Dsge Wars (Again)

There's been a small-scale revival inwards the arguments some Dynamic Stochastic General Equilibrium (DSGE) models. My thinking on these models has evolved somewhat; I holler back they are non peculiarly interesting, but the arguments over at that topographic point utilisation are somewhat misplaced.

(I am getting laid upward to caput out to the Modern Monetary Theory conference inwards Kansas City, therefore my comments hither are brief.)

Recursive Macroeconomic Theory

I started reading Recursive Macroeconomic Theory by Lars Ljungqvist together with Thomas J. Sargent this throttle (northern hemisphere...), together with it answered some of the questions I had near the DSGE approach. Other projects had popped upward (plus travelling), together with therefore I suspended my DSGE studies. This article is an impressionistic summary of my thinking.

The approach yesteryear Ljungqvist together with Sargent is much cleaner than every other exposition of DSGE mathematics that I stimulate got seen. They brand clear the beginning mathematics behind DSGE macro -- optimal command theory. This is apparently attractive to soul alongside a doctorate inwards command systems theory.

Optimal Control Theory versus Economist Mathematics

There is a stark divergence betwixt the presentation inwards Recursive Macroeconomic Theory and most "introductory" DSGE texts. The optimisation problems to last solved is clearly stated inwards Recursive Macroeconomic Theory, together with the solution techniques to a greater extent than oft than non follow accepted mathematical norms. Meanwhile, criterion introductions correct downwards objective functions, together with blindly differentiate everything inwards sight, asserting that this leads to the optimal solution.

It is obvious that nosotros cannot rely on taking derivatives of objective functions inwards the presence of constraints. For example, allow us assume that nosotros wish to abide by the maximum of the business office f which is defined by:

f(x) = -(x-10)^2.

If at that topographic point are no constraints on the solution variable x, together with therefore nosotros tin differentiate f and present that x=10 equally the maximum. However, this does non apply if x is constrained to prevarication on on the interval [0,1], in which instance the maximum is x=1.

Therefore, nosotros withdraw to bring the diverse constraints on the optimisation employment seriously, together with that is non done inwards most of the treatments of DSGE macro I stimulate got run across. The proofs rely on the "Everybody Knows That Theorem," which is non a characteristic of existent academic mathematics. Conversely, Ljungqvist together with Sargent (generally) create non skip over the details.

In the side yesteryear side section, I volition hash out the "standard" DSGE approaches, together with and therefore instruct dorsum to Ljungqvist together with Sargent's text later.

Should We Care About DSGE Macro?

In practice, the DSGE macro methodology consists of:

• Decide upon the desired conclusions.
• Write downwards a complicated mathematical backstory that has lots of symbols together with fancy equations.
• Assume that the backstory leads to the desired conclusions.

Although this sounds extremely harsh, it is the only agency to depict aspects of DSGE macro such equally the supposition that the degree of involvement rates is a key determinant of economical behaviour. In practice, this supposition is built into all mainstream models, together with the empirical methodologies stimulate got no agency of rejecting the assumption. It is non only an accident that the consensus has been shocked yesteryear the tiresome stride of recovery after modern recessions -- after all, it was believed that the degree of involvement rates was "unsustainably low." Indeed, the natural charge per unit of measurement of involvement had to last revised lower inwards lodge for the information to gibe the theory.

In other words, the whole panoply of mathematics used is a gigantic scarlet herring.

From the perspective of wanting to empathize how the economic scheme functions, at that topographic point is only i existent question: are the desired theoretical outcomes of DSGE macro practitioners useful? The fact that DSGE macro is roundly ignored yesteryear everyone whose chore depends upon beingness correct near the economic scheme is in all probability the best respond to that question. (In theory, fundamental bankers are supposed to attention near beingness correct near the economy, but inwards practice, fifty-fifty the raw incompetence displayed heading into 2007 did non cutting into retired senior fundamental bankers' subsequent speaking fees.)

From the perspective of academic economics, it is an obvious employment that this methodology has to last used inwards the "top journals." This is only a surprise if you lot assume that the academic organization shows a vogue to progress towards the truth.

Recursive Macroeconomic Theory?

The outset chapter of Recursive Macroeconomic Theory is a "literary" description (their word) of how the authors consider what the whole signal of DSGE macro is. It does non look to stand upward for to how pretty much everyone else describes the debate. It is difficult to consider the methodology equally beingness apparently wrong, although that could last my bias equally a resultant of my background inwards command theory.

I prefer to provide to their arguments at a after time. However, I would debate that the weakness is the embedded supposition that the only agency to approach mathematical problems similar this is to cast them equally optimisation problem. That was the psychology of command systems applied scientific discipline inwards the 1960s, together with I nonetheless consider that mental attitude inwards some economists together with people inwards finance. Basically, you lot say that you lot are finding an "optimal solution," together with that is supposed to halt all debate on the query whether the solution is whatever good. The reality is that whatever solution is the "optimal solution" for some objective function, together with therefore nosotros withdraw to expect for to a greater extent than sensible determination criteria. Control applied scientific discipline dropped its infatuation alongside optimal command yesteryear the early on 1980s, together with therefore seeing economists favouring the approach is an intellectual fourth dimension warp for me.

The debates near methodology are interesting, but unlikely to last resolved. As for the mathematical treatment, fifty-fifty Recursive Macroeconomic Theory gets squirrely when confronting the expanse that I stimulate got the most complaints near DSGE mathematics: equilibrium. In Section 7.3, recursive competitive equilibrium is defined. It starts alongside a lot of mathematics, but fifty-fifty then, some economist hand-waving sneaks into the definition. They utilisation price that create non look to stand upward for to criterion mathematical concepts, together with promise the reader knows what they mean. Mathematics largely consists of statements near sets together with the holding of sets; it is unclear what laid properties they are describing at key sections of their definition.

I withdraw to provide to the text later, but I but wanted to highlight that fifty-fifty the cleanest flake of mainstream economist mathematics relies on organized faith beingness extended yesteryear the reader.

Concluding Remarks

It is unclear whether DSGE macro is worth studying. The mathematics is non clearly explained, together with it is unclear whether it bears whatever relation to the fourth dimension serial beingness studied. 

(c) Brian Romanchuk 2017