#### Justifications for the Long-Run Productivity Growth Forecasts in the *Trustees' Reports*

MEMORANDUM

To: Dean Baker, Paul Krugman, Other Interested Parties

From: Brad DeLong

Date: March 25, 2005

Paul Krugman observed:

a strange asymmetry between what is updated [in the Social Security

Trustees' Reportto reflect recent data, and what isn't.... [H]igh productivity growth since 2000... seems like big news... [but] isn't factored in at all. The reason is that the trustees use an average over the past four "full business cycles," measured from peak to peak (Section IV.B.7).... [T]hey won't take the good productivity news since 2000 into account [at all in forecasting the future] until the economy [begins] another recession. There's something very wrong with that...

This raises two natural questions:

- Why have the Social Security Trustees adopted this estimating convention of taking average productivity growth over the past four peak-to-peak
*complete*business cycles and projecting it forward into the indefinite future? - How long have the Social Security Trustees been using this--peculiar--rule of thumb for long-run forecasts of productivity growth?

The answer to question (2) is simple. The 2005 *Trustees' Report* is only the second year that the Trustees have used this rule of thumb that throws away all the favorable information about productivity growth since the 2000 business cycle peak.

Back in the 1990s the Trustees formed their long-run productivity growth estimates by taking the average level of productivity growth over the previous forty years and then marking down from that average because productivity growth had declined over time. Back in 1996 when the 40-year average was 1.8% per year their forecast was 1.4%. In 1997, 1998, and 1999 when the 40-year average was 1.7% per year their forecast was 1.3%.

In 2000, 2001, 2002, and 2003 as the fast productivity growth of the post-1995 period showed that we were no longer in an ongoing productivity slowdown, and as the gap between the 40-year and the 10-year growth average fell, the Trustees shrank their markdown and brought their estimate of future long-run productivity growth toward the 40-year average: the gap was 0.4% per year in 2000, 0.3% per year in 2001, 0.2% per year in 2002, and 0.1% per year in 2003.

Then in 2004 the Trustees freeze the long-run rate of productivity growth at 1.6% per year, thus for the first time choosing a forecast of future productivity growth *lower* than both the 40-year and the 10-year average, and for the first time justifying their forecast by saying that since "productivity growth can vary substantially within economic cycles... it is more useful to consider historical average growth rates for complete economic cycles." Had the SSA Trustees followed the 2000-2003 pattern of cutting the gap by 0.1% per year, they would have forecast 1.7% per year. Had the Trustees adopted the convention of averaging the past 40-year and the past 10-year growth rates, they would also have forecast 1.7% per year.

And in 2005 the Trustees continue to freeze the long-run rate of productivity growth at 1.6% per year, again justifying it by chopping off the data at the 2000 business cycle peak. Had the SSA Trustees followed the 2000-2003 pattern of cutting the gap by 0.1% per year, they would have forecast 1.9% per year. Had the Trustees adopted the convention of averaging the past 40-year and the past 10-year growth rates, they would also have forecast 1.9% per year.

Possible answers to question (1) are left as exercises to the readers.

2005 *Trustees' Report*:

For the 40 years from 1963 to 2003, annual increases in total productivity averaged 1.8 percent, the result of average annual increases of 2.5, 1.1, 1.5, and 2.0 percent for the 10-year periods 1963-73, 1973-83, 1983-93, and 1993-2003, respectively. However, productivity growth can vary substantially within economic cycles. Therefore, it is more useful to consider historical average growth rates for complete economic cycles. The annual increase in total productivity averaged 1.6 percent over the last four complete economic cycles (measured from peak to peak), covering the 34-year period from 1966 to 2000. The annual increase in total productivity averaged 2.2, 1.2, 1.3, and 1.6 percent over the business cycles 1966-73, 1973-78, 1978-89, 1989-2000, respectively. The ultimate annual increases in productivity are assumed to be 1.9, 1.6, and 1.3 percent for the low cost, intermediate, and high cost assumptions, respectively...

2004 *Trustees' Report*:

For the 40 years from 1962 to 2002, annual increases in total productivity averaged 1.7 percent, the result of average annual increases of 2.6, 1.1, 1.6, and 1.7 percent for the 10-year periods 1962-72, 1972-82, 1982-92, and 1992-2002, respectively. However, productivity growth can vary substantially within economic cycles. Therefore, it is more useful to consider historical average growth rates for complete economic cycles. The annual increase in total productivity averaged 1.5 percent over the last four complete economic cycles (measured from peak to peak), covering the 34-year period from 1966 to 2000. The annual increase in total productivity averaged 2.3, 1.2, 1.2, and 1.5 percent over the business cycles 1966-73, 1973-78, 1978-89, 1989-2000, respectively. The ultimate annual increases in productivity are assumed to be 1.9, 1.6, and 1.3 percent for the low cost, intermediate, and high cost assumptions, respectively...

2003 *Trustees' Report*:

For the 40 years from 1961 to 2001, annual increases in total productivity averaged 1.7 percent, the result of average annual increases of 2.7, 1.4, 1.3, and 1.5 percent for the 10-year periods 1961-71, 1971-81, 1981-91 and 1991-2001, respectively. The ultimate annual increases in productivity are assumed to be 1.9, 1.6, and 1.3 percent for the low cost, intermediate, and high cost assumptions, respectively. These are the same as the ultimate rates assumed for the 2002 report...

2002 *Trustees' Report*:

For the 40 years from 1960 to 2000, annual increases in total productivity averaged 1.8 percent, the result of average annual increases of 2.7, 1.6, 1.4, and 1.6 percent for the 10-year periods 1960-70, 1970-80, 1980-90 and 1990-2000, respectively. The ultimate annual increases in productivity are assumed to be 1.9, 1.6, and 1.3 percent for the low cost, intermediate, and high cost assumptions, respectively. These are 0.1 percentage point higher than the ultimate rates assumed for the 2001 report. This increase reflects ongoing assessment of historical data, including the period of rapid productivity growth between 1995 and 2000...

2001 *Trustees' Report*:

For the 40 years from 1959-99, annual increases in total productivity averaged 1.8 percent, the result of average annual increases of 2.6, 1.8, 1.3, and 1.5 percent for the 10-year periods 1959-69, 1969-79, 1979-89 and 1989-99, respectively. The ultimate annual increases in productivity are assumed to be 1.8, 1.5, and 1.2 percent for alternatives I, II, and III, respectively. These are the same ultimate rates assumed for the 2000 report...

2000 *Trustees' Report*:

For the 40 years 1959-98, annual increases in productivity for the total U.S. economy averaged 1.9 percent, the result of average annual increases of 3.0, 1.8, 1.3, and 1.4 percent for the 10-year periods 1959-68, 1969- 78, 1979-88 and 1989-98, respectively.... The ultimate annual increases in productivity for all sectors—wage-and-salary workers, self-employed persons, and the total economy— are assumed to be about 1.8, 1.5, and 1.2 percent for alternatives I, II, and III, respectively...

1999 *Trustees' Report*:

For the 40 years 1958-97, annual increases in productivity for the total U.S. economy averaged 1.7 percent, the result of average annual increases of 2.9, 2.0, 1.0, and 0.9 percent for the 10-year periods 1958-67, 1968- 77, 1978-87 and 1988-97, respectively.... The ultimate annual increases in productivity for all sectors—wage-and-salary workers, self-employed persons, and the total economy— are assumed to be about 1.6, 1.3, and 1.0 percent for alternatives I, II, and III, respectively.

1998 *Trustees' Report*:

For the 40 years 1957-96, annual increases in productivity for the total U.S. economy averaged 1.7 percent, the result of average annual increases of 3.1, 2.0, 1.1, and 0.6 percent for the 10-year periods 1957-66, 1967- 76, 1977-86 and 1987-96, respectively.... The ultimate annual increases in productivity for all sectors—wage-and-salary workers, self-employed persons, and the total economy— are assumed to be about 1.6, 1.3, and 1.0 percent for alternatives I, II, and III, respectively...

1997 *Trustees' Report*:

For the 40 years 1956-95, annual increases in productivity for the total U.S. economy averaged 1.7 percent, the result of average annual increases of 2.8, 2.0, 1.2, and 0.9 percent for the 10-year periods 1956-65, 1966-75, 1976-85 and 1986-95, respectively.... The ultimate annual increases in productivity for all sectors—wage-and-salary workers, self-employed persons, and the total economy— are assumed to be about 1.6, 1.3, and 1.0 percent for alternatives I, II, and III, respectively.

1996 *Trustees' Report*:

For the 40 years 1955-94, annual increases in productivity for the total U.S. economy averaged 1.8 percent, the result of average annual increases of 2.8, 2.1, 1.4, and 1.0 percent for the 10-year periods 1955-64, 1965-74, 1975-84 and 1985-94, respectively.... The ultimate annual increases in productivity for all sectors - wage-and-salary workers, self-employed persons, and the total economy - are assumed to be about 1.7, 1.4, and 1.1 percent for alternatives I, II, and III, respectively...

1995 *Trustees' Report*:

For the 40 years 1954-93, annual increases in productivity for the total U.S. economy averaged 1.6 percent, the result of average annual increases of 2.4, 2.3, 0.8, and 1.0 percent for the 10-year periods 1954-63, 1964-73, 1974-83 and 1984-93, respectively.... The ultimate annual increases in productivity for all sectors - wage-and-salary workers, self-employed persons, and the total economy - are assumed to be about 1.7, 1.4, and 1.1 percent for alternatives I, II, and III, respectively.