Wednesday, 7 May 2014

Piketty and the Marginal Product of Capital

Like hordes of others I'm reading Capital in the 21st Century and so far I'm very impressed. But when I came to this, on page 213, I was shaken, not stirred:
Concretely, the marginal productivity of capital is defined by the value of the additional production due to one additional unit of capital. Suppose, for example, that in a certain agricultural society, a person with the equivalent of 100 euros’ worth of additional land or tools (given the prevailing price of land and tools) can increase food production by the equivalent of 5 euros per year (all other things being equal, in particular the quantity of labor utilized). We then say that the marginal productivity of capital is 5 euros for an investment of 100 euros, or 5 percent a year.
Why do economists do this sort of thing? Keynes gave the world a very useful term for the return which a capital asset offers, expressed as an interest rate. He called it the marginal efficiency of capital:
More precisely, I define the marginal efficiency of capital as being equal to that rate of discount which would make the present value of the series of annuities given by the returns expected from the capital-asset during its life just equal to its supply price. This gives us the marginal efficiencies of particular types of capital-assets. The greatest of these marginal efficiencies can then be regarded as the marginal efficiency of capital in general.

Now I think it's clear that Keynes and Piketty are using the same concept, but giving it different names. "So what" you ask; "isn't an author entitled to choose his own terminology?" Well yes, but the name Piketty chose happens to be the name usually given to something quite different. The marginal product of an input, as Wikipedia tells us "is the extra output that can be produced by using one more unit of the input ... assuming that the quantities of no other inputs to production change." (I know Wikipedia isn't always reliable, but trust me I can find plenty of better authorities to cite if I need 'em).

The reasons why this pisses me off somewhat are twofold. Students are regularly warned not to confuse the marginal product of capital (usually abbreviated MPK) with the marginal efficiency of capital (MEC). The MPK should be understood as units of additional output per unit of additional input, while the MEC is akin to an interest rate (it can be thought of as an internal rate of return). It's important to avoid confusion because the two terms often rub shoulders in a discussion.

The other reason why Piketty's choice of jargon is unfortunate is that there are plenty of hacks out there looking to diminish the impact of his work. It's a shame that he has given them an opening.

But it may be for the best. Samuelson remarked that one reason why Keynes's General Theory made such an impact was that the many obscure points give rise to a lot of arguments and, in order to participate, people first had to read the book. Piketty's writing is mostly clearer than that of Keynes, but it may be that it is precisely the few infelicities of language which will keep the conversation going.

Wednesday, 1 January 2014

The Grumpy John H. Cochrane succumbs to Carly Simon Syndrome

He writes:

"Paul Krugman is now reduced to making fun of my name."

Evidently he believes the term "cockroach ideas" was inspired by the first syllable of his surname. This seems unlikely. Krugman has been writing about cockroach ideas for years. Here's an early example, from March 2011:
Way back, when I spent a year in the government, an old hand told me that fighting bad ideas is like flushing cockroaches down the toilet; they just come right back. I’m having that feeling a lot lately, on at least two fronts.

One is the crowding out issue. I keep encountering both the same old misunderstanding of Ricardian equivalence, and people citing evidence from periods when the economy was nowhere near the zero lower bound. The latter was, perhaps, excusable when the idea of a liquidity trap was still new; but folks, we’ve been at the ZLB for two and a half years now:

The other is the whole “the Social Security trust fund doesn’t exist” thing. I’ll just repeat what I said back when Bush was trying to push through privatization:

Social Security is a government program supported by a dedicated tax, like highway maintenance. Now you can say that assigning a particular tax to a particular program is merely a fiction, but in fact such assignments have both legal and political force. If Ronald Reagan had said, back in the 1980s, “Let’s increase a regressive tax that falls mainly on the working class, while cutting taxes that fall mainly on much richer people,” he would have faced a political firestorm. But because the increase in the regressive payroll tax was recommended by the Greenspan Commission to support Social Security, it was politically in a different box – you might even call it a lockbox – from Reagan’s tax cuts.

Monday, 4 February 2013

The X Case: a Question

Neither of the regular readers of this blog is a lawyer, but on the off-chance that I can persuade a blogging lawyer to take a look at this post, I have a question. Since it’s hardly fair to ask you to do all the work -- no, I'm not a fee-paying client -- I’ll attempt my own answer below and you can tell me where I’m wrong (I’m @Paddy_Solemn on Twitter).

When the Supreme Court lifted the injunction preventing Miss X and her parents from travelling to London for an abortion, what was the legal essence of their decision, particularly with regard to the risk of suicide? I’ll leave it to you to decide whether I’m asking for the ratio decidendi or the res judicata or neither. Call it what you like. My reason for asking is that I often read pronouncements like this one from Lucinda Creighton TD:

The X case brought in this issue of suicide as a grounds for abortion. I think that's very tenuous. The psychiatrists who came before the Health Committee are the only people who are in a position to really speak with any expertise on the specific question of whether abortion is ever necessary to prevent a suicide. Their answer was a resounding no. That is very conclusive as far as I am concerned and draws a line under the issue. We must be guided by their expert evidence.

Now any fule kno that “suicide is a grounds for abortion” is a rather sloppy account of the judges’ decision in the X case. What they actually said can be read here. Their statements relate to the very peculiar circumstances, which cannot arise again because, in similar cases, the right to travel is now guaranteed by the thirteenth amendment. Just how peculiar those circumstances were is spelled out:

...whatever the exact numbers are, there is no doubt that in the eight years since the enactment of the [eighth] amendment, many thousands of Irish women have chosen to travel to England to have abortions; it is ironic that out of those many thousands, in one case of a girl of fourteen, victim of sexual abuse and statutory rape, in the care of loving parents who chose with her to embark on further trauma, having sought help from priest, doctor and gardai, and with an outstanding sense of responsibility to the law of the land, should have the full panoply of the law brought to bear on them in their anguish.

I said at the outset that I'd attempt an answer to my own question. As I read it, the essence of the judgement is this. If it is practicable to prevent an abortion by imposing restrictions on the movements of the woman concerned, then that should be done; but these restrictions should not be so onerous as to create a substantial risk to her life. In particular they must not create such stress as would give rise to a substantial risk of suicide.

So to what extent does the X case judgement generalize? The most obvious cases in which it applies are those of prisoners who demand abortions. I suppose it would also apply to women on bail, since typically they are not free to leave the jurisdiction.

If my reading is correct, then the “resounding” verdict of the psychiatrists, that abortion is never necessary to prevent a suicide, is a bit beside the point as well as being rather sweeping. The relevant population-at-risk consists of women who want abortions, but are prevented from leaving the country. Studies of women who are at liberty but suffering from depression are not especially relevant.

Monday, 28 January 2013


The tragic death of Savita Halappanavar has fanned the embers of the Irish abortion debate, which until then had been smouldering away, ignored by most of the population, including me. At times it seems like we’re back where we started following the launch of the Pro-Life Amendment Campaign (PLAC) in 1981, with Professor William Binchy reprising his old role as champion of the Unborn. It’s a bit like seeing Franco Nero resurfacing in Django Unchained. I thought he must be dead by this time, but actually he has worn rather well. One big difference with this flare-up is that the debate now has an international flavour as American bloggers enter the lists. I welcome this. It livens things up. But it also creates scope for confusion, since Ireland looks deceptively like a US state from certain angles. I want to address two particular sources of confusion in this post:

(1) what the Irish debate is mostly about; and

(2) the idea that Irish law has a particularly Catholic flavour.

“Hard cases make bad law.” We heard that adage frequently from PLAC in the debates leading to the Eighth Amendment (1983):

The State acknowledges the right to life of the unborn and, with due regard to the equal right to life of the mother, guarantees in its laws to respect, and, as far as practicable, by its laws to defend and vindicate that right.

What PLAC meant about hard cases, I take it, was that the Constitution should merely state the general principle and allow doctors and lawyers to decide whether, for example, a zygote is unborn and therefore has rights, and how the limits of the practicable are to be determined; trust the experts. Unlike Messrs Binchy and Nero, this dictum hasn’t aged well. That is because the only abortion cases which Irish hospitals and law courts need consider are hard cases. For the vast majority of women requiring abortions the main difference between living in London and living in Dublin is the airfare, typically around €130 return. In practical terms, there must be many locations in the US where obtaining an abortion is more difficult than it is for Irish women.

The very success of PLAC means that the Irish abortion debate is concerned exclusively with hard cases, where a pregnant woman has at least a colourable argument that her “equal right to life” is at stake. I stress this because anti-abortion campaigners are wont to frame the issue as if we were discussing abortion on demand. No doubt they fear that any relaxation of the law will put us on that slippery slope, which is quite possible, but we can’t slide very far without another referendum on the Eighth Amendment.

So the sort of thing we are debating is:

* What facilities should be in place in cases where a pregnant woman’s life is acknowledged to be in danger? The European Court of Human Rights finds it unsatisfactory that she should be expected to have her abortion in England. I certainly agree.

* What if the threat to her life arises because she is suicidal, as in the X case? Under current law, the nature of the threat to her life is irrelevant. Obviously this is totally unacceptable to anti-abortion campaigners. I expect the legislation will be a fudge, allowing an abortion in the unlikely event that two psychiatrists approve.

* Lawyers, including those representing the government, believe that the Constitution as it stands may allow abortion in cases of fatal foetal abnormality. Should that be provided for by legislation? That makes sense to me.

By Irish standards, these views are enough to make me a liberal. Pretty clearly, they are rather tame by American standards.

So much for the first confusion I wanted to address. The other one springs from the tendency to assume that Irish abortion law is written to the specifications of the Catholic Church. In reality the source, for most purposes, is the Offences Against the Person Act 1861 of the (then staunchly Protestant) UK Parliament. The consequence is that the distinction “between killing someone directly and allowing someone to die of indirect causes” which is so important to Catholic moralists, doesn’t appear to concern the Irish Supreme Court at all. I’m not a lawyer, but I’m pretty sure that any of the three methods of dealing with an ectopic pregnancy mentioned in that link could be used in Ireland without risk of prosecution. Basically, the law permits killing in self-defence, whether the threat comes from a deranged gunman or a misplaced foetus.

All this is by way of a reply to a question put to me on Twitter, where I have been sounding off under the Nom de Twit of Paddy Solemn. I have another Twitter account where I post, as I do here, under my own name. But some personal friends use that for informing the world about grave matters such as rugby and food. They follow me for my comments on these topics. I’ve concluded that it is inappropriate to bring foetuses into that.

Irish readers may already have heard of Paddy Solemn. I think he was created by Flann O’Brien but I first encountered him in an essay by Conor Cruise O’Brien: “Paddy Solemn has, however, a secret fear. It is that Ireland Will Let Him Down. Of what avail his personal respectability if he is dragged down by a national entity which refuses to be respectable?” Paddy Solemn is well suited to be my Twitter spokesman on matters such as abortion. But his twittering should not be taken as seriously as he takes himself. If I think I’ve something even slightly substantial to say, I’ll say it here at greater length.

Friday, 23 November 2012

More on Irish Maternal Mortality

[Update 25th November 2012: corrected a couple of errors.]

It's always good to follow the example of the masters, so I'll start this post in the style of Cosma Shalizi, who regularly leads off with an Attention Conservation Notice, telling his readers what return they can expect for the time invested in reading further. That's especially appropriate in this case, because Ireland's low maternal mortality figures are being cited frequently in the course of arguments against abortion liberalisation. But that's not what this post is about. To my mind abortion law has to do with rights, not numbers. I want to know more about the numbers, but even if I knew them with certainty I don't believe that would settle any moral questions.

Another issue that I'm not proposing to tackle is the underlying causes of variations in maternal mortality from one country to another. There is quite a bit of literature on that but I haven't read it. When I do, I will share whatever I learn here, so please drop by again. That's what blogging is all about: sharing one's scraps of newfound knowledge (and frequently getting told one is full of shit, usually by people who know even less).

If you're still reading I take it that you want a few numbers. So far, the best primary source I have found is the clinical reports of the Coombe Hospital, which are available online. The table below combines two tables from page 34 of the report for 2010 (click to enlarge).

We could add one more column, for 2003, by looking at the corresponding tables from the 2009 report, which tells us that 8,288 mothers attended the hospital in 2003 and there were no maternal deaths in that year. So over an 8-year period, 71,229 mothers attended the hospital and there were just three maternal deaths. That's a reasonably good outcome, with mortality averaging 4.2 per 100,000 mothers (or slightly better worse if the number is expressed as a proportion of live births). From press reports I know that there were two deaths in 2001-2002. If we include those, assuming that the number of mothers wasn't much different from 2003, we get a mortality figure of about 5.6.

Does what goes for the Coombe Hospital, go for the country as a whole? Well, maybe. The pessimist's reading is that the Coombe is an unusually well-equipped hospital so others are unlikely to do as well. The optimist's reading is that the Coombe probably handles more difficult cases -- see the footnotes to the table. The truth is that we can't safely make inferences for the country as a whole from the figures for a major hospital or even a few of them.

So we're back to the need for better data. When I wrote my previous post, I hadn't read this recent article by Niall Hunter which mentions recent research highlighting the inadequacies of CSO data. I haven't seen that research but I doubt that it would surprise me greatly.

Wednesday, 21 November 2012

Good Midwives or Bad Statisticians?

In the controversy surrounding the death of Savita Halappanavar many commentators have been quick to point out that Ireland's maternal mortality rate is really very low by international standards. I'm not disputing that, but a word of caution is in order.

According to the CSO's Report on Vital Statistics 2010, there was just one maternal death in Ireland in that year. This figure is certainly incorrect. The Rotunda Hospital recorded three maternal deaths in 2010, while the Coombe Hospital recorded one. (See this Irish Times report). I don't know what the true figure for the entire country is but obviously it can't be less than four. It is unlikely to be in double figures: maternal mortality figures are typically quoted as deaths per 100,000 live births and Ireland has about 75,000 births per year.

So the CSO's numbers are a bit dodgy. What else is new? It won't come as a huge surprise to anyone who has wrestled with CSO figures for migration and the balance of payments. As Paul Krugman remarked in the latter context, Ireland is a major importer of errors and omissions. Even so, an error of at least 300% should make us hesitate before making brash claims about the quality of medical care.

Efforts are being made to produce more meaningful figures. Until these are available, treat with scepticism anyone who refers you to numbers published by outfits like the World Health Organization, Unicef or the CIA Factbook. Their models rely in one way or another on figures supplied by national sources; garbage in, garbage out.

Once again, because I really don't want to be supporting scaremongers: I'm not suggesting that Irish maternal care is poor, even by the standards of other highly developed countries. I'm simply saying that we don't have data that entitles us to make strong claims about our relative performance. Maybe the English really are a bit worse at maternity care. Or maybe they are just a bit better at counting.

Saturday, 20 October 2012

Ronald Cruise O’Dworkin

I’m by no means the go-to guy if you want to explore “the influence of the altogether neglected Samuel von Pooped on the totally forgotten Herman von Supine”, but from time to time I’m struck by how deeply some not-especially-famous writers impress their ideas, and even their prose, on others. Thanks to a fairly harmless bit of snidery by Scott Sumner, I was reminded of this passage from Conor Cruise O’Brien’s introduction to a 1968 edition of Burke’s Reflections on the Revolution in France:

That those who advocate or approve the contemporary counter-revolution should interest themselves in the Reflections requires no demonstration. But why should those who oppose the contemporary counter-revolution, and the neo-conservatism which is among its more overt intellectual expressions, be invited to read this first modern counter-revolutionary manifesto?

The fact that such a question is certain to be asked is in itself indicative of a peculiar, and apparently deep-rooted, weakness in left-wing thinking. The intelligent rightist does not ask to be given reasons why he should read Marx and the Marxists. He reads them because they are important, and because they are on the other side. He learns from them and sometimes is warned by them....

The intellectual left on the other hand – though with some notable exceptions – has a strong tendency to neglect its adversaries and to dismiss even their most influential writings, unread, with a sneer. This is associated, I believe, with another pronounced tendency on the left: that which runs to misunderstanding and underestimating the forces opposed to it.

It seems that the right-wing enthusiasm for opposition research has flagged a little since O’Brien wrote those words. Ronald W. Dworkin, Senior Fellow at the Hudson Institute (not to be confused with legal philosopher Ronald M. Dworkin) warns his fellow conservatives against slipping into the idle habits of the left:

I believe in capitalism. Many of this journal’s readers do, too. Then why am I writing as if we can learn something from Marx?

The fact that such a question is certain to be asked is in itself indicative of weakness typically more rooted in left-wing thinking. The intelligent conservative does not ask to be given reasons why he should read Marx and the Marxists. He reads them because they are important, and because they are on the other side. He learns from them and is sometimes warned by them. The intelligent conservative makes use of Marxist insights, but for his own purposes. He learns from his adversaries about the strengths and weakness of his own position — and of theirs.

The leftist, on the other hand — though with some notable exceptions — has a strong tendency to neglect his adversaries and to dismiss even their most influential writings. Although conservatives should and do read Marx and Foucault, leftists often think they have nothing to learn from Tocqueville and Burke. Indeed, they often greet these writers with a sneer, which is why they consistently misunderstand and underestimate the forces opposed to them.

This kind of thing makes me wonder whether I shouldn’t strive for a more active role as a public intellectual. As the name of my blog indicates, I really don’t think I have any startling new insights to offer the world. Still, I have reasonably well-stocked bookshelves, internet access, and a ticket to the UCD Library. I’m confident that I could knock together a few articles on, say, the American Civil War, with style and content closely resembling Shelby Foote. Or I could offer insights into paleontology reminiscent of Stephen Jay Gould, with wonderfully apt metaphors drawn from baseball. The fact that I have never been to a baseball game, and wouldn’t know a cynodont from a triceratops anus, doesn’t seem to present any particular obstacle. The possibilities are endless. I could rework Russell or recycle Ryle. Should I offer my services to the Hudson Institute? My rates are decidedly reasonable.

(The title of this post borrows from the TLS reviewer who described O’Brien’s really excellent book, The Great Melody, as a biography of Conor Cruise O’Burke.)