Visualising NGDP Targeting

The AS-AS framework gave rise to one of the iconic images of Economics. Almost everyone who has studied or followed economics will have seen a version of the following diagram:

The AS-AD Diagram – from Wikimedia commons

Now, the stylised facts of this diagram are these

1. The supply curve is upward sloping : A higher price usually means a larger quantity can be produced. Think of how a higher price of Oil makes hard to reach reservoirs economic.
2. The supply curve goes vertical at some finite level of output. This represents real constraints on production in the economy.
3. The demand curve is downwards sloping – generally people buy a larger quantity of stuff when its cheaper.

We can understand the inflation targeting regime through the lens of this diagram. A supply shock moves the supply curve upwards. In order to return to the target price level, the central bank must move the demand curve leftwards. This is the reason to believe that inflation targeting is a sub-optimal strategy for a central bank – in this framework, in response to a positive supply shock, which decreases output, a central bank must deliberately generate a further fall in output in order to get inflation back to target. Think about that – in order to keep inflation on target in the face of a supply shock, we must deliberated produce less than we could. Moreover, in the real world, a loss of demand almost always means a rise in unemployment. So we are deliberately trading unemployment and lost production for in order to hit a 2% target.

The reverse happens in a positive supply shock. This time the supply curve is lowered, so the central bank shifts the AD curve rightwards. This rise in demand leads to a boom, and when the supply shock passes we find that the aggregate demand curve is too far to the right (policy is suddenly too loose) and we get a spike in inflation.

In the real world, its fair to say that we don’t “know” the shape of the supply curve and the aggregate demand curve. All we can measure is the cross over which actually happens i.e., we can measure the price level and RGDP and  Lets specify aggregate demand by: $P + Y = \text{constant}$, I.e demand that it slope downwards at a forty five degree angle. I am still totally free to match up to any empirical data by altering the inferred supply side curve. If we assume that we are talking about small changes in the price level and output, then $P+Y \approx P*Y = NGDP$. In that case we can draw a third axis on the graph:

This diagram is just the AS-AD diagram with a third axis drawn on to represent NGDP. The red lines are lines of constant NGDP. The inspiration for this was Minkowski diagrams for switching between space time frames by drawing on the a second frame of reference.

A supply shock hits the economy, and as a result the supply curve moves from A to B. Originally, this moves us from the point marked start, to the point marked NGDP. Under NGDP targeting, this is where the story ends, as we have moved along a line of constant NGDP. We have some slightly higher inflation, and a small decrease in output, but this output loss was inevitable, as the new supply curve goes vertical well below the original level of output. Under inflation targeting, the central bank now forces AD/NGDP onto a lower path, inorder to return the price level to its starting value, Pi. This cause output to drop from Yn to Yi. In the example that I have drawn, where the supply curve is fairly flat, the decrease in output needed to bring inflation back to its starting value was far larger than the original loss of output. This is the disaster scenario for inflation targeting, where a large loss of output is required to correct a small change in inflation. This is arguably what happened in the US in 2008, and almost certainly what happened to the Eurozone in 2011, where policy makers focused on inflation, traded catastrophic falls in output to a void small overruns in inflation.

Of course, if I had moved the start point up onto the nearly vertical part of the supply curve, then we could have traded a tiny loss in output for quite a large change in the price level. Arguably, this was the story of the 70;s and 80s, where they were in a reasonably high inflation regime, and this put them well onto the vertical part of the supply curve, this, huge changes in inflation translated into only small changes in output.

On more nice thing about this diagram: it makes it clear that what we actually have are two `real’ things, the supply curve, and the demand curve. But these are unmeasurable, and we can specify the outcomes (where the curves cross) using any two of NGDP, real output, and the price level. The price level/Real output specification seems to have an almost sacred place in economics. When given a choice of equivalent decompositions, it is almost always right to thing in terms of the things which are easiest to measure. Here that ist he Price Level, and NGDP. An independent measurement of real output is almost impossible, as it would depend on some kind of notion of intrinsic value, so in practice, RGDP is measured by applying an inflation correction to NGDP. By using a Y,P decomposition, you are cross-correlating your measurement errors.

Finally, NGDP targeting always leads to a smaller output gap but higher inflation than IT when faced with a supply shock. If we are on the flat part of the supply curve, that is a good thing, if we are on the vertical part of the supply shock, that is a bad thing. given the general downards stickiness of inflation despite enormous falls in output in the US, UK, and EZ, we are definitely on the flat part of the curve, and so should be looking to NGDP growth, rather than inflation, to guide policy.