Should the World be Flat?

Is the current proliferation of tax credits - or their better spoken sibling,  tax thresholds – inimical to the welfare potential of the economy? The following well known proposition of economic theory suggests that it is.

For any structure  of ‘threshold plus marginal rate’ there will always be some ‘flat rate scheme’that  for a given individual income tax payer will  increase the utility, consumption, labour supply and tax paid of that tax payer.

If you like, for a given income tax payer, there will always be some 'flat rate scheme' - one which abolishes the threshold and makes all income subject to a 'flat' rate of tax -  that makes both the tax payer and the government better offer.

What is going on here? How is this marvel achieved?

The answer does not lie in any strange grace of ‘simplicity’. Or in some abhorrence of nature of a vertical axis intercept. The answer lies in the incentives that a flat rate scheme offer to a person to obtain utility from consumption rather than leisure.

The explanation of this doesn't require any maths or diagrams. The logic can be conveyed solely through words.

It is easy to see the following 'trivial' proposition: there will always exist some flat rate scheme that would yield exactly the same revenue as before IF the person worked exactly the same hours as before. This is true merely by virtue of arithmetic:  as any flat rate scheme involves abolishing the tax threshold  (and so increasing the tax liability) and a cut in the marginal rate (decreasing the tax liability), there will necessarily exist some marginal rate of tax such that the person would pay exactly the same revenue IF they worked the same number of hours.  

We now persue significance of this apparently hum drum proposition ... Is it not true that to work the same number of hours as before - while paying the same tax - is to have same consumption as before? And is not working the same number of hours as before to have the same leisure as before? Thus our proposition in the paragraph above says: 'there will necessarily be a flat rate scheme such that the person could have the same leisure and the same consumption as before by the working the same hours as before'. In short, we can construct a flat rate scheme such that the person can obtain the same utility as before simply by working the same hours as they did before.

But - and this the key observation -  under this scheme, the person can now do BETTER than 'the same utility as before'; and they can do better by choosing to work MORE hours than they did before. This is because the reduction in the rate of tax has increased the consumption reward for working an extra hour. Previously, the consumption reward (in utility terms) from working an extra hour was just matched by the loss  (in utility terms) from working an extra hour (that equality was why the person worked as long as they did, and no longer). Now that the consumption reward for working an extra hour has ncreased (on account of the cut in the marginal rate),  it is now utilty increasing to to work more than they did before. Further, by working more under the hypothesised scheme they must pay more tax, as a matter of arithmatic. And they must consume more.

The proposition of the dominance of a flat rate scheme over 'threshold plus marginal rate' is suggestive of the more general proposition:

                                      

For any scheme of ‘threshold plus marginal rate’ there will always be some (i) reduction in the marginal rate, and (ii) reduction in the threshold that will, for any given income tax payer, increase the utility, consumption, labour supply and tax paid of that tax payer.

The logic is just the same. The only difference is that the size of the effect of a mere reduction in the threshold is less than the size of the effect of outright abolition. Thus reducing the threshold to zero is better than reducing it merely to a positive number.

But if reducing the threshold to zero is better than reducing it merely to a positive number, would it not be better still to reduce the threshold to a negative number? The answer is : yes, it would be better. Unlimited vistas of improvement through tax restructure seem to open up ...

Why, then, do we resist this free lunch offered by schemes to simultaneously reduce thresholds and reduce marginal rates?


One answer is that  the impacts of any given such restructure are heterogeneous and contrary across income.

The 'free lunch' proposition at stake is, recall, conditioned on a given individual income tax payer, call them X. It is clear that the restructuring that increases the utility, consumption, and labour supply of tax payer X  may have different effects on other payers. To illustrate: any individual whose income was  below the threshold obviously must now have lower utility and consumption (and pay more tax) on account of any abolition of the threshold.  It is also easy to see that the person whose income was ‘significantly' above that of tax payer X,  will win from the restructure that delivers 'lunch for free' to X. This high income person will certainly have higher utility, BUT (unlike X) they may pay less revenue. Thus what is a free lunch for X may be lunch, indeed, for those better off than X; but not, alas, a free one. And for those with incomes less than X, it may be no 'lunch' at all.

There is another reason that recommends caution against reducing thresholds and rates. Mancur Olson has suggested that Joseph Stalin used this logic to drive growth in the 1930s. That fact is an inauscipicous one. Public Choice theory can explain why what might seem like a tax reform can prove to a tax exploitation.

The next post elaborates. 

The Inconvenient Truth About Tax Credits

The Inconvenient Truth about Tax Credits

Everyone loves tax credits. At least, left of centre parties do. In 1993 Bill Clinton greatly expanded an old scheme; in Britain New Labour introduced them in imitation in the 1990s, and now the Coalition government - at Liberal Democrat instigation - have substantially increased them. The post 2007 Labor government in Australia has recently inaugurated their use there.

The beauty of a tax credit for the Left is that it is equivalent to an increase in the tax-free threshold (or ‘allowance’) that the ‘better off’ don’t get. That is to say, it is an increase in the tax-free threshold that is ‘means tested’; as income rises the size of the increase is reduced, at some point to zero. This means testing not only reduces the revenue cost of the measure (obviously), it has another merit: unlike a universal increase in the tax-free threshold, a tax credit will not reduce the supply of labour of those sufficiently well off as to not receive it. For such persons there is no incentive to ‘buy leisure’ with the tax credit, for the very solid reason that they don’t receive any credit

But all is not good. The worm in the apple is found is in very means testing of the increase in the threshold. This means testing has both an equity and efficiency cost.

With respect to equity, the ‘shading out’ of the credit as income rises clearly constitutes an increase in the effective marginal rate of tax of all those who receive a positive tax credit (but don’t get the full amount). This increase in the effective marginal rate of tax obviously doesn’t apply to anyone whose income is sufficiently high that they don’t get any credit.  The upshot is that a less well-off person on some tax credit will face a higher effective marginal tax rate than a somewhat better-off person on no credit; and the effective marginal tax rate falls with income. This seems to offend our sense of equity:  not only should average rate of tax not fall with income, the marginal rate should not fall, either. It seems inequitable, to illustrate, for a better-off person to pay in tax a smaller fraction of their extra income from, say, working a public holiday, than a poorer person.

But there is also an efficiency defect in the tax credit system. It is a simple matter to demonstrate the following proposition:

For any person you care to nominate who is receiving some credit less than the maximum, there will always be some simultaneous (i) reduction in the size of the credit,  and  (ii) reduction in the rate of shading out, that will increase that person’s hours worked, consumption, utility and tax paid.

To put it another way, for any nominated tax payer receiving some credit, one can always craft a revision of the credit that makes it smaller, but more universal, so that the person is better off; and the Treasury too!

This conclusion constitutes an inconvenient truth for tax credit schemes.  These schemes are meant ‘to help’ those receiving it. But for anyone not receiving the maximum it can always be dominated by a reworking that seems to dilute that scheme, by reducing the size of ‘help’ to those right at the bottom, but creating a ‘help’ to some towards the top who previously received nothing.

Such is one of the dilemmas of those who would contrive a tax system to secure their vision of a fairer society.

But how does the ‘dilution’ mooted above work that minor miracle of longer hours, higher consumption, increased utility and more tax paid?

Wait for the next installment.

Hayek contra Friedman

Hayek and Friedman’s Conflicting Diagnoses of the Great Depression

In the beginning was the Great Depression. 

It was from that mysterious episode that there emerged modern macroeconomic debates. Not only the familiar divide between ‘Keynes and the Classics’, but also the less well known but (I believe) ultimately more significant divide between ‘Historical Liberalism’ and ‘Neoliberalism’.

This last divide is manifested in Hayek’s and Friedman’s differing diagnoses of the Depression. Both Hayek and Friedman blamed central banking for the disaster. But for different reasons. And for different type of reason.

Put simply, Friedman had a Political Economy account of central banking’s responsibility for the Depression, whereas Hayek had a Pure Economics account of central banking’s responsibility for the Depression.

Hayek provides his account in Prices and Production of 1931, the book of a series of lectures he gave as a newly appointed professor at LSE. (The man who had him appointed him – Lionel Robbins - gave a popularised version of Hayek’s contentions in his The Great Depression of 1934.)

  

Prices and Production argued that an actively monetary policy amounted to a price distortion. Specifically, a loose monetary policy reduced the market price of investment below the opportunity cost of investment. Loose policy was, in effect, a subsidy on capital accumulation, and like all subsidies it could only do harm. Thus in the 1930s Hayek was criticising activist monetary policy on market success grounds. The free market would generate a socially efficient outcome, and active monetary policy distorted that outcome, and so wasted welfare.   

By contrast Friedman’s Monetary History of United States of 1963 criticises activist monetary policy on government failure grounds. To explain: Friedman’s case against central banking was not that central banking took something good (the free market outcome), and made it bad. That was not his position. To Friedman active monetary policy could often do good. Years later Hayek would spotlight Friedman’s optimism about the potential of monetary policy:

I don't like criticizing Milton Friedman … but …   if I told him … that I very much doubt whether monetary policy has ever done anything good, he would disagree. http://www.cato.org/pubs/policy_report/cpr-6n3-hayek.html

Friedman’s optimism about the potential of monetary policy arose from his judgement that there could be ‘market failure’ (in the form of bank runs, for example). The problem with active monetary policy was that the Central Bank did not with any reliability correct such market failures; rather it frequently mismanaged interventions that could be managed improvingly, and so making things worse. Thus Friedman’s criticism of active monetary policy was not pinned on the perfection of the market; but a defect in government.

Friedman’s position flags a key differentiation of Neoliberalism from ‘Historical Liberalism’ (that is, classical liberalism before the Great Depression): Neoliberalism shifted the burden of the case for limited government from market success to government failure.

The starting point of this shift was the Neoliberal acknowledgment that the free market outcome need not be the best of all feasible worlds. But this left neoliberal supporters of economic freedom with problem; why reject shifting that imperfect market outcome by some ‘economics of control’? To plead the incapacity of the state to implement a perfecting shift would be beside the point; the advocate of regulation hardly needs the state to be capable of a perfecting shift to make their case for regulation; an improving shift would be sufficient. And pleading the incapacity of the state to make even a small improving shift would be implausible. The inevitable bungling and ignorance of government will not convict the state of such complete incapacity. Bungling and ignorance does not (after all) imply that laws against theft are worse than useless: so why should it imply that laws against (say) monopoly pricing are worse than useless? In the face of some market failure, surely the government was capable of making things at least marginally better? As Friedman would be the first to insist, while the Fed could not have prevented a recession in 1929, it could have prevented a depression.

The riposte of neoliberalism to the regulatory advocate was not that government could not intervene improvingly, but that government would not intervene improvingly. It would choose (perhaps unwittingly) to not to intervene in a way that would be improving. This is the meaning of ‘government failure’.

Both Hayek’s and Friedman’s positions were, to be sure, underargued. There were gaps in ‘the pure economics’ of Hayek, while Friedman’s Political Economy was a collection of observations rather than a theory.

Hayek never articulated with the requisite rigor how looser a monetary policy would constitute a subsidy for investment. For it is not clear how in a competitive market a looser monetary policy can reduce ex ante real interest rates. It should only affect nominal interest rates (to the extent that the policy innovation is predicted), or ex post real rates (to extent that the policy innovation is unpredicted). But not ex ante real interest rates. In the same vein, it was also unclear how a looser policy would increase investment in the face of a wish of the public not to save any more. On this particular, Hayek’s references to ‘forced saving’ were more evocative than clarifying.

Friedman in a similar way can be criticised for having little offer in terms of a fundamental theory of government failure. With specific respect to the Great Depression, he argued that, in the absence of strong personalities, the Fed's committees drifted between policies, and never maintained a course. In post-War period Friedman’s criticism of policy drift became a criticism of policy ‘churning’; where ‘importance-maximising’ central bankers made waves in order to maintain their role as ‘players’. Both these are interesting suggestions, but far from a fully-fledged theory of government failure.

Nevertheless, one can still reasonably dichotomise criticisms of current monetary policy activism into market success critiques, and government failure critiques. Market success critiques would in the contemporary world turn, I suggest, on the thesis that monetary policy was underpricing risk; reducing the private price of risk beneath the social opportunity cost of risk. And government failure critiques ? I think they might find some material in the premium our time places on celebrity and self-dramatisation. In economic life we hail the risk-taking, rule breaking, routine-smashing ‘entrepreneur’ over the prosy Marshallian ‘saver’ and ‘firm’. And in policy I put to you we are all now Schumpertarian policy pirates; engrossed in innovative, ‘aggressive’ ‘blue-sky’ polices.

If you look at the history of financial crises, it shows that an aggressive and creative response is the best way to ensure minimal damage to the economy. 

 Ben Bernanke, Time, 27 December 2010

The Eternal Sunshine of the Wattless Mind?

The Eternal Sunshine of the Wattless Mind?

In a forbearing profile of the British Chancellor of the Exchequer, the Sunday Telegraph (18 March 2012) records,

‘George Osborne is probably the first chancellor in modern history to take a two-day holiday a week before the budget. His decision to do so speaks eloquently about his approach to the job … his predecessors are amazed at his ability to spend so little time on the job’.

Osborne returned from holiday to appear on the BBC in order to promise a ‘crackdown’ on foreigners not paying enough stamp duty on the real estate they buy in London; stamp duty on purchases over £5m will be raised from 5 to 7 percent.  Big deal. My back of the envelope calculation suggests this will raise at best £40m over 12 months, compared to forecast revenues last year of £589B. This is a made-for-television policy.

The Telegraph unwittingly put their finger on it when it concluded  ‘… we can see the outlines of Osbornism. It is not an economic doctrine: it is the absence of economic doctrine’. That captures it: the Chancellor’s mind is perfectly unsullied by any economic principle.

Of course, we get the politicians that we deserve. And their minds, too. In 1936 Keynes, in the last paragraph of General Theory, judged that his contemporary public was ‘impatient … for fundamental diagnosis’. (The completely unheralded success of the launch of Penguin books that year is one corroboration Keynes’ contention).  Did not that ‘impatience’ exert an influence on the character of the body politic? In that year a future a Chancellor of the Exchequer, Hugh Gaitskell, was head of the Department of Economics at University College, London, spending a good part of his energies mastering Hayekian trade cycle theory, and arguing against quasi-Keynesian remedies that appealed to his Labour colleagues. We cannot imagine any politician today taking difficult economic thought so seriously. But, correspondingly, we cannot imagine the public having any hunger for ‘fundamental diagnosis’. In the midst of our listing economic system, we have suddenly burgeoning not Penguin books, but Twitter.

In the Long Run ‘We’ are all … Irrelevant

In the Long Run ‘We’ are all … Irrelevant

Perhaps Keynes’ most quotable and frustrating remark is, ‘In the long run we are all dead’. To dispose of it I am tempted to brandish the riposte of Ludwig von Mises;

‘I do not question the truth of this statement: I even consider it as the only correct declaration of the 

Neo British Cambridge School’.  (Economic Planning, 1945)

But this sally is to evade Keynes’ point. Which is, as far as I can see,  that ‘the rate of discount’ is not zero;  and (to illustrate his thrust) assuring the patient that their agony will ultimately vanish hardly by itself constitutes sufficient grounds for inactivity. It would hardly constitute grounds (for example) to decline to purchase morphine.

Keynes’ remark, thus interpreted, is both irresistible and weak. It may with equal justice be retorted that time preference is not infinite. And it is not infinite; not even for that futurity when ‘we’ are dead, and gone, and wholly untouchable by events on earth. Was not Keynes himself concerned with the ‘economic possibilities of our grandchildren’?

While on the matter of mortality ….  the Australian Bureau of Statistics' just released Causes of Death gives a striking measurement of  how quickly our ‘journey’s end’ is changing. In 2001 ‘Ischaemic heart disease’ (which, of course, felled Keynes) killed 26, 234 people.  In 2010 it killed 21708 people; a decline of 4526. In 2001 3740 died of Alzheimer’s and dementia. But by 2010 9003 did.

(see: http://www.ausstats.abs.gov.au/ausstats/subscriber.nsf/0/E39670183DE1B0D9CA2579C6000F7A4E/$File/33030_2010.pdf)

The 'More is Less' Fantasy of Today's Public Finance

Richard Howard, the global strategist of the hedge fund Hayman Capital, has recently articulated thus one the popular delusions regarding current 'austerity' programs:  

‘At the moment, the peripheral countries are cutting their budgets quickly and aggressively, which is having a negative impact on their economies and making it even harder for them to reach a balanced budget.’(Business Spectator)

There you have it: to cut government spending is to make it harder to balance the budget. And conversely, to increase spending is to reduce the deficit. The might be called the More is Less fantasy. More government spending, less of a deficit.

Let me give this fancy its due: increasing government spending by $1 probably will increase GDP in many contexts; and so will increase government revenue. But will a dollar of spending increase revenue by more than a dollar? Not even the most crude, skewed and one-eyed Keynesian models will allow this conclusion.

To see this, let's travel into a Keynesian universe as far as an unhinged reason will permit.

We may begin  - in the spirit of extreme Keynesianism - by throwing out any suggestion that the economic system has a self-equilibrating tendency, and assuming the most simplistic Keynesian model of the elementary textbooks (often referred to as the 45 degree model). Such a model assumes away the possibility that in response to an increase in government spending, the interest rate might rise (and so reduce investment); or that the exchange rate might appreciate (and so reduce exports); or that the price of output might rise (and so reduce real money balances, with further negative implications for the interest rate and the exchange rate); or that consumers will perceive that any extra government debt spells future interest charges and future taxes to match; or that consumers will save almost all of any temporary increase in income that might be generated by a temporary increase in government spending.

In other words, we give everything we can to the Keynesian model. And we now give more. We suppose that there is zero 'leakage' arising from savings: that is, 100% of any extra income is consumed by households. And we assume zero leakage arising from imports: that is, 0% of any extra income is spent by households on overseas sourced goods and services.

This is the model of the ultimate 'multiplier'. In such a model if the government spends another dollar (financed by debt) then that will generate 1/t dollars of extra GDP, where t = the fraction of an extra $ of GDP that will flow to the government in higher taxes.

So what is the extra revenue from this extra GDP? Some simple algebra gives us the answer:

t * 1/t  

And  t * 1/t  equals 1.

Thus in this ultimate multiplier model one extra dollar in government spending will generate one extra dollar in revenue, exactly.

The consequence is that the slightest movement away from the 'ultra' assumptions made above implies that one extra dollar in government spending will generate less than one extra dollar in revenue

So if we allow households to save even just a few cents of extra $ of income then the multiplier will be smaller than 1/t, and so one extra dollar in government spending will generate less than one extra dollar in revenues.

And if we allow households to spend even a few cents of extra income on imports, then the multiplier will be smaller than 1/t, and so one extra dollar in government spending will generate less than one extra dollar in revenues.

Conclusion: even in this extreme Keynesian universe, More is, alas, More. And Less is Less: less government spending, less deficit.

The 'In Fifth Year of Recession' Myth
The media are full of the claim that Greece is now in its fifth year of recession. Started by various Greek finance officials, this canard has been picked up and credulously repeated by BusinessWeek and Reuters, and many others. In truth Greece has been in recession, as customarily measured, for 12 quaters, or three neat years.

Greek real GDP  (seasonally adjusted) grew until the fourth quarter of 2008. It fell again in the first quarter of 2009. Two succesively quarterly falls is usually deemed to constitute a recession. Thus Greece could be said to be in recession from the beginning of 2009.

That is 3 years.

(Data is sourced from http://stats.oecd.org/Index.aspx)