Do you calculate inflation differentials utilizing … inflation or value ranges? Comply with up on this debate from a bit over a 12 months in the past.
Right here’s a time collection plot of the log ratio of US CPI to Euro Space 19 HICP (seasonally adjusted by writer utilizing X13) (blue line, left scale), and month-on-month inflation differential annualized (tan line, proper scale).
Determine 1: Log ratio of US CPI-all city to Euro Space 19 HICP (blue line, left scale), and month-on-month annualized inflation differential, in % (tan line, proper scale). HICP seasonally adjusted utilizing X13 log remodel, X11 ARIMA seasonal adjustment. Inflation differential calculated utilizing log first variations. Supply: BLS, EC through FRED, and writer’s calculations.
Abstract of outcomes on log ratio:
- ADF unit root take a look at: fail to reject at 10% msl.
- DF-GLS (ERS) unit root take a look at: fail to reject at 10% msl.
- KPSS pattern stationary take a look at: reject at 1% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: no breaks chosen.
Abstract of take a look at outcomes on m/m inflation fee differential:
- ADF unit root take a look at: reject at 1% msl.
- DF-GLS (ERS) unit root take a look at: reject at 1% msl.
- KPSS pattern stationary take a look at: fail to reject at 10% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: no breaks chosen.
What about core?
Determine 2: Log ratio of US CPI-core to Euro Space 19 HICP core (blue line, left scale), and month-on-month annualized inflation differential, in % (tan line, proper scale). HICP seasonally adjusted utilizing X13 log remodel, X11 ARIMA seasonal adjustment. Inflation differential calculated utilizing log first variations. Supply: BLS, EC through FRED, TradingEconomics, and writer’s calculations.
Abstract of outcomes on log ratio for core:
- ADF unit root take a look at: fail to reject at 10% msl.
- DF-GLS (ERS) unit root take a look at: fail to reject at 10% msl.
- KPSS pattern stationary take a look at: reject at 1% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: 5 breaks chosen; final one at 2019M05.
Abstract of take a look at outcomes on m/m inflation fee differentials for core:
- ADF unit root take a look at: reject at 1% msl.
- DF-GLS (ERS) unit root take a look at: reject at 1% msl.
- KPSS pattern stationary take a look at: fail to reject at 1% msl, reject at 5% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: 2 breaks chosen; final one at 2013M04.
Whereas the pattern break at 2021M02/03 will not be statistically important for core (utilizing a dummy for inflation differentials, or a dummy interacted with pattern for value ratio), you possibly can see there may be an acceleration in relative core.
Determine 3: Log ratio of US to Euro Space 19 core costs, 2020M02=0 (blue). Inexperienced (crimson) arrow are deterministic tendencies with numbers (in parentheses) indicating deterministic (stochastic) pattern progress charges. NBER outlined peak-to-trough recession dates shaded grey. Supply: BLS and EC through FRED, TradingEconomics, NBER and writer’s calculations.
Taking segmented tendencies actually, US core CPI is rising 0.3 ppts sooner than the Euro space, ranging from 2021M02 onward.
For extra on testing on deterministic, stochastic and segmented tendencies, see Cheung and Chinn (Oxford Economic Papers, 1996), Cheung and Chinn (JBES, 1997), and Cheung, Chinn and Tran (AEL, 1995).
Replace, 8pm Pacific:
2slugbaits factors out that HICP and CPI deal with implied residential hire otherwise. I repeat Determine 1, however utilizing US HICP in addition to Euro Space HICP.
Determine 4: Log ratio of US HICP to Euro Space 19 HICP (blue line, left scale), and month-on-month annualized inflation differential, in % (tan line, proper scale). HICP seasonally adjusted utilizing X13 log remodel, X11 ARIMA seasonal adjustment. Inflation differential calculated utilizing log first variations. Supply: BLS, EC through FRED, and writer’s calculations.
The unit root/pattern stationary take a look at outcomes are primarily the identical as for the CPI/HICP comparability.
From 2018M02-2021M2, the ratio rose +0.4% per 12 months, and from 2021M02-2023M04, it fell 0.7%. For comparability, in Determine 1 (operating to 2023M05), the ratio rose +0.8%, then fell 0.8%. Therefore, utilizing HICPs for each areas, the shift is barely smaller.
Do you calculate inflation differentials utilizing … inflation or value ranges? Comply with up on this debate from a bit over a 12 months in the past.
Right here’s a time collection plot of the log ratio of US CPI to Euro Space 19 HICP (seasonally adjusted by writer utilizing X13) (blue line, left scale), and month-on-month inflation differential annualized (tan line, proper scale).
Determine 1: Log ratio of US CPI-all city to Euro Space 19 HICP (blue line, left scale), and month-on-month annualized inflation differential, in % (tan line, proper scale). HICP seasonally adjusted utilizing X13 log remodel, X11 ARIMA seasonal adjustment. Inflation differential calculated utilizing log first variations. Supply: BLS, EC through FRED, and writer’s calculations.
Abstract of outcomes on log ratio:
- ADF unit root take a look at: fail to reject at 10% msl.
- DF-GLS (ERS) unit root take a look at: fail to reject at 10% msl.
- KPSS pattern stationary take a look at: reject at 1% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: no breaks chosen.
Abstract of take a look at outcomes on m/m inflation fee differential:
- ADF unit root take a look at: reject at 1% msl.
- DF-GLS (ERS) unit root take a look at: reject at 1% msl.
- KPSS pattern stationary take a look at: fail to reject at 10% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: no breaks chosen.
What about core?
Determine 2: Log ratio of US CPI-core to Euro Space 19 HICP core (blue line, left scale), and month-on-month annualized inflation differential, in % (tan line, proper scale). HICP seasonally adjusted utilizing X13 log remodel, X11 ARIMA seasonal adjustment. Inflation differential calculated utilizing log first variations. Supply: BLS, EC through FRED, TradingEconomics, and writer’s calculations.
Abstract of outcomes on log ratio for core:
- ADF unit root take a look at: fail to reject at 10% msl.
- DF-GLS (ERS) unit root take a look at: fail to reject at 10% msl.
- KPSS pattern stationary take a look at: reject at 1% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: 5 breaks chosen; final one at 2019M05.
Abstract of take a look at outcomes on m/m inflation fee differentials for core:
- ADF unit root take a look at: reject at 1% msl.
- DF-GLS (ERS) unit root take a look at: reject at 1% msl.
- KPSS pattern stationary take a look at: fail to reject at 1% msl, reject at 5% msl.
- Bai-Perron structural break assessments of L+1 vs. L sequentially decided breaks: 2 breaks chosen; final one at 2013M04.
Whereas the pattern break at 2021M02/03 will not be statistically important for core (utilizing a dummy for inflation differentials, or a dummy interacted with pattern for value ratio), you possibly can see there may be an acceleration in relative core.
Determine 3: Log ratio of US to Euro Space 19 core costs, 2020M02=0 (blue). Inexperienced (crimson) arrow are deterministic tendencies with numbers (in parentheses) indicating deterministic (stochastic) pattern progress charges. NBER outlined peak-to-trough recession dates shaded grey. Supply: BLS and EC through FRED, TradingEconomics, NBER and writer’s calculations.
Taking segmented tendencies actually, US core CPI is rising 0.3 ppts sooner than the Euro space, ranging from 2021M02 onward.
For extra on testing on deterministic, stochastic and segmented tendencies, see Cheung and Chinn (Oxford Economic Papers, 1996), Cheung and Chinn (JBES, 1997), and Cheung, Chinn and Tran (AEL, 1995).
Replace, 8pm Pacific:
2slugbaits factors out that HICP and CPI deal with implied residential hire otherwise. I repeat Determine 1, however utilizing US HICP in addition to Euro Space HICP.
Determine 4: Log ratio of US HICP to Euro Space 19 HICP (blue line, left scale), and month-on-month annualized inflation differential, in % (tan line, proper scale). HICP seasonally adjusted utilizing X13 log remodel, X11 ARIMA seasonal adjustment. Inflation differential calculated utilizing log first variations. Supply: BLS, EC through FRED, and writer’s calculations.
The unit root/pattern stationary take a look at outcomes are primarily the identical as for the CPI/HICP comparability.
From 2018M02-2021M2, the ratio rose +0.4% per 12 months, and from 2021M02-2023M04, it fell 0.7%. For comparability, in Determine 1 (operating to 2023M05), the ratio rose +0.8%, then fell 0.8%. Therefore, utilizing HICPs for each areas, the shift is barely smaller.