I wondered if the behavior of Chinese inflation was abnormal. The answer to this question basically depends on (1) what model you believe in, (2) what you think the parameters of the model are, (3) what you think the input values are, and (4) whether you think the model has been stable over time. Here is an answer.
Consider the evolution of CPI inflation in China.
Figure 1: China CPI inflation quarter-on-quarter (blue), year-on-year (tan), calculated as log differences. ECRI has defined recession dates in light blue. CPI adjusted using X-13. Source: World Bank.
This is the IPC series published by Kose and Ohnsorge at the World Bank. The quarterly series is seasonally adjusted using X-13 in the levels, then the logarithmic differences are calculated. The year-over-year series is the unadjusted series calculated using log differences.
Can the evolution of Chinese inflation be explained by a Phillips curve, pre-pandemic or post-pandemic? To answer this question would require a measure of the output gap or some other measure of economic activity. Figure 2 shows three output gaps, measured using statistical methods, and real GDP growth.
Figure 2: HP-filtered GDP on the extended sample (blue), band-pass filter (Eichenbaum-Christiano) on the extended sample (red), Hamilton filter (Quast-Wolters) (green) and quarterly GDP growth (tan). Source: GDP from Higgins & Zha/Atlanta Fed, author’s calculations.
- Hodrick Prescott is a filter applied to 2-year stretched GDP data using an ARIMA(1,1,0) to account for end-of-sample estimation problems associated with the two-tailed filter.
- The band-pass filter is applied to the same extended GDP time series.
- The modified Hamilton filter is the Jim Hamilton filter setting h=4 to 12 instead of 8 according to Quast and Wolters (2023)
- The growth rate is the annualized t/t growth rate of GDP.
GDP data is Higgins and Zha (Atlanta Federation) data updated from the first quarter of 2018 using actual growth rates reported by the NBS.
I run a regression of annualized inflation q/q on the lagged measure of the output/growth rate gap, the lagged depreciation of the nominal trade-weighted exchange rate, and the contemporaneous change in the price of oil in CNY over the period 2000Q1-19Q3.
πyou = β + βgapt-1 +γ πt-1 +φΔqyou +φΔpyouoil
The estimates are shown in Table 1.
Table 1: Determinants of the Chinese inflation rate
Remarks: Bold indicates significance at 10% using HAC robust standard errors.
Note that the deviation (or growth rate) is usually significant (with the exception of the bandpass filter), while the lagged inflation is only significant when using the modified Hamilton filter. Oil prices still significant.
Here is a scatterplot of inflation (q/q AR) versus Hamilton gap (modified), 2000Q1-19Q3:
Figure 3: Quarter-on-quarter annualized inflation versus lagged spread (Hamilton filter).
Using these estimates, I predicted inflation rates (note that the inflation rate shown below does not match those reported in the press as these are seasonally adjusted q/q rates). This is a test of the stability of the regressions estimated in the post-Covid period.
Figure 4: Actual q/q inflation (black), prediction using HP filter (blue), using BP filter (red), using Hamilton filter (green), and using growth rate (tan).
The output gap based on Hamilton’s filter produces the lowest mean squared error (but underestimates the most).
Table 2: Actual minus Planned
Measures of economic activity are positively associated with inflation, after accounting for cost-push shocks (especially oil price shocks). Lagged inflation generally does not enter.