a unit root is an instability in a linear autoregressive time-series-forecasting model, leading to secular growth of the series as noise is amplified
In the analysis of time series, there is a large class of models called ARMA, for Autoregressive, Moving-Average. These are based on assuming that a certain linear function of the process and some of its lagged (past) values [this would be the autoregressive part] is equal to another linear combination of an underlying "white noise" process and some of its lagged values [this would be the moving-average part].
These linear combinations of lagged values can be used to construct certain "characteristic polynomials". If the polynomial for the autoregressive part has a root of absolute value greater than 1, then the model is numerically unstable and it amplifies the "white noise" explosively.
If the characteristic polynomial has a root of absolute value equal to 1 (a "unit root") then the model does not amplify the noise explosively, but it does amplify it leading to "secular growth". "Secular variation" is a variation that is not part of an oscillation and so is not expected to reverse itself eventually. It is a term borrowed from perturbation theory in celestial mechanics.
Unit roots can be removed by looking at the iterated differences of the process. For instance, instead of looking at GDP, look at GDP growth. I think Mankiw's point reduces to "maybe GDP growth is not the right thing to look at, and you should instead look at the year-on-year changes in GDP growth". Somebody has been spending waaaay too long thinking about linear filters and signal processing.
Like I said in another comment, as a mathematician watching a debate among leading economists, I am flabbergasted. Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
This would seem to be:
1.) Rather improbable
2.) Highly self serving if one's goal is to justify the existing system.
3.) Possibly the only assumptions that could give rise to a theory that could be successfully taught to most economics students.
How many grad students in economics are familiar with/competent in non-linear dynamics? As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."
Does this then mean that a "unit root" is the only instance that would give rise to a "Goldilocks Economy?"
What do you mean by "goldilocks economy", anyway? Most economists teach a theoretical framework that has been shown to be fundamentally useless. -- James K. Galbraith
That is a confusing statement. He uses the argument to say, that the US will grow only with the long term average growth rate. E.g. With 3%, when this was the average growth in the last 20 years, and will not sprint with e.g. 5% to make up the difference to what would have been the GDP without the crisis.
I think Mankiw is right on this and Krugman is wrong. There was a massive misallocation of capital and training to people. Capacities are not only underused, but as there is need to reallocate and retrain, capacities have been destroyed. Not completely. There maybe some catchup, but I think Krugman is too optimistic. You have read Stiglitz' 'Globalisation and its discontent'. If I remember correctly, he makes exactly the same point. Even if the long term growth trends aren't damaged by the reform, the IMF has asked e.g. Asian countries to do, the reduction in the GDP base will hurt long time. Der Amerikaner ist die Orchidee unter den MenschenVolker Pispers
This all seems sort of like what we would have expected if Ptolemy had been capable of Fourier analysis when he was accounting for retrograde motions of planets with epicycles. As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."
There is written in the end:
But to invoke the unit root thing to disparage growth forecasts now involves more than a bit of deliberate obtuseness. How can you fail to acknowledge that there's huge slack capacity in the economy right now? And yes, we can expect fast growth if and when that capacity comes back into use.
And what I say is, that this capacity isn't there or at least not fully, because it is not capacity in producing the things, that are demanded in the future. Der Amerikaner ist die Orchidee unter den MenschenVolker Pispers
He uses the argument to say, that the US will grow only with the long term average growth rate. E.g. With 3%, when this was the average growth in the last 20 years, and will not sprint with e.g. 5% to make up the difference to what would have been the GDP without the crisis.
What Krugman claims in your quote is that as long as there is unemployment, there is "unused capacity" (remember that Krugman is a semi-classical Keynesianist - he assumes that labour is the critical limiting factor in the political economy. In other words, he assumes an empty world).
So to try to translate what you quote from Krugman above: "Mankiw is saying that growth will remain at the current level. But that is bollocks, because there is unused capacity in the economy, which can be employed to produce capital goods, which can be used to increase the production of goods. Which means that if the unused capacity is employed in this fashion, growth will be higher than it is now."
Of course, once you realise that we in fact do not live in an empty world, the entire exchange becomes surreal, because Mankiw's concept of "long-run [exponential] growth" becomes self-defeating, and Krugman's insistence that labour is the only limiting factor in the economy becomes nonsense.
- Jake If you only spend 20 minutes of the rest of your life on economics, go spend them here.
What do you mean by "goldilocks economy", anyway?
