### Is inflation correlated with output growth?

Consider the AD-AS model which is often expressed in growth rates. Economists will often say that the short-run supply curve is flatter in the short-run and vertical in the long-run. In other words, aggregate demand policy can have SR output effects, and only has LR price effects. Sounds good.

But there is a lot of baggage hiding behind “*can* have effects”. Often we’ll say that lackadaisical businesses cause a flatter SRS and that businesses with rational expectations have a vertical one. Also sounds good.

What causes the steepness of the SR supply curve? I’m sure that there are multiple determinants in regard to expectations. Here’s what got me on this topic. David Andolfatto shared the below graph and asked “*Does lowflation necessarily mean low growth?*”.

Good question. My answer includes expectations concerning the monetary policy regime. Specifically, my answer was “*It does in a regime of volatile and uncertain nominal income. Surprise AD growth pushes us up the SRAS*.” Andolfatto called me out and in the right way, asking “*What’s the evidences for this?*”

I had no evidence. I had the AS-AD model in hand and some logic – but no evidence. My logic is as follows. In a monetary regime that includes a constant rate of AD growth, output and price growth are inversely correlated. If NGDP grows at 5% always, then inflation falls when output growth rises. In other words, AD is exactly what people expect – illustrated as a vertical SRAS curve.

However, expectations are different in a regime of erratic AD. Let’s say that the rate of AD growth is unknown, but that the variance is known. If this is the world that you live in, then you make hay when the sun shines. Businesses sell more in periods of higher income. And, because they’re marching up the marginal cost curve, prices also rise. Alternatively, it may be that output growth is inflexible and prices rise as a goods are rationed.

Regardless of the truth, the above explanation is just story-telling. I had no evidence. What would the evidence even be? Here’s what I settled on. First, let’s express the AS-AD model in quarterly growth rates. In order to get a handle on monetary regime AD variance, I calculated the standard deviation of the NGDP growth rate by Fed Chair. Presumably, the Fed chair has a decent amount to do with monetary policy and the rear that occupies that chair is an indicator of when a regime begins and ends. I calculated the correlation between the GDP deflator and RGDP growth rates by regime. Below is the scatter plot.

What does it tell us? It tells us that regimes of stable AD growth experience a negative correlation between inflation and output growth. It also tells us that a AD growth volatility is associated with a positive correlation between inflation and output growth. So, *Does lowflation necessarily mean low growth? It does in a regime of volatile and uncertain nominal income*.

(Of course this is all casual. It makes sense to me at first blush though. Having said that, the line of best fit also looks like it’s driven by the 2 extremely variable times: McCabe & Powell.)