I ran into a pair of articles about interest rates by neoclassicals. They are straightforward by the standards of neoclassical macro, and cover two topics of interest. The first topic is — how do neoclassicals believe that central banks control inflation? The second is on *r** estimates, which are presumably needed in order to use interest rates to control inflation according to the theory.Since I am supposed to editing my book and dealing with a new consulting project, I have had limited time to dig into these articles right now. I think they may be of interest to readers, and I hope to write more about them later.

## How Do Central Banks (Allegedly) Control Inflation?

Laura Castillo-Martinez and Ricardo Reis wrote a working paper “How do central banks control inflation? A guide for the perplexed.” Although the working paper was from 2019, it came up in discussion on Twitter. It has a fair amount of mathematics, but the mathematics is cleaner than most expositions of dynamic stochastic general equilibrium (DSGE) models. It achieves this by dropping the business sector, and just looking at how households allegedly maximise their utility.

I have a lot of complaints about most DSGE macro model mathematics which have both a household and business sector, but having just the household sector reduces the scope of neoclassicals to mangle the mathematics of optimal control. That said, I have severe concerns about a couple assertions at the beginning of the paper — before we get to what are viewed as the interesting bits. *(This is what happens in almost every DSGE paper that crosses my desk, so this is not in any sense a surprise. The fundamental problem of DSGE macro is that neoclassical economists borrowed the properly set out mathematics of optimal control theory, and are attempting to extend the theory to a problem that is not covered by the mathematics in the existing optimal control literature. They are happy to drown the reader in mathematics from optimal control, but invariably have a hard time setting up the mathematics of their problem. The reality that pretty much every one else fudges over the mathematical steps of the jump has meant that none of them even notices the issue, the usual reaction is “well, I think somebody did this properly somewhere in the literature,” which is not a statement one hears from pure mathematicians. This observation invariably gets neoclassicals extremely angry, as they are very certain of their grasp of higher mathematics, so I have largely given up on pursuing the topic.)*

If we put aside concerns about the mathematics, we have a survey of different theories as to how central banks stabilise inflation in DSGE models. For a person trying to decipher what neoclassical economists are banging on about, this might be a useful starting point.

Unfortunately for neoclassicals, explaining how central banks determine the inflation path in a household optimisation problem (if we believe the math!) does not immediately translate into how central banks influence inflation (or not) in the real world. Missing from the standard household optimisation problem are things like the external sector, capital investment, and even the housing market. Within the paper, there are assertions about “banks,” but it is unclear to me how “banks” fit into the mathematical model proposed. This is related to my mathematical concerns with the paper, but I would need to sit down with paper and pencil and trace through the mathematical logic before I can offer more detailed opinions. (To be less mysterious, I see an issue that I have run into before, but the authors proposed a different way of addressing the concern. Given the lack of mathematical precision in the statements detailing their fix, I would need to reverse-engineer their logic. Although most applied mathematics will use textual assertions as short cuts, the usual standard is to keep logic close enough to set theory to allow “reverse engineering” logic to be relatively trivial.)

The entire neoclassical theoretical edifice relies upon interest rates having a relatively strong and predictable effect on the economy. The article in question outlines various theories that result in that conclusion. The obvious concern to an outsider is whether these theoretical mechanisms empirically show up in observed data. The empirical side is beyond the scope of this paper (despite its rather expansive title). Despite the importance of this issue, I am unimpressed with the alleged empirical evidence, but I would need to bite the bullet and dig through more of the literature to see whether I can find anything that stands up to scrutiny. (One interesting observation is that many mainstream economists will loudly exclaim that the empirical evidence behind interest rate effectiveness is irrefutable, but they absolutely refuse to discuss the data demonstrating this, and instead just say “go read the literature.”)

## Worthwhile *r** Estimate

Katie Baker, Logan Casey, Marco Del Negro, Aidan Gleich, and Ramya Nallamotu recently published a (blog) article at the NY Fed: “The Post-Pandemic *r***” *The article is not mathematical, so it should be easy to follow. For those of you new to the topic, *r** can be thought of as the “neutral” or “natural” real rate of interest, but the neoclassicals finally moved away from the normative implications of the word “natural” and just went with a neutral-sounding symbol.

I wrote about *r** in 2020, at about the time its estimates blew up due to pandemic wackiness. The recent Fed article is a sign that *r** is now back.

Figure from NY Fed article – link above. |

In my previous article, I was looking at other estimation techniques. Why they blew up in the pandemic was pretty obvious to anyone familiar with those techniques. What is striking about the NY Fed article is that they refer to an estimate based on a “DSGE model,” that is described in a paper that I have not yet read. This estimate is quite different — it refers to a term structure, as is seen in the figure above. There are estimates for “short-term,” and various tenors (5-, 10-, 30-year).

Since I have not dug into the DSGE paper, I cannot offer much insight into the meaning of the above figure (e.g., what are the mathematical properties of these long-term estimates?). However, recent events are quite awkward for simple versions of *r**. Inflation peaked and turned around with real rates at quite negative levels. We are stuck with “real rates are extremely important for economies, but sometimes we need massive fudge factors to match observed behaviour.”