Xavier Sala-I-Martin once wrote a paper called *“I just ran two million regressions”*. I can’t do quite as good, but I nonetheless have had a look at the nominal GDP growth of 143 countries since 1990. My “project” is to see whether there is a correlation between the growth rate of NGDP and the volatility of NGDP. We know from inflation history that there is a pretty close positive correlation between higher inflation and higher volatility in inflation. My expectation was that that would also be the case for NGDP and NGDP volatility (measured as the standard deviation of yearly NGDP growth across 143 different countries).

But more important I wanted to see whether we could say what would be the “optimal” growth rate of NGDP. By “optimal” I (here) understand the rate of NGDP growth that minimizes the volatility of NGDP growth and hence increases the predictability of NGDP growth.

Let’s first look at the data in the must raw form. This is a plot of the average yearly growth rate of NGDP in the 143 countries against the standard deviation of the NGDP growth rate in the same countries. I have split the period 1990-2011 into four sub-periods 1990-1995, 1995-2000, 2000-2007 and 2007-2011. That gives us four observations per country – nearly 600 observations.

The graph is pretty clear – as with inflation there is a pretty clear positive correlation between the level of NGDP growth and the standard deviation of NGDP growth.

Hence, there is a clear cost of higher NGDP in the form of a more volatile NGDP development.

Therefore an NGDP target of 3 or 5% growth clearly is preferable to an NGDP target of for example 10 or 100%.

However, if lower NGDP growth reduces the volatility of NGDP why not target -10% NGDP growth or lower?

To examine this issue I take a closer look at the data.

The graph below zoom in on countries (and periods) with an average growth rate of NGDP below 30%.

Again we see the clear picture that higher NGDP growth leads to higher NGDP volatility – and this also goes for relatively low rates of NGDP growth. Hence, it is not only in hyperinflation scenarios that this is the case.

As the graph shows if we go from an NGDP growth rate of 0-6% to 14-20% the volatility of NGDP growth doubles!

However, the graph also shows that the relationship is not linear. In fact if NGDP growth drops below zero – as have been the case in many countries since 2008 – then the volatility *increases*.

The graph also shows that there historically has *not* been any significant difference in NGDP volatility countries with NGDP growth of 0-2% or 4-5%.

The graph should make Scott Sumner happy as Scott has been arguing that the Federal Reserve should target 5% growth (level targeting). Historically NGDP growth of 5% has minimized the variance of NGDP growth and there would probably be little to gain – in terms of reducing NGDP volatility – by targeting a lower rate of NGDP growth. However, there would clearly be a cost of for example targeting a higher growth rate of for example 10%.

I think there is important lessons to draw from the graphs below. First and foremost that an NGDP growth target between 0% and 6% is preferable to higher *or* lower growth rates. But it should also be remembered that this is a very simple analysis and we could certainly lear a lot more from studying the country specific data closer, but all in all I don’t think Scott is making a major mistake when he is arguing in favour of a 5% NGDP (level) target in the US.

PS Forgive me for using volatility and standard deviation synonymously, but I am sure you get the drift. And please don’t kill me for saying that minimizing the volatility of NGDP is “optimal” – that is just a figure of speech.

PPS I really didn’t do the calculations on my own – I got quite a bit of help from my young and clever colleague Mikael Olai Milhøj.

UPDATE: Another young and clever colleague of mine Jens Pedersen noted that the logic of our results actually mean that a country like China with a trend growth rate of *real* GDP well above 6% should de facto be a *deflation* target’er to minimize NGDP volatility. This is what the data is saying – at least indirectly – but I am not sure that I am ready to argue that. I am however pretty sure that George Selgin would tell me that that is in fact what China should do.

## W. Peden

/ November 7, 2012I’m with Selgin on this one. Macroeconomic policy should be consistent with what basic microeconomics tells us about the price mechanism. Stable prices are mischievous things in an unstable world. Meeting the demand to hold money is what matters.

This is a possibly good argument for a deflationary target: deflation makes the consequences of bad labour market and minimum pricing policies apparent, so it should encourage policymakers to reform in these areas.

## Lars Christensen

/ November 7, 2012William, fundamentally I agree. George is right, but I must also say that there empirically might not be a major difference between a 0% and 5% NGDP target for a country like the US.

## henry bee

/ November 8, 2012Hi Lars, it’s been a while. I’ve had a few long email exchanges with Scott related to this post. The ideal target would be a moving target based on a moving window of the trailing 10-year real GDP growth + 2% inflation. There is no ideal NGDP target because it depends on each country’s economic development phase.

Due to the short sample size, aren’t you capturing a snapshot of the growth patterns of Developed Countries vs. Emerging Countries from 1990-present? The ECs have had higher volatility or growth rate during this time but likely due to their mode of production, which is more volatile in nature. Countries like US and Europe’s mode of production is services and demonstrate lower volatility.

## nickikt

/ November 8, 2012Why is that optimal? I see no reason for that to be true. We do have clear microeconomic resons that 0% is best (Prices relative and absolute are right).

Why does going to RGDP growth + 2% help? I have never been able to understand this. Scott makes psychological arguments against it (the money illusion) but nothing I would expect to be bigger then the benefit of correct prices.

## Lars Christensen

/ November 8, 2012Nickikt, the only claim I make is for the sample I have the volatility of NGDP growth is minimized for NGDP growth between 0% and 6% and that there is no major difference between 0% and 6% so you might as well target the one or the other. 0% is fine for me – if you start off in equilibrium.