Abstract
If we agree that fertility decline occurs independently of background, we can further assume that marriages occur independently of their background. Moreover, we can express a theoretical marriage function that is background-independent as an integral equation. We begin by critically examining existing marriage functions, namely, the Coale-McNeil distribution , double exponential distribution, and the Hernes’ function . Guided by critical analyses of Hernes’ differential equation, I propose an integral equation as a marriage function based on a simple marriage model. This assumes that the probability of first marriage occurrence completely depends on the ratio of women in their first marriage within a given space. This also implies background independence of the marriage function. This integral equation not only fits the observed data well, but also provides the most likely estimations of the mean age at first marriage. This is decisive evidence that my proposed integral equation is the most reliable marriage function. To formulate marriage function is one of the requirements for predicting fertility.
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Notes
- 1.
“(dt)” indicates that this integration is a Lebesgue integration. The Riemann-Stielties integration is expressed as \(\int F(t) dt\).
- 2.
However, even the “Baby Boom” is not an exception for SDSMF. Its onset occurred as a mere historical accident, and its subsequent durability can be explained by SDSMF.
- 3.
Observed values were calculated from vital statistics that were modified in accordance with the census.
- 4.
This is an incorrect tradition that originated with L.R. Klein. We must abandon this improper way of conducting a statistical test in favor of a theory that is able to hypothesize a point null hypothesis that is not trivial.
- 5.
National Family Research of Japan 1998 was conducted by the Japan Society of Family Sociology.
- 6.
Japanese Social Stratification and Mobility Survey, 1995.
- 7.
I used data from Two centuries of Swiss demographic history —Graphic album of the 1860–2050 period [5].
- 8.
The European Social Survey (ESS) is an academically-driven social survey designed to chart and explain the interaction between Europe’s changing institutions and the attitudes, beliefs and behavior patterns of its diverse populations. The ESS was established in 2001, and was led by its founder and coordinator, Roger Jowell, until his death in December 2011 (http://www.europeansocialsurvey.org/).
- 9.
The concept of race is not scientific. Nonetheless I use “Caucasoid” to denote ethnic groups such as Anglo Saxons and Germans.
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Ike, S. (2016). Marriage Function as an Integral Equation. In: Fertility Decline and Background Independence. SpringerBriefs in Population Studies(). Springer, Tokyo. https://doi.org/10.1007/978-4-431-55151-5_3
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DOI: https://doi.org/10.1007/978-4-431-55151-5_3
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