Stock-flow confusion (wonkish)

In his latest article, Noah Smith repeats a claim that has long bothered me: that mainstream economic models are “stock-flow consistent”. Which is to imply that the very popular research agenda in monetary economics using stock-flow consistent (SFC) methods has little new to add to the mainstream. Because. You know. We got that.

I want to respond with two points about this, which also relate to Smith's general views on maths, theory, and economics. First, a theory is a concept. An idea. Theories can therefore be modelled mathematically in many ways. Second, the stocks and flows of the mainstream are different, theoretically, to those of the monetary economists.

Theories are concepts
Evolution is a theory. It requires absolutely no maths to explain it. Cell theory, is, well, a theory. Again, no maths required. Plate tectonics. Heliocentirsm. All concepts or ideas. Not equations.

Or closer to home, game theory is a concept that has many, many, mathematical representations.

I don’t see the problem with an “economics without maths” if we are engaged in debate about which ideas have merit, and can on their face, provide useful predictions. Smith cites Minksy as an economist who explains his theory of “stability is destabilising” in words. To me that’s a great example of the usefulness of theories, even without mathematical models to accompany them. After all, many mathematical methods could be used to capture the core elements of this theory.

So to say frame “broad idea-sketching” as an alternative to “formal models” is rather naive in my view. You can’t have a formal model without big ideas underneath it. After all, every variable and parameter in a mathematical equation is meant to capture some piece of reality, and you need a theory to say that such a thing even exists.

And there are still many debates about whether measured, mathematical, things have theoretical foundations that allow them to be interpreted in particular ways. Think of the capital debates. You can have many formal models with K in them, but you need a theory to say what K is in reality.

Or more recently, there has been a debate around the meaning of the number we get when we measure multi-factor productivity. Just because we measured it, and had a formal model underpinning it, doesn’t allow for an interpretation without a theory to accompany it.

SFC models use different concepts
With that in mind, we can now compare the SFC approach of monetary economics with the apparent stock-flow consistency of mainstream models. As you might have guessed, the consistency is not really there once we account for the underlying theoretical concepts.

Again I will use my mud-map of economic domains to make this point. I find this a useful way to structure economic inquiry as it makes clear the point that there are different conceptual and theoretical domains in which economic analysis takes place.

The fundamental difference is this. Standard models capture a theory about real goods and services, and real capital (the physical buildings and machines). SFC models capture transactions and balances (assets and liabilities) in money, regardless of the underlying physical attributes of the goods and capital. This means that SFC models allow for credit balances between entities, which can’t be captured in the standard economics of real goods, since credits are not physical goods or services. The image below tries to show that although standard models are consistent in their treatment of stocks of physical capital and flows of investment in that physical capital, the very concept of physical capital is different to the items accounted for in money-based SFC models.

I also try to show that the way each approach deals with aggregation can be quite different. Standard models typically pick an arbitrary level and aggregate under the assumption of a representative agent, often to the level of a whole country. But SFC models are only useful when they aggregate at the levels of economic sectors, or even more finely than that. Because after all, once you have aggregated the whole economy to a single agent, the credit balances between agents within the group all cancel out, yet the whole point of SFC models it to observe the dynamics of these balances between different parts of the economy.

The table below is from Lavoie and Godley’s Monetary Economics, which details the monetary transactions that can be accounted for in this approach, which simply cannot exist in a world of real goods and services only.

I have long held the view that many of the conflicts in economics stem from theoretical confusions. After all, once a bunch of equations are written down, it is very easy to see if the “solution” is correct.

Noah could use his unique position as a facilitator of economic debate in the blogosphere to help economists with different approaches begin to talk to each other, rather than past each other. But confusing formal models with theory, and holding alternative approaches to a higher standard to mainstream approaches, is not a great start.

UPDATE:
To make clear the idea of analysing different domains, I think a motor-racing analogy is useful. One racing "school of thought" measures stocks and flows in terms of the weight of each car each lap. They show that the flows of weight lost in fuel is consistently captured in declining stock of weight of the car. Another school of thought measures the length travelled by each car and its speed, noting how their stocks and flows of distance are also consistent.

Yet the two aren't directly comparable, even though they may both be independently, and jointly, useful approaches for understanding motor-racing. In economics we get confused because we use words like capital to mean multiple things. This problem is all too obvious if consider what sort of understanding of racing we would have if the two schools of thought used the name capital to mean both distance and weight. 

Econ-media gets fresh

A quick update on two interviews from the past week.

First, is an hour long chat with Frank Conway who hosts the Economic Rockstar podcast. We chat about many things. One big topic is teaching economics better by using the Robinson Crusoe economy as an example that opens up very broad lines of economic inquiry, rather than as a very narrow story to help learn comparative advantage. Another is how blogging has influenced by studies and career. There is also some discussion of environmental economics and rebound effects.

I also mix up my Alan’s near the end - attributing to Alan Blinder the work of Alan Kirman as well.

Here’s the podcast

Second, is a shorter interview with Colin Hesse, who hosts Radio Skid Row in Sydney. We chat about my research on relationship networks and favourable land rezoning (article here). I also talk more positively about how to crack the game of exchanging political favours, by using the carrot of the revenue that governments could raise if they charged for the new property rights they create with zoning decisions.

Economics of favours and karma

Giving gifts is often seen as a selfless act, but this is only one side of the story. The act of giving generates implicit obligations, whether we like it or not. When political donors say they are supporting a party out of a selfless respect for democracy, we know it is a lie. We implicitly understand the role of gifts in creating obligations.

At a personal level this leads to situations that seem paradoxical on the surface. For example, if you ask someone for a favour, they are more likely to give you a favour in the future.

Such findings are only interesting because they conflict with our baseline view about the rationality of giving and receiving favours. Why is this so?

I want to try and answer this question by making explicit the “favour-accounting” system between individuals that is fundamentally implicit. Such a system captures the core human desire to reciprocate.

When we do that, it becomes clear that because of our desire to reciprocate, giving a favour generates an asset in the form of being owed a favour, while receiving one creates a liability in the form of owing a favour. That is, the “favour balance sheet” looks good for those who give favours, but bad for those who receive them and are on the hook for future favours.

Think about it. Why power does a political donor really have? He has a bunch of assets in the form of politicians who owe him favours. In the table below I try to capture this situation in table form.

So you would expect that people seeking to accumulate assets and wealth would be in the business of giving favours to those with the ability to reciprocate. This is especially the case when there is a large subjective value difference between the cost of the favour given, and the value of the favour received, i.e. the cost is low for those giving the favour compares to the value of the benefit to those receiving it.

After you’ve asked for one favour, and while your credit is good, you can expect that the same person is willing to give you another favour to boost their exposure to your “favour credit”. It is common, for example, for politicians to seek extra funding from donors already contributing, rather than find new donors.

If you come through and reciprocate favours when required, you can participate as a giver and receiver in as ongoing game of favour exchange necessary to participate in social life. Maybe you can think of it as karma.

We can also see that giving favours to strangers won't always make them feel good about you, because you are creating liabilities for them. People often don't want to accept large gifts because of this.

But when we instead use money to settle “favour accounts” we are essentially saying “you gave me a favour, but I don’t want to owe you anything, so here is this money instead to cancel my obligation to you”. I don’t feel any particular need to reciprocate with my supermarket for the food I get there, but when my neighbours give me food its does end up on the social accounts.

That is why we there is such a big difference between doing something as a hobby, and doing something commercially - when you settle you accounts with money, your future cooperation can’t be assured, yet when you keep open the favour accounts, reciprocity ensures ongoing cooperation.

It stands to reason that you shouldn’t expect karma from counter-parties where you cancel obligation with money. But you should for your non-market interactions that rely on networks of ongoing exchanges of favours and implicit obligations.

Now to answer the question I posed of why our baseline intuition about favours is wrong. The reason is, I believe, that when we are implicitly thinking of favours that do not require reciprocation. We are thinking of a world were it is possible to give a favour and for the receiver to behave like a pure robot and feel not desire to reciprocate. The t-table of this situation is below.

But if this is truly the case, then there is no rational basis for ever giving a favour either, as it is a pure loss every time. Where the logic of rationality is failing is that we only look at the receiver of the favour through the lens of a perfectly rational world where no reciprocity exists. We forget that is such a world a giver of a favour with no reciprocal obligation wouldn’t exist either.

A comment on Keen’s “Credit plus GDP” measure

Background

More than anyone, Steve Keen has raised awareness of the role of banking and money creation in driving economic cycles. Not only this, he has published just about every presentation and paper of his freely online, and participated in a variety of forums online and in the media.

Not only is he out there putting forward new approaches and ideas, he is doing so in a way that allows every man and his dog to nit pick at his work. That takes guts.

Because of the public nature of his work for the past decade, his analysis and communication of these big ideas has evolved to become extremely powerful and hard to ignore. Just about everyone I talk to in the economics crowd these days has been influenced by Keen’s work in some way. For me personally, the latest lesson from Keen as been his reconciliation of accounting identities with the dynamic effect of additional demand from credit creation - a change in understanding that I think could offer a clear path forward for dynamic monetary methods. 

The issue
In the spirit of this public debate I want to take issue with one of Keen’s recent ideas; adding change in credit (debt) to GDP. But I want to do so constructively so that as a profession we can incrementally improve our economic analysis and understanding of macroeconomic phenomena. 

In this video, from 16mins onwards, Keen explains the idea and attaches a particular interpretation to the summation of GDP and the flow of new credit (change in the credit balance), as “aggregate expenditure” (AE). The slide below summarises.

Where this measure of AE differs from the standard view is that it can include expenditure on transfers, such as assets sales, rather than just newly produced goods. It therefore includes expenditure on real estate (not just new housing construction), and leveraged expenditure in equities markets. We could probably better call it “aggregate transactional expenditure”. 

What he misses, however, is that there is no one-to-one relationship between credit creation and its use in asset markets. Quite a bit of new credit is used to fund investment in new buildings, and other “capital” goods, the value of which is already included in GDP calculation. 

Let’s take an example. I build a new home. The land costs $100,000, and the building I have designed will cost $100,000 to build on that land. I buy the land using my saved wages, and borrow $100,000 to construct the building. In this case, this $100,000 of new credit created by my bank for me to pay my builder is counted as new capital (or what the Australian statistical agency calls “gross fixed capital formation”). It is in nominal GDP. Adding the $100,000 in new credit to the $100,000 of new housing in GDP makes no sense. Similar situations abound in large investment projects, where bank funding for pipelines, rail lines, energy facilities and so forth, is already part of measured GDP. 

Even in cases where new credit can appear to be pure speculation on asset markets, such as the purchase of an existing home, that credit can then be used to purchase consumer goods, which are counted in GDP. For example, the seller of the home I buy with my new mortgage can turn around and buy a car, a boat, or go on a holiday, with the new money created when I took out a loan to buy their house. The net effect is as if they had used new credit (money) to directly buy those consumer goods.

If I haven’t been clear, I don’t think the simplification of calling GDP the expenditure in a year financed by existing money is appropriate. And I am not sure what it adds to Keen's analysis, since credit dynamics alone make similar predictions of the macroeconomic cycle without adding them to GDP. If it is merely a case of "here's a metric that correlates well with the historical data", I have no issue. Whatever works is fine. But if we attach meaning to it above and beyond this, than we need to understand what the metrics really are. 

Economic domains approach
I think of this issue in terms of economic domains. GDP is not a measure of the use of money - it neither measures transactions, nor balances of accounts or any such thing. It is our best measurement of real goods and services produced by the market economy and the government sector. It only records purchases by households and governments of new goods and services, ignoring all asset market transactions, second hand goods transactions, intermediate production transactions, and so forth. In fact, in order to add up the value added of goods and services, it includes only a select few transactions to ensure no double counting, and a reasonable approximation of new production only. 

In terms of my economic domains approach to economic analysis, we can see that despite both being measured in $/period (which is simply the common measure used to aggregate different types of goods), GDP is a measure of real production, while new credit is a measure of the change in the balances of our monetary accounting system. This means that without knowing all the monetary balances and transactions in the whole economy, we can’t precisely know the link between new credit and the production of real goods and services. There are also price effects to consider, both in the real goods markets, as well as asset markets, which changes incentives for real capital investment. The question mark in the image below shows where this type of monetary analysis must focus - understanding the mechanisms by which new money creation affects GDP.

In terms of the simple examples I used earlier, the diagram below shows how some share of new credit is already counted in GDP when it funds new capital investment. But even here, it is not clear what the relationship between new credit and GDP should be like. 

Credit and GDP differently

Perhaps it is more useful to look at the effectiveness of new credit in creating goods and services instead of asset price inflation (or inflation generally). Call it “growth efficiency of credit”. And why not? That’s what the World Bank calls it.

There are two extremes I have in mind in this analysis. 

First, if all new credit is directed to new capital investments, we would expect a very close match between credit creation and increases in nominal GDP. Second, if all credit creation is to fund asset purchases, we might expect a much lower relationship between new credit and GDP growth. 

This idea fits nicely with the story that we should use the banking system to support new capital investment instead of funding asset purchases, which simply leads to asset price growth and speculative cycles. In this story it matters what new credit (money) is used for, not just the levels of new credit. 

To examine the idea of credit efficiency, I take the change in nominal GDP (increase in real market goods and services in current dollar terms) over a period, and the change in total credit (i.e. the new credit) to see how effectively the new credit is being directed towards real production instead of asset markets. The result is in the chart below. 

What a surprise! Nothing at all like I expected. I had in mind a very cyclical, hard-to-decipher, pattern. 

Instead we see two main periods of stability. Prior to 1990 the ratio was rather stable, with a mean value of 3.42, meaning that for every dollar of new credit, GDP grew by $0.29. In the second stable period, between 1993 and 2008, the ratio was 7.33, meaning that GDP grew by $0.14 for every new dollar of credit on average. 

I suspect that these stable period levels in some way reflect the prudential controls on lending that prevailed at each time period, such as loan-to-value ratio limits, savings requirements, and other such things in the case of mortgage lending. But also, I suspect there is a feedback loop at play - from more credit creation, leading to higher home prices, which leads to lower interest rates, supporting more credit creation and higher prices, and on it goes. It is these types of feedbacks that Keen's dynamic methods can capture. 

But what of the unstable periods?

There was one in 1990, which we know preceded a recession in the early 1990s. And there is a lull in credit while GDP growth remained strong in 2009-10, perhaps due to government stimulus. But now we appear to be in a period of very inefficient credit use, where a new dollar of credit has bought just $0.05 of GDP over the past three years. I suspect this has a lot to do with the winding down of mining investment (I’m unsure of the degree of domestic bank lending for these expansions), at the same time as a massive ramp up in investor mortgages in Sydney and Melbourne, which do not feed directly into consumption and investment.

Overall we could say that the patterns seen here supports Minky's idea that "stability is destabilising".

So what is the meaning of this?

It is a little worrying to see a “pre-recession” pattern forming at the moment. But without looking more widely at the predictive power of such patterns, I'm hesitant to make strong predictions, though I don't expect any surprise economic boom in the coming few years.

In terms of economic theory, at the very least I now have a story about how the money domain leads to changes in the real resources (GDP) domain through directing new funds towards new capital investment, or towards asset purchases. This is one mechanism that provides a relationship between these domains. I suspect there is a second important mechanism, and this is the effect of new credit on asset values, and the subsequent effect on brining forward or delaying investment for asset owners. In terms of my economic domains approach, this mechanisms relies on a monetary effect on the value of property rights (assets), and an subsequent effect on new capital investment because of these value changes. I have attempt to look at the second part of this mechanism before. 

There is also a literature in this area, which also looks at the “credit-to-GDP gap” (see here, here and here for examples). I see plenty of scope to reconcile Keen’s ideas (focusing on growth rather than levels) with the work of others. There is even an international database on total credit available to researchers following a lot of interest in this idea from the Bank of International Settlements. 

So what

I hope that by highlighting problematic conceptual issue with adding GPD to change in credit, this post improves future debates about the link between the monetary system and economic activity. My impression is that we currently have a group of economists looking at monetary models of the economy, and a bunch of them looking at models of only real goods and services, and they are talking past each other because the are using terms to mean different things. Using my economic domains approach makes this conflict in terminology obvious, and I hope points towards ways to reconcile approaches in a meaningful way.

Lessons from Brexit

I didn’t predict this outcome. Few did. I thought it was too soon. But I wasn’t naive about the politics of the situation. One of my main concerns was that the Remain campaigners seemed overly attached to unrealistic models of economic doom, while simultaneously accusing the other side of spreading lies.

Almost nobody I asked could give me an economic reason to be in the EU. I read nothing that made any sense from this outsider’s perspective. No one could point to a particular policy change and clearly say exactly how the economic ramifications would play out. They couldn’t really. Because nobody knew, or even knows now, what the word of UK trade and immigration policy will look like post-EU.

The whole question is political.

Let me briefly note some of the main lessons I see from this experience. This post is as much a record of my thinking as it is a commentary on politics.

1. Facts don’t matter and politics rewards lies
Anyone able to make an objective assessment of the day-to-day behaviour of successful politicians in any country knows this. Lying is the main ingredient in political success. Yet the Remain campaign seemed to somehow think that stating facts could change people’s minds. For apparently scientifically-minded technocrats, that is absurdly naive.

2. Economic effects will be serious
This is the big lie that the Remain campaign couldn’t bring itself to admit was a lie. If they could admit this, they would have seen the campaign period as a battle of lies, and get over their foolish attachment to their own truth.

That the pound dropped a touch in a short period after the referendum result is economically meaningless. All it says is that currency traders were surprised. We also live in a world embroiled in a currency war, each country looking to deflate to stimulate its export sector. Yet somehow the weak pound is a bad thing for UK.

When other countries observe how economical benign it was for the UK to leave, others will follow, and this lie will become all too obvious even to those who believe it now. As James Galbraith said “such warnings will be even less credible when heard the next time.”

3. Technocrats underestimated peoples willingness to blame outsiders
War is the nature of civilisation. People are tribal animals. Yet somehow the mental model of Remain-side technocrats was too full of ideology over observation. People always blame outsiders for their problems. Always have. Always will. There doesn’t have to be truth in it and telling them ‘facts’ can actually strengthen their beliefs.

4. Naive support for the EU rent-seekers
Many people don't actually benefit from the free movement of labour across the EU. Highly educated professionals do. But your average labourer doesn’t. For most people they see only costs to political integration with Europe. And indeed, any benefits come at the cost of an enormous layer of bureaucracy and rent-seeking.

In many minds, the question is whether you want your political rent-seekers locally raised, or part of the outsider group you are inclined to blame for your troubles. The answer here is obvious.

5. High immigration is disruptive
Take a look at Germany. The refugee crisis really gave them no choice but to accept a huge influx of new immigrants. To maintain internal cohesion will require a massive propaganda effort, coupled with a massive intervention effort to teach the language and culture to the new immigrants.

It’s something that the left doesn’t like to speak about, but the evidence is pretty clear. High rates of immigration are disruptive to social institutions that share a group’s wealth. This is a fact of human nature.

Be honest now. I’m sure you can think of some person, or some group, that you perceive as an outsider and genuinely don’t want to lend a hand to, perhaps you even want to punish them. Absolute humanism, utilitarianism, or whatever you call it, where all lives are equally important, is pure fantasy. We are tribal, and the veil of equality is always a within-group phenomenon.

Last word
In all, the political ramifications of Brexit are far less interesting than the volumes of words spilt about it suggest. Some leaders will come and go as the internal transition is navigated. It’s no big deal. One will stick eventually.

And I think the one who sticks in the UK will have a surprisingly social agenda. A pro-UK agenda. If history is a guide, this is what people want once you've choked off immigration.

Other rich countries in the EU will see how “surprisingly” successful the transition has been and also leave. The EU in its current form is over. Without direct democratic input and fiscal unification it lasted longer than could be expected. We can only hope that what comes out of the EU rubble are the peaceful nation states that it helped create, and decades on we can say that the EU served its purpose of bringing widespread peace across Europe.

Or am I too naive?

In all honesty, if I was voting I would have voted Remain. But not for any rational reason. I just would have conformed to the expectations of my social group. And because of the social reinforcement, I probably would have become very passionate about my position. As a remote observer with no particular interests, it is much easier to see the underlying logic of the situation.

Robinson Crusoe’s real economic choices

The Robinson Crusoe economy is widely used as a teaching aid in economics to explain concepts such as comparative advantage and equilibrium in an exchange economy.

In my view, the use of the Crusoe economy as a teaching aide often trains students to focus only on a few very narrow ideas, and ignore many of the fundamentally important elements involved in economic production and coordination in Crusoe's world.

This will be obvious to you when you watch the latest “stranded on an island” reality television show. The lessons of economics simply don’t correspond to the type of production and coordination I see in them.

In this post I want to show how Crusoe’s story can be an effective teaching aide, and demonstrate a structured, yet pluralist, approach to economic inquiry, in the way I have previously proposed. This structure breaks down an economic problem into various domains of interest, along with a number of guiding questions about aggregation timing, and prediction, in order to assess the types of concepts, models and analysis being applied in each domain.

Rather than use Crusoe's story to justify a concept - “This is specialisation, remember it by the story of Crusoe”, the reverse approach could be taken. “Here is the story of Crusoe, how would we understand that economics of the story?” Having a structured method of economic inquiry then allows students to ‘discover’ the economic concepts you really want to teach them.

Where would such a method of inquiry lead us in Crusoe’s story?

First, here is the standard use of Crusoe, which typically focuses on specialisation when Crusoe is joined by Friday. For some reason he has an absolute advantage in producing fish and coconuts, as each day he can produce more both than his companion Friday. But his relative advantage is in coconuts. The graph such as the one below is then used to demonstrate the gains to specialisation. The dashed light blue line is their combined output without specialisation, and the green line is with each producing the product in which they have a relative advantage, and the gap between these lines near the kink of the green line is the gain from specialisation.

This lesson is simple, and true enough on its face. But it is very incomplete.

So what about my alternative use of the Crusoe economy for teaching economics?

Social and political environment
We first inquire about how Crusoe and Friday came to understand what their social arrangements should look like, noting that any subsequent economic activity will be embedded within these social relationships. In the actual story Crusoe rescues Friday and ‘employs’ him as a servant, teaches him Christianity, and generally creates a hierarchal social relationship. Under this condition the idea that Crusoe and Friday will equally and jointly make decisions about their production activities and trade is a little strange. What will happen is that Crusoe will use the social arrangement to dictate their joint activities in order to fulfil his wishes, which are themselves a product of his previous social environment.

What other social structures could there be in a two-person economy? One case might be that the two are parent and child. In this case the parent will likely have power to dictate the activities of the child, but will also have an incentive to invest in the relationship in order for the child to reciprocate in the future.

The story can be used to open lines of enquiry about social and political structures and their analysis, revisiting this simple case to enforce the basic concepts later introduced.

Money and legal rights
Moving on from social and political environment, we can then interrogate the related economic domains of money and property rights. We can ask questions about who owns what, and how accounts will be kept. Unless we understand the rights of our two gents, we aren’t going to make much progress in understanding the situation.

For example, if Crusoe is a more productive fisherman because he excludes Friday from the most fertile fishing areas by claiming property rights over these areas, this opens up a new puzzle. Would the productivity of Crusoe and Friday be different if they had a different system of property rights? Maybe if Friday could access those parts of the island Crusoe set aside for himself, total output could be much higher. Hence this story can be used to show how understanding the distribution of property rights can help answer questions about whether there are more efficient alternative allocative institutions. For example, maybe cooperative production by fishing together one day, and then collecting coconuts together the next, is even better than any outcome from specialisation.

In the money domain we can ask how Crusoe and Friday plan to keep accounts if they specialise, as per the standard economic account, yet some days the fishing is better than others, and some seasons the coconut palms are not fruiting so prolifically. If their daily output of fish and coconuts fluctuates, we create an inter-temporal problem of smoothing production and consumption via accounting.

What would these accounts look like? Would Crusoe credit Friday some fish when coconuts are slim pickings, and vice versa? At what price could a debt in fish be repaid with coconuts. These questions about how accounts are kept and how they evolve through time really matter for how Crusoe and Friday coordinate their production.

We can use the story as a stepping stone to another story, of the Capitol Hill babysitting coop, and its monetary system, before leaping off to study large-scale monetary systems and central banking.

Real resources and welfare
In the domain of real resources we can ask questions about whether Crusoe has always been more productive, and look at how he came to be; a question of timing. Perhaps he has a fishing net that Friday cannot access. If this is that case were again need to ask the question of why it is Crusoe’s net in the first place it it washed up on the beach.

Putting this to the side, if Crusoe did specialise in coconuts while possessing a fishing net, there will be a loss in potential joint production because of the idle capital of the net. We know that the existence of fixed capital can break down the logic specialisation, undermining the clear-cut beneficial outcome that is presented in textbook economics. And even if Crusoe is somehow innately better skilled at the two activities, it merely begs the question of how he learnt to be better and what is stopping Friday from learning the skills and even surpassing Crusoe’s productivity. These lines of inquiry can lead into the study of trade, and arguments about managerial economics and learning, infant industries, trade protection, and so forth.

We can even build on the standard specialisation story. In the earlier graph I have also plotted a dotted orange line showing a 50:50 split of the output from Crusoe and Friday specialising. Notice that this line sits fully below Crusoe’s own production frontier. What this means is that while there is a gain from trade, it is not clear how it should be split. Obviously, given the existing legal situation and capital stock, Crusoe is more productive and will be able to extract a greater than half share of the resulting larger combined economic pie. But how much?

If we deal just with the kink in the combined production frontier for a moment, if Friday receives a 37.5% share of combined output he is just as well off as going it alone and not trading. At that same kink point, Crusoe is just as well off if he receives 53.9% of the combined production of fish and coconuts.

Here we have a problem. This trade produces a surplus that needs to be shared. Somewhere between 37.5 and 46.1% of combined output to Friday and the rest to Crusoe will make them both better off in pure output terms. How this surplus gets divided is a defining issue of economic distribution and welfare which is fundamentally ignored by most economists. It is a question of who gets the rights to surpluses generated by trade. If Crusoe captures all the surplus, inequality on the island will start increasing, but if Friday can capture most of it, their wealth will become more equal.

Because Crusoe and Friday now face the problem of how to allocate their economic surplus, the story allows us to introduce ideas of utilitarianism, including how welfare can be assessed or improved.

The story also provides scope to lead into questions about whether the standard story of specialisation makes useful predictions applicable to the modern world. On this account, some of the basic predictions of the standard story of specialisation and trade fail, as Hill and Myatt explain

…since the industrialized nations are so similar – similar economic structures, resources and technology – they likely have similar opportunity costs in production. Thus, they would not be expected to trade much with one another. But in fact industrialized countries trade extensively with one another. He says: ‘Over 70 per cent of the exports of industrialized countries go to other industrialized countries … These facts appear to be inconsistent with comparative advantage theory’

We should be asking why that it, and looking at what else may be happening. 

Indeed, we can take the next step after discussing specialisation to ask how the scale and diversity of Crusoe and Friday’s economic output can be increased once they have learnt to optimally collect coconuts and go fishing. We then talk about capital investment, innovation, and so forth.

So what?
The story of Crusoe is usually seen as a memorable simplification for teaching a couple of basic economic concepts. But I argue that it can instead be used to teach a structured and coherent pluralist approach to economic inquiry. In doing so, this approach makes clear the many hidden assumptions necessary to concentrate on the economic analysis of specific domains of the Crusoe economy, and ensure students understand from the very beginning that this is the norm in economic analysis, and to remain critical.

Time to revisit how we calculate expectations?

The below presentation by Dr Ole Peters opened my mind. If there was one thing I believed was a reasonable implicit assumption of economics, it was determining the expectation value upon which agents base their decisions as the “ensemble mean” of a large number of draws from a distribution. Surely there is nothing about this simple method that could undermine the main conclusions about rational expectations, whether humans act that way or not? Surely this is a logical benchmark, regardless of whether actual human behaviour deviates from it.

But now I’m not so sure. Below is a video of Dr Peters making the case that non-ergodicity (according to the physics interpretation of the word) of many economic processes means that taking the ensemble mean as an expectation for an individual is probably not a good, or rational, expectation upon which to base your decisions.

I encourage you to watch it all.


Let me first be very clear about the terminology he is using. He uses the term ergodic to describe a process where the average across the time dimension is the same as the average across another dimension.

Rolling a dice is a good example. The expected distribution of outcomes from rolling a single dice in a 10,000 roll sequence is the same as the expected distribution of rolling 10,000 dice once each. That process is ergodic [1].

But many processes are not like this. You cannot just keep playing over time and expect to converge to the mean.

Peter’s example is this. You start with a $100 balance. You flip a coin. Heads means you win 50% of your current balance. Tails means you lose 40%. Then repeat.

Taking the ensemble mean entails reasoning by way of imagining a large number coin flips at each time period and taking the mean of these fictitious flips. That means the expectation value based on the ensemble mean of the first coin toss is (0.5x$50 + 0.5*$-40) = $5, or a 5% gain. Using this reasoning, the expectation for the second sequential coin toss is (0.5*52.5 + 0.5 * $-42) = $5.25 (another 5% gain).

The ensemble expectation is that this process will generate a 5% compound growth rate over time.

But if I start this process and keep playing long enough over time, I will never converge to that 5% expectation. The process is non-ergodic.

In the left graph above I show in blue the ensemble mean at each period of a simulation of 20,000 runs of this process for 100 time periods (on a log scale). It looks just like our 5% compound growth rate (as it should).

The dashed orange lines are a sample of runs of the simulation. Notably the distribution of those runs is heavily biased towards final balances of around $1 (remembering the starting balance was $100).

In fact, out of the 20,000 runs in my simulation, 17,000 lost money over the 100 time periods, having a final balance less than their $100 starting balance. Even more starkly, more than half the runs had less than $1 after 100 time periods. The right hand graph shows the final round balances of the 20,000 simulations on a log scale. You can read more about the mathematics here.

So if almost everybody losses from this process, how can the ensemble mean of 5% compound growth be a reasonable expectation value? It cannot. For someone who is only going to experience a single path through a non-ergodic process, basing your behaviour on an expectation using the ensemble mean probably won’t be an effective way to navigate economic variations.

I see two areas of economics where we may have been mislead by thinking of the ensemble mean as reasonable expectation.

First is a very micro level concern: behavioural biases. The whole idea of endowment effects and loses aversion make sense in a world dominated by non-ergodic processes. We hate losing what we have because it very often decreases our ability to make future gains. And we should certainly avoid being on one of the losing trajectories of a non-ergodic process.

The second is a macro level concern: insurance and retirement. Insurance pools resources at a given point in time across individuals in the insurance scheme in order that those who are lucky enough to be winners at that point in time, make a transfer to those who are losers. By doing this, risk is shared amongst the pool of insurance scheme participants [2].

Retirement and disability support schemes are social insurance schemes. They pool the resources of those lucky enough to be able to earn money at each point in time, and transfer it to those that are unable to.

But there has been a big trend towards self-insurance for retirement. In the US they are 401k plans, and in Australia superannuation schemes. Here the idea is that rather than pooling with others at each point in time (as in a public pensions systems), why not pool with your past and future self to smooth out your income?

You can immediately see the problem here. If the process of earning and saving non-ergodic and similar in character to the example here, such a system won’t be able to replace public pensions, as many individuals earning and saving paths will never recover during their working life to support their retirement. Unless you want the poor elderly living on the street, some public retirement insurance will be necessary.

Undoubtedly there are many more areas of economics where this subtle shift in thinning can help improve out understanding of the world (I’m thinking especially about Gigerenzer’s ideas of heuristics approach as being ways humans have evolved to navigate non-ergodic processes).

I will leave the last word to Robert Solow, who has had similar misgivings (for over 30 years!) about our assumptions of ergodicity (a stationary stochastic process) which undermine rational expectations.

I ask myself what I could legitimately assume a person to have rational expectations about, the technical answer would be, I think, about the realization of a stationary stochastic process, such as the outcome of the toss of a coin or anything that can be modeled as the outcome of a random process that is stationary. If I don’t think that the economic implications of the outbreak of World war II were regarded by most people as the realization of a stationary stochastic process. In that case, the concept of rational expectations does not make any sense. Similarly, the major innovations cannot be thought of as the outcome of a random process. In that case the probability calculus does not apply.

fn[1]. He does not use the term as it is often used in economics as describing what often falls under the term Lucas critique, or in sociology is called performativity. Basically, it is the idea that the introducing a model of the world creates a reaction to that modal. Take a sports example. As a basketball coach I look at the past data and see that three point shots should be take more because they aren’t defended well. I then create plays (models) that capitalise on this. But because my opponents respond to the model, the success of the model is fleeting.

fn[2]. Peters himself has a paper on The Insurance Puzzle. The puzzle is that if it is profitable to offer insurance, it is not profitable to get insurance. The typical solution invokes non-linear utility to solve it. Peters offers an alternative. My take is on the economic implications of this - if people can smooth through time for retirement than there is not logic to social insurance.

The great Australian town planning give-away

It is the gift that keeps on giving for the Australian property developer lobby. Planning gains. Betterment. Whatever you call it, it is a multi-billion dollar give-away to the politically connected happening every year.

It works like this. Property developers buy land with the accompanying right to use it for a certain purpose, which is typically prescribed in the local council planning documents. They then lobby their mates in power to change the prescribed uses in the plan, in the process giving them a new property right which they did not pay the previous owner for. Nor did they pay the government for that new right. It was a gift.

But in Australia’s beloved capital city this game of giving planning gifts to your mates doesn’t work. There is no gift. In the Australian Capital Territory, if you want more property rights, you pay the government for them.

The ACT government achieves this in two ways. First, it has a public body that plays the role of land developer, the Land Development Agency, which converts land into urban uses, invests in infrastructure, and sells the new plots of land at market prices. When it sells this land it comes with the requirement to build on that land within two years in accordance with the purpose clause of the land title. By acting as the developer, 100% of the windfall planning gains goes to the government in manner that is economically efficient.

Second, if you have land that can be developed to higher uses within relevant zoning rules of the town plan, you must pay the government a Lease Variation Charge (formerly a Change of Use Charge) of 75% of the value gains to the land from allowing the higher value use.

These two schemes earned the ACT government $164 million and $19 million in 2014-15 respectively. That’s $183 million in revenue that would be given away to land developers in other states.

So how big is the great betterment give-away occurring in other states? We can scale up the ACT data to get a good estimate of the size of this give-away happening in the rest of the country.

There are two main adjustments necessary to do this. First is to adjust for the dwelling price differences across states. While the two schemes apply to all types of land, including residential and commercial, the residential values dominate. I therefore adjust the figure by the ratio of state median dwelling prices to ACT median prices to get the price ratio. I then adjust for the number of new dwellings in other states completed in that year to get the dwelling ratio. I then calculate the total scaling factor as price ratio times the dwelling ratio. Then I multiply this by the ACT betterment revenue and sum across states.

The result is summarised below. And the answer is $11 billion.

	Median price (May 2015) CoreLogic	Trend new private dwellings (ABS, year to June 2015, State)	Price ratio	Dwelling ratio	Scaling factor	Scaled revenue ($m)
Sydney	$ 691,000	51,368	1.39	14.13	19.57	3,582
Melbourne	$ 502,000	64,529	1.01	17.75	17.86	3,267
Brisbane	$ 424,000	42,055	0.85	11.57	9.83	1,799
Adelaide	$ 383,000	10,079	0.77	2.77	2.13	389
Perth	$ 528,000	30,343	1.06	8.35	8.83	1,616
Hobart	$ 299,000	2,734	0.60	0.75	0.45	83
Darwin	$ 510,000	1,648	1.02	0.45	0.46	85
Canberra	$ 499,000	3,636	1.00	1.00	1.00	183
Total						10,821

That sounds right to me. $11 billion is what the Australian states gave away to landowners and property developers in 2014-15, that they could have recouped had they had the system of betterment taxes that the ACT has had since 1971.

As a final point, you might think that the degree to which the ACT government controls land uses might have some effect on slowing new investment in dwellings. This is not the case. The ACT has the largest homes in the country, and has the same bedrooms/person ratio (a measure of dwelling stock per capita) as Queensland, slightly behind Tasmania, but in front of NSW and Victoria. While I remain cautious about the ability for such systems to be taken advantage of, I see the current system of private landowners taking planning gains and determining the new supply even more prone to political corruption and favouritism. Rezoning gifts don't even come with obligations on developers in other states to actually build what they promise. They can sell the land with the new rights the following day and cash in their gains. 

Throw out the standard urban economics model

The workhorse model of urban economics is the Alonso-Muth-Mills (AMM) model of the mono-centric city (the modern treatment is attributable to Jan Bruckner). This model is basically the representative agent optimal-control model of neoclassical economics. It is modified with additional functions that account for the cost of commuting to a city centre from different distances and allows capital, K, to be optimally geographically dispersed as well.

Sweet right?

The only problem is this. When you convert the model to English you realise it has little basis in reality. The only real pattern that is consistent with the model is that higher buildings are near the city centre. But I could come up with a million other models that are consistent with that pattern.

One of the main flaws in the AMM model is that there is no possibility for development of sites within the city into new buildings. Every site is already used at its optimal level. There are no vacant sites or sites with old buildings ready for knock-down and reuse. There is no development industry. There are no landowners.

Also because of the comparative-static nature of how the model is used, every time there is a marginal change in any of the parameters of the model — a new person moves to the city, the rental price of the second best land use increases, or the efficiency of construction methods change — the whole city is wiped clean of homes and buildings. The single social planner who controls everything in the city then dictates that the whole city will be rebuilt with a new optimal allocation of housing and commercial buildings under new conditions, and this whole new stock of buildings rebuilt in an instant to that new specification.

Don’t believe me? Here are comments from eminent urban economist David Pines from back 1987 making the same point.

The static approach in the Alonso-Mills-Muth model is useless in explaining many stylized facts regarding the urban structure and its evolution through time. In the static analysis... land is continuously utilized within the city boundaries and the city boundaries are continuously extended with income and population size.
...
The reason for the failure of the static model in explaining these ‘irregularities’ is that the housing stock is assumed to be perfectly malleable, which, of course, is highly unrealistic.

Perfectly malleable. That’s the crux here. Behinds this term hides the complete nonsense I just described about the constant rebuilding of the entire city.

This is a massive problem for anyone wishing to apply economics to urban planning. Because in the AMM model any constraint on land use — be it a natural feature such as a lake, river, or mountain, or a regulatory constraint in the form of height limits, floor area restrictions (FAR), or greenbelts — increases prices by forcing the malleable capital stock of homes and buildings to spread further from the city centre.

But this simply cannot be true outside of the model. There are so many contradictions between the model and reality that its conclusions cannot be taken seriously. For example, the existence of a development industry that takes sites that are vacant or in low-value uses and invests in new buildings isn’t captured in the model. There is no such mechanism because there is no vacant or under-utilised land. Every piece of space already has a building at the perfect economically-optimal height for that location.

I created the below image to show the common real-life elements of real cities that can’t exist in the standard AMM model. Let me explain.

The horizontal axis represents the distance from the centre of the town. Imagine taking a slice of the city along the roadside as you drive outwards from the city centre. You will see the density of buildings fall, which are represented here in dark grey. What you see in the real world is just the dark grey. 

The world of the AMM model is represented by the blue line, showing the optimal development density at each point along the road at a given time. In the city centre, where rents are highest, it is optimal to build higher buildings. Higher rents justify the investment in taller buildings. But then as you go further from the city centre, the rents at each location can only justify a smaller building on each site. I call this the “site economic frontier” because for each individual site at a given point in time, it is the economic limit of development.

In the AMM model, the whole city is full to the blue line. Always and everywhere. So you can begin to see the problem. There are substantial gaps between this model outcome and the reality of the grey buildings.

Moving along, the dashed orange line represents town planning constraints. Near the city centre I have shown how a height limit will create a gap between the site economic frontier and the “planned frontier”, or planning limit. I have also shown how such gaps are created by site-specific controls such as heritage protection (meaning you can’t demolish the building and then build to the site’s economic frontier). And I have shown how city boundaries like greenbelts or urban footprints create a similar gap.

The blue shading is therefore the economic-planned frontier gap. In the AMM model this is a problem, because before introducing such a gap the city is full to the brim, with buildings always built in every location to the economic frontier, so it results in a net loss of dwellings and buildings, even after accounting for feedback into higher prices and a higher economic frontier in other areas.

Yet in the real-world view, introducing such a gap changes nothing. Buildings are not demolished and rebuilt in different locations. Landowners in certain locations are simply limited by a “regulatory geography” rather than the “economic geography”, neither of which the city as a whole is anywhere near.

The existence of the light orange shading — the gap between the currently built city and the planned frontier — also cannot exist in the AMM model. There are no development opportunities. Even worse, there are no vacant land sites. This is an even bigger problem for the model.

I highlight this particular point by shading the gap between vacant sites and the planned frontier in darker orange because in the real world these are the most likely sites to be next developed. On the left of the diagram I also have a little curve that is supposed to show the probability of a site being developed as a function of its currently developed density or height. The smaller the current development, the more likely that site will be developed next, as there are lower costs in doing so in terms of demolition.

Overall then, we have a diagram that shows the major problems for the standard AMM model of urban economics. There can be no development industry in the AMM model because there is no planned-frontier gap. But even worse, the fact that reality doesn’t fit well to the model means that there must be some other mechanism determining the rate of investment in new housing and development. Something entirely ignored in this model. And even worse, entirely ignored in the current popular textbooks on urban economics.

I have been through this before. Vacant land is a perpetual real option to invest. The optimal timing of when to invest in a building — to exercise the development option — is when you expect that doing so maximises its value (read up on the Bellman equation if it takes your fancy). Otherwise, you wait. Because while today it might be optimal to build a five-storey building, in a couple of years it might be optimal to build a 12-storey building, providing even greater incomes. And you can’t do both.

This turns the standard model on its head. It means that because planning controls, such as height limits, take away this future option to build higher buildings, the value of waiting to build is lower, and the typical landowner will bring forward their investment, increasing the rate of new dwelling supply.

To me, the fact that the standard AMM model doesn't fit the data, and because we know land is best characterised as a real option, it must surely be time to throw out this model and update the textbooks.

Update: Read more about the option to delay development here.

The mysterious real interest rate of economic theory

The mysterious real interest rate – the one typically denoted as r in economic theory – does not have a real-life counterpart. This is a problem for economic theory. And it is a major problem for policymakers relying on monetary policy to boost economic activity.

While we think of the nominal interest rate minus inflation as getting close to the theoretical concept of real interest rates, changing this value in practice through central bank operations does not actually change the real return on capital and stimulate investment through that channel.

Why?

Because the price of capital is determined by the interest rate! We have known this for a long time. Joan Robinson wrote about the circularity of reasoning when we measure the quantity of capital by its price. She was ignored. As I expect to be.

For those who want to understand a little deeper, here are some more details. First, we take the standard economic view. In this view there is a thing called capital, K, that has a fixed cost (because it is a machine or building etc.), and each unit of K has an income-earning potential, net of depreciation, each period, which I call I. To buy each K people borrow money at the rate, r, meaning that as long as the ratio I/K > r it is profitable to invest in more capital, K.

So if my business can generate $100,000 in extra profit each from an extra machine, the business might see the value in spending $1,000,000 on that machine if they can borrow to pay for it at a 9% interest rate (costing $90,000 per year in interest), rather than an 11% interest rate (an annual interest cost of $110,000).

However here’s the circularity problem. The gains from a lower cost of new investment are made whether the investment is undertaken or not because they become capitalised in the value of the business immediately. That is because the value of the option to expand is always captured in the market value of the assets of the business.

What is this option I speak of? Where did it come from all of a sudden?

The way I snuck this into my definition of capital is part of the fundamental problem that permeates all the economic debates about capital. One group talks about capital as machines — independent robots, vehicles, machines and tools, who get to keep the returns from their existence. Yes, my bulldozer gets income from its efforts in this view, not the owner of the bulldozer. Because once you have an ownership structure overlaid, you have a system of property rights which contain real options for investment, and they have a value.

Think about land. Land is often referred to as capital, but it is nothing but a piece of paper offering a particular set of rights to a three-dimensional chunk of the universe. Land is an ownership right, not a physical object. See my mud map of economic concepts to help see what I mean here.

Once we have shifted to a view of capital of a system of property rights, some of which have physical machines attached to them — like a building attached to land rights, or a truck attached to various rights held by a trucking company — we can begin to see the circularity problem more clearly.

We now have a world were investors maximise the return on their property rights, not one where machines decide how to maximise the return on themselves.

This means that anyone making a decision to invest in new machines must take into account the current value of their property rights as part of the cost of capital. Because the full opportunity cost of the investment in a machine is the next best alternative, which is to sell the property rights at market value. In the diagram below I try to capture the idea that all physical capital — buildings, machines and so forth — are attached to property rights, and that only if we look at the value of the whole can we get the true cost of new capital investment from the perspective of owners of property rights.

Let us now see the effect of decreasing interest rates in a world of property rights, and where the value of these rights is part of the cost of capital. We will take the simplest case of a piece of vacant land, where the full value of the property right is from the option to build a $1 million building on that land to earn a future income of $100,000 per year. Here only the building is part of physical capital in standard economic theory.

We will then see what effect a reduction in interest rates has on the cost of “property plus capital”, and therefore the incentive to invest for owners of property rights. The table below summarises.

	Before	After	Further
Interest rate	11%	9%	7%
Income from investment	$100,000	$100,000	$100,000
Capitalised value of income	$909,091	$1,111,111	$1,428,571
Cost of standard K	$1,000,000	$1,000,000	$1,000,000
Return on standard K	-9%	11%	43%
Value of property right	-$90,909.09	$111,111.11	$428,571.43
Cost property rights K	$909,091	$1,111,111	$1,428,571
Rate of return on property rights K	0%	0%	0%

Let me walk you through this. The interest rate is the real interest rate. Take it as the nominal interest rate in a zero inflation environment for simplicity. The income from investment is the annual income after the building is built. The value of that income is capitalised at the new interest rate to show the static value. Then we see that when the interest rate is reduced, the $1 million building gets a positive rate of return, and hence the change to the interest rate will provide the incentive to invest.

As a side note, the alternative way to see this is to simply assume that the cost of the building is borrowed at the interest rate, as I did earlier when discussing the standard view. In this case, the cost of capital is $110,000 per year before the interest rate fall, and $90,000 per year after the interest rate drop, shifting the investment from an unviable to viable way earn the $100,000 per year.

But, if we consider the value of the property right as well, we have a different picture. Here, the value of the property right is the residual after taking the investment return (capitalised value of income) and subtracting the physical investment cost (cost of investment). With interest rates of 9% in the 'Before' case, the value is negative, and there is clearly no return on capital (i.e. for property valuers out there, this building is not the highest and best use of the land). But even after the interest rate is dropped to 9%, the return on the combined “property plus capital” is zero, because the cost of capital now includes the opportunity cost of selling the property right at a positive price.

Even if we decrease interest rates further, say to 7%, the rate of return on “property plus capital” is still zero, as I show in the last column. Owners of property rights simply gain at the expense of those in society who do not own substantial property rights and will be future buyers of those rights.

Under this view, the investment effect of lower interest rates disappears. The reason is that the capital of economic theory, and hence the real interest rate of economic theory, cannot be detached from the reality of a system of property ownership rights.

I’m not the only one to say this either. Once you are in a world of property rights and real options, the key determinant of investment is not the real interest rate of standard theory. Here’s Raj Chetty showing that increasing interest rates from low levels can bring forward investment — the exact opposite of the standard view. In a world of property rights an real options, the key factor is not what to invest, but when to invest in order to maximise the rate of growth in the value of your property rights. Hence there is a huge role for speculation on the price of property rights, and a clear logic behind following the herd during asset cycles. Under these conditions, it is also the case the reducing interest rates reduces the cost of delaying investment, and may, in fact, slow rates of investment and economic activity!

Let me summarise. First, standard theory has machines earning incomes and ignores the system of property rights it attempts to model. Second, once you incorporate a system of property rights these right have values, and the value of these rights must be added to the cost of machines to calculate the economic (opportunity cost) of capital. Third, once you have done this, changing the nominal interest rate (or even nominal rate minus inflation) changes no investment incentives, as all property rights holders immediate gain the value, which becomes a cost of investment. Finally, other factors that affect the cost of delaying investment by owners of property rights probably have a larger effect on investment, and in fact, decreasing interest rates decreases the cost of delaying investment.

This is not to say that there may be some effect of monetary policy through other channels, such as decreasing interest costs of borrowers, allowing them to increase spending. But if this is the dominant effect, without an investment incentive, then loose monetary policy may primarily inflate asset prices and not economic activity. This prediction gels with the reality of the past decade.