Rates: The Long and Short of it

A great post over at globalmacrotrading on long term global rates. We indeed have seen a large move down in bonds over the entire curve and it appears consensus that “rates are going to rise” and the market is “rotating into risk assets”. And when there’s consensus there’s usually little reason to hop on board. Here’s a longer term chart of the ten year with a back-of-the-envelope fundamental model – rolling 10 year average nominal growth plus the term premium (here I’m using Kim and Wright, 2005):

(Source: FRED/Author’s calculations)

The r-squared is about 0.92 and the current reading of about 2% suggests the ten year is a little high. And indeed it had worked it’s way down from the December 15th high of 2.6% down to about 2.3% before shooting up again yesterday on comments San Francisco Fed’s Williams, and we’re sitting close to 2.5% as I write this.

Thinking about the long term value of the ten year, we have to think about long term nominal GDP and the term premium. Decomposing nominal GDP into the real and inflation components, we see that if we assume that monetary policy has reached a state of technology that enables the Fed to control inflation, then the degree of freedom is real GDP. What does that look like long term?

I built a simple Cobb-Douglass-inspired model of real GDP growth as a function of productivity growth, growth in the capital stock, and growth in the labor force. The data go back to 1951 and the r-squared is 0.73. Here’s a table of the data for the whole period and the last 10 and 20 years:

RDGP TFP K L
1951-2014 3.18% 2.13% 3.53% 1.47%
Last 20 2.44% 2.08% 2.39% 0.88%
Last 10 1.51% 1.41% 1.76% 0.48%
Forward? 1.80% 1.43% 1.19% 0.50%

For the forward estimate of TFP and K I projected forward the recent recovery. For labor growth I used the BLS’s projection to 2022. Then if we assume an inflation rate of 2% going forward we come to a nominal GDP estimate of 3.8%. Plugging this back into our model, assuming the small term premium of today and we get about 2.6%. So most of the move might already be in. It all depends, of course, on assumptions about future growth and the term premium. I’m frankly not certain how to think about long term forecasts of the term premium, but it seems to correlate with the rate itself. For growth and inflation, if you think we’ll be stuck at 1.5% real GDP and 1.5% inflation then the 10 year moves below 2%. Think we’ll return to the nominal growth rates of the late 1990s, printing 6% per year? Then the 10 year goes above 4%. But with productivity growth averaging about 2% long term, and seeing as how we’re not likely to get a surge in immigration, skilled or otherwise, over the next eight years (yeah, I said it), and seeing as how the BLS is pretty good at what they do, any additional growth has to come from a huge increase in K. That’s another post, but the spoiler is that it’s not likely.

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