Every once in a while something just strikes you and, inexplicably, you like it. Clair Brown's American Standards of Living: 1918-1988 struck me that way.

After googling

*saving by quintile*turned up the book (see yesterday's post) I went back and started reading from the beginning. Got all the way to page six before I had to stop and write this new post. Here's the part that did me in:

Periods of economic growth traditionally are characterized by greater equality of classes. Consequently, the growth in real expenditures across classes deviates from the growth in total output, as families in a lower class experience greater growth in consumption than families in a higher class...

Since government policies heavily influence total output and relative incomes, and because each class will try to maintain its relative position, shifts in income inequality tend to have a cyclical nature, as a class that loses out relatively in one period tries to improve its position in the next period. A period of increasing inequality usually follows a period of decreasing inequality.

Now if somebody had written that for Wikipedia, there would be a comment attached to it reading

*This article needs citations for verification.*You know what? It's an important statement for me, so

*I*need citations. I need references. I need verification. I need Emmanuel Saez's graph:

Graph #1: The Top Decile Income Share in the United States, 1917-2007 From Striking it Richer (PDF, 2009) by Emmanuel Saez |

Greater equality, 1942-1978. Golden age of growth, 1947-1973.

*Periods of economic growth traditionally are characterized by greater equality of classes.*Evidence? Well, it's a start.

I particularly like the idea that inequality might run in some sort of cyclical pattern. That idea fits right in with my world view. Shows up in the graph, too.

Actually, as Arnold Toynbee may already have said, if there are cyclical patterns on a civilizational scale to be found in our world then we ought to start with that, and always remember that the details probably fit the larger pattern. You don't always need to fit details to the larger pattern. But the pattern can help to resolve ambiguities. It can provide guidance. And it can call some things plain silly, like the idea that economic growth always clings to an invariant trend.

Economists like to think economic growth tends to trend. They say things like GDP is "trend stationary". They speak of an "output gap". The output gap is the gap between where GDP is now and where it would be

*if it had stayed on trend*. People who speak of an output gap think in terms of a long-term trend of growth.

Let me see if I can get this right. "Stochastic" means "random" and is the opposite of "deterministic". At MathWorks they look at a graph of US GDP and identify it as a "nonstationary" (as opposed to stationary) stochastic process. Nonstationary, because "there is a very obvious upward trend" visible on the graph.

MathWorks calls this upward trend a "mean trend" and describes it as a "violation of stationarity". So, it is a nonstationary stochastic process. They identify two such trend types: where the mean trend is

*deterministic*, and where the mean trend is

*stochastic*. Note these two are opposites, per our introductory definitions just above.

So GDP is a nonstationary stochastic process, where the nonstationary part -- the trend part -- might be deterministic, or might be stochastic. If it is deterministic, we have a deterministic nonstationary stochastic process. If it is stochastic, we have a stochastic nonstationary stochastic process. Ain't this fun?

Anyway, the deterministic one is said to be "trend stationary". The other one (according to Eduardo Rossi's PDF, page 4) is said to have a "unit root". And this isn't just boring arithmetic. It's economics with a hard on.

Here's the thing. The path of GDP is

*something*stochastic. The stochastic part means it's random in the sense, I think, that we cannot know whether the next report will be higher or lower than anybody's guess.

That's the "marginal" piece of it, the "next piece of data" part. The other part of it is the long-term piece. You know, the trend. Is it a trend? Or is it as random as the next piece of data? Is it deterministic, or stochastic? That is the question.

But that is

*their*question. Not mine. For me, it's a Toynbee thing. Left to its own devices, the economy will follow a path of growth and decline that encompasses many centuries and many nation-states. Left to its own devices, the economy will conform to the demands of human nature and to the demands of wealth. Left to its own devices, we get what looks to us to be the rise and fall of civilizations.

It doesn't have to be that way, of course. We could understand that what's happening is the result of such forces, and we could choose a different path. But that's a difficult thing to achieve, because everyone clings to their political opinions, even when they damn well know the problems are economic.

It's a catch-22. If we leave our economy to the wiles of human nature, we end up with the decline and fall of civilization. And the only thing we have to prevent that sad end is human nature.

So... How to resolve the deterministic slash stochastic, trend-stationary slash unit-root dilemma? Think big picture. Sometimes it's one way; sometimes the other. When the economy's growing vigorously for twenty years or more, or when a nation is young and vigorous, you've got a deterministic trend.

When economic problems arise faster than we can invent solutions, and growth sucks ass, well, you get lots of people chanting "unit root, unit root, unit root". And you know what? At that moment, they're right.

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