Inflation beliefs

One of the biggest apparent puzzles in macroeconomic policy today is why inflation remains so low when the unemployment rate is at multi-decade lows. The evidence clearly suggests that the trade-off between inflation and unemployment is far weaker today than it used to be or, as the economics profession would have it, the Phillips curve is flatter than it once was (here). But as the academic economist Roger Farmer has pointed out, the puzzle arises “from the fact that [central banks] are looking at data through the lens of the New Keynesian (NK) model in which the connection between the unemployment rate and the inflation rate is driven by the Phillips curve.” But what if there were better ways to characterise the inflation generation process?

Originally, the simple interpretation of the Phillips curve suggested that policymakers could use this trade-off as a tool of demand management – targeting lower (higher) unemployment meant tolerating higher (lower) inflation. However, much of the literature that emerged in the late-1960s/early-1970s suggested that demand management policies were unable to impact on unemployment in the long-run and that it was thus not possible to control the economy in this way. The reason is straightforward – efforts by governments (or central banks) to stimulate the economy might lead in the short-run to higher inflation, but repeated attempts to pull the same trick would result in a response by workers to push for higher wages which in turn would choke off labour demand and raise the unemployment rate. In summary, government attempts to drive the unemployment rate lower would fail as workers’ inflation expectations adjusted. One consequence of this is that the absence of any such trade-off implies the Phillips curve is vertical in the longer-term (see chart).

Another standard assumption of NK models, which are heavily used by central banks, is that inflation expectations are formed by a rational expectations process. This implies some very strict assumptions about the information available to individuals and their ability to process it. For example, they are assumed to know in detail how the economy works, which in modelling terms means they know the correct structural form of the model and the value of all the parameters. Furthermore they are assumed to know the distribution of shocks impacting on the economic environment. Whilst this makes the models intellectually tractable, it does not accord with the way in which people think about the real world.

But some subtle differences to the standard model can result in significant changes to the outcomes, which we can illustrate with regard to some recent interesting work by Roger Farmer. In a standard NK model the crucial relationship is that inflation is a function of expectations and the output gap, and produces the expected result that the long-run Phillips curve is indeed vertical. But Farmer postulates a model in which the standard Phillips curve is replaced by a ‘belief’ function in which nominal output in the current period depends only on what happened in the previous period (known as a Martingale process). Without going through the full details (interested readers are referred to the paper), the structure of this model implies that policies which affect aggregate demand do indeed have permanent long-run effects on the output gap and the unemployment rate, which is in contrast to the standard NK model. Moreover, Farmer’s empirical analysis suggests that the results from models using belief functions fit the data better than the results derived from the standard model.

The more we think about it, the more this structure makes sense. Indeed, as an expectations formation process, it is reasonable to assume that what happened in the recent past is a good indicator of what will happen in the near future (hence a ‘belief’ function). Moreover, since in this model the target of interest (nominal GDP) is comprised of real GDP and prices, consumers are initially unable to distinguish between real and nominal effects, even though any shocks which affect  them may have very different causes. In an extreme case where inflation slows (accelerates) but is exactly offset by a pickup (slowdown) in real growth, consumers do not adjust their expectations at all. In the real world, where people are often unable to distinguish between real and price effects in the short-term (money illusion), this appears intuitively reasonable.

All this might seem rather arcane but the object of the exercise is to demonstrate that there is only a “puzzle” regarding unemployment and inflation if we accept the idea of a Phillips curve. One of the characteristics of the NK model is that it will converge to a steady state, no matter from where it starts. Thus lower unemployment will lead to a short-term pickup in wage inflation. Farmer’s model does not converge in this way – the final solution depends very much on the starting conditions. As Farmer put it, “beliefs select the equilibrium that prevails in the long-run” – it is not a predetermined economic condition. What this implies is that central bankers may be wasting their time waiting for the economy to generate a pickup in inflation. It will only happen if consumers believe it will – and for the moment at least, they show no signs of wanting to drive inflation higher.