Towards a Formally Defined New Economics

The discussions on reforming the economics curriculum after the crash has produced highly defensive responses from the likes of Karl Whelan and Tony Yates.  Their response being – meah – why stray from the neoclassical when you have Diamond and Dybvig and the Bernanke Financial Accelerator in your kit bag. Well that kitbag is obviously deficient if it cannot ex-plain the causes of a balance sheet recession, only reactions when you get into one.  The worst example of this was a paper by Negro, Giannoni and Schorfheide  of the NY Fed last year that claimed that DGSE was capable of explaining the Great Recession.  What they did was take the most well known New Keynsian model Smets-Wouters (2007) New Keynesian model and add on the  the “financial accelerator” model of Bernanke, Gertler, and Gilchrist (1999).  In the model credit shocks transmit through the real economy through amongst other reasons undermining the value of collateral. However all they did was take a pre-existing credit shock from Q3 2008 and predict it forward, they could not explain how that shock occurred.

But if the existing kit-bag is insufficient does that mean we should simply broaden courses to be more institutional and more cogniscent of great debates.  Certainly I have argued here that courses should focus on the contested core ideas. But that is not enough.

I said then

To my mind an economics curriculum needs to be founded around these contested core ideas, ideas such as what is interest? what are profits?  what is saving and what is the impact of saving?  What creates value?  What is capital?  There is no real agreement on any of these ideas.

Replacement of the flawed neo-classical paradigm (in the lakosian sense) requires a better replacement – but there is no consensus- at least in the post-keynsian community, what that replacement should be, we only have a broad outline.

What I am suggesting here is that we formally in mathematically and accounting consistent terms the core concepts and not let past ANY model that is not formalised.   This way we will ensure that all our models are computable, testable and formally consistent.

This approach is much more fundamental that the neo-classical core based on intertemporal optimisation of marginal values.  Marginal values of what?  Are these values observable and do they provide information for economic decisions? What is the impact of one optimization on flows affecting all other optimisations?  DGSE and similar models have a level of abstraction one step removed from the fundamental constraints of capitalism. Endowments are not accumulations of factor returns, they are a gift from heaven.  That is not to say inter temporal optimisation is not a useful second order tool, but is not a primary first order tool, those are the fundamental accounting constraints and relationships of capitalism.

I suggest four rules for a formally defined economics of this nature:

1) All economic models are constructed from formal definitions of the key relations of the economic system (capitalism in our case) which are set in accounting and stock-flow dimensionally consistent quadruple entry terms.

2) These economic relations provide information to agents only if they are observable.

3) A complete model must account for all economic gains and losses to all departments and categories agents of the economy, including banks and finance, all other models are partial.  A universal model includes all information for all agents, no model can be universal without artificially reducing the information set.

4) Only a complete model can be used to compute the path of all prices at the level of aggregation of the model.    No model can include all information so no model can be fully predictive of all prices.

 Let us explore how modelling can proceed on such axiomatic foundations.

The starting point is the fundamental equation of accounting.

Assets=Owners Equity + Liabilities

This assumes that for each modelling step we have a liability for a corresponding asset, so always more than one agent and a double entry for each, Copeland’s quadruple accounting principle.

Capital is another term for Owners Equity, so lets rearrange in terms of Capital for our Fundamental Equation of Capitalism.

Capital=Assets-Liabilities

We can refine this further by casting this in intertemporal terms.

NPV Capital=NPV Assets-NPV Liabilities

Cast in this way we can see the measure of capital is fundamentally bound up with the interest rate – now why did this issue entangle economic theory for 80 years when it can be found in one step from foundational principles?

It is more useful however for agents to base decisions on the rate of return on capital over a defined period – A to B

ROR=NPV AssetsB-NPV LiabilitiesB/NPV AssetsA-NPV LiabilitiesA

Which can be termed

ROR=Profit:Loss/Capital Advanced.

As Cameron Murray rightly advances it is ROR not marginal revenues which is the key metric for the firm.

Which gives us a definition of profit:loss

We can further breakdown the Profit:Loss account as follows:

Profit:Loss= revenues+book value assets-depreciation-expenses

Where expenses are the per moment of time cost of liabilities to the balance sheet.

So from very simple beginnings we have derived definitions of capital, profits, revenues and costs.  Breakdown the revenues accruing to factors and you have the foundations for a stock-flow consistent economic model.   We also have the tools through some simple algebra and not so simple double entry tables to model interest and banking, but that is beyond the scope of this post.  If any accountant wishes to comment on these propositions or wishes to show how they can be defined more expressively please feel free to do so.

Looking back on the writing of key classical thinkers such as Malthus and Torrens it is striking how careful they were to define these fundamentals, and how sloppy more recent practitioners are (with a few notable exceptions such as Fisher, Keynes, Kaldor and Godley)

From setting up a complete model at a relevant level of abstraction we can derive equations for market clearing prices where the flow of revenues equals the flow of costs. In capitalism most markets are not market clearing most of the time, if they were that would provide no information on where and how to invest.  This avoids the sterility of the unfortunate physical analogy of equilibrium-disequilibrium. A paradigm without agents acting on information.  The equilibrium analogy creates logical paradoxes, either equilibrium is defined in a way where it is never achieved or defined intertemporily with prescient rational agents with the same information as God which makes being out of equilibrium impossible, and eliminates all information on differential rates of profit which is the defining feature of capitalism.   A much better language to talk in non-linear dynamics terms – regions of relative stability – where limit cycles reign, and regions of instability and chaos.

There are certainly risks of Bourabaki style sterility of  axiomatic foundations.  But the issue is to get the first axoms right.  Neither Austrian human action axioms or the fashionable in the last decade graduate texts composed entirely of axoims derived from maximising agents were based on the accounting of the firm – were based on a monetary capitalist economy.

6 thoughts on “Towards a Formally Defined New Economics

  1. Pingback: Mathematical Modelling in Economics that Meets the Lawson Critique | Decisions, Decisions, Decisions

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