# Home-ostasis Is where the Heart Is

#### How quickly does the self-correcting mechanism work?

In intro macroeconomics courses, my view is that there is a certain (necessary) amount of hand-waving going on when students are taught that, in the long run, the economy will self-correct.*(See*

*here*

*for a decent explanation if you have no idea what I am talking about, or consult any macro textboook.)*

This story, as far as I know, isn't wrong. Sure, I and others would argue that modern economies don't always return to their prior long-run level of real output -- a.k.a hysteresis -- and that understanding that a recessionary gap can also be closed by a drop in long-run aggregate supply is important to the self-correcting mechanism.

But still. In my experience, intro macro doesn't go much further than that -- leaving a whole lot of questions for the wannabe economist. How long does this self-correcting mechanism take to work? How do growth rates respond over time to an output gap?

Here's where I'd normally cite the literature; perhaps I was searching the wrong terms on Google Scholar and SSRN, but I couldn't find any study which looked at how the US economy self-corrects, or returns to equilibrium. (*Note: I'm going to fold in government stabilization policy into the self-correction mechanism, as I'm not prepared to simulate several decades of counterfactuals; in any case, this post examines how the US economy corrects -- not necessarily "self" corrects -- to output gaps.)*

So I decided to do that, to attempt to answer "how long is the long-run" when it comes to the self-correction mechanism, and how growth behaves during that time frame. To that end, I took the entire data series from FRED of NGDP -- 1947 through 2012 -- and used a Hodrick-Prescott filter to determine the trend growth rate of NGDP over the years.Using that data, I found the NGDP gap in all of these quarters and the actual NGDP growth rate between that quarter and one, two, three, and so on quarters ahead, all the way through 16 quarters, or four years. Then I found the correlation of the growth rate one quarter, two quarters, and so on out with the original output gap. That tells me how much of the variance in growth rates can explained by the existence of a self-correction mechanism during that interval. The second thing I found was the slope of the regression line for the scatterplot of the output gap by the average growth rate within that quarterly interval. The slope measurement of -0.17, for example, for one quarter out suggests that for every 1 percentage point output gap, growth will be 0.17 percent higher than trend in that first quarter. This measure tells us how strong the self-correcting mechanism is over time, given an exogenously determined output gap at t = 0.

As we can see above, the self-correction process has been historically strongest between quarters 4 and 5 after the formation of an output gap in quarter 0. Before that, the self-correction process is less apparent in the data -- perhaps this reflects the time it takes for prices to adjust, or for fiscal and monetary intervention to work its way through the system. I can't explain the mechanism with this analysis -- really, we're treating the economy as a black box, shaking it, and seeing how it responds.

Now the really fun part about this is that we can build a shock model of output gaps, effectively determining the real-world impulse response function. Exciting stuff, if you find impulse response functions exciting. (And if you do, then you are an economist.)

I've done this below using our information about "slope" to determine the growth rate given an output gap, and then this growth accumulates to close the output gap. Furthermore, I've used the original data to determine the standard error from the mean growth rate to determine a 90 percent confidence interval, projecting out a high- and low-growth rate scenario. That allows me to model the output gap as a fan chart -- which unfortunately Google Docs messes up a little bit, but anyway -- we get a simple, but empirically well-founded, model of the US economy's correction of output gaps.

I've plugged in a 3 percent output gap for demonstration -- arbitrary, but in sample, given recent recessions:I feel like I understand the self-correcting mechanism so much better now.

PS. Tomorrow's post will be about the dis-equilibrating side of the American economy. Do we have a "stall speed" of economic growth, at which point we pitch like a plane into recession? How strong is the "momentum" of growth or contraction?