In this blog I always try and emphasize cyclical features of macroeconomic growth, as that is my main research interest right now. Given the extraordinary events taking place in the world of monetary policy in recent years, an important question to look at is where the long run US economic growth rate is going, as the argument has been made that the more fractured US labor market could lead to weaker economic growth going forward as US consumers are less willing to spend as they were before the great recession .

First, if you look at US economic growth, there has been a lot of talk about a decline in the long term US growth rate trend. What do I mean by this? Recent (excellent) research by some economists at Fulcrum Investments highlighted in an FT article by Gavyn Davies (see here) used something called a "Dynamic Factor Model". This research incorporated some tweaks in the overall model to allow it to "detect" where the long run US economic growth rate is headed. Their results clearly show that long term US economic growth (and growth in other major developed economies) is heading downwards. The figure below from their paper (which you can find here) shows the downward trend that they obtain for the long run US economic growth rate. In their paper the authors go on to repeat this analysis for the other major developed economies with very similar results.

Above the red line plots their long run growth rate, with the blue dotted lines showing 5 and 10 percent confidence intervals. The black much more cyclical line shows the Congressional Budget Office's measure of the growth in potential output ( - the growth in the maximum output of the economy if all factors of production were employed).

On the face of it, the red line showing their measure of estimated growth looks pretty bad - it appears to move downwards over the 55 years plotted here. But there are two points to bear in mind here though.

First, this measure does not use the official definition of economic growth, which is percentage change in real GDP

Second, I would argue that their definition of "long term" is not correct. To me, long term means something that is measured over several business cycles, not just over one business cycle. Just looking at the graph above, I would argue that for the period 1970 to 2000 their long term measure of the economic growth rate was actually pretty stable, but that their measure clearly turns downwards well after 2000. So their measure really drops decisively below 3% only in 2004 or thereabouts, only 10 years ago, and therefore not even a complete business cycle ago. To my way of thinking that is not a change in the long term growth rate, as it has only happened over the last business cycle. Why does this matter? Well it could be (as we all know from the Reinhart and Rogoff research) that the recovery from the last recession was weak because the last recession was caused by a systemic banking failure - something that takes a lot longer to recover from than a "regular" recession.

Often it is good to get a robustness check on the results from doing an exercise like this by looking at what alternative methodologies reveal about the fluctuations in economic growth that the US has experienced. So here I introduce another approach known as wavelet analysis. This type of analysis operates in what scientists call the "time-frequency" domain, as it assumes a certain degree of (regular or irregular) cyclicality.

So let's first start with what wavelet analysis does. It basically takes the data and extracts cycles that can be detected by the technique over different ranges of frequencies. This is done in certain preset ranges, and these ranges are dyadic ( - they increase in terms of powers of 2). So for example the most basic cycles in a quarterly data series can be extracted at the 2 to 4 quarter cycle, then at a 4 to 8 quarter cycle, an 8 to 16 quarter cycle etc. When you run this type of wavelet analysis ( - technically it's called multiple overlap discrete wavelet analysis), you have to specify the maximum length of cycle you want to extract. Here I specify a 16 year cycle to be the maximum cycle, so that means that we have 5 series of what are called "crystals" which include the different ranges of cycles up to a 16 year cycle. Then anything left over after cycles up to 16 years long are extracted, is also put into what is called the "wavelet smooth". It contains any trend in the series plus any cycles in the data that can be detected that are longer than 16 years in length.

So what does this look like for US economic growth?

In the chart above I have broken down the fluctuations in US economic growth by cycle range, so lyd1 (the dark blue line) represents 2 to 4 quarter fluctuations in growth, lyd2 (the bright red line) represents 1 to 2 year cycles in growth etc. The light brown line which is labelled lys5 represents everything left in the growth series after all the other cycles have been extracted, so it contains cycles longer than a 16 year duration and any trend left in the series. Following the wavelet literature, I will call this variable (lys5) the "smooth".

What I find is very different from the Fulcrum Investment research. It is clear that from around the late-1960s onwards the growth rate has fallen to a lower level than it was prior to this date. But from around 1983 we see another phenomena emerging in the data - that of the so-called "great moderation", which saw high frequency fluctuations (lyd1, lyd2 and lyd3) dampened down, but at the same time a more vigorous longer term cycle emerging, particularly in the "smooth". In a paper with Andrew Hughes Hallett (available here) we show that in fact there was likely volatility transfer from this more high frequency (shorter) cycles to the low frequency (longer) cycles. I will write more about this paper and it's implications in a future blog.

But what is clear is that the longer term trends shown by the wavelet smooth do not indicate a significant decline in the long term economic growth rate. In fact, quite the opposite: it shows that i) the longer term smooth has been falling for cyclical reasons, as it has rebounded nicely since the great recession, but also ii) the longer term trend (also captured by the smooth) is in fact moving upwards quite rapidly, signifying that the economy is still on a long cycle upswing right now. In fact it may indicate that there is a longer cycle in growth lurking in the data.

Of course which methodology is right will affect a whole lot of other variables in the economy - such as the stockmarket, the bond market, incomes and expenditures.

So which method is right? Both methods have their advantages, but both also have disadvantages and statistical flaws. Probably the honest answer is that only time will tell!

First, if you look at US economic growth, there has been a lot of talk about a decline in the long term US growth rate trend. What do I mean by this? Recent (excellent) research by some economists at Fulcrum Investments highlighted in an FT article by Gavyn Davies (see here) used something called a "Dynamic Factor Model". This research incorporated some tweaks in the overall model to allow it to "detect" where the long run US economic growth rate is headed. Their results clearly show that long term US economic growth (and growth in other major developed economies) is heading downwards. The figure below from their paper (which you can find here) shows the downward trend that they obtain for the long run US economic growth rate. In their paper the authors go on to repeat this analysis for the other major developed economies with very similar results.

Source: Antolin-Diaz, Dreschel and Petrella (2014), p21 |

Above the red line plots their long run growth rate, with the blue dotted lines showing 5 and 10 percent confidence intervals. The black much more cyclical line shows the Congressional Budget Office's measure of the growth in potential output ( - the growth in the maximum output of the economy if all factors of production were employed).

On the face of it, the red line showing their measure of estimated growth looks pretty bad - it appears to move downwards over the 55 years plotted here. But there are two points to bear in mind here though.

First, this measure does not use the official definition of economic growth, which is percentage change in real GDP

*per capita*, as it is measured here as percentage change in real GDP. In fact most economists do not either, as getting population estimates by quarter is extremely difficult and even if you do, they are only estimates as we only really take a proper guage on the US population every census year. In other words, the figure above doesn't account for the change in population growth. This is important, as in all developed countries there has been a decline in the population growth rate, so some of this fall in the percentage change in real GDP would be expected. Now the authors do attribute some of the fall in the growth rate to the fall in population growth, so this is not a fault with their analysis, but rather something that one would be expect to be reflected in the figure above, thus tending to support a fall in the long term growth rate.Second, I would argue that their definition of "long term" is not correct. To me, long term means something that is measured over several business cycles, not just over one business cycle. Just looking at the graph above, I would argue that for the period 1970 to 2000 their long term measure of the economic growth rate was actually pretty stable, but that their measure clearly turns downwards well after 2000. So their measure really drops decisively below 3% only in 2004 or thereabouts, only 10 years ago, and therefore not even a complete business cycle ago. To my way of thinking that is not a change in the long term growth rate, as it has only happened over the last business cycle. Why does this matter? Well it could be (as we all know from the Reinhart and Rogoff research) that the recovery from the last recession was weak because the last recession was caused by a systemic banking failure - something that takes a lot longer to recover from than a "regular" recession.

Often it is good to get a robustness check on the results from doing an exercise like this by looking at what alternative methodologies reveal about the fluctuations in economic growth that the US has experienced. So here I introduce another approach known as wavelet analysis. This type of analysis operates in what scientists call the "time-frequency" domain, as it assumes a certain degree of (regular or irregular) cyclicality.

So let's first start with what wavelet analysis does. It basically takes the data and extracts cycles that can be detected by the technique over different ranges of frequencies. This is done in certain preset ranges, and these ranges are dyadic ( - they increase in terms of powers of 2). So for example the most basic cycles in a quarterly data series can be extracted at the 2 to 4 quarter cycle, then at a 4 to 8 quarter cycle, an 8 to 16 quarter cycle etc. When you run this type of wavelet analysis ( - technically it's called multiple overlap discrete wavelet analysis), you have to specify the maximum length of cycle you want to extract. Here I specify a 16 year cycle to be the maximum cycle, so that means that we have 5 series of what are called "crystals" which include the different ranges of cycles up to a 16 year cycle. Then anything left over after cycles up to 16 years long are extracted, is also put into what is called the "wavelet smooth". It contains any trend in the series plus any cycles in the data that can be detected that are longer than 16 years in length.

So what does this look like for US economic growth?

Source: Calculations by author |

What I find is very different from the Fulcrum Investment research. It is clear that from around the late-1960s onwards the growth rate has fallen to a lower level than it was prior to this date. But from around 1983 we see another phenomena emerging in the data - that of the so-called "great moderation", which saw high frequency fluctuations (lyd1, lyd2 and lyd3) dampened down, but at the same time a more vigorous longer term cycle emerging, particularly in the "smooth". In a paper with Andrew Hughes Hallett (available here) we show that in fact there was likely volatility transfer from this more high frequency (shorter) cycles to the low frequency (longer) cycles. I will write more about this paper and it's implications in a future blog.

But what is clear is that the longer term trends shown by the wavelet smooth do not indicate a significant decline in the long term economic growth rate. In fact, quite the opposite: it shows that i) the longer term smooth has been falling for cyclical reasons, as it has rebounded nicely since the great recession, but also ii) the longer term trend (also captured by the smooth) is in fact moving upwards quite rapidly, signifying that the economy is still on a long cycle upswing right now. In fact it may indicate that there is a longer cycle in growth lurking in the data.

Of course which methodology is right will affect a whole lot of other variables in the economy - such as the stockmarket, the bond market, incomes and expenditures.

So which method is right? Both methods have their advantages, but both also have disadvantages and statistical flaws. Probably the honest answer is that only time will tell!