Sunday, January 24, 2010

Taylor Rule and Output Gaps

Taylor wrote:
Taylor Rule is pretty simple. It just says, the interest rate should equal 1 1/2 times the inflation rate, plus 1/2 time the GDP gap, plus 1.

I'm beginning to have doubts.

Using this formula to calculate the proper target for the federal funds rate using different estimates of the output gap naturally results in a variety of targets.

Using the GDP deflator and the Laubach and William's measures of the output gap, the CBO measure of the output gap and the gap between real GDP and its trend results in the following paths for the federal funds rate since 1984:

For the Laubach and Williams' one way measure, (LW1) the highest target was 7.97 percent in the third quarter of 2005. It was nearly as high, 7.73 percent in the first quarter of 2007. The most recent target, for the second quarter of 2009, was -.19 percent, the only negative nominal interest rate.

For Laubach and Williams' two way measure, (LW2), the highest interest rate was 8.22 percent during the first quarter of 2007. It was 7.03 percent during the third quarter of 2008. The lowest is the target for the second quarter 2009, is negative -.19 percent. Again, this is the only negative rate during the period.

The CBO measure generates a high interest rate target of 8.9 percent in the first quarter of 1990. It also suggests a high rate at the beginning of the Great Recession, 8.09 in the first quarter of 2007. The low is second quarter 2oo9, at -1.66 percent. However, the nominal interest rate was also negative in the fourth quarter of 2009, -.1 percent.

The gap between the trend growth path of real output and real GDP suggests a federal funds rate that reached a high of 9.21 percent in the first quarter of 2000. It also suggests an interest rate of 6.7% for the first quarter of 2007 and 4.97 for the third quarter of 2008. It turns negative as nominal income began to fall, -1.83 in the fourth quarter of 2008, -.32 in the first quarter of 2009, and -3.59 for the second quarter of 2009.

These applications of the Taylor rule do call for negative nominal interest rates, but for some of them, the negative rates are not much different from zero, and only apply to a single quarter.

Of course, these calculations are using the GDP deflator, which includes all goods and services. The standard approach is to ignore capital goods and government goods and instead just look at the prices of some consumer goods--well, everything other than food and energy. Further, these calculations used the current inflation rate and output gap to find the proper information. The Taylor rule needs to use available information. Look for another post later.

1 comment:

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