This is week four of my posts featuring research presented at the conference on Applications of Behavioural Economics, and Multiple Equilibrium Models to Macroeconomics Policy Conference held at the Bank of England on July 3rd and 4th 2017.

Today’s memo features two economists working on models of multiple equilibria from different perspectives. George Evans is a pioneer in models of adaptive learning, a topic he has worked on for more than thirty years. George presented his joint work with Seppo Honkapohja, Deputy Governor of the Bank of Finland, and Kaushik Mitra, Professor of Economics at the University of Birmingham. Patrick Pintus, a Researcher at the Banque de France, presented a co-authored paper with Yi Wen, an Assistant Vice-President at the Federal Reserve Bank of St. Louis and Xiaochuan Xing from Yale University. The papers presented by both of these authors make small changes to a relatively conventional monetary Dynamic Stochastic General Equilibrium (DSGE) Model. Both of them reach non-mainstream conclusions by exploiting the fact that monetary equilibrium models always contain multiple equilibria.

George Evans began his work on adaptive learning in his Ph.D. dissertation at Berkeley in the early 1980s. When the rest of the profession was swept up by the rational expectations revolution, George persevered with the important idea that perfectly correct beliefs about the future cannot be plucked from the air, they must be learned. For an introduction to George’s work, I highly recommend the book co-authored with his long-time co-author, Seppo Honkapohja.

The paper of Evans, Honkapohja and Mitra (EHM), begins with a theme we met in post two where I discussed the fact that the standard New Keynesian model, in which the central bank follows a Taylor Rule, has two steady state equilibria. The intellectual foundation for that idea comes from the work of Jess Benhabib, Stephanie Schmitt Grohé and Martín Uribe, (BSU). BSU pointed out that the money interest rate cannot be negative. It follows from that observation that the Taylor Rule must be non-linear.

The evidence for multiple steady states is presented in Figure 1 which is taken from George's paper. The dashed line is called the Fisher equation, after the American economist Irving Fisher. This graphs the relationship we would expect to hold between the money interest rate and the inflation rate if the real interest rate is constant. The solid line is an estimated Taylor Rule that takes account of the non-linearity in the central bank’s response to inflation that arises from the existence of the lower bound. A steady state is an inflation rate and an interest rate that satisfies both of these equations. Notice that these two curves intersect twice, one at an interest rate of roughly 2.5% and one with an interest rate close to zero.

Evans, Honkapohja and Mitra (EHM) build on this idea by adding a theory of adaptive learning. I am often asked how my own work on the belief function is related to George’s work on adaptive learning. They are very closely linked. I agree with George that expectations, aka beliefs, are not plucked from the air. They must be learned. In models where there is a continuum of equilibria, like the ones I work with, it is beliefs that select which equilibrium will prevail. George’s work on adaptive learning provides a micro-foundation for what I have called the belief function.

Previous work has shown that, in the basic New-Keynesian model, the upper steady state is stable under adaptive learning but the lower steady state is not. They modify the basic model by adding the assumption that the rate at which prices and output can fall has a lower bound. They show that this assumption implies that there exists a third steady state in which recessions can be persistent and deep.

Figure 2 illustrates the dynamics that arise from adaptive learning in their model. The three steady states, A B and C are respectively the target 2% inflation steady state, the zero-lower bound steady state and the deflation steady state that arises from EHM’s assumption that deflation is bounded below. Importantly, steady states A and C are stable; steady state B is not. Most of the time, the economy is hit by shocks that keep it in region A. But occasionally a large shock, like the Great Recession, knock it over into region C and, when that happens, it may be very difficult to escape.

George and his co-authors use their analysis to argue that a large fiscal intervention, a short-sharp shock, can knock the economy out of region C and back into region A. Readers of this blog will know that I have expressed scepticism of that idea in the past, largely because I am not a big fan of the basic NK model. However, this is the most convincing rationale in favour of a large fiscal stimulus that I have yet seen. The mechanism that ESM propose works by permanently shifting expectations; that mechanism is likely to be at work in many economic models and I am pleased to see the George’s agenda is once again getting exposure. If you are a young researcher who is thinking of working in macroeconomic theory and policy, consider working on models of expectations formation.

Next, I will turn to the work of Patrick Pintus, Yi Wen and Xiaochuan Xing (PWX). I have been a fan of Patrick’s work since he was a graduate student in Paris working with Jean-Michel Grandmont and I have followed Yi Wen’s papers closely since we first met at a conference in New York many years ago. Yi wrote the state of the art paper on why models of increasing returns to scale should be taken seriously and it is no surprise that a collaboration that involves the two of them would produce ideas worth listening to. This is my first exposure to Xiaochuan Xing, and I am sure we will hear much more of him in the coming years.

PWX take up a puzzle that has long been known to plague the equilibrium real business cycle (RBC) model that has dominated macroeconomic theory for more than thirty years. That model predicts that when interest rates are high, the economy will soon enter an expansion. The reality is different. High interest rates are an omen that a recession is coming down the road. What are the features of the real world that are missed by the classical RBC paradigm?

PWX relax the RBC model in two ways. First, they introduce the realistic assumption that it is difficult or impossible to borrow in large amounts without providing collateral. Second, they recognize that many loan contracts are arranged with variable-rates as opposed to fixed-rates. By combining these two assumptions with an otherwise standard business cycle model, they arrive at a model where many different outcomes can occur in equilibrium. The alert reader will by now, have picked up the theme: this is a model with multiple equilibria where outcomes are driven by beliefs.

The fact that PWX are able to construct a theoretical model with multiple equilibria is a first step: But does this model help to explain data? Until recently, much of the work on multiple equilibria consisted of esoteric calibrated theoretical models. The reason for that was two-fold. First, most graduate students were not exposed to the potential for multiple equilibrium models to explain data. And second, the techniques that were available to confront those models with data had not been developed. That began to change when Thomas Lubik and Frank Schorfheide showed in 2004 how to estimate a model with a set of indeterminate equilibria. That agenda was advanced further when Farmer, Khramov and Nicolò (FKN) developed a simple method for implementing their idea using standard software packages. FWX use the FKN technique to estimate their model using US data and they find that roughly 25% of the variance in GDP is caused by animal spirits. You can hear Patrick discuss these ideas in the video linked above.