Introduction
Background on the Hukou System
Personal Engagement: Why This Topic?
My interest in the Hukou system stems from its profound impact on China’s social and economic landscape, but also from my experiences growing up in the rustic region of the country.
I tried to document the history and memories of my hometown through publishing books. Despite my best efforts to detail the chronicle of my people, there is no doubt that one pen does not have the power to overturn the decline of agriculture, exodus of young people, and abandoned farmland that signal the profound impact that industrialization has had on Bei-Wang-Jia. The fields, once filled with the smell of harvest, are now silent, and the golden waves of wheat no longer sway in the wind. Brain drain echoes in the abandoned homes littering once cheery streets, and the soul of the land mourns in the shadow of rapid progress.
That's why I choose to research and model mathematically to see the quantifiable dynamic of the situation. And, as I believe, with urbanization and modernization accelerate globally, understanding the mechanisms that govern internal migration becomes increasingly important. This math exploration allows me to combine my passion for mathematics with a desire to analyze real-world social issues.
Formulating the differential equations provided an opportunity to predict how changes in policy might influence migration patterns. For instance, I hypothesized that relaxing Hukou restrictions would significantly increase the urban Hukou population while reducing the floating population. Through numerical simulations, I tested this prediction and analyzed the results, gaining deeper insights into the complex interplay between policy and migration.
Aim of the Exploration
Hukou is the household registration mechanism established in the 1950s, under which citizens of China are classed according to their birthplace and then granted either rural or urban status. The Hukou system is one of the major tools for the government of China in managing internal migration and resource distribution. The Hukou system ties access to basic social services like education, healthcare, housing, and job opportunities with one's registered place of residence, which in essence often prevents the free mobility of persons within the country. Those who migrated without their Hukou status changed usually face numerous hurdles when attempting to access such services in their new locations, thus dividing the society into categories with migrants as the underprivileged "floating population".
The rapid economic development in China over the past few decades has caused accelerated urbanization, which drove millions of rural residents to seek better opportunities in urban centers. Undeniably, the Hukou system has made this migration process more complex. On one hand, cities enjoy labor supply provided by migrants, but on the other hand, the migrants themselves often cannot integrate fully into urban society because of their Hukou status. This sets up a dichotomy that has deep implications for social equity, economic efficiency, and urban planning.
Motivation for the Study
Understanding the dynamics of migration of population under Hukou is important to policy makers, economists, and urban planners. Traditional demographic analysis does provide a considerable amount of insight, but is unlikely to capture adequately the interactions among policy, economic incentives, and population movements. A mathematical model can be an appropriate conceptual structure in which these interactions can be quantified and forecasts about future developments may be given.
I can formulate this into a more dynamic model using differential equations to take into account the rate of population changes over time, with alternations that may be imposed by policy strictness, economic disparities, and personal decisions on migration. This model should permit the analysis of different scenarios, such as policy reforms or changes in economic conditions, with quantifications of plausible outcomes for new migration patterns. More importantly, such models will be able to indicate the equilibrium states and stability conditions, hence giving further insight into what long-term implications the Hukou system might have for China's demography.
Research Question
This IA seeks to explore and answer the following research question:
How can differential equations be utilized to model population migration under the Hukou system in China?
Addressing such a seemingly large question (and large indeed), I would like to attempt to:
By this mathematical probing, I wish to add a quantitative contribution to the discussion of internal migration in China, highlighting how biopolitical restrictions like the system Hukou have shaped demographic trends. The theoretical understanding developed in the present study gives insights that are practical at the same time and capable of enlightening policy decisions with regard to the balance between economic development and social equity.
Mathematical Modeling Framework
To model the population migration under the Hukou system using differential equations, I need to construct a framework that captures the dynamics of rural-to-urban migration, the influence of Hukou policies, and economic factors affecting migration decisions (maybe also the willingness of reproducing, as previous researches show that there might have been a negative correlation between education level and reproducing rates, and urban tends to be of high education generally speaking) [1].
This section will develop a set of differential equations representing these dynamics, provide reasoning for each component, and incorporate policy effects.
Fig 1. Spatial distribution of interprovincial migrant workers' hukou transfer intentions in China.[2]
Fig 2. Spatial distribution of Hukou Attraction Index[3]
Fig 3. Spatial distribution of Hukou Exclusion Index[4]
Fig 4. Hotspot analysis of hukou exclusion pattern of provincial‐level units in China[5]
Fig 5. Table using the gravity model[6]
1. Defining Variables and Parameters
References
Gu, Hengyu, Ziliang Liu, and Tiyan Shen. "Spatial Pattern and Determinants of Migrant Workers' Interprovincial Hukou Transfer Intention in China: Evidence from a National Migrant Population Dynamic Monitoring Survey in 2016." Population, Space and Place 26, no. 2 (2020): e2250. https://doi.org/https://doi.org/10.1002/psp.2250. https://onlinelibrary.wiley.com/doi/abs/10.1002/psp.2250.
Appendix:
import numpy as np
from scipy.integrate import solve_ivp
import matplotlib.pyplot as plt
# Time span
t_start = 0
t_end = 20 # years
t_eval = np.linspace(t_start, t_end, 1000)
# Initial populations (in millions)
R0 = 800 # Rural Hukou holders
U0 = 200 # Urban Hukou holders
M0 = 50 # Floating population
# Total population (constant)
N = R0 + U0 + M0
# Parameters
alpha_0 = 0.05 # Baseline migration rate to urban areas without Hukou change
beta_0 = 0.01 # Baseline Hukou conversion rate
gamma_0 = 0.02 # Baseline return migration rate
delta_0 = 0.005 # Baseline urban to rural migration rate
kappa = 1.0 # Sensitivity of alpha to policy strictness
lambda_ = 1.0 # Sensitivity of beta to policy strictness
mu = 0.1 # Sensitivity of migration rates to economic disparity
theta = 1.0 # Policy strictness parameter (baseline)
E = 1.0 # Economic disparity (baseline)
K = 1000 # Urban carrying capacity (in millions)
# Define E(t) and theta(t) for scenarios
def E_t(t):
return E # Constant for baseline
def theta_t(t):
return theta # Constant for baseline
def f_E(E):
return 1 + mu * E
def alpha(t, R, U, M):
theta_current = theta_t(t)
E_current = E_t(t)
return alpha_0 * np.exp(-kappa * theta_current) * f_E(E_current) * (1 - (U + M) / K)
def beta(t):
theta_current = theta_t(t)
E_current = E_t(t)
return beta_0 * np.exp(-lambda_ * theta_current) * f_E(E_current)
def gamma(t):
theta_current = theta_t(t)
return gamma_0 * (1 + theta_current) # Assuming h(theta) = 1 + theta
def delta(t):
E_current = E_t(t)
return delta_0 * (1 - mu * E_current) # Assuming n(E) = 1 - mu * E
def migration_model(t, y):
R, U, M = y
R = max(R, 0)
U = max(U, 0)
M = max(M, 0)
alpha_t = alpha(t, R, U, M)
beta_t = beta(t)
gamma_t = gamma(t)
delta_t = delta(t)
dR_dt = - (alpha_t + beta_t) * R + gamma_t * M + delta_t * U
dU_dt = beta_t * R - delta_t * U
dM_dt = alpha_t * R - gamma_t * M
return [dR_dt, dU_dt, dM_dt]
# Initial conditions
y0 = [R0, U0, M0]
# Solve the system for baseline scenario
sol = solve_ivp(
migration_model,
[t_start, t_end],
y0,
t_eval=t_eval,
method='RK45'
)
# Plotting baseline scenario
plt.figure(figsize=(12, 6))
plt.plot(sol.t, sol.y[0], label='Rural Hukou Holders (R)')
plt.plot(sol.t, sol.y[1], label='Urban Hukou Holders (U)')
plt.plot(sol.t, sol.y[2], label='Floating Population (M)')
plt.xlabel('Time (years)')
plt.ylabel('Population (millions)')
plt.title('Migration Dynamics Under the Hukou System (Baseline)')
plt.legend()
plt.grid(True)
plt.show()
[1] Life expectancy would also be a point here cause we have to consider the death rates as the natural part of the population to decrease. As China faces severer problems of aging population and low birth rate issue, the death rates can be seen as generally increasing.
[2] Hengyu Gu, Ziliang Liu, and Tiyan Shen, "Spatial pattern and determinants of migrant workers' interprovincial hukou transfer intention in China: Evidence from a National Migrant Population Dynamic Monitoring Survey in 2016," Population, Space and Place 26, no. 2 (2020), https://doi.org/https://doi.org/10.1002/psp.2250, https://onlinelibrary.wiley.com/doi/abs/10.1002/psp.2250.
[3] Gu, Liu, and Shen, "Spatial pattern and determinants of migrant workers' interprovincial hukou transfer intention in China: Evidence from a National Migrant Population Dynamic Monitoring Survey in 2016."
[4] Gu, Liu, and Shen, "Spatial pattern and determinants of migrant workers' interprovincial hukou transfer intention in China: Evidence from a National Migrant Population Dynamic Monitoring Survey in 2016."
[5] Gu, Liu, and Shen, "Spatial pattern and determinants of migrant workers' interprovincial hukou transfer intention in China: Evidence from a National Migrant Population Dynamic Monitoring Survey in 2016."
[6] Gu, Liu, and Shen, "Spatial pattern and determinants of migrant workers' interprovincial hukou transfer intention in China: Evidence from a National Migrant Population Dynamic Monitoring Survey in 2016."
[7] These people are mainly workers, called 农民工(Nong Min Gong) in Mandarin.
[8] This especially applies to the mega cities like Beijing/Shanghai/Guangzhou/Shenzhen.
[9] Or "deurbanization" if we use the human geography term; this could be due to the pressures from environmental pollutions or costs of living. Given the relatively poor economic performance (especially on the job markets), this rate might start to continuously increase in the near future.
[10] This varies with time and leaders. For example, now it's easier to move Hukou to Shanghai compared to Beijing as if one graduated from QS-Rank-Top-50 school, he/she/they'll be able to move within a short amounts of time.
[11] This is essentially the degree or extent of siphon effects in China, which can be worsened (increased) if equity is not of priority or improved (decreased) if the Revitalization Policy is of importance. [See, Government of China. (2024). Central Document No. 1: Opinions of the Central Committee of the Communist Party of China and the State Council on Learning from the “Thousand Villages Demonstration, Ten Thousand Villages Renovation” Project to Effectively Promote Comprehensive Rural Revitalization. Beijing: Government of China.]
[12] Words Count Limitation, in a word.
[13] How many people can land feed (without harming potential).
[14] There are also different kinds of migrations I can discuss on (from Human Geography).
[15] This part is yet to be executed.
[16] Actually, speaking of this, there are some calls to abolish the Hukou totally like abolishing the Agricultural Tax in 2006 (proposed by many law scholars but also high-level officials; Xi's PhD Thesis has the conclusion is to be finished in the foreseeable future).
[17] Check Appendix.
