Policy makers at central banks have been puzzled by the fact that inflation is weak even though the unemployment rate is low and the economy is operating at or close to capacity. Their puzzlement arises from the fact that they 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.

In a recent paper joint with Giovanni NicolÃ², we compared two models of the interest rate, the unemployment rate and the inflation rate. One theory, the NK model, consists of a demand equation, a policy rule and a Phillips curve. The other, the Farmer Monetary (FM) model, replaces the Phillips curve with a new equation: the belief function. We show that the FM model outperforms the NK model by a large margin when used to explain United States data.

To make this case, we ran a horse race in which we assigned equal prior probability to two models. One was a conventional New Keynesian model that consists of a demand equation, a policy rule and a Phillips curve. The other was the FM model. The FM model shares the demand curve and the policy rule in common with the NK model but replaces the Phillips curve with a new equation; the belief function.

The belief function captures the idea that psychology, aka animal spirits, drive aggregate demand. It is a fundamental equation with the same methodological status as preferences and technology. To operationalise the belief function, we assumed that people make forecasts of future nominal income growth based on observations of current nominal income growth. If *x* is the percentage growth rate of nominal GDP this year and *E*[*x*â€™] is the expected rate of growth of nominal GDP growth next year we assumed that *x* = *E*[*x*â€™].

We estimated both models using Bayesian statistics and we compared their posterior probabilities. Our findings are summarised in Table 2, reproduced from our paper. The table reports what statisticians call the posterior odds ratio. As is common in this literature, we compared the models over two separate sub-samples; one for the period from 1954 to 1979 and the other from 1983 to 2007. Our findings show that an agnostic economist who placed equal prior weight on both theories would conclude that the FM model knocks the NK model out of the ball park. The data overwhelmingly favours the FM model.

We explain our findings in the paper by appealing to a property that mathematicians call hysteresis.

Conventional dynamical systems have a stable steady state that acts as an attractor. The economy will converge to that steady state, no matter where it starts. The FM model does not share that property. Although the economy follows a unique path from any initial condition, the FM model has a continuum of possible steady states and which one the economy ends up at depends on initial conditions.

The FM model explains the data better than the NK model because the unemployment rate in US data does not return to any single point. In some decades, the average unemployment rate is 6%: in others, it is 3%. And in the Great Depression it did not fall below 15% for a decade. The unemployment rate, the inflation rate and the interest rate are so persistent in US data that they are better explained as co-integrated random walks than as mean-reverting processes. The FM model captures that fact. The NK model does not.

What does it mean for two series to be co-integrated? I have explained that idea elsewhere by offering the metaphor of two drunks walking down the street, tied together with a rope. The drunks can end up anywhere, but they will never end up too far apart. The same is true of the inflation rate, the unemployment rate and the interest rate in the US data.

As I have argued on many occasions, the NK model is wrong and there has been no stable Phillips curve in the data of any country I am aware ever since Phillips wrote his eponymous article in 1958. My paper with Giovanni provides further empirical evidence for the Farmer Monetary Model, an alternative paradigm that I have written about in a series of books and papers. Most recently, in Prosperity for All, I make the case for active central bank intervention in the asset markets as a complimentary approach to interest rate control.

In a separate paper, Animal Spirits in a Monetary Model, Konstantin Platonov and I have explored the theory that underlies the empirical work in my joint work with Giovanni. The research programme we are engaged in should be of interest to policy makers in central banks and treasuries throughout the world who are increasingly realising that the Phillips curve is broken. In Keynesian Economics Without the Phillips Curve, we have shown how to replace the Phillips curve with the belief function, an alternative theory of the connection between unemployment and inflation that better explains the facts.