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As basic indicators for measuring inflation, the relationship and transmission mechanism of consumer price index CPI and producer price index PPI have always been core issues in macroeconomic research. (Click “Read the original text” at the end of the article to get the completecode data) .
Research on this issue obviously has important academic value and practical significance: when PPI leads changes in CPI, it means that upstream prices have a positive conduction effect on downstream prices, and prices may rise due to the impact of supply factors, and This leads to the risk of “cost-push inflation”. At this time, inflation management should focus on “supply control”; conversely, when CPI guides changes in PPI, it means that there is reverse pressure from downstream prices on upstream prices. Mechanism, prices may rise due to the impact of demand factors, which may lead to the risk of “demand-pull inflation”. At this time, inflation management should focus on “demand control”.
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Data: CPI and PPI monthly year-on-year data
Read data
head(data) ## Year-on-year CPI PPI for the month ## 1 36556 -0.2 0.03 ## 2 36585 0.7 1.20 ## 3 36616 -0.2 1.87 ## 4 36646 -0.3 2.59 ## 5 36677 0.1 0.67 ## 6 36707 0.5 2.95
CPI data
## ## Residuals: ## Min 1Q Median 3Q Max ## -4.3232 -1.2663 -0.5472 0.9925 6.3941 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 1.05348 0.30673 3.435 0.000731 *** ##t 0.01278 0.00280 4.564 9.05e-06 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 2.1 on 187 degrees of freedom ## Multiple R-squared: 0.1002, Adjusted R-squared: 0.09543 ## F-statistic: 20.83 on 1 and 187 DF, p-value: 9.055e-06
1. Unit root test
After reviewing the data, I found that seasonal adjustments are needed.
gives the output:
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R language ECM error correction model, equilibrium correction model, restricted VECM, cointegration test, unit root test spot interest rate market data
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## Augmented Dickey-Fuller Test ## ## data: x ## Dickey-Fuller = -2.0274, Lag order = 0, p-value = 0.4353 ## alternative hypothesis: explosive
## ############################################ ## ## # Augmented Dickey-Fuller Test Unit Root Test # ## ############################################## ## ## Test regression trend ## ## ## Call: ## lm(formula = z.diff ~ z.lag.1 + 1 + tt) ## ## Residuals: ## Min 1Q Median 3Q Max ## -2.66698 -0.36462 0.02973 0.39311 1.97552 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) 1.063e-01 9.513e-02 1.117 0.2653 ## z.lag.1 -4.463e-02 2.201e-02 -2.027 0.0441 * ## tt 4.876e-05 8.954e-04 0.054 0.9566 ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.6307 on 185 degrees of freedom ## Multiple R-squared: 0.0238, Adjusted R-squared: 0.01324 ## F-statistic: 2.255 on 2 and 185 DF, p-value: 0.1077 ## ## ## Value of test-statistic is: -2.0274 1.5177 2.255 ## ## Critical values for test statistics: ## 1pct 5pct 10pct ## tau3 -3.99 -3.43 -3.13 ## phi2 6.22 4.75 4.07 ## phi3 8.43 6.49 5.47
PPI data
## Augmented Dickey-Fuller Test ## ## data: x ## Dickey-Fuller = -1.3853, Lag order = 0, p-value = 0.1667 ## alternative hypothesis: explosive
(1) If there is a unit root, use the differential sequence to perform steps 2, 3, and 4;
(2) If there is no unit root, use the original sequence.
Therefore, both data are differentiated.
data$CPI=c(0,diff(data$CPI))
2. Testing the cointegration relationship – EG two-step method
Give the output
(1) If there is long-term cointegration, use the VECM method to linearly filter, and use the filtered “residual component” to proceed to steps 3 and 4;
(2) If there is no long-term cointegration, there is no need to filter and proceed directly to steps 3 and 4.
Establish a long-term equilibrium model
## Call: ## lm(formula = PPI ~ CPI, data = data) ## ## Residuals: ## Min 1Q Median 3Q Max ## -3.6930 -0.5071 -0.0322 0.4637 3.2085 ## ## Coefficients: ## Estimate Std. Error t value Pr(>|t|) ## (Intercept) -0.03678 0.06428 -0.572 0.568 ## CPI 0.54389 0.10176 5.345 2.61e-07 *** ## --- ## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 ## ## Residual standard error: 0.8836 on 187 degrees of freedom ## Multiple R-squared: 0.1325, Adjusted R-squared: 0.1279 ## F-statistic: 28.57 on 1 and 187 DF, p-value: 2.615e-07
Plot residuals
ts.plot(residual
If there is no long-term cointegration, there is no need to filter and proceed directly to steps 3 and 4.
3. Nonlinear test – RESET test method
Give the output
## RESET test ## ## data: data$PPI ~ data$CPI ## RESET = 0.28396, df1 = 1, df2 = 186, p-value = 0.5948
4. Establish VAR model and Granger causality test
Establish VAR model to give output results
## $Granger ## ## Granger causality H0: CPI do not Granger-cause PPI ## ## data: VAR object var.2c ## F-Test = 5.1234, df1 = 2, df2 = 364, p-value = 0.006392 ## ## ## $Instant ## ## H0: No instantaneous causality between: CPI and PPI ## ## data: VAR object var.2c ## Chi-squared = 15.015, df = 1, p-value = 0.0001067
The p value is rejected if it is less than the given significance level. Generally, the p value is less than 0.05, and can be relaxed to 0.1 in special cases. The f-statistic is greater than the quantile point. Generally look at the p value.
The Granger test mainly looks at the P value. For example, if the P value is less than 0.1, the null hypothesis is rejected and there is Granger causality between variables.
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This article is selected from “R language EG (Engle-Granger) two-step cointegration test, RESET, Granger causality test, VAR model analysis of the relationship between CPI and PPI”.
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