73.
Fabricant Solomon (1942). Employment in Manufacturing, 1899 1939: An Analysis of Its Relation to the Volume of Production. NBER Books
Floud, Roderick and Deirdre McCloskey (eds) (1994) The Economic History of Britain since 1700. Vol 2: 1860 1939. Cambridge University Press.
Foreman Peck, J. 1995. A History of the World Economy: International Economic relations since 1850. Pearson Education Ltd.
Gordon, Robert J. 2004. Productivity growth, inflation, and unemployment: the collected essays. Cambridge University Press.
Grabowski, R., Self, Sh., Shields, M. 2007. Economic Development: A Regional, Institutional, and Historical Approach . Sharpe.
Hobsbawm, Eric. 1989. Industry and Empire, Penguin Books.
IMF Global Financial Stability Report. Navigating the Financial Challenges Ahead. October 2009. http://www.imf.org/External/Pubs/FT/GFSR/2009/02/pdf/text.pdf Chapter 4.What is the Damage? Medium Term Output Dynamics after Financial Crises. http://www.imf.org/external/pubs/ft/weo/2009/02/pdf/c4.pdf
Johnson, S. 2009. “The Global Crisis: Is It Over Yet?” MIT Sloan School of Management. http://baselinescenario.files.wordpress.com/2009/06/global crisis for wbank abcde korea june 21 2009 final.pdf
Kendrick John W. (1982) International Comparisons of Productivity and Cases of the Slowdown , American Enterprise Institute for Public Policy Research Kendrick, John W. (1961), Productivity Trends in the United States . "National Bureau of Economic Research Number 71, General Series," "Princeton University Press,
Kennedy, Kieran A . 1971 Productivity and industrial growth: the Irish experience . Clarendon Press, Oxford University Press.
Keynes, John Maynard. 1937. “Alternative theories of the rate of interest”. Economic Journal.. 47, 241 252.
Kindleberger, Charles. 2006. A Financial History of Western Europe. Routledge, 2006.
Kolmogorov, Andrey N. (1941). "The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers". Proceedings of the USSR Academy of Sciences 30: 299–303. (Russian) , translated into English "The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers". Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences 434 (1980): 9–13.
Krugman, Paul. 1994. Rethinking International Trade. MIT Press.
Lorenz, Edward. “Designing Chaotic Models”. Journal of the Atmospheric Sciences : 2005. Vol. 62, No. 5, pp. 1574–1587.
Minsky, H.P. (1986) Stabilizing an Unstable Economy . New Haven : Yale University
Press.
Olson James S. 2001 . Historical dictionary of the Great Depression, 1929 1940. Greenwood Press.
Pisani Ferry, Jean and Bruno van Pottelsberghe. “Handle with Care! Post Crisis Growth in the EU”. Bruegel Policy Brief . 2009/02. April 2009. http://aei.pitt.edu/10780/01/pb
2009 02_170409.pdf
Roberts J., (1989). Europe 1880 1945 . Second edition. Longman, Roberts P.. (2004). The End of Oil . Houghton Mifflin Company,
Salter, W.E. (1960) Productivity and Technical Change . Cambridge University Press,
Scott, Maurice F. (1991) A ew View of Economic Growth. Clarendon Paperbacks.
Taleb, Nassim Nicholas . The Black Swan: The Impact of the Highly Improbable. 2007. New York: Random House.
Taylor, John B. 2008. The Financial Crisis and the Policy Responses: An Empirical Analysis of What Went Wrong. http://www.stanford.edu/~johntayl/FCPR.pdf
Torretti, R. 1984 Philosophy of geometry from Riemann to Poincaré. Dordrecht Boston.
Wragg, R., and Robertson, J. (1978). Post war trends in employment, productivity, output, labour costs and prices by industry in the United Kingdom. Dept of Employment Research Paper no. 3 Dept of Employment. London.