Should asset prices be included in inflation?

According to Zhou Xiaochuan, governor of the People’s Bank of China (PBOC) for over 15 years until 2018, the answer is yes:

Zhou argues that central banks could adopt a broader concept of inflation, something like the cost of living index flagged by US president-elect Joe Biden, with the measure of inflation going beyond the existing consumer price index (CPI) by factoring in asset prices as well as the cost of public services.

In the euro area, it seems that the only way assets are taken into account is indirectly as rental – and here the weight is 6.5%, which seems a bit low.

What would be the effect of including asset prices on measured inflation? According to this paper from 2002:

We find that the failure to include asset prices in the aggregate price statistic has introduced a downward bias in the U.S. Consumer Price Index on the order of magnitude ofroughly ¼ percentage point annually. Of the three broad assets categories considered here—equities, bonds, and houses—we find that the failure to include housing prices resulted in thelargest potential measurement error. This conclusion is also supported by a cursory look at some cross-country evidence.

Given the large growth in assets prices due to QE, that bias has certainly increased in magnitude.