Reddit reviews Recursive Macroeconomic Theory

"Saltwater" and "freshwater" are terms that grew out of the late 1970s and early 1980s and reflected substantive disagreement in macroeconomic modeling and methodology.

"Freshwater" schools were located near the Great Lakes and included Minnesota, Chicago, Rochester, Carnegie-Mellon, and Penn. These schools focused their training on dynamic macroeconomic models and emphasized rigorous microfoundations and then-cutting-edge mathematical techniques. Their models tended to be broadly "conservative" in their policy implications.

"Saltwater" schools were located on the coasts and included Harvard, MIT, Berkeley, and Stanford. These schools favored a more ad-hoc approach to macroeconomic modeling and were slower to adopt cutting-edge mathematical techniques. Because their models admitted "Keynesian" features more easily, their policy prescriptions tended to be more interventionist than their freshwater counterparts.

This all basically vanished by the mid-1990s, where the freshwater guys won on technique and the saltwater guys won on substance. Everyone now learns the dynamic mathematical tools in their first year and learns a healthy mix of modeling techniques, and everyone learns standard New Keynesian models that were initially developed in saltwater schools.

The terms just aren't meaningful now - there has been convergence in technique and there is more agreement on what constitutes policy-relevant modeling. That's not to say that "all is well" in macro-land, but it is to say that graduate training in the field has largely moved on. There are some holdouts. "Minnesota Macro" (that is, the ethos of the freshwater school) remains alive and well at, um, the University of Minnesota.

But you're going to use Sargent-Ljungqvist (a quintessential "freshwater" book) in your first year and Woodford (a solidly saltwater text, but with all the dynamic math) in the money block or in your second year, pretty much wherever you go to school.

A good popularly-accessible book-length treatment of these issues is available in David Warsh's Knowledge and the Wealth of Nations, which I highly recommend to those who are interested in the history of modern economic thought.

Oh boy, this shall be fun, it's a little disappointing that people are downvoting this, as I think it's a fairly reasonable question given the idea's spat out about economics from politicians and journalists.

Edit (this paragraph is the edit, not the huge wall of text, that was always there): Also I think one of the other problems seen is often it's not actually the economists who even get to make the important decisions in the end, time after time I have seen politicians implement policies that economists will repeatedly facepalm over. My biggest issue with modern day politics is that it is a popularity contest, rather than vote between the most qualified people of who we think could do the right job, we vote mostly on unqualified people who we think would do the least bad job, or for most people, who they think appeals the best to their self interests. I don't have a perfect solution, but fuck, there must be a better way.

(also part of edit) I guess you also have the problem of the agenda of the economist, are they trying to optimise social welfare, their own interests, or the interests of someone providing for them by other means.

I myself am still only an undergraduate, I graduate at the end of this year with majors in analytical economics, computer science and pure mathematics. Next year I am doing an honours year in just mathematics, followed possibly by a 2 year masters in the same three area's my undergrad is in, then I'm not really sure what I will do my PhD in yet, other than the topic will most probably be on game theory. I also work as a research assistant for a somewhat well known macroeconomist at my uni who also has a research position at Cambridge (they're actually over there for a month at the moment).

What I will say I have come to find holds across all fields of science, only in the social sciences there seems to be a greater number of pseudoscientists (my personal branding of them). Basically, any of the topics termed a science, whether they be a natural or social science, are really complex. Most of the mathematics scientists find useful can be used across any of these fields, and one can't necessarily say that a physicist is smarter than say a political scientist, or that the work the physicist is doing is harder than that of the political scientist.

One can however, obviously, point out that the average (take any measure of that you want) person that studies physics is generally smarter, knows a lot more maths etc. than the average political science or economics student (hell, I even think the average economics student learns a lot more than the average political science student). I think this is sad, I don't necessarily expect quite the same level, but people are given economics degree's these days without even taking a multivariable calc course, that should be illegal! (only half /s).

Okay, now to kind of move onto what you were asking. If you want resources that debunk economic models, then you merely need to find an economic model you have a problem with and search for criticisms of that, I expect it works much the same for any other science.

If you as a mathematician were interested in actually learning a bit about how real economists model different aspects of the economy, here is a bit about some of the main subject areas (there are a lot of sub-areas to these and somewhat large area's that fit into multiple or none of the areas well), any of the texts linked you could acquire off rapidlibrary for a look if you want, or should be in the library of any uni you are at.

One must remember that economics deals with a subject that has a lot of randomness (much like biology, giving a natural science counterpart), so a lot of the models don't give an exact answer, or even model anything that you can assign good specific numbers to, a lot of the time you are just trying to model as many of the effects of different things as you can, then trying to see what happens when you control certain things like interest rates, or how consumers can optimally make decisions etc.

Microeconomics tends to deal with the economic decisions faced by individual entities, whether it be people/consumers or firms/producers etc. This is where game theory is probably used more than any other area of economics, but it certainly isn't the only area.

Consumer theory is basically built up on the idea of utility, which is basically defined as someone's "enjoyment" of consuming something (one can have negative utility for something, sometimes referred to as a bad rather than a good for obvious reasons). Utility is only defined to be ordinal, so one can say someone strictly prefers one good to another for example, but not that they like it twice as much or anything like that.

Utility also has to satisfy a few assumptions (which is where it is mostly criticized) for the theory that gets developed to mostly hold, but on the most part they aren't too bad if the person is actually trying to make an optimal decision, they are things like preferences should be complete, transitive, consistent etc.

One of the simple first models one would be taught in microeconomics is that of a simplified world where there is one consumer trying to pick a consumption bundle out of 2 existing goods that will maximise their level of utility (very straight forward constrained maximisation problem). If you ever hear someone say that microeconomics is just one simple constrained optimisation problem, it's because they are under the impression that "microeconomics == n-good utility maximisation problem", which it is not.

A lot of the main theory for micro now works with general equilibrium models, which has n-consumers and n-producers. The maths for this gets rather messy, and I wont try to explain it here, if you want to learn more about microeconomics with a background in mathematics I would suggest you pick up Microeconomic Theory. This is essentially the text used by most post grad micro courses at the better universities.

Macroeconomics tends to deal with the aggregate effects in economy. What's going on with the interest rate/price level, what is the aggregate level of income inside the economy, what is the average level of welfare for a person. For example a model I did in my third year macro unit was the central banks problem of setting the interest rate to help optimise an objective of the bank. Basically the bank has a target interest rate and target level of output, then it models the effects in the economy (which direction the forces are on inflation and output, given any output gaps and the interest rate) and sets the interest rate to minimise the weighted sum of difference from target inflation and target output. Looking back it was very much an optimal control problem in disguise.

From what I have been able to gather (I have managed a postgrad micro unit during undegrad but not macro) most of modern day macro models are built up using dynamic programming methods (I just took a course on calculus of variations with a large chunk on optimal control theory which was awesome, I love it). If you want to learn more about that go look at Recursive Macroeconomics.

Game Theory (which you might have actually learnt something about) is also vital for modern economic theories, as essentially it is the study of agents optimal decisions when interacting with other self thinking agents. This is where my main interest is along with micro, if you wanted to learn about this I would suggest Myerson's Analysis of Conflict book, or possibly Fudenberg or Tiroles, as it covers more, but I don't think it's as good for an introduction, and trust me, game theory takes a bit of work to learn properly.

There are many different kinds of games, strategic deals with situations where all players make their move (surprise) simultaneously, extensive form will allow turn based games. Then you have a whole array of others, Bayesian games deals with players having multiple possible types, differential games is basically multiplayer optimal control theory (set of state variables and control varaibles, each player tries to find optimal control function given others will be doing the same to maximise their utility of the terminal state), stochastic games is similarly pretty much multiplayer dynamic programming I think.

Like I previously mentioned, game theory is my main love, I am currently working on a fairly large game theory library in c++ which I'm hoping may end up being the standard tool for research in game theory, and economics certainly isn't the only area currently interested in game theory, there are biologists, computer scientists, mathematicians, political scientists etc. that are doing research with it as well. (<3 Von-Neumann!).

Where are you in economics right now? Undergraduate? Graduate?

Advanced mathematics appears everywhere in economics, though your mileage may vary depending on your definition of "advanced". As a mathematician, I suspect that quantitative finance contains the most advanced mathematics, since in modern mathematics research the majority of interaction with economics is through quantitative finance. But unless you plan on doing the most advanced math, there's more than enough advanced math in non-finance economics to keep you interested.

Generally speaking, professional economists build up some skill in real and functional analysis, as well as a variety of other skills like optimization, stochastics, and PDEs, depending on their specific research interests. These are all graduate-level math topics, so I'd consider them reasonably advanced. Take a look into econ PhD prelim coursework. When I took the sequence, we used the texts Microeconomic Theory by Mas-Colell-Whinston-Green, Recursive Macroeconomic Theory by Ljungqvist and Sargent, and Econometrics by Hayashi. I think they're good springboards for you to evaluate the math in higher economics.

In quantitative finance, I'd maybe start by checking out Portfolio Risk Analysis by Connor, Goldberg, and Korajczyk, then if you're still interested, I'd pick up measure-theoretic probability. I recommend Probability with Martingales by Williams. Once you're comfortable with measure theory, look through Stochastic Calculus and Financial Applications by Steele. You'll very quickly enter the area of research mathematics while studying quantitative finance, e.g. jump-diffusion models and Levy processes appear in the pricing of exotic derivatives, and they're heavily studied by even pure mathematicians.

The standard grad school text these days for dynamic macro is Ljungqvist & Sargent's Recursive Macroeconomic Theory. You won't need to go through the whole thing necessarily, but to be able to tackle the Woodford book, I would think chapters 1-4, 7-8, 12-13, 16-17 and 24-26 would be quite helpful.

There's also Simon & Blume's Mathematics for Economists, which is a good reference book should you need it. For example, the discussion and motivation of Lagrange multipliers and the Kuhn-Tucker optimization conditions is very good.

One noteable omission from both of those books which you will likely encounter at some point is continuous-time optimization/optimal control. This topic is often covered in the appendices of various grad-level macro textbooks, but perhaps the best I've come across is Chapter 7 of Daron Acemoglu's Introduction to Modern Economic Growth. The appendix to Barro & Sala-i-Martin's Economic Growth also has some pretty good coverage.

By the way, if you hunt around, all of these textbooks can be found online for "free".

To add on. If you have a lot of math and are a bit of a masochist Sargent and Ljungqvist is the phd level standard.

For graduate (at quals-level) courses my undergrad institution used Mas-Colell, Whinston, and Green's Microeconomic Theory and Ljungqvist and Sargent's Recursive Macroeconomic Theory.

Yeah macroeconomics is a very chaotic field right now and it can be very overwhelming, especially when you are first starting out. If you are interested in DSGE and have a decent mathematics background, this book Recursive Macroeconomic Theory is a good starting point.

I would also add that you should ask your professors for input. They are usually very supportive and will help give you research ideas as well as to refine them.

http://www.amazon.com/Recursive-Macroeconomic-Theory-Lars-Ljungqvist/dp/026212274X/ref=sr_1_1?ie=UTF8&s=books&qid=1291526398&sr=1-1