Arnold Kling  

Trend vs. Random Walk

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I am starting to re-read Ed Leamer's textbook, Macroeconomic Patterns and Stories. Very early, he presents a graph of real GDP from 1955 to 2005 on a log scale, showing that it grows at a trend rate of 3 percent, with hardly any years where it grows faster than 6 percent or slower than 0 percent.

In the 1980's, folks like Nelson and Plosser argued that such a graph was really deceptive. They argued instead that real GDP behaved statistically more like a random walk with drift.

It makes a huge difference today which model you believe. If there truly is a trend, then one believes in mean reversion. Given how much real GDP fell, that implies at some point that we will see very rapid real GDP growth in the future, probably the fastest on record.

On the other hand, if real GDP is a random walk with drift, then it just is where it is. Going forward, it does not know that it has to "make up" for any subpar growth. It is just going to try to grow at the trend rate of 3 percent (the "drift"), not get back to the trend level.

I worry that the multi-decade time-series properties of GDP could be determined in part by mechanical factors related to how the Commerce Department undertakes calculations, particularly the inflation adjustment. I think that if I were looking at trend vs. random walk, I would be more inclined to focus on payroll employment as my indicator of economic activity, because you don't have to worry about inflation adjustment.

My opinion, which is just a gut feeling that I cannot justify, is that employment is more of a trend than a random walk. That is, I continue to expect that employment growth will be much faster than normal at some point. So my gut tells me to dismiss stories of permanent labor market dislocation, such as the health insurance hurdle.


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COMMENTS (10 to date)
Hyena writes:

Shouldn't we expect this anyway? It would be odd if underutilized resources did not become, over time, more utilized. It would tend to defy everything we know about biology and adaptive, entropy-resisting systems.

Doc Merlin writes:

In markets with a large barrier to entry (for example pig farming where there is a ~2 year difference between making new pigs and them being food) you see /very/ wild swings in price from modest changes in demand.

Also, in such markets you see years that have price points far below cost are followed by years with very high prices and vice versa. (volatility is highly serially correlated in these markets.)

The total effect of the insurance barrier will not just be lower employment in the short run, it will result in MUCH too high employment at some future time, and correspondingly excessive wages. This period will then be followed by a period of far too low wages and employment.

Anyway, my point is that barrier such as this will increase serial correlation in volatility and increase volatility in the labor markets. This is very pro-cyclical and very bad.

Keith E writes:

Mean Reversion to Trend or Random Walk?

Is the question what type of pattern did the economy appear to follow in the past or what drives these patterns?

If we assume that the economy automatically follows some specific pattern, we might assume that the policies and actions we take do not matter. If policies and actions do matter, future growth patterns need not follow past patterns.

Defining economic growth as an increase in goods and services produced, I assume economic growth is driven by savings being invested to grow our capacity to produce the goods and services people want to buy (the Solow Growth Model approach). Given this, I would expect randomness in growth data as the success rate of investment varies, as random noise of weather and other things shift consumption and production around year to year, as subjective desires shift year to year, as variations in population growth and movement shift things around, etc. I'd expect a mean reversion only so long as we maintain the policies that support the steady allocation of income toward savings so that investment can accumulate capital used for producing goods and services.

We should always be careful when assuming that past patterns will continue into the future because the underlying mechanisms that created those patterns can likely be changed.

david writes:

Further to Hyena's comment, Say's Law implies a trend.

I suppose one might ask whether years with above trend GDP growth typically started from below trend GDP levels.

Arthur_500 writes:

I have looked at those very trends over the past fifty years and we are currently exactly where we "should" be. However, we have seen meteoric rises and falls, especially at the end of the 1990's and once again in 2008. I doubt the economy has a brain necessary to reach certain goals.

We have noticed that our economy continues to rise over time with those nasty periodic drops. This is the conundrum that many an economist has worked hard to predict and explain to no avail. I really don't think it is a random walk, however.

Any business will have its cycles of growth, steadying off, dropping and return to growth (or collapse). This has as much to do with technology and lifestyle changes as anything else.

Our most recent collapse really had as much to do with lifestyle changes and new financial products (technology) as it had to do with those nasty bankers. Over time we see growth as a steady march. In spite of those few runners and joggers most of the population will walk and some will crawl.

Various writes:

Wow Arnold, you get at the heart of a very profound question. Personally I think that the model you describe for predicting GDP trajectory depends on the particular circumstances. I certainly agree with you that, with normal policy inputs and ebbs and flows in the economy, that the "trend" model is the better one. However....to the extent that fundamental and long-lasting changes are made to the economy or more specifically, changes in gov't regulation, taxation and the like affect the economy, then I should think the economy will probably shift onto another semi-permanent trend line, either higher or lower than the original one.

I can think of several obvious cases of this that are rather extreme, but do illustrate the point. An ultra-extreme example would be East Germany after WWII. Economic output in that country was way below trend, and this was made obvious by its lagging below per capita output of it's nearly previously identical Western counterpart. That became apparent after the wall came down. There were probably similar factors at work in the U.S. during the 1930s. The shift in GDP growth after it shifted radically to the left is probably another good example.

So....I personally think that it is possible that healthcare reform has or will be a not-so-subtle punch in the gut to our economy, at least until it is amended or gutted. This could take a while for citizens to become aware of the nasty side effects of HC Reform. Anywhere from 1 year to 10....and exactly at what point they conclude the cause-and-effect is anybody's guess I think

jeppen writes:

To a large extent, technology, education and population growth determines potential GDP. So, since these things are barely affected by economic downturns, it is no wonder that GDP returns to trend after recessions instead of exhibiting random walk properties.

Piet le Roux writes:

Adding to first comment: GDP and employment are of two different categories. GDP is potentially infinite and not drawn from a pool. Employment not infinite - drawn from limited pool, maximum 100%.

Dave writes:

This reminds me of Mankiw's Unit Root Hypothesis, which caused Krugman to call him evil and for Mankiw to ask for a wager on the subject that Krugman never accepted.

Carl The EconGuy writes:

Arnold, you wrote this:

"On the other hand, if real GDP is a random walk with drift, then it just is where it is. Going forward, it does not know that it has to "make up" for any subpar growth. It is just going to try to grow at the trend rate of 3 percent (the "drift"), not get back to the trend level."

... which is just plain wrong, as you well know. In a random walk with drift, actual growth rates will be higher/lower than the trend rate, depending on the distribution of the error term. So, you cannot dismiss the unit root hypothesis by guessing that there will be a higher than trend rate recovery for a while; in fact, this is absolutely implied by the equation. Short term growth rates are pulled from a distribution, typically assumed normal, around the trend -- so, if the distribution is stable (which requires long time series to ensure), then short term poor performance must be matched by an equal weight of above-trend performance. If that weren't true, the drift would not be constant.

But you will never make up for lost GNP, and that's the point. The economy is like a Leijonhufvudian drunk who at every step can choose any number of corridors to stumble through -- once he chooses one, all the others are no longer available. Then he wobbles down his corridor, until he picks a new one, with exactly the same width as the previous one. But he'll never know where he might have gone in any of the other corridors, they are closed off. He just wobbles at exactky the same average pace, through an infinite number of corridors with the same width, and he randomly picks one at every step. Those are the only stable laws of macroeconomics that we have found after all these years of pointless theorizing and model building! The rest, as someone said, is all in the supply and demand of the economy -- I think I know who said that, but maybe you can remind me?

And, if you think that payroll employment is a better indicator than other time series, why don't you do the statistical tests yourself and check whether trend stationarity or random walk is the better explanation for the statistical properties? After all, you don't dismiss the tests as analytically incorrect, do you? Testing is better than believing, don't you think? I have a hunch which way the test will come out ...

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