Recursive Macroeconomic Theory

"Sargent went into the engineering literature, he took the tools and techniques that engineers use to do things like make sure your television is clear, and he brought them over into economics. There were all these tools that scientists were using to control systems. An engineer might build a TV that has a feedback mechanism. Somehow, it can look at the picture and if the picture isn’t right, it can go back and adjust the inputs in a way that clarifies it. If there is a horizontal scroll or a vertical scroll, it does something internally to stabilise the system, and makes sure it doesn’t get out of whack. All the same tools that engineers use to stabilise your television picture can be used to stabilise the economy. The difference – this is an important difference, and where Sargent’s contribution comes in – is that when I do something with a TV, it doesn’t try to get out of the way to protect itself. It doesn’t say, “Oh! I don’t like having a little more green in my colour, so I’m just going to turn it back down.” Unlike TVs, people have brains and they respond to policies. If you try to tax them, they try to get out of the way of taxes. If you try to tax a TV, it has no way of getting out the way. That’s where rational expectations comes in. When you’re trying to control a person instead of a TV, you have to take into account their expectations – how they’re going to respond to the things you do as a policy-maker. Sargent took all these tools and techniques for optimal control that were being used in engineering, all this heavy mathematics, brought it over into economics, added rational expectations to it which made it even more complicated mathematically and harder to use than it already was in the engineering literature. Yes. It wasn’t so much that he was this grand theorist – although he is certainly good at that – it was more the tools and techniques that he brought to the profession. He gave us the tools and techniques we need to analyse the crisis and build the models that we need to build to understand it. But it’s not as though he built those models themselves. He built the hammer, not the house. This is the textbook I use in my PhD macro courses. In fact, it’s used in almost all of the major PhD programmes in the US right now – any respectable programme most likely uses this book. It’s a book of tools and techniques to solve what are called recursive macroeconomic models. Modern macroeconomics uses DSGE models – dynamic stochastic general equilibrium models. That’s a bit of a mouthful, but all dynamic means is that it’s a model which explains how things move through time. So it explains what GDP will be today, tomorrow, the next day and the day after that, and how it might change if the government does different things or if certain things happen in the economy. It’s really a model of how the economy transitions from one point to the next – how it goes into recessions et cetera. Those models are extraordinarily difficult to solve. What this book shows us – and this is the recursive part in the title – is a way of breaking down this really hard problem into little tiny pieces. You can actually solve a much simpler problem when you only have to look at how the economy moves from today to tomorrow. I don’t have to look at how it moves from tomorrow to the next day and all the way out as far as I can see. We can break down these really hard problems into a recursion between today and tomorrow. It’s probably one of two. In macro there really aren’t very many. There’s this book, and there’s a book by David Romer of Berkeley. So this is sort of the Bible right now."

"It is a way of recasting any dynamic problem in macroeconomics in a specific analytical way, that is called a recurse. It is the book over which generations of PhD students in macroeconomics have sweated blood. And any good book for PhD students in macroeconomics should be stained with sweat and blood, because it needs to be highly technical. This book is. “Any good book for PhD students in macroeconomics should be stained with sweat and blood” It’s really difficult from a mathematical point of view. Doing the problem sets is like writing papers. Going through each chapter and then the problem set of the chapter is really challenging and it takes a long time. To cut a long story short, it’s probably the most technical and difficult book you can think of if you want to study macroeconomics. But, obviously, it is the one that pushes you at the frontier. If Romer was the introduction to the frontier in a very broad sense, this one really is the frontier, but in a very narrow sense. The book covers a wide range of topics, but all the topics that the book covers can be recast in this particular analytical form that is called ‘recursive’. Yes. And understanding how you can apply those tools in specific contexts and to particular problems. How, for example, if there are missing markets in insurance, and you cannot insure against a state of the world, you can use these recursive methods to find the solution to that."