How Does the Fed Measure Inflation?

Please explain thoroughly with explanations and thoughts.

Reference Link;

https://media.pearsoncmg.com/ph/bp/bp_hubbard_econ_5/MTC/ch26/MTC2603.html

In addition to the first question, please respond to the two posts on the bottom on your thoughts about how the fed measure inflation? Do you agree, disagree with this person's post? Why? Please include all of your thoughts and not short explanations.

Post #1 to respond to;

The Federal Reserve measures inflation using several key indicators to look for variations in consumer prices in the long term. Measures of inflation can vary substantially over short periods. However, the two most used measures of inflation are the Consumer Price Index (CPI) and the Personal Consumption Expenditures Price Index (PCE). According to the video, in 2000, the Federal Reserve announced that it would focus more on the PCE than on the CPI in tracking inflation. The PCE has three advantages over the CPI. First, it is a chain-type price index, as opposed to a market-based index. Second, the PCE includes the prices of more goods and services than the CPI. Finally, past values of a PCE can be revised, which allows one to keep track of historical trends of inflation better. In 2004, the Federal Reserve decided to rely on a sub-category of the PCE called core PCE. The core PCE excludes food and energy prices. Inflation as measured by Core PCE has been much more stable than inflation as measured by CPI or regular PCE, according to statistics. When PCE and CPI were measuring deflation between 2009 and 2010, Core PCE was still measuring inflation to be over 1%. It is here where the main difference can be seen.

Post #2 to respond to;

Due to the volatile nature of inflation, the Federal Reserve utilizes multiple price indexes when evaluating the rate of inflation. Price indexes measure changes in the price of a group of goods and services over a specified period of time rather than the increase in those prices relative to one another. The two price indexes most commonly used by the Fed is the Consumer Price Index (CPI) produced by the Bureau of Labor Statistics and the Personal Consumption Expenditure Index (PCE) produced by the Bureau of Economic Analysis. Prior to the year 2000, the Fed's Federal Open Market Committee (FOMC) focused more on CPI but found that it did not account for consumer substitutions of goods and services, did not have as comprehensive of coverage of goods and services, and could not be revised adequately in the long-term as opposed to the PCE. There is a further sub categorization of PCE referred to as "core" PCE that the Fed announced higher reliance on in 2004 that excludes food and energy prices due to their short-term volatility thus making the underlying inflation more difficult to analyze with them included. With this exclusion of food and energy prices, data comparing the price indexes from 1999-2013 showcases the stability of core PCE over CPI and PCE, with a particular note of so in 2009 when the CPI and PCE indexes were indicating negative economic deflation while the core PCE was showing inflation rates above one percent.