Q. Inflation data and Purchasing Power Parity (including cost of living, CPI, PPI, etc.)?

Consult the ACCRA Cost of Living Index.  Electronic holdings begin in 1990. For prior to 1990, consult the print. Firestone HD6983 I57, available in print (1981-2010). The preceding title was Cost of living indicators. Inter-city index report. Holdings are spotty and under call numbers HD6983.A7 (1972, 1978) and HD9004.A4 (1979-1981). 

For international consumer prices indexes, use World Development Indicators or EIU Country Data. For detailed purchasing power parity data, see the World Bank's International Comparison Program (2017).

For global pricing before 1950, see the Global Price and Income History Group.

Cost of Living Survey Series consists of 4 studies: "Cost of Living of Industrial Workers in the United States and Europe, 1888-1890", "Cost of Living in the United States, 1917-1919", "Study of Consumer Purchases in the United States, 1935-1936", and "Cost of Living Index for the American States, 1960-2003".

For the United States CPI Detailed Report go to CPI Detailed Report
For the United States PPI Detailed Report go to PPI Detailed Report

One can also get CPI Detailed report back to 1978.  To download many places use the FTP site.  CPI detailed reports back to 1953 can be found on FRASER.  For 1952, see "Consumers’ price index and retail prices of food" - Firestone HD6983 .A12.

Consider using these free websites for quick look ups:

• Bureau of Labor Statistics. Consumer Prices Indexes
• AIER Cost-of-Living Calculator (historical)
• Bestplaces.net
• Salary.com

Take a look at Inflation Calculator

To calculate the worth of the US dollar from 1913 to the present , go to Federal Reserve Bank of Minneapolis What is a Dollar Worth?
 

In addition, Global Insight has historical data.
Once in Global Insight, Choose the bank name  U.S. Economic - Historical and enter keywords to search for CPI in the database.

Also, try EIU City Data (contains price data on over 160 products & services in 140 cities worldwide from 1990+) and Counting the Costs City Data (contains city data for Bolivia, Colombia, India, Malaysia, & Sweden).

For historical try the Current Value of Old Money.

The Value of a Dollar: Colonial Era to the Civil War 1600-1865

The value of a dollar: prices and incomes in the United States, 1860-2019 / by Scott Derks.

The Value of a Pound: Prices and Incomes in Britain 1900-1993
(DSS) HB235.G7V438 V358 1995

How Much is that in Real Money
(DSS) HB235.U6 M39 2001

Wholesale Prices for 213 Years 1720 to 1932
(DSS) HB235.UW52

See Prices and Wages by Decade (courtesy of University of Missouri).  Covers 1700+.