stock flow consistent models

Consistent modelling and inconsistent terminology

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Simon Wren-Lewis has a couple of recent posts up on heterodox macro, and stock-flow consistent modelling in particular. His posts are constructive and engaging. I want to respond to some of the points raised.

Simon discusses the modelling approach originating with Wynne Godley, Francis Cripps and others at the Cambridge Economic Policy Group in the 1970s. More recently this approach is associated with the work of Marc Lavoie who co-wrote the key textbook on the topic with Godley.

The term ‘stock-flow consistent’ was coined by Claudio Dos Santos in his PhD thesis, ‘Three essays in stock flow consistent modelling’ and has been a source of misunderstanding ever since. Simon writes, ‘it is inferred that mainstream models fail to impose stock flow consistency.’ As I tried to emphasise  in the blog which Simon links to, this is not the intention: ‘any correctly specified closed mathematical macro model should be internally consistent and therefore stock-flow consistent. This is certainly true of DSGE models.’ (There is an important caveat here:  this consistency won’t be maintained after log-linearisation – a standard step in DSGE solution – and the further a linearised model gets from the steady state, the worse this inconsistency will become.)[1]

Marc Lavoie has emphasised that he regrets adopting the name, precisely because of the implication that consistency is not maintained in other modelling traditions. Instead, the term refers to a subset of models characterised by a number of specific features. These include the following: aggregate behavioural macro relationships informed by both empirical evidence and post-Keynesian theory; detailed, institutionally-specific modelling of the monetary and financial sector; and explicit feedback effects from financial balance sheets to economic behaviour and the stability of the macro system both in the short run and the long run.

A distinctive feature of these models is their rejection of the loanable funds theory of banking and money – a position endorsed in a recent Bank of England Quarterly Bulletin and Working Paper. Partially as a result of this view of the importance of money and money-values in the decision-making process, these models are usually specified in nominal magnitudes. As a result, they map more directly onto the national accounts than real-sector models which require complex transformations of data series using price deflators.

Since the behavioural features of these models are informed by a well-developed theoretical tradition, Simon’s assertion that SFC modelling is ‘accounting, not economics’ is inaccurate. Accounting is one important element in a broader methodological approach. Imposing detailed financial accounting alongside behavioural assumptions about how financial stocks and flows evolve imposes constraints across the entire system. Rather like trying to squeeze the air out of one part of a balloon, only to find another part inflating, chasing assets and liabilities around a closed system of linked balance sheets can be an informative exercise – because where leverage eventually turns up is not always clear at the outset. Likewise, SFC models may include detailed modelling of inventories, pricing and profits, or of changes in net worth due to asset price revaluation and price inflation. For such processes, even the accounting is non-trivial. Taking accounting seriously allows modellers to incorporate institutional complexity – something of increasing importance in today’s world.

The inclusion of detailed financial modelling allows the models to capture Godley’s view that agents aim to achieve certain stock-flow norms. These may include household debt-to-income ratios, inventories-to-sales ratios for firms and leverage ratios for banks. Many of the functional forms used implicitly capture these stock-flow ratios. This is the case for the simple consumption function used in the BoE paper discussed by Simon, as shown here. Of course, other functional specifications are possible, as in this model, for example, which includes a direct interest rate effect on consumption.

Simon notes that adding basic financial accounting to standard models is trivial but ‘in most mainstream models these balances are of no consequence’. This is an important point, and should set alarm bells ringing. Simon identifies one reason for the neutrality of finance in standard models: ‘the simplicity of the dominant mainstream model of intertemporal consumption’.

There are deeper reasons why the financial sector has little role in standard macro. In the majority of standard DSGE macro models, the system automatically tends towards some long-run supply side-determined full-employment equilibrium – in other words the models incorporate Milton Friedman’s long-run vertical Phillips Curve. Further, in most DSGE models, income distribution has no long-run effect on macroeconomic outcomes.

Post-Keynesian economics, which provides much of the underlying theoretical structure of SFC models, takes issue with these assumptions. Instead, it is argued, Keynes was correct in his assertion that demand deficiency can lead economies to become stuck in equilibria characterised by under-employment or stagnation.

Now, if the economic system is always in the process of returning to the flexible-price full-employment equilibrium, then financial stocks will be, at most, of transitory significance. They may serve to amplify macroeconomic fluctuations, as in the Bernanke-Gertler-Gilchrist models, but they will have no long-run effects. This is the reason that DSGE models which do attempt to incorporate financial leverage also require additional ‘ad-hoc’ adjustments to the deeper model assumptions – for example this model by Kumhof and Ranciere imposes an assumption of non-negative subsistence consumption for households. As a result, when income falls, households are unable to reduce consumption but instead run up debt. For similar reasons, if one tries to abandon the loanable funds theory in DSGE models – one of the key reasons for the insistence on accounting in SFC models – this likewise raises non-trivial issues, as shown in this paper by Benes and Kumhof  (to my knowledge the only attempt so far to produce such a model).

Non-PK-SFC models, such as the UK’s OBR model, can therefore incorporate modelling of sectoral balances and leverage ratios – but these stocks have little effect on the real outcomes of the model.

On the contrary, if long-run disequlibrium is considered a plausible outcome, financial stocks may persist and feedbacks from these stocks to the real economy will have non-trivial effects. In such a situation, attempts by individuals or sectors to achieve some stock-flow ratio can alter the long-run behaviour of the system. If a balance-sheet recession persists, it will have persistent effects on the real economy – such hysteresis effects are increasingly acknowledged in the profession.

This relates to an earlier point made in Simon’s post: ‘the fact that leverage was allowed to increase substantially before the crisis was not something that most macroeconomists were even aware of … it just wasn’t their field’. I’m surprised this is presented as evidence for the defence of mainstream macro.

The central point made by economists like Minsky and Godley was that financial dynamics should be part of our field. The fact that by 2007 it wasn’t, illustrates how badly mainstream macroeconomics went wrong. Between Real Business Cycle models, Rational Expectations, the Efficient Markets Hypothesis and CAPM, economists convinced themselves – and, more importantly, policy-makers – that the financial system was none of their business. The fact that economists forgot to look at leverage ratios wasn’t an absent-minded oversight. As Oliver Blanchard argues:

 ‘… mainstream macroeconomics had taken the financial system for granted. The typical macro treatment of finance was a set of arbitrage equations, under the assumption that we did not need to look at who was doing what on Wall Street. That turned out to be badly wrong.’

This is partially acknowledged by Simon when he argues that the ‘microfoundations revolution’ lies behind economists’ myopia on the financial system. Where I, of course, agree with Simon is that ‘had the microfoundations revolution been more tolerant of other methodologies … macroeconomics may well have done more to integrate the financial sector into their models before the crisis’. Putting aside the point that, for the most part, the microfoundations revolution didn’t actually lead to microfounded models, ‘integrating the financial sector’ into models is exactly what people like Godley, Lavoie and others were doing.

Simon also makes an important point in highlighting the lack of acknowledgement of antecedents by PK-SFC authors and, as a result, a lack of continuity between PK-SFC models and the earlier structural econometric models (SEMs) which were eventually killed off by the shift to microfounded models. There is a rich seam of work here – heterodox economists should both acknowledge this and draw on it in their own work. In many respects, I see the PK-SFC approach as a continuation of the SEM tradition – I was therefore pleased to read this paper in which Simon argues for a return to the use of SEMs alongside DSGE and VAR techniques.

To my mind, this is what is attempted in the Bank of England paper criticised by Simon – the authors develop a non-DSGE, econometrically estimated, structural model of the UK economy in which the financial system is taken seriously. Simon is right, however, that the theoretical justifications for the behavioural specifications and the connections to previous literature could have been spelled out more clearly.

The new Bank of England model is one of a relatively small group of empirically-oriented SFC models. Others include the Levy Institute model of the US, originally developed by Wynne Godley and now maintained by Gennaro Zezza, the UNCTAD Global Policy model, developed in collaboration with Godley’s old colleague Francis Cripps, and the Gudgin and Coutts model of the UK economy (the last of these is not yet fully stock-flow consistent but shares much of its theoretical structure with the other models).

One important area for improvement in these models lies with their econometric specification. The models tend to have large numbers of parameters, making them difficult to estimate other than through individual OLS regressions of behavioural relationships. PK-SFC authors can certainly learn from the older SEM tradition in this area.

I find another point of agreement in Simon’s statement that ‘heterodox economists need to stop being heterodox’. I wouldn’t state this so strongly – I think heterodox economists need to become less heterodox. They should identify and more explicitly acknowledge those areas in which there is common ground with mainstream economics.  In those areas where disagreement persists, they should try to explain more clearly why this is the case. Hopefully this will lead to more fruitful engagement in the future, rather than the negativity which has characterised some recent exchanges.

[1] Simon goes on to argue that stock-flow consistency is not ‘unique to Godley. When I was a young economist at the Treasury in the 1970s, their UK model was ‘stock-flow consistent’, and forecasts routinely looked at sector balances.’  During the 1970s, there was sustained debate between the Treasury and Godley’s Cambridge team, who were, aside from Milton Friedman’s monetarism, the most prominent critics of the Keynesian conventional wisdom of the time – there is an excellent history here. I don’t know the details but I wonder if the awareness of sectoral balances at the Treasury was partly due to Godley’s influence?

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On ‘heterodox’ macroeconomics

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Noah Smith has a new post on the failure of mainstream macroeconomics and what he perceives as the lack of ‘heterodox’ alternatives. Noah is correct about the failure of mainstream macroeconomics, particularly the dominant DSGE modelling approach. This failure is increasingly – if reluctantly – accepted within the economics discipline. As Brad Delong puts it, DSGE macro has ‘… proven a degenerating research program and a catastrophic failure: thirty years of work have produced no tools for useful forecasting or policy analysis.’

I disagree with Noah, however, when he argues that ‘heterodox’ economics has little to offer as an alternative to the failed mainstream.

The term ‘heterodox economics’ is a difficult one. I dislike it and resisted adopting it for some time: I would much rather be ‘an economist’ than ‘a heterodox economist’. But it is clear that unless you accept – pretty much without criticism – the assumptions and methodology of the mainstream, you will not be accepted as ‘an economist’. This was not the case when Joan Robinson debated with Solow and Samuelson, or Kaldor debated with Hayek. But it is the case today.

The problem with ‘heterodox economics’ is that it is self-definition in terms of the other. It says ‘we are not them’ – but says nothing about what we are. This is because includes everything outside of the mainstream, from reasonably well-defined and coherent schools of thought such as Post Keynesians, Marxists and Austrians, to much more nebulous and ill-defined discontents of all hues. To put it bluntly, a broad definition of ‘people who disagree with mainstream economics’ is going to include a lot of cranks. People will place the boundary between serious non-mainstream economists and cranks differently, depending on their perspective.

Another problem is that these schools of thought have fundamental differences. Aside from rejecting standard neoclassical economics, the Marxists and the Austrians don’t have a great deal in common.

Noah seems to define heterodox economics as ‘non-mathematical’ economics. This is inaccurate. There is much formal modelling outside of the mainstream. The difference lies with the starting assumptions. Mainstream macro starts from the assumption of inter-temporal optimisation and a system which returns to the supply-side-determined full-employment equilibrium in the long run. Non-mainstream economists reject these in favour of assumptions which they regard as more empirically plausible.

It is true that there are some heterodox economists, for example Tony Lawson and Ben Fine who take the position that maths is an inappropriate tool for economics and should be rejected. (Incidentally, both were originally mathematicians.) This is a minority position, and one I disagree with. The view is influential, however. The highest-ranked heterodox economics journal, the Cambridge Journal of Economics, has recently changed its editorial policy to explicitly discourage the use of mathematics. This is a serious mistake in my opinion.

So Noah’s claim about mathematics is a straw man. He implicitly acknowledges this by discussing one class of mathematical Post Keynesian models, the so-called ‘stock-flow consistent’ models (SFC). He rightly notes that the name is confusing – any correctly specified closed mathematical macro model should be internally consistent and therefore stock-flow consistent. This is certainly true of DSGE models.

SFC refers to a narrower set of models which incorporate detailed modelling of the ‘plumbing’ of the financial system alongside traditional macro Keynesian behavioural assumptions – and reject the standard inter-temporal optimising assumptions of DSGE macro. Marc Lavoie, who originally came up with the name, admits it is misleading and, with hindsight, a more appropriate name should have been chosen. But names stick, so SFC joins a long tradition of badly-named concepts in economics such as ‘real business cycles’ and ‘rational expectations’.

Noah claims that ‘vague ideas can’t be tested against the data and rejected’.  While the characterisation of all heterodox economics as ‘vague ideas’ is another straw man, the falsifiability point is important. As Noah points out, ‘One of mainstream macro’s biggest failings is that theories that don’t fit the data continue to be regarded as good and useful models.’ He also notes that big SFC models have so many parameters that they are essentially impossible to fit to the data.

This raises an important question about what we want economic models to do, and what the criteria should be for acceptance or rejection. The belief that models should provide quantitative predictions of the future has been much too strongly held. Economists need to come to terms with the reality that the future is unknowable – no model will reliably predict the future. For a while, DSGE models seemed to do a reasonable job. With hindsight, this was largely because enough degrees of freedom were added when converting them to econometric equations that they could do a reasonably good job of projecting past trends forward, along with some mean reversion.  This predictive power collapsed totally with the crisis of 2008.

Models then should be seen as ways to gain insight over the mechanisms at work and to test the implications of combining assumptions. I agree with Narayana Kocherlakota when he argues that we need to return to smaller ‘toy models’ to think through economic mechanisms. Larger econometrically estimated models are useful for sketching out future scenarios – but the predictive power assigned to such models needs to be downplayed.

So the question is then – what are the correct assumptions to make when constructing formal macro models? Noah argues that Post Keynesian models ‘don’t take human behaviour into account – the equations are typically all in terms of macroeconomic aggregates – there’s a good chance that the models could fail if policy changes make consumers and companies act differently than expected’

This is of course Robert Lucas’s critique of structural econometric modelling. This critique was a key element in the ‘microfoundations revolution’ which ushered in the so-called Real Business Cycle models which form the core of the disastrous DSGE research programme.

The critique is misguided, however. Aggregate behavioural relationships do have a basis in individual behavour. As Bob Solow puts it:

The original impulse to look for better or more explicit micro foundations was probably reasonable. It overlooked the fact that macroeconomics as practiced by Keynes and Pigou was full of informal microfoundations. … Generalizations about aggregative consumption-saving patterns, investment patterns, money-holding patterns were always rationalized by plausible statements about individual – and, to some extent, market-behavior.

In many ways, aggregate behavioural specifications can make a stronger claim to be based in microeconomic behaviour than the representative agent DSGE models which came to dominate mainstream macro. (I will expand on this point in a separate blog.)

Mainstream macro has reached the point that only two extremes are admitted: formal, internally consistent DSGE models, and atheoretical testing of the data using VAR models. Anything in between – such as structural econometric modelling – is rejected. As Simon Wren-Lewis has argued, this theoretical extremism cannot be justified.

Crucial issues and ideas emphasised by heterodox economists were rejected for decades by the mainstream while it was in thrall to representative-agent DSGE models. These ideas included the role of income distribution, the importance of money, credit and financial structure, the possibility of long-term stagnation due to demand-side shortfalls, the inadequacy of reliance on monetary policy alone for demand management, and the possibility of demand affecting the supply side. All of these ideas are, to a greater or lesser extent, now gradually becoming accepted and absorbed by the mainstream – in many cases with no acknowledgement of the traditions which continued to discuss and study them even as the mainstream dismissed them.

Does this mean that there is a fully-fledged ‘heterodox economics’ waiting in the wings waiting to take over from mainstream macro? It depends what is meant – is there complete model of the economy sitting in a computer waiting for someone to turn it on? No – but there never will be, either within the mainstream or outside it. But Lavoie argues,

if by any bad luck neoclassical economics were to disappear completely from the surface of the Earth, this would leave economics utterly unaffected because heterodox economics has its own agenda, or agendas, and its own methodological approaches and models.

I think this conclusion is too strong – partly because I don’t think the boundary between neoclassical economics and heterodox economics is as clear as some claim. But it highlights the rich tradition of ideas and models outside of the mainstream – many of which have stood the test of time much better than DSGE macro. It is time these ideas are acknowledged.