# Long-Term Impact of Interregional Migrants on Population Prediction

^{*}

## Abstract

**:**

## 1. Introduction

**CWR**) is considered to be an aggregated decisions made by females or couples to maximize their utility [11]. In developed countries, women emphasize professional careers and begin postponing family formation and childbearing [12]. Furthermore, the social and economic environments of families with children are substantially different between urban and rural areas. Therefore, the promotion of children in a family requires several policies with complex and comprehensive viewpoints, and countermeasures that account for regional differences in the living environment.

**CWR**will affect on the transitions in the population distribution of children, women, and the elderly in municipalities, compared with conventional CCA. The second question is which cohort will be more attracted to urban agglomeration in the output of the proposed CCA model. The third question is how interregional migration in our model is related to the level of urbanization. This question will be tested through the use of urbanized indices in terms of the industrial characteristics.

**CWR**. Concluding remarks and future challenges are presented in Section 7.

## 2. Review of the Literature

**CWR**), and migration rate [15,30]. CCA has the advantages of simplicity and interpretability, and it is used as a standard model for regional population prediction in the U.S., Japan, and other countries [4,5,6,7]. For instance, Vanella and Deschermeier [31] proposed a probabilistic CCA that uses simulation techniques based on stochastic models for fertility, mortality, and migration, to forecast the population according to age and sex. In addition, Smith et al. [6] conducted a population prediction under acceptable parameter assumptions using different sources of data.

## 3. Description of the Japanese Population, Migration, and Urbanization Trends

## 4. Existing Methodology: Cohort Component Analysis

**P**(i, t) is the initial population of municipality i at initial year t, and

**NC**(i, t) is the natural increase (or decrease if it is negative) in the difference between births and deaths between t and t + k.

**NM**(i, t) is the net migration: the difference in the number of immigrants and emigrants into or from municipality i, between t and t + k. In this study, k is ordinarily set to 5, because of the Census interval of Japan.

Parameter | Descriptions |
---|---|

Initial Population (Pin (i, x∼x + n)) | (2010) 5-year age cohorts for both sexes in Japan at the municipality level. |

Survival Rate (S i, x∼x + n)
| $\frac{P\left(i,\hspace{0.17em}x\hspace{0.17em}+\hspace{0.17em}n\right)}{P\left(i,\hspace{0.17em}x\right)},x=0,5,10,\dots ,90,n=4,\mathrm{constant}\mathrm{for}t$ |

Cohort Age-specific Child–Women Ratio (CWR i, x∼x + n)
| $\frac{P\left(i,\hspace{0.17em}0\sim 4\right)}{P\left(i,\hspace{0.17em}f,\hspace{0.17em}x\sim x\hspace{0.17em}+\hspace{0.17em}n\right)},x=15,20,\dots ,45,n=4,\mathrm{constant}\mathrm{for}t$ |

Relative Disparities forCWRi, t (R i) | $\frac{\sum CWR\left(i,\hspace{0.17em}2010,\hspace{0.17em}x\sim x\hspace{0.17em}+\hspace{0.17em}n\right)}{CWR\left(2010\right)},\mathrm{constant}\mathrm{for}t$ |

Child–Women Ratio ($(\mathbf{C}\mathbf{W}{\mathbf{R}}_{\left(i,\hspace{0.17em}t\hspace{0.17em}+\hspace{0.17em}k\right)}$) or Fertility Rate ($\mathbf{T}\mathbf{F}{\mathbf{R}}_{\left(i,\hspace{0.17em}t\hspace{0.17em}+\hspace{0.17em}k\right)}$) | $CW{R}_{\left(t\hspace{0.17em}+\hspace{0.17em}k\right)}\ast R{}_{\left(i\right)}$, $CW{R}_{\left(t\hspace{0.17em}+\hspace{0.17em}k\right)}$ is adopted from national population projection data. |

Sex Ratio (SR) for Ages 0–4 | $\frac{P\left(m,\hspace{0.17em}0\sim 4\right)}{P\left(f,\hspace{0.17em}0\sim 4\right)},\mathrm{constant}\mathrm{for}t$ |

**CWR**).

**CWR**is measured at the municipal scale, which assumes that the relative disparities of the municipalities are held, by dividing the total

**CWR**of the municipality by the average

**CWR**of the initial year, 2010. This assumption is commonly introduced for the reference (conventional)

**CWR**and our proposed model. The future

**CWR**for municipalities is calculated by multiplying the average

**CWR**of the predicted intervals, which are adopted from the national population prediction data of Japan, 2010–2040, with the medium-fertility assumption that relative disparities in the municipalities are held. The sex ratio at birth (

**SR**) was set as the average value of 105.2 from the actual observations from 2006 to 2010, and was assumed to be constant for both models.

## 5. Proposed Model System: Integration of CCA with the SAR Model

#### 5.1. Spatial Autoregressive Model (SAR)

**Y**is the georeferenced dependent variable. Matrix

**X**contains exogenous explanatory vectors, and

**β**is the associated regression parameter vector. In our approach, the model will result in a spatial correlation between the explanatory variable and the error term. Therefore, the SAR specification can include the spatial correlation in “

**Xβ**.” SAR was used because we assumed that dependent variable

**Y**(number of migrations) would be an index of regional attractiveness or job opportunities.

**W**is a weighting matrix with neighboring regions, and the associated scalar parameter ρ reflects the strength of spatial dependence. The spatial weight matrix,

**W**, is an $nxn$ nonnegative matrix that has an element of

**W**, which gives the weight at two locations, i and j. In this model, (

**I**− ρ

**W**)

^{−1}is non-singular, and product of (

**I**− ρ

**W**)

^{−1}$\mathsf{\epsilon}$, which equals the variance–covariance matrix, is positive-definite. The error vector in Equation (6) shows the dependent structure among the regions. For spatial correlation, we considered the observations as being independent of one another, with each being identically distributed. In this study, we used contiguity matrices to show two spatial correlations with their shared boundary. For contiguity matrices, an element, w[i, j], has a value of 1 if units i and j share a common border, and 0 for the others.

#### 5.2. Summary of SAR Estimation

## 6. Discussion

#### 6.1. Comparison between CCA Output and the Proposed Approach

#### 6.2. Distribution of Urbanization Indices: Retailers and Manufacturing Employees

^{2}(red and orange colors), and these were primarily distributed in four main metropolitan areas (Tokyo, Yokohama, Osaka, and Nagoya). The 1195 municipalities with retailer densities of less than 50 persons/km

^{2}(blue color) were distributed in all of the other areas. However, in 2040, as shown in Figure 4b, only 39 municipalities will have retailer densities that are larger than 1000 persons/km

^{2}(red and orange colors), and the number of municipalities with retailer densities of less than 50 persons/km

^{2}(blue color) will increase to 1300. Comparing the estimated retailer densities during 2010 and during 2040, 73% of municipalities will lose retailer workers by 2040, including the major metropolitan areas.

^{2}(red and orange colors) amounted to 56, most which are distributed within four main metropolitan areas: Tokyo, Yokohama, Osaka, and Nagoya. The number of municipalities with a manufacturing employee density of less than 50 persons/km

^{2}(blue color) was 1100, which were distributed in all other areas. The distribution of manufacturing employees can also be observed in the coastal regions, as specific industrial zones are mainly located on the coast of Japan. As shown in Figure 5b, we can observe that, in 2040, manufacturing employees will be distributed in municipalities with population densities that are larger than 1000 persons/km

^{2}in all 14 major urban areas: Tokyo, Yokohama, Osaka, Nagoya, Sapporo, Fukuoka, Kobe, Kawasaki, Kyoto, Saitama, Hiroshima, Sendai, Chiba, and Kitakyushu. Even in rural areas, 890 municipalities will enjoy an increase in manufacturing employees by 2040.

**Figure 4.**Distribution of estimated retailer density. (

**a**) Distribution of estimated retailer density in 2010; (

**b**) Distribution of estimated retailer density in 2040.

**Figure 5.**Distribution of estimated manufacturing employee density. (

**a**) Distribution of estimated manufacturing employee density in 2010; (

**b**) Distribution of estimated manufacturing employee density in 2040.

#### 6.3. Transition of Population According to Urbanization Indices

#### 6.4. Population Distribution in Terms of Child–Women Ratio (CWR)

**CWR**and the population distribution across all regions, which is significant in terms of the long-term demographic dynamics. Note that we assumed that the relative distribution of the

**CWR**over the region did not change, but that its average over the period changed. According to Figure 7, the average

**CWR**in 2015 was 1.3798. It is expected to gradually decrease until it reaches 1.3302 by 2025, whereupon it will increase slightly starting from 2030, and reach 1.3457 in 2040. The rates have increased slightly as the

**CWR**for women in their 30s and 40s have increased in recent years. Figure 8a,b show the distributions of

**CWR**across all municipalities in 2010 and 2040, respectively, to confirm the relationship between newborn cohorts and the population distribution. From these figures, we can see the spatial distribution of

**CWR**. Some municipalities in Okinawa and Hyogo will enjoy a higher

**CWR**of over 1.9, and 129 municipalities will be consistently above the national average of 1.3457. Almost all urban municipalities, especially Tokyo, Hokkaido, and Kyoto, will have the lowest

**CWR**in 2040.

**CWR**and the three population groups—children, female childbearing, and the elderly—demonstrates how the population is distributed according to the municipalities’

**CWRs**. Figure 9a–c show the relationship between municipalities’

**CWRs**and the three groups of populations in 2010 and 2040, respectively. All graphs revealed that the relationship changed over time for all of the age groups. According to Figure 9a, the peak of the CWR with the children’s cohort changes from around 1 in 2010, to around 0.8 2040. The approximated normal curve in 2040 shifted slightly to the left from that in 2010. Figure 9b illustrates that from 2010 to 2040, all female childbearing groups will move from municipalities with higher CWR to those with lower CWR. Figure 9c shows that the spatial distribution of the elderly group was distributed to municipalities with higher CWRs in 2010, and that it will not significantly change by 2040. According to Figure 9a–c, the municipalities with CWRs ranging between 0.8 to 0.9 will have the highest populations for all age groups, and the overall population will shift to municipalities with lower CWRs.

**Figure 7.**Medium CWR assumption (Source: https://www.e-stat.go.jp, accessed on 1 March 2021).

**Figure 9.**Distribution of population by

**CWR**(2010 to 2040). (

**a**)

**CWR**with children population (0 to 14); (

**b**)

**CWR**with female childbearing population (15 to 49); (

**c**)

**CWR**with elderly population (65 and over).

## 7. Conclusions

**CWR**to observe shifts in the distribution of children, women, and elderly populations between regions in the future. In addition, by comparing both methods, we can observe how population distributions differ under different assumptions.

**CWR**. If this trend continues, Japan’s population will continue to decrease in the future. Regarding the second question, our proposed approach predicts higher populations among the middle-aged cohorts than the conventional CCA. One reason for this outcome is that foreign migrants are counted in our model, because the inclusion of foreign migrants is referenced in the dataset. Foreign migrants will also attract to urbanized areas with more retailers and manufacturing employees. The future population will be highly concentrated in urbanized areas, because domestic migrants will have moved from rural areas to urban areas, and migration from overseas will also be concentrated in urban areas.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Variable | Moran’s I | Expected I | Variance | Z-Score | p-Value |
---|---|---|---|---|---|

Male Total Immigration | 0.39692 *** | −0.00072 | 0.00856 | 45.28304 | 0.00000 |

Male Total Emigration | 0.41763 *** | −0.00072 | 0.00859 | 48.67499 | 0.00000 |

Female Total Immigration | 0.39061 *** | −0.00072 | 0.00857 | 45.66852 | 0.00000 |

Female Total Emigration | 0.37421 *** | −0.00072 | 0.00556 | 43.8016 | 0.00000 |

No: of Employees in 2nd Industry | 0.34752 *** | −0.00072 | 0.00726 | 47.94531 | 0.00000 |

No: of Retailers | 0.34389 *** | −0.00072 | 0.00726 | 47.44475 | 0.00000 |

Cohorts | Spatial Correlation Parameter ($\mathsf{\rho}$) | |||
---|---|---|---|---|

Male Immigration | Male Emigration | Female Immigration | Female Emigration | |

0–4 | 0.196 *** | 0.238 *** | 0.195 *** | 0.056 |

5–9 | 0.0868 * | 0.113 * | 0.121 ** | 0.0949 * |

10–14 | 0.0848 * | 0.130 ** | 0.152 ** | 0.0895 |

15–19 | 0.157 ** | 0.126 * | 0.11 * | 0.0688 |

20–24 | 0.137 *** | 0.199 *** | 0.145 *** | 0.0693 |

25–29 | 0.142 *** | 0.199 *** | 0.210 *** | 0.185 *** |

30–34 | 0.210 *** | 0.294 *** | 0.234 *** | 0.196 *** |

35–39 | 0.209 *** | 0.242 *** | 0.234 *** | 0.127 *** |

40–44 | 0.117 *** | 0.213 *** | 0.144 *** | 0.0693 * |

45–49 | 0.0746 * | 0.135 *** | 0.0987 ** | 0.129 *** |

50–54 | 0.0599 | 0.146 *** | 0.181 *** | 0.172 *** |

55–59 | 0.0748 | 0.111 ** | 0.212 *** | 0.0979 ** |

60–64 | 0.0908 * | 0.0913 * | 0.131 *** | 0.0657 |

65–69 | 0.173 *** | 0.198 *** | 0.161 *** | 0.176 *** |

70–74 | 0.220 *** | 0.259 *** | 0.292 *** | 0.204 *** |

75–79 | 0.284 *** | 0.334 *** | 0.221 *** | 0.101 * |

80–84 | 0.349 *** | 0.304 *** | 0.236 *** | 0.0863 |

85–89 | 0.284 *** | 0.345 *** | 0.168 *** | 0.0348 |

90–over | 0.456 *** | 0.514 *** | 0.193 *** | 0.0934 |

Total | 0.338 *** | 0.524 *** | 0.415 *** | 0.416 *** |

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**Figure 6.**Distribution of population according to urbanization indices (2010 to 2040). (

**a**) Retailers with children population (0 to 14); (

**b**) Retailers with female childbearing population (15 to 49); (

**c**) Retailers with elderly population (65 and over); (

**d**) Manufacturing industry employees with children population (0 to 14); (

**e**) Manufacturing industry employees with female childbearing population (15 to 49); (

**f**) Manufacturing industry employees with elderly population (65 and over).

Variable | Mean | Std. Dev | Min | Max |
---|---|---|---|---|

Population | 66,763.36 | 97,183.621 | 178 | 903,346 |

Net Migration | 29.337 | 1685.814 | −8279 | 68,917 |

Male Net Migration | 17 | 776.239 | −1044 | 31,822 |

Male Immigration | 1660 | 8195 | 0 | 337,629 |

Male Emigration | 2401 | 13,230 | 6 | 547,290 |

Female Net Migration | 19 | 903.962 | −896 | 37,095 |

Female Immigration | 1460 | 7506 | 2 | 309,618 |

Female Emigration | 1387 | 6297 | 6 | 258,300 |

Working-age Population (15–64) | 27,390 | 46,094.009 | 0 | 573,317 |

Number of Employees in Secondary Industry | 7426.012 | 9922.661 | 13 | 96,761 |

Number of Retailers | 10,949.84 | 7716.154 | 4 | 18,670 |

Initial Year 2010 Population (Person) | Final Predicted Year 2040 Population Using CCA (Person) | Final Predicted Year 2040 Population Using Proposed Approach (Person) | |
---|---|---|---|

Total | 128,057,352 | 110,923,739 | 109,728,234 |

0–4 | 5,322,799 | 3,536,609 | 3,453,977 |

5–9 | 5,593,452 | 4,195,635 | 4,112,763 |

10–14 | 5,910,750 | 4,205,658 | 4,122,782 |

15–19 | 6,160,687 | 4,268,129 | 4,267,003 |

20–24 | 6,518,181 | 4,367,966 | 4,363,330 |

25–29 | 7,352,494 | 6,561,470 | 6,586,601 |

30–34 | 8,358,745 | 6,245,334 | 6,266,845 |

35–39 | 9,748,001 | 7,291,696 | 7,325,188 |

40–44 | 8,743,156 | 6,542,081 | 6,566,990 |

45–49 | 8,038,243 | 5,409,622 | 5,421,565 |

50–54 | 7,649,769 | 5,118,017 | 5,126,621 |

55–59 | 9,042,016 | 6,214,705 | 6,235,866 |

60–64 | 10,372,889 | 7,848,735 | 7,888,604 |

65–over | 29,246,170 | 39,118,082 | 37,990,098 |

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Oo, S.; Tsukai, M.
Long-Term Impact of Interregional Migrants on Population Prediction. *Sustainability* **2022**, *14*, 6580.
https://doi.org/10.3390/su14116580

**AMA Style**

Oo S, Tsukai M.
Long-Term Impact of Interregional Migrants on Population Prediction. *Sustainability*. 2022; 14(11):6580.
https://doi.org/10.3390/su14116580

**Chicago/Turabian Style**

Oo, Sebal, and Makoto Tsukai.
2022. "Long-Term Impact of Interregional Migrants on Population Prediction" *Sustainability* 14, no. 11: 6580.
https://doi.org/10.3390/su14116580