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Tuesday, March 4, 2014

SFC Modelling And Government Finance Catastrophes

I am now looking at using Stock-Flow Consistent (SFC) modelling to describe (central) government finance. This is a much simpler task than attempting to model everything within the economy, so I do not have to worry about a lot of thorny problems. In this article, I explain a rule of thumb to deal with long-term fiscal policy expectations. To illustrate, I give an example of an obviously unsustainable fiscal policy that gives rises to an expected future inflationary catastrophe. This article is mainly about model-building; I will discuss in a future article how this relates to the real world fiscal outlook.

As an immediate disclaimer, I will state that I am approaching this from the outside of the field. I have a lot of experience with mathematical modelling and applied economics, but I do not know the economic literature. As a result, it seems likely that what I am writing here was discussed before, but I have not seen prior versions of it (that I can remember; I may have read something similar and just internalised the idea). In consequence, I make no attempt to offer references of who discussed this technique first.


I have been looking at developing SFC models (further description here) of fiscal dynamics using a framework that is similar to that described in the text by Godley and Lavoie. (Affiliate link: Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth.)

Since I am interested in long-term trends, I am able to ignore a lot of things that complicate other modeling approaches. (For an example of a more complicated SFC model, see Nick Edmonds’ model of the UK.) I typically shock the economy with a recession, then let the economy go back to a “steady state” configuration (as the economy is stabilised by the automatic stabilisers of the welfare state), which is the technique used within Godley and Lavoie. I do not attempt to model future recessions, which means that the long-term trajectory is unrealistically smooth. But if you view the model trajectory as being a trend that the economy will bounce around, this is not a big problem.

Similarly, I typically duck the question of modelling inflation by often assuming that inflation is exogenous – usually a constant value. (See this article for an explanation of exogenous.) However, in doing that, I assume that the policy interest rate is varying in response to the economy; in other words the “exogenous” inflation rate assumption is really just assuming that the Central Bank is always hitting its (exogenous) inflation target. If we are explicitly ignoring the wiggles in the economy, such an assumption is a reasonable approximation of reality.

However, assuming that inflation is exogenous is in obvious contradiction to Functional Finance, which holds that the risk associated with loose fiscal policy is inflation. I have thus assumed away the negative effects associated with fiscal deficits, and so my models, taken at face value, would allow a modern government to run deficits of 75% of GDP with no ill effects. (Huge deficits were run during wartime, but at the cost of effectively nationalising production, which is obviously not being done at present.)

The reason I am willing to accept this somewhat dubious assumption is that my models are meant to approximate fiscal settings we see over the past couple of decades, which tend to be stable and somewhat tight. They correspondingly have little measurable impact on inflation, and/or Central Banks have been very effective in hitting their inflation targets. The models do not leave this zone of operation, despite wide swings in the model debt/GDP ratio (which is what we see empirically).

But what happens if there is a fiscal catastrophe of some sort, which forces the country out of that zone of operation? I explain how existing models could be used, at least indirectly, in that case.

Fiscal Catastrophe 2034

In order to simplify things, imagine that we have a parallel universe United States that is similar to the real world U.S. economy, but we make the following changes:
  1. Government policy has achieved price stability - 0% inflation – and this policy is seen as being credible for all concerned. The price level (and the level of wages) are where they are now (in 2014).
  2. Fiscal policy settings are such that nobody (other than a few fiscal nutters) has any worries about the long-term fiscal position of the U.S. Federal Government. (This helps reinforce Assumption #1.)
  3. There are no worries about the external balance, or natural resources/ecological catastrophes over the next twenty years.
Under these assumptions, expectations are for price stability and stable government debt dynamics as far as the eye can see.

Imagine then that a powerful political coalition forms, and enacts the following policy, and that there are no expectations that it will be reversed:
  1. In order to fix the retirement planning problem for everyone aged 45 and under in 2014, starting in 2034 (in 20 years) every citizen who reaches age 65 will be given a tax-free lump sum payment of $1 million.
  2. To “pay” for this programme, everyone who will be in that age bracket has to pay a special 2% increase on their income taxes. (Therefore, people over age 45 will not receive the payment, but do not pay the extra tax.)
What are the consequences of the introduction of this programme?

The Heuristic Response

I would use a heuristic method (a mathematical term which is a fancy way of saying of rule-of-thumb) to approximate the answer that question. I would use a model similar to one of my existing SFC models, but one in which inflation is truly endogenous (determined within the model); in other words, the Central Bank can miss its target. I would then run it forward 20 years, and see what happens.

My current models are backward-looking, in that they do not explicitly attempt to model the future. They could embed pseudo-expectations, in that model entities use historically available data to make guesses about the future, but without explicitly running the model forward in time.

The implication is that the model output appears rather perverse:
  1. Since there is an immediate tightening of fiscal policy, there would be a contraction of growth, and the price level would presumably fall. 
  2. The effect of tightening would dampen out, and the economy is largely at “steady state” by 2034 (as the result of monetary policy and the automatic stabilisers).
  3. In 2034 (and thereafter), a massive fiscal stimulus hits, as the first wave of payments in the programme are made. Inflation would scream higher in response to higher demand (since supply has not increased). Even if the central banks reacts, it will not help; if anything, hyperinflation would ensue. This is because the fiscal deficit would go hyper-exponential as a result of interest costs.
Taken literally, this makes very little sense. Anybody would see that this fiscal policy was unsustainable, and would start taking action in 2014, not 2034 (e.g., by hoarding real assets).

However, this could be immediately seen, even with my backward-looking model. The model output is incompatible with the assumption of price stability, and inventory hoarding would be extremely profitable for model entities. Therefore, at the minimum, one can state the policy is “unsustainable” under current policy settings (in the sense the output violates reasonable assumptions about the behaviour of the state trajectory).

But it would be possible to take this a step further, and force inflation to follow some trajectory defined by a single parameter (at the simplest, a constant inflation rate). It would then be possible to then solve for what inflation rate would give a trajectory that would be consistent with reasonable market behaviour.

For example, you might find that a constant inflation rate of X% gives a sensible-looking forward trajectory, in the sense that there is no overwhelming incentive for entities within the model to hoard inventories. You find X by repeatedly solving the model, and searching for a value of inflation that appears consistent with “reasonable” behaviour. (You would probably want the inflation rate to be somewhat front-loaded than a constant inflation rate over the 20 years. So you would fix some functional form for the inflation rate, and solve for the free parameter value(s) that give a “reasonable” model trajectory.)

Although I have no idea what the exact market response would be (panic, presumably), using this rule-of-thumb, you may have a hope of being within an order of magnitude of being correct.

(As an aside, my modelling framework differs from the Lavoie/Godley models as a result of this line of thought. My models are not specified directly as equations, rather as a group of programming entities that are linked by rock-solid accounting identities. It is possible for a model entity to embed another complete SFC model within its decision function, allowing it to run models iteratively to solve problems as I stated above. However, I have not yet attempted this particular feat of software engineering, which is why I am not reporting simulation results.)

Relation To The Mainstream

This procedure probably looks ridiculously primitive to a mainstream economist – “This problem was solved a long time ago, you ignorant blogger. You just model this in a state-of-the-art Dynamic Stochastic General Equilibrium (DSGE) model. Expectations are explicitly built into the model. Case closed.”

My response can be summarised:
  • The inter-temporal governmental budget constraint (“Ricardian Equivalence”) that is embedded in these models is incorrect, in that term risk premia introduce arbitrarily large pricing errors into the “equation”*. Even if we make the assumption that term risk premia are zero (which is obviously wrong), the constraint is either tautological or incorrect (my formal proof of this assertion is on my “To Do” list.)
  • In general, these models are not truly solved, and my view is that the true solutions do not look anything like what the mainstream economists think they look like (article link). They only attempt solve for small deviations from a constant steady state (“linearisation”), which is obviously not a good description of my example.
My heuristic could be interpreted as an attempt to approximate a “Rational Expectations” equilibrium using a mathematical modelling technique that at least has a chance of working (without dragging in the incorrect Ricardian equivalence notion). In other words, it is doing what mainstream macro claims to be doing, but at least attempting to get close to the correct solution.

Up Next: What About The Real World?

In a follow up article, I will discuss how this example applies to the real world fiscal catastrophe that is supposed to be facing Western governments as the result of demographics.


* As I note in my response to Palley, there are two parts to the Inter-temporal Budget Constraint. The first part is an accounting relationship which describes during a single budget period, which is obviously correct, but contains no behavioural information. The second part – a constraint which allegedly holds over the behaviour as time passes to infinity – is what I refer to as “Ricardian Equivalence”, and is the part that is either wrong or tautological (a statement that is trivially implied by assumption).

(c) Brian Romanchuk 2014


  1. This comment has been removed by a blog administrator.

  2. I think that how people react to changes in their pension rights is quite a difficult issue. You could argue for rational households who take full account of the rights. In reality I suspect much of it is ignored, but not all. In by UK model, I incorporate a small impact on ongoing contributions from revaluations in pension fund assets due to market movements. This seems to me consistent with anecdotal evidence.

    I don't understand your modelling structure without equations, but I'd be interested to see more. I was going to ask if you could put a listing somewhere, but I guess not.

  3. I am planning to release the code when it is ready for prime time. There are equations implicitly within the code, but they are defined as interactions amongst the "objects". For example, I define spending for households on the basis of it already receiving its salary for the period, and it can do its spending/saving allocation as a stand-alone operation. I do need to validate the "household budget constraint" with all the variables in one shot, rather the identities hold for each set of transactions.

    I have not yet triedthe trick of embedding another model within an entity's decision function, but it should be possible. Since the model is just an object, I would just need to instantiate another obviously has to be a version of the model without an embedded model, as that would regress to infinity.

    1. As a further example, I do not attempt to calculate a same-period fiscal multiplier for fiscal policy, as in Godley and Lavoie. Instead, I am currently having the business sector react to historical demand. Since I have only had passive fiscal policy in my models, this was no big deal. However, I have left the model structure so that the business sector could react to fiscal policy so as to create a same period multiplier, but there could be errors in how the expectations are formed. Assuming I get my hands on the right Python libraries, I should be able to replicate the results of Godley and Lavoie (I need to solve some simultaneous equations).

    2. As a final addendum, one reason for waiting to put out my code is that I want to look at the legal aspects of open source licences. The code is fairly basic now, but it is set up in a fashion so that I could expend a lot of effort improving it. I do not want to accidently lose control of my efforts. If anyone has ann interest inn this, and expertise in open source licensing models, I would be happy to hear about it.

    3. I don't really know much about licensing, but I was advised to use the Creative Commons licensing for my stuff and to put the link on the blog. Not that I'm that concerned, really.


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