The Perplexing Problem Of Credit In Macro

One of the major issues with the internal logic of neoclassical macro is the handling of credit risk. The problem of credit is acute for Dynamic Stochastic General Equilibrium models because they are allegedly based on “microfoundations.” However, the theoretical problems remain for any aggregated mathematical model. The advantage of heterodox economists is that they do not make a big deal about the alleged internal consistency of their mathematical models, and so they are more willing to hand wave around the issue.

Towards A MVP ABM

I have been catching up on some of my programming backlog, and I think I am in position to aim for a minimum viable product (MVP) version of my Python agent-based model (ABM) project. The figure above shows the visible progress made so far — which is not not at first glance an economic simulation. (In case you are wondering, the green balls are planets, and the blue box is supposed to be a spaceship flying between them. Or the balls could be island cities in an ocean at night, and the blue box is a container ship. Whatever.)

The challenge I face with this project is that every single aspect can explode in complexity, and so I can be paralysed by the need to deal with every potential quirk in the simulation. For this reason, I need to force myself to aim at a MVP, and worry about the cut corners later.

Parameter Uncertainty Is Not The Same Thing As Model Uncertainty

One way to model model uncertainty is to have uncertainty about model parameters. Although there can be times where this technique is adequate, it does capture the true nature of model uncertainty. Model uncertainty refers to situations where a baseline model is missing dynamics found in the real world system. Ideally, analysis should be robust to this type of uncertainty.

The Perils Of Non-Causal Models: r* Edition

One important property of time series is models is whether they are causal or non-causal. A non-causal model has the property that future values of inputs affects the current values of outputs. For time series, the calculation implies the use of a time machine, which is generally not available. One needs to be careful of the issues posed by non-causality in financial model building, since time series libraries treat time series as single units, and contain many non-causal operations. However, as I discovered the hard way, the Holsten-Laubach-Williams (HLW) model is non-causal, and the 2020 spike causes some serious issues (figure above). I previously analysed the model, but had not realised the magnitude of the problem associated with 2020. Although my qualitative analysis was not greatly affected, the charts were perhaps too sensationalistic. 

Falling r* Is No Accident

A great deal of significance has been attached to the fall in r*, which is the current preferred term for what was known as the natural rate of interest. My belief is that this fall is not due to structural factors in the real economy, rather it is an artefact of the means of estimating r*, as well as the reaction function of New Keynesian central bankers.

Nonlinear Models Give No Escape From r*

The dynamic stochastic general equilibrium (DSGE) model literature is ever-growing, and new features are being continuously added. This makes it difficult to make generalisations about the literature. However, from a macro modelling perspective, we are mainly interested in models that might be used by a central bank to set interest rates. Even if we are not central bankers ourselves, we presumably want to understand how central bankers see their policy lever as working.

In an earlier article (link), I discussed how all linear models end up with a notion that there is a "neutral" interest rate at any given time -- a policy rate which does not lead the economy to accelerate in one direction or another. If we add standard assumptions made by neoclassical economists, we can get to the concept of r* -- which is a steady state neutral rate. (If we are away from that steady state, the neutral rate within a linear model at any given time is determined by the deviations of other values from their steady states.)

Empirical Testing Of Macro Models

From a bond market practitioner's perspective, model testing is straightforward: does it make money? The ability to make money after model implementation (and not just "out of sample") is a simple quantitative metric -- although one might need to wait for a large enough sample to test this. Not everyone is a market participant, and they want to evaluate models on other metrics (e.g., does it help guide policy decisions?). However, the key insight of the "does is make money?" metric is that it is related to the more vague: "does it offer useful information about the future?" It is entirely possible for a model to have some statistical properties that are seen as "good" -- yet offer no useful information about the future. 

All Road Lead To r*

One of the major theoretical tasks facing neoclassical economists is the estimation of the variable r*, which is similar to what was termed the natural rate of interest. This concept has a long history, and as will be discussed here, this will continue so long as mainstream economics bears any resemblance to the current consensus theory. The reason is straightforward: if one assumes that the real rate of interest is a major driver of economic outcomes, we need to estimate what the neutral position of the control variable is.

Primer: Teaching Models Versus Empirical Models

I divide macroeconomic models into two classes: teaching models, and empirical models. Teaching models are far more common, and most economic arguing about these models. An alternative name for them is "toy models," which points to the weakness of this class. They are not fit to real-world data, and so there is no reason to expect them to offer useful predictions. More dangerously, the class of teaching models is so wide that almost all scenarios can be seen as the result of such a model (barring things like violating accounting identities). This explains why we can find neoclassical economists arguing the opposite sides of political issues, despite being in the same theoretical school of thought. Empirical models offer predictive content, and to what extent they are accurate, can possibly offer concrete estimates of the trade-offs between policy choices. The problem is that fitting these models to data is difficult. Certain teaching models can be fit to data -- and thus fall into this class -- but one needs to be very careful about what model we are talking about.

Arbitrage-Free Pricing For Linear Instruments

The core of any fixed income pricing model is a yield or discount curve. The discount curve allows for arbitrage-free pricing of all instruments without optionality -- which I refer to here as linear instruments (which may be a slight bending of terminology). Instruments with optionality are nonlinear instruments, which add considerable complexity to fixed income option pricing. This article discusses the properties of the part of the model that prices the linear instruments. Since the linear pricing is only dependent upon the expected value of the probability distribution -- and not the shape of the distribution -- it is unaffected by option pricing, and so it can be fitted before attempting to price options.

Arbitrage In Practice And Theory

 Arbitrage is a core concept in financial mathematics, and often comes up in discussions about markets. Although it is a key concept for pricing securities, the practical applications are more limited -- since dealers do not set prices in a way to set themselves up to be arbitraged. 

The textbook "The Mathematics of Financial Derivatives: A Student Introduction" by Paul Wilmott, Sam Howison, and Jeff Dewynne (Amazon affiliate link) is a standard introductory text, and describes arbitrage in the following fashion.

This [arbitrage] can be loosely stated as "there is no such thing as a free lunch." More formally, in financial terms, there are never any opportunities to make an instantaneous risk-free profit. (More correctly, such opportunities cannot exist for a significant length of time before prices move to eliminate them.)

Macro Models Aren't Useful Now, And That Is Perfectly Fine

There has been a small flurry of publications by neoclassical economists attempting to fit a pandemic into standard frameworks. This is what to be expected, as neoclassical models are frameworks designed to maximise the amount of publications over time. However, aggregated models are not particularly useful right now. This is true both for neoclassical as well as traditional heterodox macro models. The reason is that they do not offer much insight into either forecasting, nor are they useful for policymakers. That will change, but we are not there yet.

Interesting Article On Mathematics Of Community Transmission

I ran into an interesting paper on community-based analysis of the COVID-19 virus by Alexander F. Siegenfeld and Yaneer Bar-Yam*. Since I assume that at least some of my readers enjoy looking at mathematical models, this paper may be of interest.

MMT And Policy Variables

One of the distinctive features of Modern Monetary Theory (MMT) is the choice of variables used by policymakers to guide he economy. The choices are unconventional: interest rate policy is downplayed or even eliminated, while the requisition price used by the fiscal arm of government is emphasised. This can be seen in the structure of the Monetary Monopoly model (link).

The Monetary Monopoly Model

What I refer to as the Monetary Monopoly Model is the simplest possible mathematical model that captures basic concepts from Modern Monetary Theory (MMT). Despite its simplicity, it gives a good feeling of how a sovereign could pin down the value of a brand new currency (relative to existing currencies, or the value of real goods or services). However, the model makes almost no assumptions about private sector behaviour, and such assumptions would be needed to simulate an existing industrial capitalist society. The reason to start with this model is that the discussion of those behavioural assumptions will drown out the MMT-specific parts of the model.

Why Rate Expectations Dominates Bond Yield Fair Value Estimates

Although there are various attempts to downplay rate expectations as an explanation for bond yields. the reality is that they dominate any other attempt to generate a fair value estimate by using "fundamental data". (Since we cannot hope to explain every last wiggle of bond yields without having a largely content-free model, we need to look at fair value estimates.) The reasoning is rather straightforward: so long as the risk free curve slope is related to the state of the economy, bond yields are pinned down by the front of the curve, and the slope.

Primer: Causality In Models

One important consideration for indicator construction is the notion of causality (using systems engineering terminology). A non-causal model is a model where the output depends upon the future values of inputs. In the absence of access to a time machine, such a model cannot be directly implemented in the real world. In practice, a non-causal model output is “revised” as new datapoints are added to input series. The result is that we cannot use the latest values of the series to judge the quality of previous “predictions” of the model.

Quick Update On Recession Probability Models

This is a short update of an article I wrote on activity-based recession probability models (link). The difference between this class of models and those relying on forward-looking information is better underlined as a result of recent events. Activity-based models are much less jumpy than those that rely on the yield curve (for example).

Recession Probability Forecasting Models

This article discusses a wide class of models: models which attempt to offer a recession probability estimate, based on variables that are not just aggregate activity variables. Models with inputs that are aggregate economic variables were the subject of a previous article and can be viewed as offering an alternative recession definition. Therefore, they are essentially coincident indicators of recessions – although they might offer a recession diagnosis earlier than “official” recession determinations are made. Instead, the models of interest here are those that use variables that are believed to have some leading information, and so can offer an inflation forecast ahead of the actual recession start.

(Note: This is an unedited excerpt of a section of a manuscript of the first volume of a book on recessions. It is an expanded version of a previously published article on my website.)

Recessions As A Random Walk

One possible way of viewing recessions is that they are essentially a form of a random walk. We can imagine that the economy can transition to a "low growth" state, and then it is easier for random fluctuations to result in a recession. This is often referred to as the economy being near its "stall speed." (An aircraft that drops below its stall speed cannot generate enough lift from its wing surfaces to overcome gravity.) This is a plausible way of looking at empirical recession models, but it dodges the theoretical question as to why the fluctuations happen.