Longterm inflation expectations should not be sensitive to a sudden move in either oil prices or equity prices as timely monetary policy adjustments from policymakers are supposed to offset those shocks.
The main short-term leading indicator of inflation is labor unit costs, which is used as an indicator of inflationary pressure on producers. Interestingly, after soaring to 12.2% in the second quarter of 2020, annual change in unit labor costs dropped to -8.9% in Q3 2020 and is currently pricing in further downside in core CPI.
Another important ‘short-term’ driver of inflation is the velocity of money (M2), which could be defined as the number of times the one US dollar is spent to buy goods and services per unit of time. While the money supply has skyrocketed since March, all the money ‘printed’ by central banks in the past year has no velocity and is currently pricing in significant fall in core CPI.
These short-term leading indicators are mostly showing that the US economy is very likely to experience disinflationary/ deflationary pressures in near to medium term (12 to 18 months).
An additional popular inflation leading indicator is the Underlying Inflation Gauge (UIG, full dataset), which is reported by the NY Fed shows that the UIG has historically led core CPI by 15 months and has been constantly plunging in the past two years; even though UIG rebounded in recent months, it is far from pricing in rising core prices in the coming year.
Also the NFIB small business surveys, which is an indicator of the health of small businesses in the US shows that the NFIB is still standing at low levels and is also not showing any signs of rising inflation in the next few months.