CYCLES, POPULATION

A population cycle occurs when the growth rate of population varies over time in some fairly recognizable fashion. This might be due to changes in patterns of migration, or fluctuations in birth and death rates. Although it is generally accepted that there are cycles of varying length in economic activity, there is less agreement on the topic of population cycles.

T. R. Malthus was the first to posit the existence of population cycles, which he argued were the result of a pattern of economic and demographic feedback. An abundant harvest might temporarily raise wages, but the higher wages would cause an increase in birth rates, leading in turn to an increase in the number of laborers and hence to a decline in real wages. This decline in real wages would be met either by reduced birth rates (the "preventive check") or by an increase in mortality rates (the "positive check"). In either event, Malthus suggested that these fluctuations would cause population growth rates–and real wages–to cycle about some fairly constant level.

Later theorists thought that Malthus's theory was rendered obsolete by technological innovation, as the industrial revolution produced steady increases in both population and real wages. But the theory of population cycles was revived by the economist Simon Kuznets (1901–1985), who studied patterns of growth in the nineteenth and early twentieth centuries in the United States and identified what have come to be known as "Kuznets cycles": pronounced fluctuations of 15 to 25 years' duration in the growth of population, labor force, households, output, and capital stock. He suggested that an increase in the demand for labor, spurred perhaps by technological innovation, might generate increased immigration rates, and the new immigrants would further increase the demand for labor because of increased demand for housing and other goods and services. This feedback effect would gradually die away, returning population growth to its preimmigration level. Such cycles were not thought to be self-generating, but rather were the result of an exogenous change in the demand for labor.

Richard Easterlin suggested that these Kuznets cycles changed significantly in the second half of the twentieth century because of changes in immigration policy. With tighter restrictions on immigration, any exogenous growth in the demand for labor could not be met through increased immigration, and would instead produce higher wages for the indigenous labor force, especially for younger workers. These improved wages would then result in an earlier age at marriage and higher birth rates, generating an urban economic boom and thus further increasing the demand for labor.

Easterlin's emphasis on younger workers, and on their wages relative to those of older workers, was a significant extension of Kuznets's original theory, since it introduced for the first time a credible mechanism for creating self-generating population (and economic) cycles. Easterlin developed this concept more fully in his later work, where he hypothesized that the small Depression-era birth cohorts of the 1930s had experienced a significant increase in their relative wages because of imperfect substitutability between older and younger workers: the younger workers were in short supply relative to older workers, and thus benefited most from the post–World War II economic boom. They married earlier and at higher rates, and exhibited a sharp increase in fertility rates that produced the 1946–1964 baby boom. When the large baby-boom birth cohort entered the labor market in the 1970s, however, they had the opposite experience: they were in excess supply relative to older workers. Their reduced relative wages caused them to postpone or forgo marriage and childbearing, producing the low birth rates of the post-1960s "baby bust."

Easterlin's model failed to predict actual events in the 1980s, however, when it was expected that smaller birth cohorts would begin to experience improved labor market conditions. Diane Macunovich (1999) has suggested that the effects of birth cohort size may produce asymmetric population cycles. When the size of birth cohorts entering the labor market is increasing, young workers not only supply labor for the economy, they also add to demand for goods and services as they set up their own house-holds–an effect similar to that observed by Kuznets. Thus, when the size of the cohort entering the labor market is increasing, the negative effect of their over-supply of labor is offset to some extent by a stimulative effect on the economy, as producers expand production capacity to meet demand. The opposite would occur when the size of entry-level cohorts begins to decline and producers find themselves with excess production capacity. This latter effect would have been masked for the small birth cohorts entering the labor market in the 1950s because of the pent-up demand from the war years, but it was experienced fully by the cohorts entering the labor market in the 1980s. This suggests that if self-generating population cycles do occur, they cannot be expected to have a regular period or amplitude.

Several researchers have focused on determining whether population cycles are theoretically possible–that is, whether they can be represented by a formal mathematical model–and whether the observed U.S. cycles conform to an acceptable theoretical model. Ronald Lee (1974) defined a family of models that might encompass an Easterlinian feedback mechanism, identifying two types of cycle that could be generated: short-term or transient cycles, and longer-term sustained cycles. Lee concluded that parameter values for what he termed a cohort model estimated from the U.S. experience between 1917 and 1982 could not sustain longer-term cycles. However, he suggested that longer term cycles could be generated by what he called a period model, in which period fertility depends on total labor force size.

In parallel with this work, Paul Samuelson (1976) developed what he termed "an oversimplified version of the Easterlin theory" using a two-generation overlapping generations model–a model that Gustav Feichtinger and Gerhard Sorger (1989) later extended to a continuous-time model. Using nonlinear differential equations, Feichtinger and Sorger were able to generate an Easterlin cycle with a period of about 43 years. They pointed out that a discrete-time framework, although more appropriate for describing population dynamics, does not yield the period length of the Easterlin cycle.

Frank Denton and Byron Spencer (1975) and Joseph Anderson (1982) presented simulation models examining the cyclical implications of an Easterlinian model, demonstrating that demoeconomic behavior is predominantly nonperiodic, hence essentially unpredictable.

Kenneth Wachter attempted to determine the characteristics of a "viable feedback model" for sustained fertility cycles, and concluded that "there are viable feedback models for U.S. births, but very few, and they are very special." He demonstrated that an Easterlin type of relative cohort size model can be one of these "special" cases–especially if the timing as well as the level of the younger cohort's fertility is affected by relative cohort size. Alternatively, the Easterlin model can produce sustained cycles if a "bandwagon" effect causes the fertility of other age groups to follow that of the younger cohorts. However, Wachter emphasized that institutional factors and period effects make it very difficult to test for population cycles given the relatively short time period of available data (p. 124).

C. T. Cyrus Chu and Huei-Chung Lu (1995) again took up the models specified by Lee and Wachter. They tested a version that incorporated both Lee's period and cohort models, and found that "there indeed exists a limit cycle solution for the U.S. fertility data; however, this limit cycle solution is not stable, and therefore the population trajectory will not converge to that limit cycle" (p. 54). However, their model made no allowance for specific period effects that might have influenced the observed pattern of fertility in the second half of the twentieth century. Thus, as Chu and Lu emphasize the existence and nature of population cycles remains an area for further research.

See also: Baby Boom; Easterlin, Richard A.; Economic-Demographic Models; Kuznets, Simon.

bibliography

Anderson, Joseph M. 1982. "An Economic-Demographic Model of the U.S. Labor Market." In Research in Population Economics, Vol. 4, ed. J. Simon and P. Lindert. Greenwich, CT: JAI Press.

Chu, C.T. Cyrus, and Huei-Chung Lu. 1995. "Toward a General Analysis of Endogenous Easterlin Cycles." Journal of Population Economics 8:35–57.

Denton, Frank T., and Byron G. Spencer. 1975. Population and the Economy. Lexington, MA: Lexington Books.

Easterlin, Richard A. 1968. Population, Labor Force, and Long Swings in Economic Growth: The American Experience. New York: National Bureau of Economic Research.

Feichtinger, Gustav, and Gerhard Sorger. 1989. "Self-Generated Fertility Waves in a Non-Linear Continuous Overlapping Generations Model." Journal of Population Economics 2: 267–280.

Lee, Ronald Demos. 1974. "The Formal Dynamics of Controlled Populations and the Echo, the Boom and the Bust." Demography 11: 563–585.

——. 1976. "Demographic Forecasting and the Easterlin Hypothesis." Population and Development Review 2: 459–72.

Macunovich, Diane J. 1999. "The Fortunes of One's Birth: Relative Cohort Size and the Youth Labor Market in the U.S." Journal of Population Economics 12: 215–272.

Samuelson, Paul A. 1976. "An Economist's Non-Linear Model of Self-Generated Fertility Waves." Population Studies 30: 243–248.

Wachter, Kenneth W. 1991. "Elusive Cycles: Are There Dynamically Possible Lee-Easterlin Models for U.S. Births?" Population Studies 45: 109–135.

Wachter, Kenneth W., and Ronald Demos Lee. 1989. "U.S. Births and Limit Cycle Models." Demography 26(1): 99–115.

Diane J. Macunovich