Couples and the K-wave.

Alison Marshall,  March 2008. [with later additions in square brackets.]
Long wave economic depressions may be caused by population cycles nearly two generations long.

Marriage Markets.

A marriage squeeze is a problem of unbalanced supply and demand in the marriage market.  An example is Britain in the 1920s. It’s well known that for many British women at that time it was difficult to find husbands, because so many British men had been killed in the 1914-1918 war. (Nicholson, 2007).  But a similar problem in the 1970s was not widely recognised.  Men tend to be slightly older than women when they marry, and for baby-boom women there weren’t enough slightly older men.

In Britain in 1921 there were 27% more women aged 20 to 24 than men aged 25 to 29. In 1951 there was an 8% deficit of women in these age groups, and in 1971 there was a 15% surplus. (Mitchell, 1988).

In the US the baby boom was more extreme.  In 1920 there were 5% more women aged 20 to 24 than men aged 25 to 29, in 1950 there was a 2% deficit of women in these age groups, and in 1970 the surplus was 28%. (U.S. Bureau of the Census, 1975).

A mating or marriage squeeze can affect fertility by influencing sexual permissiveness, age at marriage, marital breakdown, and feminism, as well as rates of marriage. (, 2007). Demographers have predicted that as many as a quarter of American women born between 1956 and 1972 will never have children. (Mencimer, 2001).

Would polygamy be better? I don’t think so. If men could have multiple wives, there would be surplus men instead of surplus women. In general there would be more dissatisfied unpartnered people in a polygamous society than in a monogamous one.

Here are some extracts from wikipedia on polygamy:

In polygyny, the most common form of polygamy, a man is either married to, or involved in sexual relationships with, more than one female at one time. According to the Ethnographic Atlas Codebook, of 1231 societies noted, 186 were monogamous, 453 had occasional polygyny, 588 had more frequent polygyny, and 4 had polyandry.  An early Christian leader, Saint Augustine, wrote in The Good of Marriage: “Now indeed in our time, and in keeping with Roman custom, it is no longer allowed to take another wife, so as to have more than one wife living.” In 1650 a parliament at Nurnberg, in Germany, decreed that because so many men were killed during the Thirty Years’ War, every man was allowed to marry up to ten women. A 19th century limerick by William Cosmo Monkhouse mentions bigamy, in which one individual is married to two people at the same time:

There was an old fellow of Lyme
Who lived with three wives at one time.
When asked, ‘Why the third?’
He replied, ‘One’s absurd,
and bigamy, sir, is a crime.’

(, 2007).

Mating arrangements have physical effects as well as social ones. Female gorillas are monopolised by dominant males, who maintain their dominance by fighting rival males. So natural selection has favoured large male body size, and the males are twice as heavy as the females. Gibbons are monogamous and the sexes have similar body sizes.  Chimpanzees are promiscuous and a lot of male resources go into being highly fertile. In humans, gender differences are intermediate between those in these three other species. (Morgan, 1991).

Population cycles.

A mathematical study of population data has found that feedback cycles nearly two generations long may develop, if fertility varies in response to partner supply within a range that includes the replacement rate. (Marshall, 1995).

Age-specific fertility rates and responses to partner supply were estimated from data from England and Wales, the USA, and New Zealand, from the late 19th century to the late 20th century. The demographic transition of the early 20th century was included in the model, and future populations were predicted from each of the 37 historical populations. Stable 43-year cycles appeared in each series of predicted populations and continued with undiminished amplitudes for thousands of years. The cycles stabilised quickly in populations predicted from the 20th century, but in the predictions from 19th century data the amplitudes of the cycles increased slowly for hundreds of years before stabilising.  (Marshall, 1995).

Further predictions were made using the same range of reproductive ages but different fertility rates, and persistent cycles always appeared when three conditions were met. These were:

1. Fertility varied in response to partner supply.
2. The range of total fertility rates included the replacement rate, a little more than 2 children per woman.
3. The difference between the minimum and maximum limits of the range of total fertility rates was at least 1.5 children per woman.

(Marshall, 1995).

These conditions were met by the fertility rates estimated from 20th century data from England and Wales, the USA, and New Zealand, as the limits of the estimated range of total fertility rates were 2 to 3.5 children per woman. The limits before the demographic transition, estimated from 19th century data, were 3.3 to 4.1 children per woman, and in a similar study of Japanese data from 1925 to 1995, the estimated limits were 0 to 1.9 children per woman.  In the Japanese study the cycles in the series of predicted populations had amplitudes which decreased and became negligible after about four generations, and the cycle length was 41 years. (Marshall, 2001).

The influences on the numbers of births in this model are the number of potential mothers and the severity of the marriage or mating squeeze. A cyclical minimum occurs in the numbers of births when the mothers are women who were born about two-fifths of the way through the cycle from the previous minimum, after the [steepest] increase in the birth rate but before the cyclical maximum in the numbers of births. The cycle is completed when these women reproduce, and so the time taken for a generation to replace itself is three-fifths of a cycle.  The cycle length is therefore 5/3 or 1.7 generations.

Economic cycles.

Economic conditions also seem to vary in long waves with wavelengths longer than one generation. These cycles have been related to fertility by R.A. Easterlin, Edward Cheung, and others, and to investment, innovation, and war by K-wave theorists.

In 1961 Easterlin investigated the relationships between post-war fertility, absolute income, labour market entry, and a marriage squeeze variable. In 1978 he attributed the baby boom of the 1950s and 1960s to the increased income of young men relative to their material aspirations. But by the 1990s it was still not clear that relative economic status could cause “self-generating population cycles”, although “a great deal of work” had been done “to identify the necessary characteristics of models consistent with such cycles”.  (Macunovich, 1998; Wachter, 1991).

Cheung’s book “begins by examining the population growth rates of the United States and Canada from 1789 to the present. . .  When birth rates increased, baby booms were created and when birth rates decreased, Generation Xs were born. These changes in population growth have created recurring themes in history. . . shifts in expenditures and lifestyles of Baby Boomers caused shifts in aggregate demand, producing the long-wave economic cycle.”  (, 2007).

The K-wave is an economic long wave with a wavelength a little longer than the population cycle.  This may be due to disturbances such as war or migration, so “K-waves” and “Easterlin cycles” may be two aspects of one cyclical process. “K-wave” is a shortened form of other names, Kondratieff or Kondratiev waves or cycles. Nikolai Kondratiev was a Russian statistician who discovered the long waves while analysing prices, and he predicted the economic depression of the 1930s. Economic long waves were also described by J. van Gelderen and Samuel de Wolff in 1913. (, 2007).

The majority opinion about K-waves is perhaps that they don’t exist. By about 1980 other opinions had coalesced into three groups: Ernest Mandel’s Trotskyist capitalist crisis group, capital investment modellers led by Jay Forrester at MIT, and Schumpeterian innovation theorists including Gerhard Mensch in Germany and Christopher Freeman in  England. W.W. Rostow and Jacob Van Duijn combined innovation and capital investment theories, and Alfred Kleinknecht related innovation to capitalist crisis. (Goldstein, 1988).

Joshua Goldstein’s analysis in the mid-1980s found longwaves tentatively corroborated in 5 variables: production, investment, innovation, prices, and wages. The evidence for innovation and capital investment was weakly supportive. For prices high-quality data are available and price waves were found to have existed for nearly five centuries, since the start of the longest data series, from 1495 to 1980. For price indexes “since at least the late eighteenth century prices in all five countries closely follow the long wave phases, indicating a synchrony in these core economies”. For commodity prices the “fit of price series to the long wave phase periods in preindustrial times decreases”  in an order “corresponding roughly with outward movement from the core of the European world economy”.  (Goldstein, 1988).

In Goldstein’s theory price cycles are seen mainly as a reflection of more important elements, production and war. War cycles have usually been considered separately from economic cycles, on the other side of the academic boundary between economics and political science. Goldstein compares economic cycles with the war cycles, 50 to 57 years long, which were attributed by Quincy Wright and Arnold Toynbee to the social memory of war. The “memory of recent severe war works against its recurrence”, and so “the relatively fixed length of a generation becomes a clock that links long waves to calendar time.”  But Goldstein is “not sure that social memory can be shown to play a role in the long wave”, although it has “a certain theoretical appeal.”  (Goldstein, 1988).

In 1989 Goldstein elaborated a four-phase dating scheme and fifteen years later he found his conclusions had strong predictive power regarding the transition in the early 1990s from the “stagnation” quarter-phase of the K-wave to the “rebirth” quarter-phase. (Goldstein, 2006).

Cause and effect.

In the century-and-a-half for which there are data, mating squeezes in the economically dominant countries occur at about the same time as peaks in the Kondratieff wave. Van Duijn’s dates for the last three Kondratieff peaks are 1872, 1929, and 1973 (van Duijn, 1983).  Partner supply, estimated from census data as the ratio of males aged 25 to 29 to females aged 20 to 24, was lowest in 1870 and 1970 in the U.S., and 1861 and 1921 in England and Wales.  It was also at a cyclical minimum in 1930 in the U.S. and 1971 in England and Wales. (Mitchell, 1988; U.S. Bureau of the Census, 1975).

Japan seems to be having a separate K-wave of its own. In the early 1990s when the K-wave in the US and the UK was moving from stagnation to growth, in Japan it was moving the other way. The Japanese economy peaked in 1989, and Japanese partner supply was at a cyclical minimum in the early 1990s. (Ministry of Health, Labour and Welfare, 2007).

Germany as well as Japan had an economic boom in the 1980s and a recession in the 1990s, and in a comparison of data from 18 countries from 1997 to 2006, house price inflation relative to disposable incomes was lowest and negative in Japan, Germany, and Korea.  It was positive and close to the median value in the US, and highest in Ireland, the Netherlands, the UK, and France. (Kaletsky, 2007).

But although the German K-wave seems to match the Japanese one, its population wave doesn’t. Between 1950 and the 1970s the birthrate trends for West Germany and the UK were very similar, and quite different from the Japanese ones. (OECD, 1979).  There has been no census since 1981 in East Germany and 1987 in West Germany, and current population statistics for Germany are extrapolations based on the last censuses. (Deutsche Welle, 2007).

Economic and population waves may be separate processes, or one may be a side-effect of the other, or each may depend on the other as interacting parts of one process. I think economic long waves are a side-effect of the series of long population waves that tend to follow any change in birth or death rates. (Marshall, 1995).  After decades of investigation any other explanation remains elusive. (Wachter, 1991).

[USA data.

For a graph showing numbers of births in the U.S. from 1909 to 2010, see]

[A 19th century cycle.
From the London Review of Books, Vol. 24 No. 20, 17 October 2002.

The Age of Revolution, The Age of Capital, The Age of Empire and Age of Extremes can be regarded as a single enterprise – a tetralogy which has no equal as a systematic account of how the contemporary world was made. . . when we come to the second major epoch of industrial expansion, the global take-off of the 1850s that is the starting point of The Age of Capital, a gradual lowering of explanatory pressure sets in. . . At the next crucial juncture of the world economy, the slide into the Great Depression of 1873 . . . scarcely any causal analysis of it is ventured. Rather, when the tide turns again with the upswing of the 1890s, Hobsbawm simply notes that the whole period of The Age of Empire appears to have moved to a Kondratiev rhythm – some twenty years of recession, followed by twenty of expansion. But ‘since we cannot explain them, the Kondratiev periodicities do not help us much.’ . . . Perhaps abstention from deeper probing of difficult questions like these is the price of the streamlined elegance of the trilogy, whose pace militates against the patient economic excavation Hobsbawm practised in essays such as ‘The Crisis of the 17th Century’ (1954).]


Deutsche Welle, 21 September 2007, ‘Germany Paves Way for First Census in 20 Years’. Accessed 13 December 2007 at,2144,2791286,00.html.
van Duijn, J.J. (1983) The Long Wave in Economic Life, London, Allen & Unwin.
Goldstein, J.S. (1988) Long Cycles: Prosperity and War in the Modern Age, New Haven, Yale University Press. Accessed 27 june 2007 at,,, and, and 18 December 2007 at
Goldstein, J.S. (2006)  ‘The Predictive Power of Long Wave Theory, 1989-2004’, in T.C. Devezas, ed., Kondratieff Waves,   Warfare and World Security. Amsterdam, IOS. Accessed 27 june 2007 at, accessed 21 November 2007., accessed 16 December 2007., accessed 23 December 2007., accessed 17 September 2007.  Product Description for Cheung, E. (1994, 2007) Baby Boomers, Generation X and Social Cycles, Toronto, Longwave Press.
Kaletsky, A. (2007) ‘Black clouds loom on horizon after years of plenty’, The Times, 22 October, p.39.
Macunovich, D.J. (1998) ‘Fertility and the Easterlin Hypothesis:  An Assessment of the Literature’. Journal of Population Economics, vol.11, pp.1-59. Accessed 3 January 2008 at
Marshall, A.M. (1995) ‘A Model of Numbers of Births in Three Countries, with Persistent Forty-Year Cycles’. Mathematical Population Studies, vol.5, no.2, pp.171-182. [ ]
Marshall, A.M. (2001) ‘Economic and fertility cycles in Japan’. Not published.
Mencimer, S. (2001) ‘The Baby Boycott’, Washington Monthly, June 2001. Accessed 17 November 2007 at
Ministry of Health, Labour and Welfare, Summary of vital statistics. Accessed 5 August 2007 at
Mitchell, B.R. (1988) British Historical Statistics. Cambridge, Cambridge University Press.
Morgan, E. (1991) The Scars of Evolution, pp.145-6. Harmondsworth, Penguin Books.
Nicholson, V. (2007) Singled Out: How Two Million Women Survived Without Men after the First World War. Viking.
OECD (1979) Demographic trends 1950-1990. Paris, OECD Publications.
U.S. Bureau of the Census (1975) Historical Statistics of the U.S., Colonial Times to 1970. Washington, D.C.
Wachter, K.W. (1991) ‘Elusive cycles: Are there dynamically possible Lee-Easterlin models for U.S. births?’  Population Studies, vol.45, pp.109-135.

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