Thinking about macro-economics hurts my head. I can’t explain why without getting pretty technical, so feel free to skip this post if you’re not a fan of calculus.

*The economy*, measured by GDP, is often thought of as a being a stock, and is described as growing and shrinking. When GDP grows, the economy is booming, which is good. When GDP decreases, the economy is in recession or depression, which is bad. When GDP growth is smaller over a period of time, that’s stagnation, which is also bad.

This all makes sense if you think of GDP as a stock, but it’s not. It’s a flow. (Click here for groovy graphics about stocks and flows) Human wealth, which is actually the most important thing, *is* a stock. GDP affects wealth; it’s an input to wealth’s first derivative. Change in GDP affects wealth; it’s an input to wealth’s second derivative. But the conversation about the strength of the economy should start with wealth, not GDP.

In order for wealth to increase, GDP growth does not need to be high. GDP growth doesn’t even need to be positive. So long as GDP exceeds depreciation, wealth increases over time. That is, so long as we produce more value in a year than the annual decrease in value of our possessions, we get wealthier. Ideally, wealth not only increases, but grows as a quadratic function, which occurs when GDP growth is positive. And even more ideally, wealth grows as a juicy quadratic function, rather than a less juicy quadratic function, which occurs when GDP growth is high. But that’s icing on the cake.

Have I made your head hurt yet? No? Read on.

When Tyler Cowen links favorably to this post by David Beckworth, which uses this chart, I ask myself, and David Beckworth and Tyler Cowen, why are you using a logarithmic scale? If Total Factor Productivity is an input to the first derivative of wealth, and it’s grown steadily, then wealth has grown as a quadratic equation. If you display the growth of TFP on a logarithmic scale, it will appear to slow down, because *that’s what logarithmic scales do* to linear growth rates. That doesn’t mean it’s an actual problem.

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## One Comment

I’m not familiar with the concept of TFP, but if I understand it correctly, it’s output, divided by labor and wealth (so, it controls for population). In calculus terms, it’s output/input*input, sort of, except the two inputs are in different units. Does that mean we can compare it to acceleration? (e.g., meters vs. meters/second, meters/second squared). I have no idea.

A logarithmic scale is helpful for showing slowing growth rates, which is what they’re trying to do, I think. They are trying to say the growth rate of TFP is slowing. If we stick with the physics analogy, that means acceleration is slowing, and the “jerk” is declining. That is not a trivial point.

Quick math: It looks like, from the graph, in 1947, TFP was about 40k (10^4.6), in 1973, it was 126k (10^5.1), and in 2007, it was 251k (10^5.4). This means that the annual growth rate from ’47 to ’73 was 12%, and from ’73 to ’07, it was 6% (I think; I always forget the CAGR formula). So, annual growth rate, as a percent, was half as high during the “stagnation.”

I get what you’re saying: we’re still growing. And 6% growth rate on the larger amount in ’73 vs. ’47 means that we’re still growing at a linear rate.

But, I think, the case they’re trying to make is that the returns on technology are declining, because the “jerk” is smaller than it used to be. Is that a fair analogy? I have no idea. My brain just died.