For Japan and South Korea, we have the observations for school children, 12 age classes from age 6 to 17, every year from 1955 to 2010 for Japan and 1965 to 2010 for South Korea [5,6]. For China, the observations are limited, age from 7 to 18, at 5 year-intervals, from 1985 to 2019 [7]. The author decided not to take every year but 1965, 1970, ---, 2005 and 2010, at 5 year-interval for Japan and South Korea.

Data for age 6, the first year in primary school for Japan and South Korea, are dropped. Also, age 18 is dropped for China, in the recognition that differences between 17 and 18 in mean height are actually very small. Since national surveys are conducted in the first month of the school year, mean height at the beginning of junior school is almost identical to that of the end month of primary school. Thus, age 7 to 12 may actually represent the primary school. In short, we apply the A/P/C model to the two age groups, primary school, from 7 to 12 in age and junior-senior high schools from 12 to 17, uniformly for the three countries.

Findings from the A/P/C model, as applied to changes in male school children’s height, Japan, South Korea and China in the past half century 

We have two sets of data of male school children’s mean height by age, 7 to12 for primary school years and 12 to 17 for junior and senior high school years, uniformly for the three countries, based on national health surveys^*1 conducted by the national governments.

The author derived age, period and cohort effects of student’s mean height, by two age groups of 6 to 12 and 12 to 17 in Japan, South Korea and China in the past half century.

The basic structure of the A/P/C analysis is presented in equation (1)^*2, stated above and looks easy to solve by the ordinary least square approach. However, when k represents birth cohort, p= i + k, the typical multi-collinearity is observed, called “identification problem” in cohort analyses. The author adopts the Nakamura’s Bayesian model, which is based on a natural assumption about gradual changes between adjacent parameters, mechanically judged by the objective standards, Akaike’s Bayesian Information Criteria [8].

^*1 People vary substantially in height between urban and rural areas and by geographical locations, north-eastern and south-western provinces in China [9], whereas disparities by regions, north and south have virtually disappeared in Japan [9]. The author has no idea of how national average figures of mean height were worked out in the CNSSCH, Chinese National Surveys of Students’ Constitution and Health.

^*2 For those readers who are not familiar with cohort analyses, it is recommended to refer to declining orange consumption in Japan―generational changes or something else? ERS#71, USDA, Mori, Dyck et al, 2009, pp.23, described for non-mathematicians [10].

First, primary school years, Tables 1-A, B and C:

Grand mean effects for Japan and South Korea are 129.3 and 128.9 cm, respectively, with very small SDs.

Age effects, from 7 to 12, are quite similar in the two countries, ranging from -13 cm for the 1^st grade to 13 cm for the end of 6^th grade.

Period effects are not similar at all between the two countries. Japan increased from -3.0 cm in 1965 to 1.6 cm in 2010, whereas South Korea increased from -6.8 cm to 7.2 cm over the same period. South Korean primary school boys increased in mean height by 9.4 cm more than their Japanese peer.

Cohort effects may signify various effects on height incurred during the pre-survey years. Honestly, the author can’t explain what they are from (1) to (15) in Tables 1-A and B. What the author suspects is that the Korean primary school boys should carry little bid negative effects on their height in pre-survey years such as insufficient food intakes, as compared with their Japanese peers. But the differences are not large and insignificant statistically.

Second, junior-senior high school years, Table 2-A, B and C:

Grand mean effects for Japan and South Korea are 163.1 and162.1 cm, respectively, with very small SDs in both cases.

Age effects, from 12 to 17, for Japan and South Korea are also similar at all ages, ranging from -13.0 cm for 1^st graders in junior-high in both countries to 7.0 cm for high school seniors in Japan and 8.2 cm in South Korea with meaningful SDs.

Period effects are quite different at all years. Period effects for Japan in 1965 are -4.4 cm, as compared to -7.6 cm for South Korea. Japan reached the greatest period effects in 1995-2000 at 1.7 cm, whereas South Korea reached the highest period effects at 5.0 cm in 2005. South Korean students increased by 12.6 cm, substantially more than Japanese, which increased by 6.1 cm.

The author does not fully comprehend what “cohort effects” imply in this version of analysis^*3. The only thing he can see is that Japan and South Korea are quite similar in patterns and the estimates of cohort effects are not large in value as age and period effects.

^*3 When the model is applied to food consumption, age effects refer to pure age, the one in the teens or the fifties, for example, whereas cohort effects refer to generations, such as those born in the 2000s, compared to older generations, born in the 1960s, for example [11].

Table 1(A): Changes in mean height of primary school boys in Japan decomposed into age, period and cohort effects, 1965 to 2010.

Grnd Mean Effect=129.33(0.04); ABIC=88.82