Sunday, March 30, 2014

Uncertainty is not what you think it is


One strange claim in the economic debate that followed the financial crisis was the impact of uncertainty on the path of investment and subsequently the recovery in economic activity. Taking just one example, it was claimed here that “fiscal policy uncertainty has directly harmed the American economy by increasing the unemployment rate by 0.6%, or the equivalent of 900,000 jobs.”

Often the idea of uncertainty is captured in economic debates by labelling its inverse, a high degree of certainty, ‘confidence’, or when being a little more critical, the ‘confidence fairy’.

It was never particularly clear to me exactly what ‘high’ or ‘low’ uncertainty was supposed to mean, since the future is always uncertain and investment is always risky, and current policy decisions are not set for eternity. In this post I will dig down into the economic theory of real options that forms the basis for claims that uncertainty alone can greatly reduce investment activity. By doing so I hope the reader will develop a considered level of scepticism about such claims.

First, we should acknowledge just how widespread the idea that uncertainty hampers investment has become. There is a website devoted to providing national indices of policy uncertainty, which itself rests on two decades of effort in academic circles to endeavour to capture this mirage-like phenomena. Even now, India’s growth slowdown is being blamed on this mythical beast.

As a general observation, it seems there is no economic ill that cannot be blamed on government policy-induced high levels of uncertainty.

The economic origins of the idea start with Black-Scholes, and were more fully developed in the general sense in terms of capital investment by Dixit and Pindyck in what is generally known as real options theory. While I have concerns about how real options is applied (which I will get to in a moment), the fundamental principle embodied in real options theory is crucial to understanding economics.

The basic idea is this. If the future is uncertain, such that your future revenues and costs won’t be exactly what you expect, then you may choose to delay investment in order to get new information about the best investment choice.

Thus, when there is more uncertainty, or what would technically enter the real options model as a larger standard deviation on the expectations of price movements, then the value from delaying investment in order to better asses new information is greater.

Under these conditions firm value maximisation occurs not by profit maximising, but by maximising the rate of change of profit over time, or the rate of return on firm equity. The idea here is that investors choices based on expectation of both price levels and the rate of change in prices.

That’s whole idea right there. If you follow that through without thinking too much more about it, you can end up at the point of advising governments to ‘fix up certainty’ in order to bring forward investment decisions in order to reduce unemployment and increase economic growth.

But that ignores some very important points, which I haven’t seen properly addressed in the application of real options theory.

First, why is a perfectly known probability distribution in any way uncertain? We have done the old trick of calling the distribution of expectations (or for that matter simply the distribution of past price movements) uncertainty instead of its usual label, risk. Unquantifiable Knightian uncertainty remains ignored. Which means that even if the distribution of price expectations narrows, and real option theory says that such a thing will encourage investment, there remains a value to delay at all times if there is even a trace of unquantifiable uncertainty.

For me, this lack of distinction removes the possibility for real options theory as it stands to provide insights into the business cycle, particularly in relation to the type of herding behaviour we see both in financial and real resource investments. My personal view is that ubiquitous unquantifiable uncertainty is fundamental to understanding why investors can appear irrational, and why our innate herding behaviour is often a more useful and actionable decision rule for investment.

Second, even accepting that risk appropriately captures the rationale for delaying investment, changing the average expectation doesn’t change uncertainty. Most commentators who argue that their policy proposals reduce uncertainty are actually more concerned with shifting the average expectation of price movements upwards. But if the whole distribution shifts, but doesn’t narrow, then uncertainty is unchanged and it remains equally rational to delay investment in the face of increasing prices.

Third, it is not at all clear what the implication for real options is when rather than shrinking the spread of the distribution, the complete nature of the distribution changes. What I mean by this is that if risk appears normally distributed at some point in time, but events occur that change expectations of future price outcomes to be exponentially distributed. Moreover, there is no real understanding of the emergent properties of agents interacting with different risk expectations - are these interactions already captured in perceptions of risk, or do they add an additional dimension which take risk perceptions into the territory of pure uncertainty?

Finally, it is well known that even in the absence of uncertainty there can still be a value to waiting to invest for current asset owners. For example, if I own a piece of land with scope for development, in the case where there is uncertainty about future prices it may be optimal to wait to see which direction prices move in order to determine the optimal building type and size to construct to maximise my land value. But even if I know exactly what prices and construction costs will be over the course of the next few years, I may still choose to delay if I expect (perfectly, with no uncertainty) the value of the land in its undeveloped state to increase at a faster rate than when it is developed. Or indeed, to not lose value as quickly if it were the case that prices are falling.

So while claims of policy uncertainty having large real impacts in investment may appear well-grounded in economic theory, the theory still has many problems when applied to real policy, real investment and a real world of fundamental Knightian uncertainty. However I do hold out some hope that the core elements of real options theory, which are substantial improvements on the usual equilibrium theory of mainstream economics, can be more successfully incorporated into our understanding of investment and the business cycle.

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Thursday, March 27, 2014

Intuition in economics can't replace reason


One thing you will notice early on about economics is the overuse of the term intuition. Typically the term is used like this “Let me give you the intuition behind this model”. Or something.

Let’s take a look at the common definition of intuition for starters. Google tells us that intuition is the ability to understand something instinctively, without the need for conscious reasoning.

Which, when you think out it (when you reason) you see that intuition is merely an excuse NOT to reason - it is instead a way to latch onto ideas that support pre-existing beliefs.

When I hear a seminar presenter say “let me give you some intuition”, I now translate it in my mind as “let me align my theory with your beliefs so you will have trouble disagreeing with me regardless of the strength of my reasoning and the evidence I present."

I find the elevation of economic intuition to a skill in itself to be very unscientific.

In physics, for example, I see people discussing intuition as either experience with certain types of mathematics (you internalise the steps of mathematical logic), or as experience in the physical world - of taking one’s lived experiment and applying what are now intuitive results to problems. You know a lever works because you have used levers many times. The results do not contradict your lifetime of personal trial and error and therefore the result is intuitive. But from my experience, this is not what economists mean.

Duncan Watts describes much better how intuition pervades social sciences and stifles scientific advancement, particularly in economics.
Part of the problem is also that social scientists, like everyone else, participate in social life and so feel as if they can understand why people do what they do simply by thinking about it. It is not surprising, therefore, that many social scientific explanations suffer from the same weaknesses—ex post facto assertions of rationality, representative individuals, special people, and correlation substituting for causation—that pervade our commonsense explanations as well.
In many ways, intuition from experience should be irrelevant to individuals analysing complex systems from within them, since the properties of the whole are typically unrelated to the properties of individual parts. 

With so much emphasis on intuition over reason, it is no wonder that a fair portion of economic debate has not progressed in 140 years.

Thursday, March 13, 2014

Spartan Morality


I want to show how the morality on display in the movie 300, in which babies are cast into a chasm for minor deformities or other weaknesses and illnesses, is easily compatible with utilitarian logic. In doing so I hope to show that utilitarianism provides completely insufficient scaffolding around moral reasoning to eliminate almost any policy, norm or cultural practice you desire.

I was motivated to write this post after discussions that were stoked by my take on the moral foundations of economics, particularly in relation to health policy. Why it is optimal from a utilitarian point of view to allocate medical resources to the young rather than the elderly? While my personal view is that in our current social and political environment this is probably appropriate, it is by no means a superior position by utilitarian reasoning, and certainly there remains debate about such welfare foundations. 

To get this brief analysis started, here is a Wikipedia excerpt about life in Sparta
Shortly after birth, a mother would bathe her child in wine to see whether the child was strong. If the child survived it was brought before the Gerousia by the child's father. The Gerousia then decided whether it was to be reared or not.
It is commonly stated that if they considered it "puny and deformed", the baby was thrown into a chasm on Mount Taygetos known euphemistically as the Apothetae. This was, in effect, a primitive form of eugenics.
Sparta is often portrayed as being unique in this matter, however there is considerable evidence that the killing of unwanted children was practiced in other Greek regions, including Athens.
Here’s that basic utilitarian rationale for the ‘Spartan morality’ of disposing of sick children. It requires a number of starting propositions.
  1. That people with life-long physical disabilities or other chronic illness have lower utility than those without
  2. The existence of these ill people reduces the utility of their carers
  3. The reduced ability to contribute to productive activity of disabled and their carers (and medical professionals) reduces the utility of others in society
  4. Disposing of sick children brings forwards births of non-sick children because of replacement reproductive effort
  5. There is relatively low utility loss from mothers and family of disposing of their sick child
In fact, we need not even invoke the 2nd and 3rd propositions in order for Spartan morality to be utilitarian, since the 1st, 4th and 5th clearly show that infanticide of the sick, “puny and deformed”, would be a straight substitute of one lifetime of low utility for one lifetime of high utility.

And that’s just about all you need. 

I hope that this challenges your faith in the objectiveness of economic reason. As Joan Robinson would say, utility is a mere meta-physical construct - its existence resting on a series of circular reasoning, defining it in terms of itself. 

Similar utilitarian reasoning could be applied to the subjects of gay marriage, slavery, or other such social practices to support any desired outcome.

We shouldn’t feel helpless in the absence of an objective method of social reasoning. We should feel freed from its shackles to debate the our underlying moral values, and why they are appropriate for a modern wealthy society. 

Applying utilitarianism means you can support mutually contradictory ends and means. You can end up at the repugnant conclusion, or justify slavery to a 'utility monster'. Or if you take an average  principle of utilitarianism, you can get to the point of justifying killing disabled children by appeal to Spartan morality. Or, as we deem currently acceptable, arrive at the point where we should allocate the medical resources to children above the elderly in accordance to ‘need’. 

There is no absolute reference point in utilitarianism. It is always applied with reference to current norms, customs and practices and can evolve to support different conclusions as society evolves.

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Sunday, March 9, 2014

17million Reasons Rent Control is Efficient


The case of Herbert Sukenik being paid $17million in 2005 to leave his rent-controlled NYC apartment has been receiving a great deal of attention online recently. 

At the risk of perpetuating the brilliant viral marketing campaign for Michael Gross’ new book, which is in fact the source of the story, I want to make a brief comment about it to counter some of the bizarre, emotional, and inconsistent reactions I have seen.

A short version of the story is that billionaire developers Arthur and William Zeckendorf paid $401million for the Mayflower Hotel adjacent Central Park, planning to turn the site into 202 super-luxury apartments.

The building was occupied by many long-term tenants under New York’s rent-control laws. This meant that tenants could only be evicted upon mutual agreement, which in turn led to the new owners offering attractive lump sum payments to tenants for them to leave the building. While most tenants accepted offers ranging from $650,000 to $1million, the final tenant held out for an astonishing $17million lump sum payment, in addition to the developers offering him another apartment to live in for the rest of his life for a peppercorn rent of $1 per month.

To me the most astounding part of the story has been the reaction by the press and social media, which has been of outrage over the injustices of rent control - that for some reason poor old Sukendik didn’t deserve the money.

There have also been cries of rent-control hindering development - that somehow rent-control is ‘inefficient’.

This absolutely wrong. Wrong, wrong wrong.

First, almost everyone has ignored the key fact that a developer buying the building knowing that rent-controlled tenants are occupying it should have expected these expenses and subtracted them from the purchase price. Thus, the tenants win at the expense of the previous building owner. The developer does not lose unless some unexpected legal loophole was exploited (which doesn't appear to be the case) - it is merely that the economic rent was shared between the previous owner and the previous tenant.

It is therefore not any less efficient than in the absence of rent control. No one sees the previous building owner holding out for $401million as inefficient, yet it is exactly the same dynamic at play. 

The second point routinely ignored is that rent-control describes a general set of rules about renting. That the NY set of rules allows this to happen doesn't mean that another set of rent-control rules could be implemented that had mechanisms for relocation and prescribed methods for calculating compensation payments to tenants. After all, in the freehold world there are generally accepted methods for compensation for land owners upon compulsory acquisition by a government authority.

Third, if Sukenik owned his apartment in freehold he would have had the same power to hold out and extract this price from the developer. This happens routinely in Australia and elsewhere when strata-titles buildings are redeveloped. The last hold out seller extracts a massive payout. Yet we see nothing at all wrong with that because they have ‘the right’ to do it. Yet under a different set of laws, tenants could also have such rights, which they did in this case. 

What really surprises me is that almost everyone who has written a reaction to the incident seems to fall on the side of the developer. If the developer had kicked out the tenant for $10,000 it wouldn't be news, but it would have been equivalent to 'Developer screws tenant of their rightful $17million compensation’.

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Friday, March 7, 2014

Wrong lesson from Adam Smith's pin factory


We commonly use stories to teach new ideas, but all too often end up taking the wrong lessons from them. My favourite example is the Coase theorem. Economics textbooks describe theorem as saying that it doesn’t matter where you place the liability for pollution, because in a world of zero transaction costs the right to pollute will end up in the hands that value is most. This is the exact opposite of the point Coase made. As Deidre McCloskey wrote,
Economists have gotten the “theorem” wrong; in fact, backwards

Coase’s actual point, the core of a Coasean economics, was to note what happens in the many important cases in which transactions costs cannot be neglected. If the situation does have high transactions costs, then it does matter where the liability for pollution is placed.
I was alerted to another example in Joan Robinson’s long forgotten textbook. In it she dismisses the division of labour as a primary factor in the great surge in productivity of the industrial revolution, noting that this is the wrong lesson to take from Adam Smith’s pin factory story.

First let me recount the relevant part of Smith’s writing where he describes the productivity boon enabled by the division of labour.

To take an example, therefore, from a very trifling manufacture; but one in which the division of labour has been very often taken notice of, the trade of the pin-maker; a workman not educated to this business (which the division of labour has rendered a distinct trade), nor acquainted with the use of the machinery employed in it (to the invention of which the same division of labour has probably given occasion), could scarce, perhaps, with his utmost industry, make one pin in a day, and certainly could not make twenty.  
But in the way in which this business is now carried on, not only the whole work is a peculiar trade, but it is divided into a number of branches, of which the greater part are likewise peculiar trades. One man draws out the wire, another straights it, a third cuts it, a fourth points it, a fifth grinds it at the top for receiving the head; to make the head requires two or three distinct operations; to put it on, is a peculiar business, to whiten the pins is another; it is even a trade by itself to put them into the paper; and the important business of making a pin is, in this manner, divided into about eighteen distinct operations, which, in some manufactories, are all performed by distinct hands, though in others the same man will sometimes perform two or three of them.  
I have seen a small manufactory of this kind where ten men only were employed, and where some of them consequently performed two or three distinct operations. But though they were very poor, and therefore but indifferently accommodated with the necessary machinery, they could, when they exerted themselves, make among them about twelve pounds of pins in a day.  
There are in a pound upwards of four thousand pins of a middling size. Those ten persons, therefore, could make among them upwards of forty-eight thousand pins in a day. Each person, therefore, making a tenth part of forty-eight thousand pins, might be considered as making four thousand eight hundred pins in a day.  
But if they had all wrought separately and independently, and without any of them having been educated to this peculiar business, they certainly could not each of them have made twenty, perhaps not one pin in a day; that is, certainly, not the two hundred and fortieth, perhaps not the four thousand eight hundredth part of what they are at present capable of performing, in consequence of a proper division and combination of their different operations.

This insight has attracted so many followers and is so embedded in economic thinking, that it was quite a shock for me to see it dismissed. Robinson merely states that people can equally divide their own labour across different tasks through time and thus Smith is incorrect in attributing the productivity of the pin factory to the division of labour.

The 18 distinct operations Smith recounts could just as easily be conducted by the same labourer on 18 different days to create the same output per person over an 18 day period as in the case where labour is divided between workers.

I’ll be honest. Dismissing one of the key elements of accepted economic theory in a single sentence is bold. But again, Robinson had a lot to get through in a short book.

So what is the real lesson? To me the lesson of productivity is not about division of labour, but of capital accumulation. 

Smith suggested it was the division of labour that had ‘given occasion’ to the invention of machinery. But this gets causality backwards; it is the new tools and production techniques that allowed both the division of labour and the great increase in efficiency. 

Imagine that each on the 18 separate tasks could be achieved more efficiently with 18 different new tools. Drawing the wire used a particular apparatus, straightening another, and cutting yet another, and so on.

For the individual labourer to be equally efficient as the factories of the time, each labourer would need 18 different tools that each sat idle for 17/18ths of the time. Thus it is the search for returns on the investment in new tools and equipment that allowed for both the observed division of labour and the radical increase in productivity.

You might interject that if 18 labourers joined together they could each buy a single different tool and simply share their own tools on the off days, that they would be equally efficient as a group. But in fact, they would simply be a factory, with the only difference to Smith’s example that workers owned all the capital.

Thus it is capital investment that leads to larger firms, internal coordination via division of labour, and increases in productivity. That is the real lesson of Smith’s pin factory.

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Wednesday, March 5, 2014

Are Australian universities just not good enough?

The reserved and mild-mannered American Canadian law Professor James Allan, who works at an under-performing Australian university, has recently written a long tirade against the bureaucratisation of higher education in Australia.

While it contains a few home truths which need public acknowledgement - like the centralisation of decision-making and the power of university executives to make inappropriate rules, and also set their own pay - it also misses important context, and offers personal biases and anecdotes instead evidence and constructive suggestions for improvements.

I want to respond here to that article. First let me attempt to summarise Allan’s points about what is wrong with Australian universities.
  • University administrators seem to value research grants as outputs rather than inputs
  • Bureaucratic decisions at universities are quite centralised
  • Students work and study, meaning they want lectures recorded and don’t want to do extra reading
  • Students don’t travel to other cities to study
  • University ranking tables are a sham, and Australian universities are not performing as well as these tables make out
However Allan doesn’t actually explain what a suitable output performance measure should be for a university. The most we get is this
In Canadian law schools (and US ones, and UK ones) you are expected to be working on your degree full-time. You are expected to do lots of reading. You are expected to think. You are expected to pursue things on your own. You are not expected to schedule classes all on two days of the week so you can work the other three. Or tell your professor that you can’t do something because it conflicts with work. Or be so tired that you do as little reading as you can get away with. 
Yet that is now standard practice in Australia. I can still, just, get away with refusing to record any of my lectures and so insist that students come (or not, since as adults it is up to them, but if not they are on their own). But the university administration detests that position and is making it harder and harder to take. As I came to Australia already with a chair I can ignore the students who get infuriated about this practice of mine in their course evaluations. But no junior academic wanting to be promoted can do so. It is no exaggeration to say that the incentives are slanted heavily in favour of caving in, of spoon-feeding students, of recording all lectures for viewing from home (with much reduced class attendance as a result)—anything to facilitate the job commitment of the supposedly full-time undergraduate. 
The flip-side of this situation is that the demands on students (even at our Group of Eight universities) are noticeably below what they are in good Canadian and UK and US universities. As for a serious Ivy League or Oxbridge undergraduate education, well, we are not in the same league as those institutions because we demand so little of our students.
Australian universities are not good enough, apparently, because students need to read more, and think, and pursue things on their own. 

He also makes a personal judgement that what you learn at university must be superior to the skills you learn at work, or that working and earning a living is not ‘pursuing things on your own’. That doesn’t really sound like a typical Australian attitude to me. My personal experience in economics is that a degree gets you in the door, then it is all down to experience. Working while studying, especially in your chosen field, is quite advantageous.

But he really doesn’t elaborate any further. Is university performance measured by research output? Is it measured by revenue? If so, he doesn’t have much of a case against the administrative bias towards academics who generate research grants.

Or is it the number of peer reviewed journal articles? If so, is it quantity or quality? Who will judge quality? Is it student numbers per academic? Or is it student quality? Who will assess that? Or do we judge performance on the gut feel of visiting academics with their own personal biases?

I don’t want to sound harsh, but for a senior academic writing about the underperformance of Australian universities, a little note about what underperformance really means, framed within the role of universities within society, would be nice. He signals that it should be research output, noting that people
…could see the difference between judging people based on what they wrote and produced versus one that judged them based largely on winning as many grants as possible.
but fails to return to how this measure fits into his picture of a competitive university system.

Whinging about the rules doesn’t really help. It is like an Apple employee coming into the company and saying they have a lot of centralised decision-making and that engineers were slugged with bureaucratic tasks, such as getting central approvals to spend money on new equipment. Whereas at their last job they could do as they please.

Sure, from the employee perspective this seems like a horrible system to work in. But any outsider assessing the performance of the company as a whole would feel it is worth it. That’s because we have an agreed measure of what company performance is. For universities we don’t, and that is usually the recipe for a growing bureaucracy.

Allan lays some of the blame at a lack of competition, perhaps due to some cultural norm of families not sending their sons and daughters interstate to the ‘best’ university in their field. Apparently this lack of competition means that universities can slack off and amuse themselves with ever more burdensome central rule-making and ever-greater executive pay.

Allan writes
In this sense, Australia and its universities are at a disadvantage. Imagine what would happen if parents were as likely to send their kids to Melbourne University as to Sydney University or the University of Queensland or Australian National University, and the deciding factors came down to what the universities had to offer, say in terms of class sizes or contact with professors or the “undergraduate experience”.
There are two problems with this point. First, is that the universities are full of international students. Outside of law especially. Surely these students are discerning about their university choice and hence provide a great deal of competitive pressure. According to the ABS 22% of students at university in Australia are international students, while at some universities that figure is over 40%. Monash and Melbourne universities seem to be competing quite fiercely, with Melbourne experimenting with student offerings at great risk.

Second, the central rules that Allan hates so much are just as much the result of competitive forces, than on the lack of such forces; of trying to attract students by ensuring the get the easiest path through their study. We’ve seen the gimmicks about giving new student iPads. Allan mentions the imposition of consistent marking systems, PhD criteria for lecturing positions, timing of student evaluations; all of these are about managing university-wide quality in order to assure new students of what they will be getting. Haven’t you seen advertisements?

This is what happens with competition for students (customers), and students mean revenue. If you want universities run competitively like private businesses, you must expect that they will measure their success in similar ways.

So where does research output fit into his competitive picture? It certainly doesn't raise revenues, and most undergraduates, the customers of universities, wouldn’t have a clue about their school’s research anyway.

Regarding the lack of travel to university, if I can sum up the Australian view very roughly, it is that university is more like advanced vocational training. Degrees that used to be provided by technical colleges are now integrated into universities. Students don’t travel because their local university usually maintains standards high enough to get them into their chosen field. Why travel if you can be assured of equally good local training? After all, once you are in the door, your experience counts much more than your degree in most fields.
He writes
When I try to point out the advantages of sending one’s kids away to university here in Australia I am generally met with blank stares of incredulity.
But of course, he didn’t mention any of those advantages in his article. Could it be that there really aren’t many? Or is he saying that Australians are just too stupid to see them?

Which leads to the more entrenched problem. The competition that drives student selection and travel for study in the US and the UK is the result of monopoly power of universities so that students must compete rather than universities. And this competition between students is also driven from a higher level. Reputation and insider connections within top universities to political and corporate elites means the payoff to getting into those universities is much higher. A degree at Princeton or Harvard is a meal ticket with a value far higher than cost of tuition itself. This not only means that students want to travel to get in to these universities, but that they (and their parents) are willing to pay through the nose for it as well. Here’s just one example of the political connections a degree at Oxford brings.

In Australia we don’t have that ‘boys club’ mentality to such an extent, especially not in most degrees. Having a teaching degree from QUT doesn’t open doors at Goldman Sachs, unlike a finance degree from MIT.

While I am sure Allan feels much better getting this all off his chest, I can’t help but think he has missed the important points to focus on his personal gripes. He overlooks exactly why Australian universities aren’t good enough, and then appeals to competition as some magical remedy to all organisational problems like some evangelical Chicago economist. Lastly, his suggestions for improving the situations include a bunch of central administrative tools!

One of his suggestions, the publication of remuneration of the highest paid employees, is generally already complied with in the annual financial accounts, where executive pay is itemised (here’s UQ, here’s QUT). But of course, executive pay exploding is not limited to universities. It is a general problem of power that competition alone does not solve.

Another suggestion is to publish the ratio of academic to non-academic staff, which is essentially a meaningless ratio because it absolutely depends on the tasks each staff is responsible for. If administrative staff are freeing up time for academics, then that is a good thing. I could imagine these suggestions being implemented and a future version of Professor Allan writing another article deriding them!

He suggests scrapping the ARC grant system, but makes no suggestion of alternative funding allocation mechanisms, as if by magic money will find worthy researchers. I agree the system is poor, but we need to be discussing better alternatives. Why didn’t Allan tell us a bit about the funding systems in those hot-shot universities he so reveres?

When push comes to shove Allan goes for the practical over the ideological, which is a good thing. But it leaves you wondering what the point of all those words really were. Will they merely be interpreted as at the ravings of a sheltered and entitled academic? We have quite enough of that already.

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Monday, March 3, 2014

Wages share and investment

Kieran Latty produced this chart on wages share and investment share in OECD countries. If we take this at face value it implies the existence of a wage share that maximises investment - which in the long run is what makes us wealthier. 


To me this seemed a little too neat. Economists love the inverted U-shape relationship, or concave relationships in general, because it implies the existence of some kind of equilibrium - just set labour share correctly and you will maximise investment. Or something like that.

It turns out to produce the ‘inverted U-shape’ curve Latty used a time fixed effect and a non-linear estimator on data from AMECO. While this may be somewhat normal in the literature on this topic - for such reasons as removing the effects of international business cycles and to control for any secular trend in international growth rates - ultimately these model choices fundamentally determine the results. Like most observational data from complex systems, we are applying models as mere plausible stories, with no objective criteria for assessing their validity.

Often the details (including the outliers) in these types of international comparisons reveal much more of the story than the general trends. To satisfy my curiosity I constructed a similar chart from OECD and World Bank data.

Below is the scatterplot of my sample (you will notice the chart is animated to show country data connected through time) . Eyeballing the data there seems to be no general time-independent inverted U-shape. This is confirmed by regressions on the sample without controls, and indeed, with a quadratic specification we find a positive coefficient on the squared term.
 



Notice that each country seems to occupy a distinct section of the chart. Such divergence between countries should be of great interest to macroeconomists. In my smaller sample below Japan has consistently high labour share and investment share, while New Zealand is consistently low on both measures. Then we have the US and UK with consistently low investment accompanying a rather high labour share. 




My expectation is that a high labour share of income would result in greater investment share, if only because owners of capital would have greater incentives to invest and innovate in order to gain a return, rather than simply hold existing assets. Who knows whether this is the case at all. But it’s my current speculation.

What is, for me, more fascinating in this data is the trend over time. We know that the labour share of national income has been falling in most countries since the 1970s. We can see that trend, along with short-term cycles, in the animated chart below that tracks my six country sample since 1970. 



In broad terms the maturing nature of these economies may mean that such a downward trend in labour share is naturally expected. Or it could be that policy choices for the past four decades have directed national income towards owners of capital, which resulted in lower investment in some cases but not others. The answer still seems completely unclear. If you want more analysis, you can read the Productivity Commissions recent work on the topic. 

Like many macroeconomic curiosities, the relationship between wage share and investment is a puzzle unlikely to find a satisfactory conclusion any time soon.