The innumerate case against Keynsianism

The basic idea of the multiplier, a concept in Keynesian economics, is extremely simple.  Imagine a seaside town in winter.  Everyone’s business is geared up to make maximum profits in the summer.  In winter, there’s excess capacity and no-one makes a lot of money.

Then suppose a visitor comes to town.  He buys some apples at the greengrocer’s.  This is good, not just for the greengrocer, but also for the hairdresser, as the greengrocer decides to spend his new income on a haircut. The hairdresser, in turn, spends their money at the dairy, buying milk.  And so on.

So if A is the additional spending and Y is the previous total of economic activity, we can say that ΔY, the total change in the quantity of economic activity, equals some multpiple (call it M) of A, i.e:

            ΔY = M.A

M would be 1 if the greengrocer put all his new income under his pillow, but if he spends some, M can be greater than 1.  M is the multiplier. It’s that simple.

Can we estimate the multiplier? Supposing that everyone is equally inclined to spend the same proportion of any extra income they receive.  This proportion is called the marginal propensity to consume (I’ll represent this as x).  The visitor spends A.  The greengrocer receives A as extra income and spends x * A.  The haridresser receives (x * A) as extra income and spends x(x * A). And so on, to infinity.

In mathematical terms, we have an infinite series whereby:

            ΔY = A(1 + x + x² + x³ +…)

And fortunately, if 0 >= x <= 1, mathematicians can sum the infinite series – the series sums to 1/(1 – x).  Thus as we have already defined M thus

            ΔY = M * A

It follows that:

            M = 1 / (1 – x)

Now, how can we estimate the marginal propensity to consume? We estimate it as the current share of consumption of the total economic activity.  If economic activity consists of consumption (C) and non-consumption (NC):

            Y = C + NC

Then

            M = 1 /(1 – (C / Y)) = 1 /(1 – (C / C + NC))

And if consumption occupies 4/5 of the current economy, this gives us a multiplier of 5.  If consumption occupies ½ of the current economy, this gives us a multiplier of 2.  And so on.

The multiplier is often used by Keynesians to argue that a small ammount of additional government spending can have a big impact on the real world economy.  Is there a catch? Well, supposing the additional visitor comes to town in the middle of summer.  Because there are lots of other visitors in summer, the greengrocer can sell all his apples already, the hairdresser is fully booked, and so on.  So the additional demand created by the visitor will merely increase competiton for resources and drive up prices.  In real terms, there will be no net increase in economic activity, because the economy was already as capacity.  So the multiplier will be 0.  Indeed, if government spending competes for resources that the private sector was previously spending more efficiently, it’s even possible that the multiplier can be negative.

Economists have tried to calculate multipliers empiracally, from real world data – what effect have changes in governement spending had on the real world economy? It’s clear that the multiplier depends on the state of the economy.  An argument may be made against increased government spending by arguing that, under current economic conditions, the multiplier is likely to be small or negative.

But this is not what Stephen Landsburg does in this article.  Instead, he attempts to disprove the theory of the multiplier.  Here’s how he does it.

Landsburg starts by stating the economy consists of consumption, governement spending G, and private investment I, so:

            Y = C + G + I

Which is just an identity, true by definition.  He then says, supposing 80% of the economic activity is occupied by consumption. So:

            C = 0.8 * Y

And therefore:

            Y = (0.8 * Y) + G + I

And therefore:

            0.2 * Y = G + I

And finally:

            Y = 5(G + I)

In this way, Landsburg claims to have derived the Keynesian multiplier, which we remember was 5 when the marginal propensity to consume, and the current proportion of spending on consumption, was 0.8.  But he hasn’t.  The multiplier was found in a formula describing ΔY (the change in economic activity). Landsburg’s formula describes Y (the previous total of economic activity).  All Landsburg has done is restate his starting premise: that the total ammount of economic activity is 5 times the level on non-government spending.  This is nothing to do with the multiplier – but it happens to be the same number (because the chosen identity for Y splits the economy into spending on consumption and non-consumption, the same factors that determine the multiplier). Having performed this bad derivation of the multiplier, Landsburg then claims you can apply the same logic to any other accounting identity, i.e. any other definition of Y. So if we consider that the economy comprises my consumption (C1), and all other expenditure (O), and that other expenditure consumption is almost the entirety of the total economy, he applies the same reason applied previously to move from the starting propositions:
            Y = O + C1

            O = (99,000,000 / 100,000,000) * Y

To arrive, correctly but banally, at the conclusion

            Y =  100,000,000 * C1

But then ludicrously implies that this means that the Keynesian multiplier is 100,000,000.

To be clear: he has done nothing but restate is premise,  that the total economy is 100,000,000 times larger than his own personal consumption.  As the multiplier is a function of the proportion of the economy as a whole occupied by all consumption, and total consumption is not identified as a separate entity in his starting identity, the same algebraic manipulation no longer has anything to do with the multiplier. The premise you can apply the same logic to any other accounting identity is simply false: the multiplier is derived from one particular component of the national economy, not from any component of any accounting identity for total economic activity that you care to define.

In other words, Landsburg accuses Keynesians of being idiots, only by being idioitc himself.  And the strange thing is, that the multiplier is not an esoteric concept that is hard to understand (consider again my initial story of the seaside town).  It’s as if Landsburg was trying to disprove the existence of the moon: necessarily, the logic is bad, because it’s being deployed in a nonsensical cause: disproving something obviously true.  Again, it’s true that the real world multipliers are less than the theoretical multiplier in the absence of any crowding out of private sector activity, but this isn’t Landsburg’s point: he’s arguing (badly) that the theoretical concept makes no sense.

Landsburg is a well-known idiot, but it’s quite common for more reputable commentators to make bad arguments against Keynsian models.  Consider this exchange between Tyler Cowan and Brad deLong.  Cowan argues that IS-LM, a commonly used Keynesian framework, is too simplified to accurately represent the real world economy.  But as deLong points out, in place of IS-LM, Cowan only proposes even simpler intellectual frameworks, models which, by his own criteria, can only be less illuminating.

So how come?  Keynes argues that, in certain circumstances, additional government spending can boost the economy.  Some people don’t like this.  Three possible reasons for this are:

(i)            the belief that government is generally less efficient in spending money than the private sector.  This is a serious objection if the economy is at full capacity, when the multiplier will be low due to crowding out.  But if there is economic capacity currently unused by the private sector, any productive use of that capacity is better than none. The relative efficiency of the public and private sectors ceases to be important. 

(ii)          the fact that governement activities are generally financed by the wealthy.  This can be considered damaging to incentives, morally wrong, or simply against your own interests (if you are among the wealthy youself).

(iii)         that government spending is hard to reverse; thus even if beneficial in the short term, it is undesirable because of its longer term consequneces.  A form of this argument was made by Milton Friedman,

When the economy is unlikely to be at capacity, argument (i) doesn’t hold, while argument (iii) involves sacrifcing the possiility of solving today’s actual problems to avoid other problems that may or  may not arise in future.  Arguments of type (ii) may be politically difficult – effectively, requiring that the unemployed make sacrifices for the benefit, at least in the short term, of the wealthy.  Thus believers in this sort of argument need to frame their case in a different way.  Additionally, some believers in the general efficiency of the private sector may find the Keynesian conclusion, that under some circumastances the government can boost the economy, too counter-intuitive to grasp.

Note Landsburg's headline, which is a re-hash of the argument that ‘Keynesians believe you can create wealth by creating money’.  Yet almost everyone agrees that money emerged in our societies precisely because, by facilitating trade and thus specialisation, it led to the creation of wealth.  Keynesians argue that, because prices do not adjust instantly to balance supply and demand, that the amount of money and its rate of circulation can (up to the natural capacity of the economy) indeed create wealth (indeed, even Friedman agreed with this). Yet even this basic idea gets misrepesented, as, more greviously, do Keynesian models.  Meanwhile, Henry Hazlitt, the author from whom (by way of Murray Rothbard) Landsburg ultimatley borrows his example, also famously and deliberately misconstrued Keynes’ views on the long and short term. His method: take a famous quote from Keynes out of context, attack its implied meaning, and defend himself from the charge that he had misrepresented Keynes by asserting that he could not have done so because he had not attibuted the quote!
What none of this explains is, how come Landsburg has a position as a Professor of Economics?

The 1% and moral absolutism

Harvard economist Greg Mankiw’s paper in defence of current levels of income inequality have been widely attacked: Jon Chiat skewers him as effectively as anyone here and here.  But there’s one particular piece of Mankiw’s argument that intrigues me.

Mankiw, like Robert Nozick before him, attacks utlilitariansim on the grounds that a perfectly utilitatian society would be a horrible place.  But this argument completely fails to grasp the nature of society.  We might like to maximise welfare (utilitarianism); we might also like to maximise economic growth, protect property rights, and free people from oppressive government.  The problem is that some of these goals are contradictory.  Growth that benefited only a few, and impoverished everyone else, would hardly be desirable; absoulte property rights create a tyranny of the property owners over everyone else; even Nozick accepted that a world without any government would be a Hobbesian nightmare, where the war of all against all prevailed and life was nasty, brutish and short.  Indeed, compared to these models, Mankiw’s arguments appear to be arguments for ultitarianism in the form of Churchill’s famous argument in favour of demoncracy; horrific but less so than any of the alternatives.

But in fact, we’re not in such a bad shape.  This is because we can aim for a compromise society, where we balance our different objectives. The argument for a certain level of additional redistribution is based on the notion that the current imbalances of wealth in our society are (i) not widely beneficial and (ii) that the downside of doing so is outweighted by the upside.  As practically no-one is arguing for 100% top tax rates, the point that a perfectly utilitarian society would be unwelcome is completely irrelevent.  Alternatively, one can think of this as a form of meta-utilitariansim, in which among the benefits to be maximised include growth, property and freedom, as well as wealth; the case for limits to redistribution can also be seen in ulititarian terms.

The strange thing about Mankiw’s argument is that the notion that individuals choose between alternatives, and how much more of something we might want depends on how much of it we already have (and how much we are lacking in our other desires) is one of the most basic principles of economics.  You get a pay increase and you buy a car; once you have a car, you spend your next pay increase on a better house, or nicer food, and so on. Mankiw’s argument (that a little utliitarianism is bad because you wouldn’t want a wholly utilitarian society) is like saying you shouldn’t by a car with your pay rise because you wouldn’t want to spend all your money on automobiles. Indeed, it’s hard to see how economics can work without some sort of (opportunity) cost – benefit going on, the sort of calculation that Mankiw derides as impossible to perform. One of his arguments is that you can’t show redistribution actually increases welfare, because the benefits cannot be measured – whereas the whole basis of economics is that people are capable, at least approximately, of personal utility maximalisation.

Nozick has been here before Mankiw, and I think that some of the explanation of the apparent idiocy lies in the heart of libertarian politcs. The appeal of libertarianism is based on its logical consistency: take one principle, the primacy of property, and extend that to constructing a vision of a coherent society.  But human society is a complex place, and its arguable that no simple principle is alone sufficient to describe the sort of world in which we might actually want to live. Showing extreme utilitarianism is logically absurd, whereas extreme libertariansim is not, might appear to be a victory to those aiming to reduce ethics to logic.  But the theoretical possibility of a purely libertarian world does not make one desirable; except to those who crave intellectual certainty where none exists; and  also, of course, to the owners of property who stand to benefit the most from having their rights recognised as absolute.