# The Dynamic Effects of Urban–Rural Income Inequality on Sustainable Economic Growth under Urbanization and Monetary Policy in China

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review and Hypotheses

#### 2.1. The Effect of Urban–Rural Income Inequality on Economic Growth

**Hypothesis**

**1.**

#### 2.2. The Effect of Urbanization on Economic Growth and Urban–Rural Income Inequality

**Hypothesis**

**2.**

#### 2.3. The Effect of Monetary Policy on Economic Growth and Urban–Rural Income Inequality

**Hypothesis**

**3.**

## 3. Methodology and Data Description

#### 3.1. Methodology

_{1},…, Z

_{q}represent p × p variable coefficient matrices, y

_{t}represents p × 1 vector of observable variables, and the disturbance e

_{t}represents p × 1 structural shock, which is supposed to obey a Gaussian distribution with the expression e

_{t}~G(0,ΣΣ), where:

_{i}= M

^{−1}Z

_{i}for I = 1,…,q. The new equation reorganizes the coefficient matrices D

_{i}. We stack the row’s elements of the new matrices. Then, we obtain R

_{t}= I

_{p}⊗ (${y}_{t-1}^{\prime}$,…,${y}_{t-s}^{\prime}$) and the p

^{2}q × 1 vector ϕ, where ⊗ represents the Kronecker product. Based on this, the equation can be represented by the following form:

_{t}, vectors, ϕ

_{t}, and covariance matrices of disturbances, Σ

_{t}, can all vary over time.

_{t}= (m

_{2,1}, m

_{3,1}, m

_{3,2}, m

_{4,1},…,m

_{p}

_{,}

_{p−1}) represent the stacked vector of the elements below the main diagonal in M

_{t}, and let v

_{t}= (v

_{1}

_{,}

_{t},…,v

_{p}

_{,}

_{t}) obey the expression v

_{j}

_{,}

_{t}= log σ2 j,t for j = 1,…,p, t = q + 1,…n. More specifically, the dynamics of the parameters that can vary with time in Equation (6) are assumed to obey the following form:

_{q}

_{+1}~G(μ

_{ϕ},Σ

_{ϕ}

_{0}), m

_{q}

_{+1}~G(μ

_{m}

_{0},Σ

_{m}

_{0}), and v

_{q}

_{+1}~G(μ

_{v}

_{0},Σ

_{v}

_{0}) for t = q+1,…,n.

_{ϕ}

_{0}= μ

_{m}

_{0}= μ

_{v}

_{0}= 0, and the covariance matrices are Σ

_{ϕ}

_{0}= Σ

_{m}

_{0}= Σ

_{v}

_{0}= 10 × I. All elements belonging to the i-th diagonals of the covariance matrices obey the prior probability distributions: ${({\Sigma}_{\varphi})}_{i}^{-2}$~ Gamma(40,0.02), ${({\Sigma}_{m})}_{i}^{-2}$~ Gamma(4,0.02), and ${({\Sigma}_{v})}_{i}^{-2}$~ Gamma(4,0.02), where Gamma represents the gamma distributions, which is in accordance with Nakajima [66].

#### 3.2. Data Description

## 4. Empirical Results and Discussion

_{t}= (MP

_{t},UR

_{t},II

_{t},EG

_{t}). Following the beginning burn-in period aimed at removing the reliance of the simulation chain upon its starting values, the joint posterior density will converge to stationary. A correctly deduced and executed MCMC algorithm will then produce the samples. We conduct 20,000 MCMC samplings and burn-in the very first 2000 initial subsamples.

#### 4.1. Parameter Estimation

#### 4.2. The Time-Varying Effects of Urban–Rural Income Inequality on Economic Growth

#### 4.3. The Time-Varying Effects of Urbanization on Urban–Rural Income Inequality and Economic Growth

#### 4.4. The Time-Varying Effects of Monetary Policy on Urban–Rural Income Inequality and Economic Growth

#### 4.5. Policy Recommendations

**Figure 7.**Urban–rural income inequality and Gini coefficient in China: 1978–2019. Notes: Before 2013, the NBS surveyed urban and rural households separately. After that, the NBS carried out reforms, and urban and rural households were surveyed according to a unified standard and caliber. Sources: Urban–rural income data are from the NBS. The NBS has been publishing Gini coefficient data since 2003, and the data for 1978 to 2002 are from Chen et al. [81]. The graph was drawn by the authors.

#### 4.6. Strengths, Limitations, and Further Research

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Estimation results of parameters in the TVP-VAR Model. Notes: In the panels of the top row, the vertical axes are the sample serial correlation functions, and the horizontal axes are the number of iterations. In the panels of the middle row, the vertical axes are the sample stochastic realizations, and the horizontal axes are the number of iterations. In the panels of the bottom row, the vertical axes are the probability density, and the horizontal axes are the sample value. Sources: Raw data are from the NBS and the PBC, and the graph was drawn by the authors.

**Figure 2.**Time-varying impulse responses of EG to II. Sources: Raw data are from the NBS and the PBC, and the graphs were drawn by the authors. (

**a**) Time horizons graph; (

**b**) timepoints graph.

**Figure 3.**Time-varying impulse responses of II to UR. Sources: Raw data are from the NBS and the PBC, and the graphs were drawn by the authors. (

**a**) Time horizons graph; (

**b**) timepoints graph.

**Figure 4.**Time-varying impulse responses of EG to UR. Sources: Raw data are from the NBS and the PBC, and the graphs were drawn by the authors. (

**a**) Time horizons graph; (

**b**) timepoints graph.

**Figure 5.**Time-varying impulse responses of II to MP. Sources: Raw data are from the NBS and the PBC, and the graphs were drawn by the authors. (

**a**) Time horizons graph; (

**b**) timepoints graph.

**Figure 6.**Time-varying impulse responses of EG to MP. Sources: Raw data are from the NBS and the PBC, and the graphs were drawn by the authors. (

**a**) Time horizons graph; (

**b**) timepoints graph.

**Figure 8.**Urbanization in China and selected other countries: 1978–2020. Sources: Raw data are from the World Bank database, and the graph was drawn by the authors.

**Figure 9.**The evolution of household income composition in urban and rural China: 2000–2020. Notes: Panel a is the urban household income composition, and Panel b is the rural household income composition. Before 2013, the NBS surveyed urban and rural households separately. After that, the NBS carried out reforms, and urban and rural households were surveyed according to a unified standard and caliber. Sources: Raw data are from the NBS, and the graphs were drawn by authors. (

**a**) Urban household; (

**b**) rural household.

Variable | Mean | Std. Dev. | Minimum | Maximum | Skewness | Kurtosis |
---|---|---|---|---|---|---|

MP | 0.0348 | 0.0146 | 0.0084 | 0.0995 | 1.5544 | 7.4454 |

UR | 0.1889 | 0.1097 | −0.3317 | 0.4539 | 0.4539 | 8.5182 |

II | 2.7901 | 0.1982 | 2.4192 | 3.4887 | 0.7532 | 3.8577 |

EG | 0.0366 | 0.0207 | −0.0526 | 0.1429 | 0.7918 | 14.003 |

Variable | Test Type (C,T,K) | ADF Statistic | 5% Critical Value | Prob. | Result |
---|---|---|---|---|---|

MP | (C,T,0) | −6.6939 | −3.4684 | 0.0000 | stable |

UR | (C,T,1) | −7.7469 | −3.4692 | 0.0000 | stable |

II | (C,T,0) | −3.5489 | −3.4684 | 0.0412 | stable |

EG | (C,T,0) | −10.1983 | −3.4684 | 0.0000 | stable |

Parameter | Mean | MSEs. | 95%L | 95%U | Geweke | Inef. |
---|---|---|---|---|---|---|

(Σ_{φ})_{1} | 0.0229 | 0.0027 | 0.0184 | 0.0288 | 0.743 | 4.35 |

(Σ_{φ})_{2} | 0.0218 | 0.0023 | 0.0178 | 0.0270 | 0.094 | 3.77 |

(Σ_{m})_{1} | 0.0829 | 0.0372 | 0.0417 | 0.1760 | 0.704 | 38.69 |

(Σ_{m})_{2} | 0.0862 | 0.0380 | 0.0425 | 0.1762 | 0.846 | 39.93 |

(Σ_{v})_{1} | 0.4326 | 0.2114 | 0.1358 | 0.9759 | 0.515 | 98.53 |

(Σ_{v})_{2} | 0.5741 | 0.1575 | 0.3271 | 0.9394 | 0.461 | 33.03 |

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**MDPI and ACS Style**

Cheng, J.; Lin, F.
The Dynamic Effects of Urban–Rural Income Inequality on Sustainable Economic Growth under Urbanization and Monetary Policy in China. *Sustainability* **2022**, *14*, 6896.
https://doi.org/10.3390/su14116896

**AMA Style**

Cheng J, Lin F.
The Dynamic Effects of Urban–Rural Income Inequality on Sustainable Economic Growth under Urbanization and Monetary Policy in China. *Sustainability*. 2022; 14(11):6896.
https://doi.org/10.3390/su14116896

**Chicago/Turabian Style**

Cheng, Junli, and Feng Lin.
2022. "The Dynamic Effects of Urban–Rural Income Inequality on Sustainable Economic Growth under Urbanization and Monetary Policy in China" *Sustainability* 14, no. 11: 6896.
https://doi.org/10.3390/su14116896