Estimating Multi-Factor Productivity

In my post on neutral interest rates I mentioned productivity figures. I wondered whether the reason the estimate of the (real) neutral interest rate of 1.8% (which is implausibly high) is a function of (i) using the wrong productivity measure; (ii) the problems with UK productivity measures. Labour market productivity is released each quarter, but ideally we want to use MFP.

The closest I've come is a January 2014 ONS estimate of MFP. It's labelled "experimental" but at least provides annual data from 1997-2012. It looks like this:

If anyone is aware of quarterly estimates, I'd be interested to know.


The neutral interest rate is currently 1.8%

Having begun with such a confident headline, the rest of this post will involve a lot of backpeddling. For many economists (not just Austrians) the Wicksellian rate of interest (or "natural" or "neutral" rate) is of central importance for macroeconomic stability. In fact, one might argue that it isn't merely an indicator of the monetary stance - it is the stance.

Indeed David Beckworth and George Selgin argued this in a 2010 working paper. This morning I thought I'd attempt to make a very rough estimate of what interest rates would be in the UK - if they were at their natural rate. Their method is based on a Ramsey growth model that says that the neutral rate of interest is a function of productivity growth, population growth, and time preference. For simplicity, they focus on the component that is likely to be most volatile - productivity. Their equation for their estimate of the neutral rate is as follows:

In other words, the neutral rate today is equal to the long run steady real interest rate, plus the difference between expected Total Factor Productivity Growth, and the long run average TFP growth rate.

Following them, I assume that the long run steady real interest rate is 2%. For the productivity figures I used the quarter on quarter growth rate of output per worker (series code A4Y0). I then calculated expected TFP using the following approximation of an exponentially weighted moving average:

Again, following Beckworth and Selgin I set the coefficient at 0.7. The output is as follows:

Once I've had a think about possible errors I've made, and corrected them, I will add this to the data section of the Kaleidic website, and update it regularly. I think the chart broadly fits with intuition - fluctuation between 2%-3% prior to 2008, and then crashing into negative territory. Post crisis the rate is noticebly lower than before, with the latest estimate (Q4 2013) at 1.8%

We cannot observe the real neutral interest rate. But we do know that the long run average should roughly equal any actual long run value, and we do know something about the underlying determinants. I think Beckworth and Selgin have made an important contribution. A few discussion points to bear in mind:

  • I've not factored any population changes in, but an increase in working age population should increase our estimate. 
  • I used quarter on quarter growth rates because they lead to less volatile results but Beckworth and Selgin use year on year rates
  • This estimate is a real rate, so shouldn't be compared to a nominal policy rate without correcting the latter for inflation.
  • Beckworth and Selgin are obviously comparing this to a real Federal funds rate in order to get a measure of the monetary stance. The Bank of England's Bank rate isn't the same thing as the Federal funds rate, however, so it might be better to compare the estimate of the natural rate with an overnight interbank measure for the UK. 

UK monetary aggregates are concerning

One of the big warning lights in the pre 2008 boom was when broad money breached a 10% year-on-year growth rate. Since then, however the Bank of England have switched its preferred measure of M4 to M4ex. Can we use the same rules of thumb when the measure changes? I'm not sure. The chart below shows M4ex recently. One of the reasons I've not been too concerned about UK monetary aggregates is that M4ex is pretty stable, growing between 3%-5% since May 2012. 

Indeed if we add the 3 month annualised growth rate (hashed line) it's risen from -0.4% in Feb 2014 to 8.4% just 2 months later (its highest rate in the series).

This morning saw the release of Eurozone M3 data, which you can see below:

After the dramatic slowdown (note: not a contraction) that bottomed out in 2010, it's not just that the rising growth rates haven't been sustained, but have continued to fall. Looking at M3 for the UK we see the following:

The 12 month growth rate was between 2% and 4.3% from Dec 2012 through Nov 2013, but has since dropped dramatically. Despite a blip in Feb 2014 it's now actually contracting. 

As recently mentioned, price inflation is also slowing. PPI is weak and CPI is way below target. Food for thought.  


Producer Price Inflation is very low


Capital based macroeconomics is flourishing

Most of the readers of this blog are UK-based non academics. But everyone interested in macroeconomics from an Austrian perspective should be aware of some fantastic new work, seeking to bridge Hayek's insights with the literature on corporate finance. In 2011 I organised a talk by Joel Stern in London - I teach Economic Value Added (EVA) in my classes, and feature it in my forthcoming textbook. But I've not sought to introduce it into my research.

One of the very best books on capital theory is Capital in Disequilibrium, by Peter Lewin. And one of the most productive members of an emerging band of youthful Austrians is Nicholas Cachanosky. So it's really exciting to see the outcome of their collaborations. In particular:

Highly recommended.