(There is some unavoidable overlap with my earlier article which discussed post-Keynesian critiques of mainstream thinking on inflation.)

## Introduction

The business cycle book is supposed to be written at a higher level than my previous books (excluding the upcoming breakeven inflation book). If I were to rate my books, almost all of the existing ones would be at the "introductory" level, and the existing SFC models, and upcoming breakeven inflation, and business cycles at the "intermediate" level. (My blog articles are mainly at the "introductory" level.)In my blog articles, I generally stay away from equations (other than very basic algebra), although I did go nuts at a few points. At the intermediate level, I will use equations where necessary; generally speaking, I am unconvinced about the use of mathematics to explain concepts (despite my applied mathematics academic training).

The discussion of neoclassical (DSGE) models is rather awkward. They involve a lot of equations, but as I discussed earlier, the mathematical conventions used by economists is at best awkward. I would only be happy if I translated the DSGE mathematics to what I see as the correct formalism, which raises all kind of technical issues.

Since my views about DSGE mathematics would be disputed by many mainstream economists, I will attempt to sidestep the debate. I will instead give what I view as a relatively sympathetic summary of standard macro models, and then discuss the issues for business cycle analysis.

## Prices at the Core of the Model

It is hard to generalise about DSGE models; academics and central bankers have been churning them out for decades. There are some standard classes of models, but any particular generalisation one can make is probably contradicted by some model in some sense. The summary here are generalisations about basic DSGE macro models based on a representative household, and they will largely apply in some sense to other major classes of DSGE models.The key in the neo-classical approach is that economic outcomes are the result of optimising decisions by economic entities (households, firms, government). Behavioural economics may muck things up, but even there, I think there are similarities to my description.

For a variety of reasons, much of the analysis is household based. Firms attempt to maximise profits, but they are typically assumed to be constrained by competition. Therefore, the driver for economic outcomes is household utility maximisation.

Households aim to maximise lifetime utility, where utility is derived from consumption. The models incorporate forward markets to create "dynamics," and so utility is also derived from expected future consumption (where expected is the usual mathematical definition of a probability-weighted average of future outcomes).

If we assume an individual is a price taker, they are confronted by a set of prices for all goods and services, now and in the future (including the dim future). They presumably have the ability to lock in their entire live's consumption habits by entering into forward contracts. (This obviously sounds ridiculous, but since these futures markets are never really fleshed out in the models, this assumption can be viewed as a mathematical convenience.)

What happens is that there is a key decision: does the household spend money *now* for goods and services, or save to purchase goods and services in the next (or later) accounting period? We end up with trade-offs:

- the price of goods now versus their expected price in the next period (equivalently, the inflation rate);
- the ability to save at a nominal interest rate;
- the loss of utility from the time-discounting in the utility function.

In summary, expected inflation is going to be related to the relative desire to defer consumption.

## Equilibrium Discontents

The next leg of mainstream thinking is the issue of equilibrium. This is an old area of contention in economics. The only observation I can offer is that I have no seen a convincing definition of equilibrium that applies to a multi-sector economy. (That is, it is easier to define equilibrium if we have a model that consists only of households, or only firms, but things break down when we try to stuff both types of entities in the same model.)Mainstream economists will probably assert that this is just a reading comprehension issue on my part, so I will not attempt to go to far with that discussion. So I will just try to come up with a qualitative description that is sympathetic to the way I see the concept being used by mainstream economists.

Observed economic outcomes -- e.g., what are the measured levels of GDP, inflation, etc. -- are assumed to be

*equilibrium*outcomes. If we drop the mystical concept of "equilibrium," it is the solution of the optimising problem that the economic model represents. Among mainstream economists, there is a great deal of chatter about "multiple equilibria" and "disequilibria," but from my perspective, they might as well be speaking in an unknown foreign language, as it is unclear how these concepts relate to the solution of the optimisation problem written down.

## The Ugly Question of the Initial Price Level

One of the theoretical problems with DSGE macro theory is the question of the determination of the initial price level. The theory pins down the ratio of current prices to the next period, but what determines the price level in the initial period?From my outsider perspective, the answer appears to be that there is no good answer; there are a few debates of a somewhat theological nature, but none of the discussion has much connection to real world behaviour.

## Equilibrium Prices and Market Clearing

One concept that has survived from classical economics is the idea that we could avoid recessions if wages were sufficiently flexible. The idea is that if those darned workers were not so unreasonable, they could accept lower and lower wages to keep the economy at full employment.Although this idea is popular among free market-leaning economists (somewhat unsurprisingly), it is unclear how well supported this folklore is within mainstream economics. It shows up in the quest for labour market "flexibility," but I am not sure how much credence this effect is given in business cycle analysis in practice. Since the flexibility of wages is itself not particularly flexible, it does not lend itself to explain cyclical fluctuations.

## Inflation Buried so Deep that it is not Causal?

Inflation and price level determination is buried in the core of the equilibrium model: prices and activity are determined simultaneously. From the perspective of business cycle analysis, this means that inflation cannot be thought of as a causal force: it just moves with the business cycle.

In other words, despite the importance of price level determination in mainstream theory, we cannot say that a change in the inflation rate will cause other variables like real GDP to move. At most, inflation rates are determined simultaneously with something like real GDP, however, the usual view is that inflation is a lagging variable. If it is indeed a lagging variable, it is

*caused*by the coincident variables (e.g., real GDP, the output gap, employment variables). This means that we need to forecast what will happen to activity variables, and then we can back out what is happening to inflation.
Of course, it should be noted that the mainstream focuses on

*inflation expectations*, and that is what is viewed as the explanatory variable. However, my argument is that inflation expectations -- to what extent that they can be measured -- is a completely different economic time series than realised inflation. When most people talk about*inflation*, they are talking about the rate of change of the CPI index (or the PCE deflator). Although expectations and future realised inflation are supposed to end up close to each other, there is no reason to believe that this is always the case.
This explains why I hope to plausibly remove "inflation" from my business cycle book, and yet cover mainstream economic theory. I can discuss the relationship between "inflation expectations" (which is in fact a fairly nebulous concept) and the cycle, without worrying whether realised inflation is coming along for the ride.

## Concluding Remarks

The preceding arguments were highly qualitative, but I think they explain what I see as a gap between empirical and theoretical mainstream analysis. This gap is that the price level is extremely important in mainstream economic theory, yet realised inflation rates are not used as an explanatory variable. Instead, the focus is on inflation expectations. However, we are not normally interested in inflation expectations when we discuss "inflation," we want to know what realised inflation will be.

(c) Brian Romanchuk 2018

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