In the Moment
Does the American economy behave like an inertial mass?This will be a short post, because I'm not feeling very well, and because this took me a long time to figure out how to do correctly -- blame my cold, I suppose.
I'm following up on yesterday's post, which examined the role of the output gap in predicting above- or below-trend growth, and build a model of how the US economy grows in response to an initial output gap. Now we put aside the output gap and investigate the inertial tendencies of the American economy: in short, how much does present growth determine future growth how far into the future?
This graph, which comes from the same data as yesterday, shows that growth in quarter 1 is highly correlated with growth in quarter 0. In fact, "growth inertia" can explain exactly half of all quarterly growth in the postwar era. That, at least to me, is striking -- although when I think about it differently, perhaps not so surprising. Economic growth tends not to go "from 0 to 60," so to speak, or from 60 to 0, all that quickly in the modern United States. Rather, there is a lumbering-about which seems to, sooner or later, converge to a trend.
Growth inertia doesn't last very long, though, as we can see. Only a third of growth in quarter 2 is explained by growth in quarter 0. By quarter 3, the inertial effect loses statistical significance.
Another way we can look at inertia is by the slope of this correlation. A hypothetical economy whose growth was entirely inertial would have a slope of 1 in every quarter; however, the real American economy data shows a slope first of 0.25 and then descending towards 0. What this tells us is how quickly inertia dissipates: if the economy is growing at an quarterly growth rate of 2 percent in quarter 0, and the average quarterly growth rate is 0.8 percent (as it is), then the growth in quarter 1 is predicted to be around 1.3. The lower the slope, the weaker the ability of growth to stay above or below the trend rate during that time interval. This too suggests that growth inertia vanishes in around three quarters.
Related to this is the error we should associate with our predictions. Using a 95 percent confidence interval, we can say that, for our prior example, annualized growth will be 1.3 ± 0.2 percent in quarter 1.
Again building a mini-model which I will eventually combine with yesterday's, imagine you have an economy growing at that quarterly rate of 2 percent -- pretend, perhaps, that it's some quarter in 1983, and this song is on the radio incessantly. How does the US economy respond, given its inertial tendencies? (For the sake of simplicity, I'm only using the single-quarter inertial data,; things would not be significantly different.)Notice that our model directly matches up with the discussion of the empirical data, as it should -- the inertia is gone within three quarters, for example. Tomorrow, I hope to figure out what I tried to do but was unsuccessful with today -- building a logistic model of growth slowdowns to answer the question of if the US economy has a "stall speed." In other words, is there a threshold level of growth that, when we go below it, we continue to fall all the way into recession? Suggestions of how do to that would be appreciated.