Inflation Vs. P/E Ratio

Inflation is negatively correlated to the P/E ratio. 

PCE Vs. GDP

The significance of consumption and the secondary effect it has on the other contributors to GDP, allows economists to use PCE as a proxy to forecast economic growth.

The PCE is correlated to GDP.

Personal Consumption Expenditures Fall off a Cliff

This won't bode well for the inflation numbers.

PCE Vs. CPI

The CPI and PCE are both important indicators of U.S. inflation. While CPI is more important from the perspective of an individual, PCE is more important from the perspective of monetary policy. 

The CPI and PCE do not cover identical categories of personal spending. The PCE has a broader scope than the CPI, as it captures the expenditures by both rural and urban consumers. Unlike the CPI, the PCE includes expenditures from non-profit institutions that serve households.

The Fed has given preference to PCE due to its broader scope and “chained base” for calculations.