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It is no secret that long-term interest rates have been kept down by the U.S. Federal Reserve for some time. In fact, that was exactly the aim of the Fed's Quantitative Easing (QE) program: To stimulate the U.S. economy by reducing the long-term cost of capital for households, businesses and governments. For the past three years, we have been used to having the Fed buy a lot of long-term Treasuries, enough, in fact, that it now owns close to 50 per cent of outstanding government debt with maturities of more than 10 years.

Before the first warning from Fed chairman Ben Bernanke in May about the coming tapering, real rates (nominal rates minus inflation) had even been negative in most of the developed world for more than a year, something that is not too common historically.

As the financial world readies itself for the coming tapering of the QE program, with improvements in labour markets and a potential budget deal in sight, the question we ask ourselves is: Assuming a neutral monetary policy stance at the Fed by the end of 2016 (meaning that the Fed funds rate returns to close to 2.50 per cent), how high can U.S. 10-year bond rates go by then?

We'll address this matter through basic empirical macroeconomics. A country's 10-year bond rates tend to follow, on average, the annual growth rate of nominal gross domestic product. This relationship is seen across the globe and can be traced back to the 1950s, when U.S. data began being tracked. Based on this observation, we fully expect 10-year U.S. Treasury rates to converge toward nominal GDP growth within the next few years.

When I look at my Bloomberg screen, I see that the consensus currently expects U.S. nominal GDP to grow by 4.5 per cent in 2014 (2.6 per cent real GDP growth plus 1.9 per cent inflation) and by 5.1 per cent in 2015 (3 per cent real GDP plus 2.1 per cent inflation). As the charts demonstrate, (U.S., Canada) this relationship does not hold true at all times, but it does give a ballpark of where rates are headed.

This simple estimation of equilibrium long-term rates actually has a very good track record. We back-tested the approach using data covering the past 20 years, and found that the results were fairly close to reality.

We took the OECD's estimation of the annual growth rate of real potential GDP in the U.S. for 1991 to 2013 (2.6 per cent) and used it as our approximation of the growth rate of real GDP. Then we added an inflation target of 2 per cent (which was not an official target until recently, but is reasonable to consider as the unofficial target of the Fed during its Alan Greenspan era). The sum of these two components gives us an estimation of equilibrium nominal GDP growth for the period of 4.6 per cent, meaning that 10-year rates should have averaged close to this figure. We then averaged the monthly 10-year rates over that span and found a mean of 4.9 per cent – not too far off the mark.

Then we went one step further and did the same calculation for Canada, the U.S., the euro zone and the U.K. from 2001 to 2007, the pre-recession period for which the OECD has published a common set of real potential GDP growth estimates. The predictions proved quite accurate in Canada and the U.S., less so in the euro zone, and adequate for the U.K. All in all, good enough results and further confirmation of the value of this pretty simple approach.

So, long rates should march toward a range of 4.5 per cent to 5 per cent eventually, but how fast will they get there? This is not an easy question. The Fed is making clear that it intends to maintain an accommodative monetary policy for some time after its QE program has expired, thus anchoring the short end of the yield curve and pressuring down long rates. In other words, tapering is not the same as tightening – at least not entirely.

In a nutshell, when the Fed finally puts an end to QE, which should happen by the end of 2014, long-term rates should march up toward about 3.5 to 3.6 per cent, a rise of 75 basis points from current levels. But 10-year rates should only return to a more "normal" level of around 4.5 per cent when the Fed brings its monetary policy back to neutral, which would be in line with a Fed funds rate of about 2.5 per cent to 2.75 per cent.

Clément Gignac is senior vice-president and chief economist at Industrial Alliance Inc., vice-chairman of the World Economic Forum Council on Competitiveness and a former cabinet minister in the Quebec government.

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