Ex-Post Social Discount Rates

Wednesday January 18, 2012

When performing ex post analysis for net social benefits, there is surprisingly little guidance on the matter of selecting a social discount rate. This is remarkable given the handwringing by the Office of Management and Budget, the Congressional Budget Office, and many others over the matter in ex ante regulatory analysis. Regardless, it is sometimes important to consider the historical impact of a program to provide a framework for understanding changes to that program, similar new programs, or simply to see if the benefits projected at the start materialized.

One school of thought when perform ex ante regulatory analysis is to estimate the social discount rate at the using the governmental borrowing rate. (Other potential rates are discussed in, among others, Cost-Benefit Anaylsis: Concepts and Practice by Boardman, et al.) I think when performing an ex post analysis, there is significant justification for using the governmental borrowing rate and it is convenient is the borrowing rate is both observable and known. For this, I have created a pair of tables available as Google Tables, that represent the annualized borrowing rate for the United States government for calendar years and fiscal years. Each table provides the base cost for borrowing at one, two, three, five, seven, ten, 20, and 30 year terms. Below is an abbreviated sample.

Year 1-Year 10-Year 30-Year
2009 0.47 3.26 4.08
2010 0.32 3.22 4.25
2011 0.18 2.78 3.91

The fiscal year table provides each from 1977 onward, due to the shift in the federal fiscal year to October 1-September 30 beginning that year. There are gaps in the 30-year rate for 2003, 2004, and 2005 and in the 20-year rate from 1988 through 1993 due to a lack of date. The calendar year table provides the one, three, five, and ten year rates from 1962 onward. Other rates start in different years after 1962,

This data was compiled from the H.15 public release (Selected Interest Rates) of the Federal Reserve Board (disclaimer: I am employed by the Federal Reserve Board) using the Treasury constant maturities data sets. The calendar year data is comes directly from the historical section’s annual tables for each maturity. The fiscal year is the arithmetic mean of the monthly rates during the fiscal year. Generally speaking, this is not the actual borrowing rate but instead represents the expected borrowing rate for the federal government during the time frame in question for the given maturity. As a result, this is a close approximation to the rate necessary for ex post social discounting.