Saturday, May 12, 2012

Correlations Across Time - NGDP and Bond Yield Edition

There's a lot of interest in using futures to help determine expectations: TIPS spreads are used to forecast expected inflation, 10-year bond yields are used to forecast expected NGDP growth, and in Scott Sumner's market monetarist nirvana the central bank would use NGDP futures to help forecast NGDP growth exactly.  The central bank would then only worry about that one expectation, vastly simplifying monetary policy.

In this post, I want to focus in on the NGDP growth and bond-yield correlation.  David Beckworth offers pretty convincing evidence that bond yields are highly correlated with NGDP growth forecasts:

Forecasting can be a bit inaccurate, so Lars Christensen  has a very nice graph showing how the 10 year bond yield has been tightly coupled with the year to year growth in NGDP in any given year.

But how do these correlations or trends change throughout time?  From the FRED data, I computed foward looking NGDP growth in 10-year windows from the second quarter of 1964 to the first quarter of 2002.  I then computed the correlation between actual NGDP growth and the bond yield in 10 year windows for each date, with 19 quarters of the window before the given date and 20 quarters of the window after the given date.  With the correlation, I also computed the OLS regression slope for the regression of bond yield as the explanatory variable and NGDP growth as the response variable.  It turns out that the NGDP growth and  the bond yield have had a very tight correlation in recent windows, but that this was not always the case.

On the graph in the second half of the 1970's (which would have been the correlations between the data from 1970 to 1985 on the NGDP growth from 1980 to 1995), we can see that there is actually a negative correlation between the bond yield and NGDP growth.  This likely could have been the result of tightening by the Federal Reserve in the 1980's in response to the oil shocks.  As a result, NGDP was pushed down against expectations, thereby creating a negative correlation.  The correlation is stronger in recent times, as the 1997 data point includes data from 2012, but still the correlation is not as strong as the one Beckworth and others find for forecasters.

Another interesting point to note in recent times is that although the correlation between NGDP growth and bond yield has been fairly high, , the OLS coefficient is rather low.  Bond yield does predict NGDP growth, but not in a one-to-one relationship.  In the most recent window, a 1% increase in bond yield predicted a 0.47% increase in NGDP growth.  What's interesting about the OLS coefficient that the correlation hides is that the OLS coefficient has been increasing in recent history.  I'm still not quite sure what that means, but I feel it should have important implications for the safe assets hypothesis and expectations of future economic growth.

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