^{1}

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With the development of economy, more and more attention is paid to the relationship between money supply and inflation in the economic field. This paper chooses consumer price index (
*CPI*) as an important index to measure the level of inflation, by choosing between January 2008 and March 2019 money in circulation
*M0*, narrow measure
*M1*, broad measure
*M2*, consumer price index
* CPI* monthly data as sample, building a vector autoregressive (VAR) model and using econometric methods of impulse response function and variance decomposition, and finally characterizes money in circulation
*M0*, narrow measure
*M1*, broad measure
*M2* and the relationship between consumer price index
* CPI* and different sizes of the impact of inflation in the money supply relationship.

With the continuous development of China’s economy, indicators such as gross national product, consumer price index and money supply have been important indicators to judge the state of macroeconomic development. Consumer price index (cpi) [

Vector autoregression (VAR) [

In 1980, C. A. Sims introduced VAR model into economics, promoting the wide application of dynamic analysis of economic system. The mathematical expression of VAR (P) model is:

y t = Φ 1 y t − 1 + ⋯ + Φ p y t − p + H x t + ε t , t = 1 , 2 , ⋯ , T (1)

y t is the column vector of endogenous variables in k dimension, x t is the column vector of exogenous variables in d dimension, p is the lag order, and T is the number of samples. k × k dimensional matrix Φ 1 , ⋯ , Φ p and k × d dimensional matrix H are coefficient matrices to be estimated. ε t is a k dimensional disturbance column vector, which can be correlated with each other synchronously, but not with its own lag value and not with the variables on the right-hand side of the equation.

Proposed by Granger (1969) [

Consider the mean square error (MSE) of the march period prediction:

MSE = 1 s ∑ i = 1 s ( y ^ t + i − y t + i ) 2 (2)

This can be expressed as follows: if the mean square error obtained by predicting y t + s based on ( y t , y t − 1 , ⋯ ) for all s > 0 is the same as the mean square error obtained by y t + s based on both ( y t , y t − 1 , ⋯ ) and ( x t , x t − 1 , ⋯ ) , then y is not caused by x Granger.

Vector autoregression model (VAR) [

First i endogenous variable of an impact not only directly affect the first i variable, and pass through the dynamic structure of the VAR model to other endogenous variables, impulse response function attempts to depict the influence of trajectory, shows how an arbitrary variable disturbance affect all other variables through model, finally and feedback to the process itself.

In 1980 [

y i t = ∑ j = 1 k ( θ i j ( 0 ) ε j t + θ i j ( 1 ) ε j t − 1 + θ i j ( 2 ) ε j t − 2 + θ i j ( 3 ) ε j t − 3 + ⋯ ) , i = 1 , 2 , ⋯ , k ; t = 1 , 2 , ⋯ , T (3)

V a r ( y i ) = ∑ j = 1 k { ∑ q = 0 ∞ ( θ i j ( q ) ) 2 σ j j } , i = 1 , 2 , ⋯ , k (4)

We know that the contents of the brackets are the sum of the influences of the j disturbance term ε j from the infinite past to the present time point on y i .

In this paper, the consumer price index (CPI) cover 8 types of goods and services consumed nationwide, and the calculation formula of CPI is

C P I = ∑ i = 1 n C P I i × W e i g h t i

Data are derived from Wind database. Figures 1-4 are the sequential trend charts of CPI, M0, M1 and M2 from January 2008 to March 2019. As the observed trend charts are not stable, the stationarity of unit root test series is further adopted.

In this paper, ADF unit root test was adopted to test the stationarity of the original sequence. The test results are shown in

Therefore, the first-order difference is carried out for the above sequences, and then the unit root test is carried out for the new sequences. The obtained results are shown in

As can be seen from

D C P I = 6.4339 e − 05 ∗ D M 0 ( − 1 ) + 3.4488 e − 05 ∗ D M 0 ( − 2 ) + 0.1177 ∗ D C P I ( − 1 ) + 0.080 ∗ D C P I ( − 2 ) + 4.9877 e − 05 ∗ D M 1 ( − 1 ) + 1.9733 e − 05 ∗ D M 1 ( − 2 ) − 3.8129 e − 07 ∗ D M 2 ( − 1 ) − 3.6004 e − 06 ∗ D M 2 ( − 2 ) − 0.0062

Variable | ADF test value | The critical value at the 1% level | The critical value at the 5% level | The critical value at the 10% level | P values | Conclusion |
---|---|---|---|---|---|---|

CPI | −320194 | −3.479656 | −2.883073 | −2.578331 | 0.9177 | Non-stationary |

M0 | −2.488793 | −3.484653 | −2.885249 | −2.579491 | 0.1207 | Non-stationary |

M1 | 0.225702 | −3,480038 | −2.883239 | −2.578402 | 0.9733 | Non-stationary |

M2 | 2.070928 | −3.484653 | −2.885249 | −2.579491 | 0.9999 | Non-stationary |

Variable | ADF test value | The critical value at the 1% level | The critical value at the 5% level | The critical value at the 10% level | P values | Conclusion |
---|---|---|---|---|---|---|

CPI | −11.21752 | −3.480038 | −2.883239 | −2.578420 | 0.0000 | Non-stationary |

M0 | −9.797663 | −3.484653 | −2.885249 | −2.579491 | 0.0000 | Non-stationary |

M1 | −13.92312 | −3.480038 | −2.578420 | −2.578420 | 0.0000 | Non-stationary |

M2 | −3.258272 | −3.484653 | −2.885249 | −2.579491 | 0.0191 | Non-stationary |

LogL | LR | FPE | AIC | SC | HQ | |
---|---|---|---|---|---|---|

0 | −4152.109 | NA | 2.62e+22 | 62.97134 | 63.05870 | 63.00684 |

1 | −4076.024 | 146.4052 | 1.05e+22 | 62.06097 | 62.49776* | 62.23846 |

2 | −4048.308 | 51.65193* | 8.83e+21* | 61.88346* | 62.66968 | 62.20294* |

Note: *represents the optimal lag order of the corresponding criterion; LR represents likelihood ratio statistic; FPE represents the final prediction error statistic; AIC represents the chi information criterion statistics; SC represents Schwartz statistic; HQ represents the hannan-quinn information statistic.

After the estimation of the model, the inverse roots of the AR characteristic polynomial of the model should be tested, and the AR root diagram and tables can be obtained, as shown in

According to

Granger causality test can further determine the causal relationship between each variable. The Granger causality test is conducted below, and the test results are shown in

According to the data in

According to the impulse response diagram in

By observing the impulse response diagram in

By observing the impulse response diagram in

Variance Decomposition

Root | Modulus |
---|---|

0.343647 − 0.543592i | 0.643106 |

0.343647 + 0.543592i | 0.643106 |

−0.564894 | 0.564894 |

−0.290970 − 0.442758i | 0.529809 |

−0.290970 + 0.442758i | 0.529809 |

0.505074 | 0.505074 |

−0.272000 − 0.017187i | 0.272543 |

−0.272000 + 0.017187i | 0.272543 |

The null hypothesis | The F value | Probability (P value) | Conclusion |
---|---|---|---|

DCPI is not the granger cause of DM0 | 0.810061 | 0.6670 | Accept |

DCPI is not the granger cause of DM0 | 17.99314 | 0.0001 | Refuse |

DCPI is not the granger cause of DM0 | 0.029371 | 0.9854 | Accept |

DCPI is not the granger cause of DM0 | 40.54574 | 0.0000 | Refuse |

DCPI is not the granger cause of DM0 | 3.940281 | 0.1394 | Accept |

DCPI is not the granger cause of DM0 | 0.394868 | 0.0008 | Refuse |

the first period, CPI was only affected by itself. With the passage of time, the contribution rate of CPI itself is gradually decreasing and the contribution rate of money supply variance is steadily rising.

Through correlation analysis such as impulse response function and variance as impulse response function and variance decomposition, the following conclusions can be drawn.

It is observed that the cumulative effect values of the corresponding impulse response functions M0, M1 and M2 are greater than 0, and it can be concluded that the increase of M0, M1 and M2 will increase CPI. From the variance decomposition, it can be concluded that contribution rate of different money supply to CPI is different.

The impact of CPI is a certain lag, and the lag index M1 is the leading indicator. Therefore, from the perspective of money supply, we should pay more attention to the change of M1 indicator, and then pay attention to the change of M2 indicator.

However, there is a significant short-term relationship between China’s inflation and money supply, and money supply has a significant impact on inflation. This relationship is very obvious in the short run. In the long run, the influence of money supply on inflation will gradually weaken and stabilize at a relative level, and the volatility will gradually stabilize.

Therefore, it can be concluded that there is no inflation in China’s economy in a short time, but it does not mean that the economy will develop steadily in the future, and stagflation may occur. At the same time, the monetary policy also has some lag and limitations. Therefore, we should establish a preventive mechanism in advance, and constantly improve some fiscal policies, formulate relevant systems, laws and regulations, so as to avoid some adverse impacts brought by inflation.

This work is supported by the National Natural Science Foundation of China (No. 11561056) and Natural Science Foundation of Qinghai (No. 2016-ZJ-914).

The authors declare no conflicts of interest regarding the publication of this paper.

Shen, S.C. and Dong, X.Y. (2019) The Structural Relationship between Chinese Money Supply and Inflation Based on VAR Model. Applied Mathematics, 10, 578-587. https://doi.org/10.4236/am.2019.107041