Self-defeating deficit reduction?

Karl’s post yesterday led to an important exchange about the possibility of self-defeating deficit reduction, with particularly important contributions from Michael Burke and Michael Taft.   If multiplier and automatic stabiliser effects are sufficiently large, the understandable concern is that cuts in the discretionary deficit could actually raise the deficit overall.  We end up with the worst of both worlds – a deeper recession and a larger deficit. 

Effectively, the argument is that the deficit reduction measures slow the economy, and this leads to automatic stabiliser effects (falling tax revenues and rising expenditures) that offset the discretionary effect (i.e. the underlying change in the deficit holding GDP constant).  

While plausible, I believe the claims for self-defeating deficit reductions are wrong – or at least wrong in the context of the simple (and I believe essentially correct) model that I think all the main participants in the debate are using.   I sketch this model here.   Using the model, it can be demonstrated that a discretionary deficit cut will lower the overall deficit for any (non-negative) values of the deficit multiplier and automatic stabiliser coefficient.   Moreover, it can be shown that the deficit as a share of GDP also falls with a reduction in the discretionary deficit, even as this reduction slows the economy through a multiplier effect. 

Of course, a simple model cannot provide the last word on the issue.   But hopefully it will at least help us pinpoint better the sources of the disagreement. 

Those arguing against the need for austerity point out that the underlying deficit has grown with previous rounds of austerity.   While I agree that these measures have slowed the economy, I do not believe that they have actually caused the deficit to rise.   Unfortunately, there are other contractionary forces at work, not least the overhang of debt that is curbing business and household spending and also bank lending.   With bond yields where they are, I assume we all agree that we cannot avoid a bailout/default without putting the deficit quickly on a downward path.   I don’t see we have any choice now but to pursue tough deficit reduction measures.   It is not going to be pleasant. 

95 replies on “Self-defeating deficit reduction?”

“Unfortunately, there are other contractionary forces at work, not least the overhang of debt that is curbing business and household spending and also bank lending.”
In addition to this, there is an overhang of interest payments. As interest rates rise, more money is taken out of the economy. As most of the funding for the banks is external to the economy, increases in mortgage rates lead to more capital leaving the economy. As most sovereign debt is held externally, increases in interest rates and increasing debt also lead to more capital leaving the country.

Anyone who argues for a positive multiplier for government spending, must also accept that there is a negative multiplier to the same value for both interest and capital repayments.

In a low inflation eurozone, it is not enough to say that “governments don’t pay back debt”. The negative effects of the interest bill must be assessed and matched against the positive effects that would accrue from not paying back the debt/taking on more debt.

The same is true of household balance sheets. The overhang of private sector debt is having a negative effect on not just sentiment, but on available capital. The absolute level of capital needs to be reduced. Any talk of over-saving is missing the point. During the bubble, massive amounts of spending were brought forward, either a continuing unproductive interest burden or a painful period of capital repayment has to take place.

Nice model but completely implausible in the absence of real-economy empirics. The proof of the pudding is in the eating. Substantial cuts will slow growth which will in turn remove the capacity for real consolidation. The evidence is overwhelming.

John – just add some non-linearity and the model falls apart. For example, put a deficit squared term into the output equation and you can generate regions where policies to cut the deficit actually cause the deficit/GDP ratio to rise. The intuition is just as people propose: if output falls sharply with the deficit, then the ratio of deficit/output can rise as you cut the budget deficit. Your model shows it can’t do this forever because we will have some output if we have no government at all, so we know there is a point where the deficit/GDP does hit zero. But we are a long way from zero, and this linear approximation doesn’t make sense for large shocks to the deficit. [Also, there are surely many equilibria here, with one being we all flee our banks and riot in the street, so if budget cuts incite that then you would need some new terms in the model.]


The model is more robust to non-linearities than you allow. From Figure 1, all that is needed to generate the basic result is that the GDP curve slopes upwards and the deficit curve slopres downwards. Besides, having to depend on non-linearities is always a good sign that an argument is non-robust.

Some remarks from Michael Taft today at the TASC conference:

-3 austerity budgets has taken €12bn out of the economy – equivalent to 7 percent of GDP in the midst of a recession. The purpose was to lower the budget deficit. The deficit will be higher next year than this year.
You can only repair public finances during a period of high growth and high job creation.
The government is no longer practicing economic policy. It is practicing alchemy.
The dividing line in the debate is not between lots of austerity and less lots of austerity.
The dividing line (is) between those who want fiscal expansion and those who want fiscal deflation.
The Irish economy has collapsed by €21bn Euro. Investment is back to 1998 levels. We need sustained, substantial and smart investment.
Opposition to investment is based on the claim that we are broke. The ESRI shows that Ireland hows the highest level of cash and assets available to an EU government.€50bn – equivalent to 30 percent Not all of the €50 billion is available due to FF’s banking policy.
You cannot cut your way to recovery. You cannot deflate your way, but you can invest your way.
€20bn is ambitious because the window for investment is closing. €15bn is available from cash and assets.
This investment would become embedded in the economy and make possible a growth friendly fiscal consolidation by 2014 – starting with the most wealthy in society.
The social and physical infrastructure is so degraded that we have a lot of vital work to do. Work that would be needed even outside a recession.
One of the legacies of FF is that we are ranked 64th in the world for our physical infrastructure. Many land locked countries have more developed ports than we do (an island country dependent on trade).

There is one requirement for deficit spending:

The funding for it has to be available. There are two sources: Use savings or borrow from someone.

Irelands savings are not sufficient for continued deficit spending.
Irelands ability to borrow can be seen as severely limited.

If deficit spending is not possible, what can be done?

Increase revenues (taxes) and decrease spending.

Debates on the multiplier on possible deficit spending are interesting but for Ireland I believe they are only of academic interest.

The deficit sooner or later has to be turned into surplus otherwise borrowing can’t be repaid. (True irrespective the size of the GDP)

Anyone considering lending to Ireland might be looking at the taxation system and how money is spent to see if Ireland will get a surplus in the foreseeable future. The questions for a potential lender are:
-Will future taxation system raise sufficient revenue for the current spending?
-Will future spending be reduced to the level of revenue the current taxation system raises?
-(or a combination of the above)

Anyone believe that tax-revenues will go back to what they were in the bubble years without a change in taxation system?
Anyone believe that Ireland can afford not to make ALL easy savings? (like stopping the lunacy of unvouched expenses)

Dr.Thomas Palley at the TASC conference said:

-The neo liberal paradigm is exhausted and cannot be revived.
We need to expose the neo-liberal economic model as the cause of the crisis. We then need to offer a compelling alternative.
Milton Friedman once said “Only a crisis produces real change. When that crisis occurs, the actions that are taken depend on the ideas that are lying around”
You do not get a bubble and crisis of the current magnitude simply because of regulatory failure.
We need to overthrow the neo-liberal paradigm and replace it with structural Keynesianism.
The forces of conservatism will try to drown out alternative explanations.
The economics profession is captured by the neo liberal framework. Our task is to persuade progressive politicians to ignore mainstream economists, who peddle toxic ideas.-

John – just take your GDP curve and make it steep at the start then flatten out to have a small slope when it crosses the deficit line. You’ll see the deficit to GDP (represented as the slope of a line from the origin) will rise with fiscal cuts over regions where the GDP curve is flatter than the slope of that line from the origin.

Your comment: ” Besides, having to depend on non-linearities is always a good sign that an argument is non-robust.”

I wasn’t arguing my point was robust, rather your conclusion is not robust (if we add very simple non-linearities to your model). I think your point is well-illustrated in any case – the slope of the GDP line is unlikely to get so flat for reasonable parameters, but, such claims are complicated in a world where strikes and riots can make that slope awfully flat for sustained periods.

An alternative way to state your point is that “as long as cuts are large enough, they are bound to bring the deficit down”. That comes from the undeniable point that if we abolish all government spending we must have a zero deficit/GDP ratio.

“having to depend on non-linearities is always a good sign that an argument is non-robust.”

THis is the kind of thinking that got us into the crisis.

@ Kenneth: “You cannot cut your way to recovery. You cannot deflate your way, but you can invest your way.”

Spot on! Except those pesky rates is near zero! And there is that little problem of the FIRE economy. This must be snuffed out PDQ.

“Milton Friedman once said “Only a crisis produces real change. When that crisis occurs, the actions that are taken depend on the ideas that are lying around”

Yep again. “… on the ideas that are lying around.” Ah, but whose ideas might them be? The usual suspects I suspect. Its their Frame! They be very ‘loss averse’, they be!

“The economics profession is captured by the neo liberal framework.”

Maybe, but I reckon its more likely they were exposed to a particular dose of ‘received wisdom’ and may not have taken the bother to subject their economic beliefs to genuine scientific scrutiny. If they had done so, some would have been most unhappy, but they would have been in the minority. And we know what happens to minorities! Think Soddy and Georgescu-Roegen.

“Our task is to persuade progressive politicians to ignore mainstream economists, who peddle toxic ideas.-”

Jeeze Kenneth, do you know any of these politicians? I assumed they were extinct by now. And bye-the-bye, toxic ideas will always trump common sense. Don’t give up. Don’t assault the glacis – seek out the weak spots.

Brian P

Would this be god of the neo-liberals Milton Friedman, or some other Milton Friedman who was a structural keynsian?

If we can’t borrow more to achieve investment, we need to alter current spending. Thus we should slash the health budget (keeping people alive is expensive) and use the savings to invest. Equally, we should cut welfare payments because they are not as productive as seed capital for small business…

You chaps might want to be careful what you propose.

Anyone who thinks that they can reduce fiscal debt and somehow miraculously in the future think that bank credit can flow again from the surplus created is just plain crazy.
This is not the mid 1980s – there is no more surplus capital in the world to run down in this monetory system.
Capital will have to be revalued upwards by a massive amount to re balance to a new equilibrium.
This development will not come from Ireland – we should not sacrifice ourselves on a austerity alter as any surplus we create will be extracted by other regions.

This is clinical insanity or a lack of understanding of money and its flows which is just a energy token.
Ireland should game the system like everyone else – we are like a honest poker player sitting on rigged table full of sharks.

Curiously our saviour could be Uncle Ben – there will be no more QE as we have come to know it – The CBs are going to revalue Gold to the Moon.

US dollar capital will stop flowing east – oil will fall dramatically in Gold terms.
After 40 years of capital rundown in America its infrastructure will be rebuilt as capital will again flow inwards to the States.
China will be a economic wasteland – the global wage / tax arbitrage system is coming to a end.
Ireland should be aware of these coming developments and postion ourselves accordingly – lets not sacrifice our old sick and vulnerable on the alter of a dying monetory system.

Having been there and done that I would say we are at least 30 months late. As conditions worsened all around them our politicians were transfixed like deer in the headlights (or rabbits in the dazzler). The downward spiral has to stopped in its tracks early in the game. Government has to act promptly, decisively and ruthlessly to curb spending. In the case I was involved in we immediately cancelled all RFI, RFQ and all contracts where we were not legally bound to spend. Where we were legally bound we negotiated an exit where it was cost effective. Employees over 55 were offered buyouts, some severance and reduced pension penalty if they went voluntarily. If they did not accept the offer it was implied they would get far less generous treatment in a forced layoff.
An immediate hiring freeze, all term and contract employees let go immediately. Employee travel stopped immediately. A wage freeze including increments and contractual increases (largely unionized work force). One of the beauties working for gov’t is that they make their own rules, and laws, rules, regulations and policies can be quickly changed even if it requires legislation. Statutory entitlements were reduced, this required legislation. Transfers to lower levels of gov’t were reduced, this required only the signature of the responsible Minister. At this stage the rot has set in and the gov’t is damned if it does and damned if it doesn’t. In a downturn as severe as we have now the gov’t should only spend on projects with a high domestic labour and material content that will improve productivity as the economy improves. Instead our gov’t subsidises car purchases that have over 90% foreign content, multi million footpaths to nowhere, canals that will be loss makers for eternity. From where I look at it the question is are we dealing with drunks, clowns or fools.

Do you think if we can cut far enough we can offset the consumption increases in China ?
This is now the ECBs problem not ours – but do you want to facilitte the raping of Ireland so that London , Frankfurt and Paris can get two more years of interest income from Ireland ?

@John McHale

In this bit

“Those arguing against the need for austerity point out that the underlying deficit has grown with previous rounds of austerity. While I agree that these measures have slowed the economy, I do not believe that they have actually caused the deficit to rise. ”

You are presumably referring to the deficit, not deficit as % of GDP?

The two might be rather different.


The two are indeed rather different. But I believe the statement above applies to both.

“It is not going to be pleasant.”

I love this phrase. It’s very popular with the pro-austerity crowd. What it’s trying to say is, “I’m a serious person telling you hard truths you need to hear and that is why I’m right.” It’s a cute little psychological trick.

To be blunt, that’s crap. Some painful things are good for you, some aren’t. It does not belong in a serious economic argument.

By all means hunt down and remove waste in the civil service. Reduce spending in areas that don’t increase economic activity. Sure, good plan. But right now land is cheap. Construction workers are cheap. And in the last boom we saw serious issues with transport, hospitals, schools, energy and communications.

Now is the time to spend money fixing these things. Now is the time to build the infrastructure the next boom will depend on. Now is the time to lay the foundation to grow the economy.

Exporting people and cutting spending are a recipe for reducing the size of the economy.


Apologies for irritating you with that closing sentence. It was unnecessary. For what it’s worth, let me say something about where I am coming from. I see myself as a Keynesian on macro issues, and have a degree of sympathy for the TASC position. Until quite recently I have been an advocate of backloading the adjustment. I believed that advocates of front loading were underestimating Ireland’s creditworthiness; and also that if the projections of a reasonably rapid return to a strong underlying growth rate meant there was some scope to smooth the shock. While I continue to believe that the market’s default pessimism is overdone, in the end there is no arguing with the fact that investors do not view Ireland as creditworthy. I have also become a bit more circumspect about the underlying medium-term growth path rate given the way that impaired balance sheets are weighing on spending (and lending) across the economy. Thus if we want to steer our way through this while retaining economic sovereignty, I reluctantly have come to the view that we have to stick to the four-year timeframe and three percent target. I am still hopeful that if we can put in place a credible plan — which requires commitments to real measures, not some vague outline of options –we can avoid hitting the economy hardest when it is at its weakest in terms of the size of the output gap. Unfortunately, the more we look like we don’t have the political capacity to push through the needed measures, the more unpleasant it will be.

These are qualitative results but I would like them to be made quantitative. In particular, I would like to know by how much GDP will have to shrink, cet par, to hit existing deficit/GDP targets. This matters since markets will not judge as credible a plan that involves GDP shrinking too much, and unemployment rising too much. So: what are m and b anyone?

(Yes, I know that the whole plan is predicated on ceteris not being paribus, but the rush to austerity in the rest of Europe is making this happy outcome more unlikely.)

@ KC
China’s role in this is that it has triggered a Schumpeterian recession/depression in the developed countries starting with Japan where property values are now what they were in 1983. China is not alone it is acting with Taiwan, Korea, Malaya, Singapore and the sum total is devastating to the US and the EU. The ECB has been more than generous to Ireland and if our gov’t had a splink of sense they would have turned things around before we became so risky an investment that our cost of money increased dramatically. Nobody held a gun to the gov’ts head and forced them to back stop our banks, cronyism, nepotism, greed and force of habit did that. We have to stop pointing fingers and looking for external scape goats we have enough blame to place domestically that it will keep us going for the rest of the century. Every gov’t makes mistakes the difference is that most of them face reality and do what needs to be done. In our case we are in a state of denial, it is a pity the British left in 1921 everything could be neatly place at their door.

@Kevin O’Rourke

One of the most frustrating things about dealing with this policy challenge is that when it comes down to it we have such a poor grasp of the key quantitative parameters.

However, I would say that a value of 1 for m and 0.5 for b are conservative (i.e. at the upper end of the plausible range) for Ireland. This puts 1/(1+mb) at two-thirds (a conservatively low estimate). That is, two-thirds of the discretionary deficit reduction would end up as an actual deficit reduction. Of course, the multiplier of 1 is the really unpleasant part. We have to destroy national income equal to the amount of the actual deficit reduction that we achieve. That is the kind of “waste” that I hoped we could avoid.

I can’t remember who said it (James Tobin maybe), but was well said that it takes a “lot of Harberger triangles to fill an Okun gap”. It is a real shame when we have to pursue policies that make that gap bigger.

@John, thanks.

I do wonder if investor confidence is low because of the lack of political will to do things that need to be done. Things like dealing with corruption – unless you have connections, investing in Ireland can be tricky. When I’ve asked about why public transit systems don’t get more investment vs. roads, I’ve been told that well-connected local people can do the latter but not the former for instance. Dealing with waste – the HSE is apparently administratively heavy; electricity prices and services are poor; etc.

Sustainability of sovereign debt requires that real interest rates do not exceed real growth rates for any significant length of time (we have already had over 2 years of this). It is a balancing act of reducing interest rate spread (and therefore interest rates) hopefully (or expectedly) through lowering budget deficits at the same time not dampening growth by a larger amount.

To a large extent the Irish government has only an indirect effect (apart from the direct effect of reduced government expenditure) on growth rates. Whereas it might be perceived that it has a more direct effect on interest rates spread by way of its 4-year budgetary plan. With strategic micro decision on the budgetary side it can mitigate against large negative demand shocks (primarily by not leaving the burden of reductions fall on lower income households) and at the same time benefit from reduced interest rate spread.

Is there other ways in which interest rates spreads could be reduced? If interest rates fell close (within 50 bp) to the bund rate then it would make sense to tackle the debt sustainability issue by way of stimulating growth. Given that the EC has approved (signed off on) all of the Irish Government “Banking decisions” they are in some way culpable (they did not want to see rising systemic risk) for a large part of Irish debt – maybe by way of an EC guarantee of €50bn Irish debt (might have the effect of reducing the spread)!

Abba Lerner the brilliant Russian-British-American economist did some very clear thinking about what makes currencies credible. His ideas have been put into practice around the world, most recently in 2001 in Argentina where states and cities issued scrip to pay their contractors and employees under a system known there as Pocones. It would help if more people knew what alternatives are available. The Kingdom of Kerry could issue scrip with the Killorglin puck goat surrounded by a golden halo on one side and St. Brendan on the other. Good quality linen paper with a hologram and we would be off to the races. Who needs Dublin or Frankfurt. It would need to be endorsed by a serious economist, Karl Whelan for example. Is the O’Brien that used to sign the British notes still around?

“I would like to know by how much GDP will have to shrink, cet par, to hit existing deficit/GDP targets.”
It may be that we are aiming at the wrong thing.

Rather than aiming at a percentage of GDP, perhaps the government would do better to aim for a deficit as a proportion of income? Or as a fixed number?

@John Mc
First, thanks for the paper. Interesting reading. Now, I’ll ask some silly questions and probably show how long it’s been since I did partial derivatives.

First, like hoganmahew and others (if I paraphrase), I guess I’d like to see some sigmas as well as all the deltas. The cumulative position is the one that quickly dominates.

If I assume that taxation as a % of GDP (or GNP for Ireland, but let’s not quibble) has some limit, then don’t we simply reach a point where the accumulated interest payments overcome the stimulus effect of deficit unless the deficit increases continuously (and geometrically?) Don’t we already know this?

Is the most interesting equation the one you didn’t do, a variant of Eq1? Should that be something like Y=Yo+mD-iSigmaD-P, where i is the interest and sigmaD is the accumulated deficit and P is a capital repayment, although we might set P to zero for the short term? The interaction between i, m, b and SigmaD makes it all beyond my late night maths, but still..

The other point that I wonder about, and one that may be pertinent when considering the keynes approach, is that in many ways Ireland thought it was running a balanced budget in the period around the middle of the decade but was actually engaging in a deficit funded stimulus. We just picked up the bill quite late in the day when we bailed out the bank’s creditors, retroactively picking up the tab for spending in the previous several years.

If we were actually running a stimulus in the run up to the crash, does this tell us anything about the stability of multipliers? Now it was private creditworthiness that collapsed and state credit may still be good, but it’s interesting nonetheless.

I’ll have to re-read in the morning! Thanks for making me go “d what?” for the first time in a while.

After the war we have went through the inflation of Europe , then Japan and now China – now we have run out of planet.
What has goverment got to do with anything but redistributing credit and surplus to manage the banking machine of capital extraction.
Do you think ANY goverment in Ireland could have implemented a austerity programme 10 years ago or more – impossible.
The neighbourhood was controlled by the drug pusher not the flawed parents struggling to control their young who were about to repeat the mistakes of their Parents who eventually needed to become popular and fashionable in order to be accepted by their sons and daughters as modern fashionable role models.
Goverment is merely a adminstrative section of banking – nothing more.

@ Mickey Hickey

China’s role in this is that it has triggered a Schumpeterian recession/depression in the developed countries starting with Japan where property values….In our case we are in a state of denial, it is a pity the British left in 1921 everything could be neatly place at their door.

Ireland is a failed state in denial as Greece was until it had no choice but to face some home truths that had been ignored for decades.

It’s striking that despite the economic emergency, not one collective interest, representing workers, business and the professions, have seriously embraced urgent change in response to the bursting of a bubble that had resulted in most sectors of society being overpaid.

Bodies such as the universities have also failed to respond to the new reality. Reintroducing fees could be a solution but as with the unreformed country, who could have confidence that the money would be spent wisely? Can excellence only be achieved through lavish spending while revenue whether from tax funds or fees comes from a virtual monopoly situation?

In Sept 2009, Minister for Health Mary Harney said Irish GPs were being paid almost five times more to administer the seasonal flu vaccine to patients than their counterparts in the UK. The litany could go on and on but what illustrates how rotten the system has become is that Harney herself in common with others, were like children let loose in Willy Wonka’s chocolate factory, in their lavish misuse of public funds on themselves.

An Bord Snip proposed over €5bn in cuts; 88 planning authorities seems a little excessive and so on.

There can be a case made for some targeted stimulus projects including infrastructure but what’s the case for turning a blind eye to wanton waste and feather-bedding or protecting public staff pensions of more than €50k from cuts?

China and other Asian countries have used a model similar to Ireland’s to develop.

The US consumer binge was financed through equity release loans on homes and consumption rose to a record 72% of real GDP in 2007.

Should China be blamed or the US which wants public services, cheap imports and low taxes?

Foreign-invested enterprises in China account for 22% of tax revenues, 28% of added industrial value and 55% of foreign trade and 45m jobs.

Ireland is over-dependent on FDI which accounts for 90% of tradeable exports. It is also over-dependent on US chemical firms which face revenue losses of $100bn in the next 5 years.

Irish exports from such firms have grown in recent years but job creation has been almost static.

This week, IBM said it would shift 190 jobs from Dublin to China; H-P said it would create 120 jobs for people who have multilingual skills; Google was reported to be routing UK revenues through its Irish unit for onward transfer to Bermuda.

While FDI employment is back to the 1998 level, many of the jobs in companies such as Microsoft and Google are taken by foreign workers because of the language skills required.

We couldn’t even revive our own language, because like much else, we chose the easy option.

On the bright side, there is an interesting travelog in the NYT: ‘Lost in Ireland.’

Then it began to rain.

Often, I wondered whether I’d been misled about Ireland. This was, I’d gleaned from books and movies, a nation of loquacious gabbers, silver-tongued schmoozers, ostentatiously oratorical pub-dwellers, but were they as mythical — and dismissibly stereotypical — as leprechauns? Or was their replacement by taciturn introverts telling me something else? The FM radio D.J.’s — my most constant companions — spoke almost every day about the implosion of the Irish economy, the lack of faith in government and the increasing departure of Irish people for other lands. I seemed to have driven into a country mired in depression both financial and emotional: Beckett’s world, not Joyce’s. Even the D.J.’s pope jokes fell flat.

Rental cars in Dublin are highly affordable

The best I can say of Irish pub food is that it’s filling. Menus may be beautifully written, but don’t let evocative descriptions of cattle breeds and root vegetables trick you into ordering a flavorless Irish stew.

A lot of economic theory is about incentives, for consumers, for firms etc. I was thinking about the Fine Gael announcement during the week (reported in the Irish Times front page on Thursday) that the Department of Finance is ‘not fit for purpose’ and that FG intend after the election to clear out Finance’s senior management and replace them with political nominees.

Well, right now, those same senior mandarins are preparing the four year plan and the Budget and if Michael Noonan is to be believed are holding regular meetings with the European Commission and ECB to stave off Ireland being bailed out by the IMF and European Stabilisation Fund. Yet these self same senior mandarins know they probably will be out of a job in six months or so (or moved sideways to the vehicle licensing centre or some other similar public sector quango).

What kind of incentive system does that create for the mandarins ?

Well done Fine Gael – you seem to have managed to give the Finance mandarins every incentive not to care if we end up in an IMF / ESF bailout.

Why does this matter – well just look at what the IMF do when they go into countries.

Across the board cuts of 25% in university budgets anyone ?

@ joseph,
First of all, I am not sure the FG policy actually envisages replacemnt with political appointees. Secondly, the facts are clear that DOF and indeed public sector management has been awful…probably worse than the banks. That is why there needs to be a clearout. In fact there already has been a clear out of sorts. Jim O’Leary has been brought into the budget divsion from outside as an adviser.

Frankly speaking, most of the senior management in the CS are not fit to run a vehicle licesnsing centre. Many of them have got to were they have got to by telling FF ministers what they have wanted to hear.

You are right about the IMF.

@ Joseph O’Toole

Well done Fine Gael…

Well done for defending the status quo, a broken system and appealing to the self-interest of academics!

What should Richard Bruton advocate? Baby-steps that the forces of conservatism and self-interest would also oppose?

This is what was reported:

Bruton was particularly harsh in his criticism of the Department of Finance and said the party was committed to a radical shake-up of it in its forthcoming proposals. He described the department as “unfit for purpose”.

First, the most senior officials would be “hand-picked managers from the top echelons of the private and public sectors”. Second, named officials would be responsible for all major change initiatives. Finally, the new structure would be scrutinised on an ongoing basis by a “high-level, expert and credible advisory and implementation board”.

Of the six other divisions in the Department of Finance, Fine Gael believes that the Budget and Economic Policy division is key. Mr Bruton says that in order to regain lost credibility it would be necessary to have an open recruitment process to appoint its director. This person would then have the power to “hand pick his or her own team”.


Who will do the handpicking of the mandarins ? The Minister of the day most likely.

We will be essentially moving to an american style of administration – with the senior ranks of the public service political appointees for fixed terms.

This may be a good system.

@John McHale
In one sense I think it boils down to whether or not you academics think you owe a duty of care to the Irish economy.
When you write down a model that spells out the logic of deficit reduction and the arithmetic possibility of reaching a specific target you do nothing wrong or anything that violates economic theory. But I think it simply isn’t good enough to give an academic shrug and say nothing else. It’s the truth but it certainly is not the whole truth.
I think you need to make explict the economic consequences of the size of the cuts that you say are absolutely necessary because of the Brussels/Bond market constraint. I think you need to tell us what your simple models say will be the unemployment consequences.
In addition, again in the spirit of telling the whole truth, you need to explore that binding constraint. Sure, the Brussles constraint is explicit. But, from a funding perspective, the only one that matters is the bond market. Is it not theoretically possible that we could return to the bond market next year at acceptable rates if we follow a deficit reduction plan different to the one imposed by Brussels?
I ask this because spreads in the bond market indicate, logically, that it wants either a different plan or that the government cannot pursue the brussels plan. Either way, something very serious is up with the credibility of Irish fiscal policy.
And here’s the thing. I think the bond market is smarter than you and Karl (no offence). It realises that the economic, particularly unemployment, consequences of what you propose render those proposals incredible.


Interesting observations about the bond market constraint and its reaction to austerity.

But your observations about “duty of care” are ridiculous. I gave up a chunk of yesterday to write up a simple little device that I thought people who are thinking hard about the challlenges facing the economy might find useful. The debate about the effects of deficit reduction measures on the actual deficit seemed to be going around in circles, and I think the simple model helps clarify a few things. To argue that we shouldn’t write anything down that does not address everying is absurd. From your earlier comments I would have thought you understand that that is not how economics works.

I think you may have misunderstood me. I, nor anybody else as far as I can see, find no fault with the proposition that reaching the 3% target is a matter of arithmetic. Both you and Karl have made that point and made it well.

But I also thik that if these points are to be made, they need to be complete. There is no point responding to a request for directions with a simple ‘turn left, turn right go straight for 5 minutes’ if what you leave out is ‘and by the way, you have walk on broken glass for most of the journey which might mean you bleed to death before you get there’.

My point is this: you run the risk of seeming to believe that getting to 3% is a simple matter of cutting large, cutting quick and then sitting back to enjoy a nice cup of tea.

I’m guessing that you don’t mean that at all, but I think we need to be explicit and play this game of consequences to the fullest possible extent.

“Is it not theoretically possible that we could return to the bond market next year at acceptable rates if we follow a deficit reduction plan different to the one imposed by Brussels?”

For that to work, Brussels and the govt would have to conclude that the current plan was long longer sensible. There is no evidence that this dialogue is even taking place.

Alternatively, Biran Lenihan could stand up on Budget day and anoounce that after consulation with you, David Begg and sundry other that he was implementing a longer adjustment period stretching out to some time in the futrue, defined by you. Then the excrement would hit the air conditioning in Brussels and Frankfurt. There would be much wagging of the finge by the Commission and the ECB etc. There is simply no chance of a return to the bond market in these circumstances.

I think you are missing a point in all of your macro analysis. The EU thinks we are overpaying public servants, over generous as regards welfare and have a crazy income tax system with anomolies at the bottom and the top of the pay scale. Sorting this out, involves fiscal pain.

@Hugh Sheehy,

Read some of Jim O’Leary’s other articles over the years on the folly of benchmarking and on joining the euro.

Again, thanks for the non Sunday paper reading material.
On your suggestion that values for m and b could be as high as 1 and 0.5, while I understand that the discussion on m could be open ended, can’t we make a better stab at b? Isn’t it related to the overall tax take? For Ireland, whether we’re talking of GNP or GDP, can’t we set a tighter band around that one?

Then, while I’d set m at a low number (0.5, maybe less) I understand that others believe in very high numbers. Either way, can’t we also consider the mechanisms whereby increases in D, and particularly SigmaD, could cause m to be negative at specific times for any positive deltaD?

We may be already approaching such a moment, where unless deficits fall we see not only a decrease in private investment but also an actual disinvestment where money flees the country. Even if enough bond lenders will lend to us at 6.5%, it doesn’t mean that all the money already in the country believes in the same scenarios. Although our MoF doesn’t believe this can happen – we’re an island, apparently – there is anecdotal evidence that deposits are fleeing Ireland and private investment is certainly pretty low. Confidence, to put it in non mathematical terms, may be inversely correlated with overall indebtedness. Once any significant part of the confidence distribution loses faith you’ve got a major problem.

John McHale
That would be a triumph for Keynesianism!!

So it is not true. Klugman is still barking mad….

This is a reflection on the consumer society, where retail supports quite a pyramid. Each level attracting “low” taxation. Undoubtedly the loss of spending by government etc will also have knock-on effects. Hence the need to find the true level of the economy as soon as possible. Taxes will support government spending …… Oh Dear, I seem to be a cracked record, repeating myself over and over…..

More taxes, now! Try to front end it as much as possible.

Anyone who does not leave, may well be losing more than they realize as the Euro falls and falls, keeping house prices in six figures and creating jobs as food prices rise and rise…….. as do taxes, while services fall. Malaysia seems good, Indonesia even cheaper…?

Best thing to do is to have had a job where you have a defined benefit pension, say like the losers who end up as civil servants? Oh I forgot, they are no longer losers, they are now leaches who caused this depression! The Irish narrative changes so often…..

Kondratieff, anyone? Life is full of cycles. So get on your bike and find a job!

Simple indeed! Economists are not here to make Irish lives easier…… So what are they useful for? I have written on that and not been contradicted. They have no duty to anyone. I only wish they would stop confusing people as the truth is rather simple and their main job is to hide that!

Irish Civil Servants are not stupid, just playing a role. When CJH threatens to have opponents killed, they tend to become very careful what they do. When it suits powerful interests to damage the Irish economy, Irish CS do nothing to stop it. None of this reflects on their ability. Their spine and honesty, however ….. You also assume they are neutral when they often are related to the elite, those who end up with what others once had, when all the fuss dies down and the economy resumes “normalcy”! Many people knew what was going to happen, Tull, even if you did not!


yes taxes will go up but spending on lavish and excessive unfunded PS pensions will come down.

Michael Hennigan

You would write excellent editorials and it would add to your Finfacts blog. Please consider it? Further examples of Malay life and cost of living might be an eye opener?

Your point about the institutional lack of comprehension of what a mess the country is in is well worth repeating, so I do! It reflects the cosy corruption caused by wealth that is rapidly disappearing but once existed. No one “belongs” to others any more, they are too busy competing and screwing the “system”. One of the worst symptoms of cheap money! Greed once excited, is difficult to turn off! GNH is more important than GNP!

Reflecting on that neat Model by JMcH I started to wonder; perhaps this is how many economists frame reality – as a virtual model whose logic is nearly flawless, whereas real reality is an irrational mess. If you persist in this belief, then things may not turn out as your model predicts.

That ‘Multiplier’ thing has me puzzled. Maybe a biochemical analogy will illustrate my miunderstanding.

You isolate and perfuse a whole tissue (an intact liver is a reasonable analogy for an economy). The tissue in a ‘steady state’. You infuse 100 units of energy (stimulus) and and a little later you notice an energy output of 101 units.



Correct! For every, genuinely needed, project (at lower cost now because of lower expectations) the government can print money. Obviously the ECB will not allow the printing, but borrowing will mean tax revenues. This is classic thirties remedy and it works! History. Simple. Austrlia embarked on such public works, Snowy Mountain scheme? and printede all the cash for the work. Non-inflationary and antideflationary. People spent that money. Australia gave $1000 to every one in Australia recently. Remember, Ken, that under EU rules the work can be done by Greeks…..!

Looks like I have a slight glitch in my uploading module!

contd: …

1. Liver cells are exempt from Laws of Thermodymanics. Not possible.

2. The input stimulus activated an intracellular (endogenous) energy source and it was responsible for the energy output – please note that you have to account for the frictional losses of energy assimilation and production!

3. The pre-existing intracellular resources showed no change. Hence, there is, as yet, an undiscovered intracellular energy source.

OK. So now to those Multipliers. What exactly are they – their component parts, and how do those component parts interact, following a stimulus, to produce an amount of output greater that the input amount? Or vice versa. Output is less that input.

If we are considering that the whole system is a mathematically modelled virtuality – then I can understand it. However if it is a real system … …?

Brian P

No, no, no. I do not think that unilateral declaration of fiscal independence is credible either. As you well know, I have thought the game was up for a long time. Right from the night the State took the entire banking system on to its balance sheet. I think I wrote about the Monty Python dead parrott sketch a long time ago. Dead parrotts are dead. Insolvent States are insolvent. We have to get beyond denial.
Look up your history. Plenty of States in the USA have defaulted. They are still there.


I am confused as to what you are are advocating. at one point you agree that “the Brussles constraint is explicit”, which I take to mean that we have been ordered to strive to get to 3%& that is binding. At another point you seem to imply that the bond markets would fund a policy with less austerity or as you call it more credibility. Or is that too much of a stretch.

From my point of view that would involve a dispute with EU. The bond markets would just say no thanks at that point.

In either event,we are back to the same point. We are not coming back to the bond markets next year. We are heading down the same route as Greece. That will involve painful fiscal correction. It is possible that it might not be as painful as outright default, since that would surely involve a zero primary deficit now.

I think you are wrong on the guarantee as well, The EU/ECB would not have allowed us not to stand behind the banks, given that it operated and still does operate a no senior bond holder left behind. Our fate was sealed by the decision not to regulate the system from around 1999. A less blanket guarantee might have been better and saved a few bob but it would not have changed the maths. But we have been down that road before.


You are correct in stating that some US states defaulted in the 1830s. Correct me if I am wrong but were Missouri and Mississippi among them. These rank 49 and 50th in the rankings of quality of life etc. Hardly a good testiment to default.

Again, excuse me if I’m repeating questions that are standard in the field…deficit financing wasn’t a big part of my macro classes. We focused on trade more than national accounts.

Anyway, earlier I wondered before if your eq1 should be something like Y=Yo+mD-iSigmaD-P, where i is the interest and sigmaD is the accumulated deficit and P is a capital repayment.

Should it perhaps be Y=Yo+mD-(1+m)iSigmaD-(1+m)RP, where R is now either a factor related to the speed at which principal is being paid back or a sort of Ricardian equivalence factor. If we arbitrarily set P to be SigmaD/50, then R would be a bit of a fiddle factor. I suppose you could set it as anything from 0 to maybe 1.3 or 1.5.

Anyway, as I say, this may be all very well understood all ready so sorry if I’m only catching up! Also, not sure if those should be (1+m) or just m.

In any case, wouldn’t such an equation be a simple way of forcing a discussion using our actual circumstances? Most numbers will probably sit within a narrow range, so even if the ESRI model is too complicated to understand a simple equation like yours ought not be too hard – even for solicitors and barristers maybe….and me.

Thanks John for writing this down. I have just read it — yes, I managed to spend all of Saturday without reading the IE blog!

I had been thinking of writing a post that went over these issues but I’m glad you beat me to it because your model is far clearer than what I would have written down.

Essentially, I agree with each of the points that you make here. A 1% of GDP spending cut “impetus” doesn’t reduce the deficit/GDP ratio by 1% but it does reduce it (it certainly doesn’t increase it.) Those who argue that

(a) The current level of the deficit is not sustainable

(b) A strategy of tax increases and spending cuts won’t bring the deficit down

are simply engaging in wishful thinking.

This might sound a bit left but it’s not meant to be.
In the UK cuts were announced with a clear declaration of values – NHS and education were to be spared. It is good for people to hear this.
There has been no declaration of values here. The only value I have seen expounded is – as long as somebody else is taking the pain that’s alright with me.
A simple mission statement could be
1: Everybody is entitled to a good quality primary and secondary education (after that they can fend for themselves)
2: Everybody is entitled to affordable good quality healthcare (need not and probably should not be free).
3: Everydoby is entitled to have crimes dealt with fairly and capably.
The focus on cutting services and not increasing taxes will lead to a society where the rich will buy the services they need and the rest will have to make do. This is actually a perfectly reasonable position to have. But it is now clear that Fianna Fail being the Republican party has much more to do with American connotations of that word than the Irish.
If there are painful decisions to be made it is really imortant that we have guiding principles so that our society ends up like a crafted sculpture rather than the aftermath of the Texas Chainsaw Massacre with BL calling to a public service near you!

Perhaps we should abolish the Irish exchequer and pay all tax revenues directly to the ECB as William Pitt did in the 19th century – it would certainly make the whole process of administration much more cost effective.
Why debate about efficiencies in this country if all our future surplus goes to a central bank and its clients ?

Just a note to say that once again the discussions on this blog are very worthwhile reading. I don’t have much to add to the debate apart from saying that I think we need to manage the cuts in a way that shapes the kind of society we want – protecting children, encouraging business both from home and overseas, investing in education and infrastructure and doing away with all waste and excessive pay. I think we have to make deep cuts to show our creditors we are serious about getting our finances in order. But more important is how we do that and how we set about reforming this country not just in the next few years but for the rest of the century and beyond. If we can get set out how we would like to see the country in 5, 10, 15, 20 years and beyond and decide on how best we can govern ourselves then this crisis will not have been wasted. Real political and public sector reform is required. Thanks again to those who contribute and post so frequently to this blog it is good to read real debate and detailed discussions on economic policy. And I’m sure there must be many more readers like me out there who read this blog and who only post infrequently or not at all that get a lot of value from it.

@Karl Whelan
“(a) The current level of the deficit is not sustainable”
I presume you mean IS sustainable (since you are saying that someone who thinks that is engaged in wishful thinking).

@John McHale

I think the linear model is too simplistic. Let’s say that current GDP is Y1 and current deficit is D1. Then on a linear model m is equal to (Y1-Y0)/D1 and b=(D0-D1)/Y1. When we now substitute into your formula for Y* and D* lo and behold we find that they are equal to Y1 and D1 respectively i.e. there is no possible equilibrium other than the current one.

Obviously that is ridiculous as is the conclusion that as m and b approach infinity we still have positive first derivative of the deficit ratio to the deficit.

There has to be very significant higher degree effects in any credible model. At the boundary, for example, Y cannot fall below 0 and so linearity has to break down to satisfy this boundary condition.

Intuitively I believe that there can be a situation where the correction causes the economy to implode and the deficit/GDP ratio to spiral.

This seems to me all about managing those higher degree effects. Too quick on the first derivative and the higher derivatives could take over.

John McHale

many thanks for providing this contribution. Apologies for daly in my response. I would like very much to come back to this in detail.

Just one point for now. No-one (I think) argues that the entirety of the subsequent contraction in output in 2009 and collapse in government finances was the result of fiscal austerity measures. The private sector was struggling.

But you agree that the govt. measures slowed the economy. This will have had a negative impact on government finances (ex the ‘saving’ from tax increases and spending cuts). My contention, and that of others, is that the saving is a mirage.

We believe we know 3 factors for 2009:

GDP fell by €20.3bn (if you prefer, GNP fell by €23.4bn)
The fiscal measures amounted to €10.6bn
Govt. finances deteriorated by €7.8bn [Table 11 of SGU]

Now, from your model, the underlying deterioration in govt. finances (udGf) is (7.8 + 10.6) = 18.4

That is, every €1 fall in output led to €0.91 in udGF (18.4 / 20.3)

If the multiplier was 1:1 from govt. spending then the govt.s share of the of the deterioration of its own finances would be (10.6/20.3) * 18.4 = 9.6

That is, a 10.6 fiscal contraction led to a saving of 1 (10.6-9.6)

If, on the other hand, the mutiplier is 1:0.5 (ie, contrary to empirical evidence, the private sector rushed to provide offsetting activity from withdrawn govt. spending so as to reduce its effects by half)

then the output effect would be 10.6/2 = 5.3

and the govts share of the udGF would be (5.3/20.3) * 18.4= 4.8

but that would mean the private sector’s share of the GDP decline would be (20.3- 5.3) = 15

and its share of the udGF is (15/20.3) * 18.4 = 14

this again is a (private sector) fiscal sensitivity of 14/15 = 93%

Now, I know some here complain that taxes are too high, but the SGU puts tax revenues at just over 34% GDP in both 2008 & 2009 (and tax revenues fell as % of collapsing GDP from 23.7 to 21.4 in 2009).

These implied sensitivities make the model less than credible.

@ John McHale

I’m afraid the model is fundamentally mathematically flawed. You have two relationships one for Y on D and a second for D on Y. That can’t be right. There is one single relationship between Y and D depending on m and b and other factors.

dY/dD exists at any time as the tangent to the Y-D curve. m impacts it positively, b negatively but it seems reasonable to posit that overall it is positive.

The sign of d(D/Y)/dD is that of Y/D – dY/dD. A priori this can be positive or negative. If we assumed that dY/dD was reasonably stable then the lower Y/D (higher the deficit ratio) the more likely that reducing the deficit is self defeating. However, it is not that simple because the very reason the deficit ratio is high might be because dY/dD has fallen i.e. the non government savings ratio has risen.

To summarise, in the current situation, reducing the deficit will be self defeating if dY/dD is higher than 1/13% i.e. c. 7. It seems difficult to believe that it would be that high.

John – thanks very much for this helpful contribution (and I fully appreciate the time you took on this). This will hopefully force all of us to take particular care in assessing the impact of either fiscal contraction and expansion on growth and the deficit. I have approached this problem with the aid of the ESRI fiscal multipliers – especially as it allows an assessment of policy variations. My main concern in the debate has been to dispel the notion that (a) a 1% fiscal contraction = a 1% reduction in deficit and (b) that the ‘pain up front’ (the shock of fiscal adjustment) disappears in subsequent years.

Let me start by accepting that in Year 0 a reduction in spending or an increase in taxation will reduce both the absolute and relative size of the deficit (which is not the same as discovering whether the deficit declines in the context of falling output, an output that accelerates as the Government reduces spending/increases taxes, which may produce the perverse results as Michael Burke points out above). However, in the spirit of helping pinpoint areas of disagreement, may I ask if extending your model beyond Year 0 would be able to capture the effect of accelerated deflationary GDP impact and diminished deficit-reduction benefit? Let me give a couple of examples.

(a) The ESRI estimates that cutting €1 billion in Government consumption results, in Year 0, in a GDP deflation of 0.8% and a deficit reduction of 0.2%. In Year 1 deflation is 0.9% with a deficit reduction of 0.1% – a significant deterioration to the extent that the relative deficit rises (though trivially). By Year 3 the numbers return to Year 0.

(b) The ESRI estimates that raising €1 billion in income tax results, in Year 0, in a GDP deflation of 0.2% and a deficit reduction of 0.4% – a better result than cutting Government consumption. In Year 1 the GDP deflation rises to 0.3%, the deficit reduction remaining at 0.4%. But in Year 4 the GDP deflation rises again – to 0.4% – while deficit reduction falls to 0.3%.

In both cases the GDP deflation rises over time.

A second issue – and this is not a criticism of your model – is that the contraction may be working on the deficit, not through impacts on GDP, but on GNP, even if only partially. For instance, a €1 billion Government consumption contraction produces a GNP deflation of 1.0% rising to 1.3% in Year 1 – though income tax remains the same. The reason we should be alert to this is that the DoF admitted that rises in GDP will not be tax-rich. If so, it will not be deficit-reduction rich. The Central Bank projects that domestic demand will flat-line next year even as exports rise by 5.1% – much higher than the Government projected; suggesting that disproportional impacts on domestic demand will not be cancelled out by rising exports. In this respect, Michael Burke’s own calculations may be closer to the mark than mine when working purely with GDP data.

And none of this includes the IMF’s hyper-deflationary impacts – which if it came true (and I don’t think it will but that might be more might hope than a rational calculation), would bring us into a new equilibrium.

To sum up, while accepting in most cases in most years that x contraction will result in a fall of absolute and relative deficit, the positive impact on deficit reduction will slowly wind down. If GNP impacts play a part, this deficit-reduction will be even less. The issue is not whether cutting will reduce the deficit – it is whether it will reach the deficit target before we hit a new equilibrium. We may be cutting to reduce, not realising that we are running out of road. I hope to produce some numbers in the short future to illustrate this.

Michael Burke,

Many thanks for taking the time to respond.

You will probably not be too surprised to hear that I don’t think we have quite converged yet.

I have two disagreements with your response:

1. Your calculation of the b parameter in the model, which you calculate based on 2009 data as 0.91. This was a year in which capital transaction related taxes collapsed due the continuting deflation of the property bubble. I don’t think we can get a good measure of b (the sensitivity of the deficit to GDP) from that year. I still think that putting it at 0.5 is actually on the high side.

2. Focusing on the case where the multiplier is equal to 1 (to minimise disagreement), your calculation of the actual deficit reduction does not capture the complete outcome. Identifying the full comparative static effect is an advantage of the model. In terms of Figure 1 from the model, you essentially take the discretionary adjustment (€10.6 bl.) then calculate the fall in GDP assuming a multipier of 1, and then identify the rise in the deficit related to the fall in GDP. In the figure, these steps be traced following a cobweb type pattern. The figure is useful in showing that this is not the end of the process, as a larger deficit itself stimulates the economy, etc. The model shows us where this cobweb pattern leads. Even if your estimate of 0.91 for b was correct, the overall impact on the deficit would be roughly half the discretionary adjustment. (This rises to two thirds if we put the multiplier at 0.5, again assuming for the sake of argument a b coefficient approximatly equal to 1.)

I doubt if you are convinced yet. But as I see it, the main space between us is that you are using two high a number for b, and you are not following through to the final equilibirum effect on the deficit after the discretionary deficit cut takes place. The formula 1/(1+mb)allows us to identify htis equilibrium change.

It is encouraging to me that we really are approaching the issue in the same way, so hopefully we can eliminate the disagreement soon.

There is no rocket science here. It is very elementary math. Reducing the deficit will be self defeating in terms of reducing the deficit/GDP ratio if and only if the sensitivity of GDP to deficit exceeds 7. That is unlikely to be the case.

Michael Taft,

I hope your conference went well yesterday.

Thanks also for the useful comments. Taking the points in reverse, you may well be right that it is better to do the analysis in terms of GNP. The model goes through either way, though of course the multiplier (m) and automatic stabiliser (b) parameters are likley to be somewhat different. I must admit that I don’t have a good empirical sense of how the change to GNP would ffect the results, and particularly the size of the key 1/(1+mb) measure.

On the point about the dynamics, there is no doubt that the multiplier will change over time. I would think that in the present depressed environment multiplier effects are likely to last longer than would be the case if we were operating closer to potential. Generally we think of impact multipliers being highest with the effects of (sustained) deficit changes fading over time. It is possible, however, that the size of the multiplier might rise initially, and so it could be that the reduction in the actual deficit as a share of the discretionary reduction falls initially, before rising later on as the size of the multiplier falls back. I think you raise an interesting point in relation to these dynamic effects, but I don’t see it as changing the basic conclusion of the model.

Again thanks for the engagment.

Brian Woods,

Thanks also for the comment. But I must admit to not being sure if you are just pulling my leg. If not, I suggest you read up a little on simultaneous equations. 🙂

@ John

Maybe some day we can have a math challenge.

Meanwhile, let’s look at your “simultaneous” equations

(1) dY/dD = m
(2) dD/dY = -b

Only possible if mb = -1. Interesting theory but I would like to see an economic justification why mb would always equal -1.

The following is a mathematical truism quite independent of any model for the economy or indeed what Y the dependent variable or D the independent variable stand for.

The sign of d(D/Y)/dD is the same as that of [Y/D – dY/dD].

So to answer the question put by your opener, deficit reduction will be self defeating in terms of reducing D/Y iff dY/dD > Y/D. Y/D is about 7 so that would need dY/dD to exceed 7. I suggest, admittedly without any of your expertise in econometrics, that this is unlikely. Do you accept the econometric criterion? If so do you think that it is met?

@Michael Burke
“The fiscal measures amounted to €10.6bn”
I don’t see how you can say this.

For it to be true, either spending would have to have fallen by 10.6bn or taxes risen or some other combination of the two between 2008 and 2009.

My memory is a little fuzzy, but I seem to recall the full year tax implications to be 1.5 bn?

According to the Stability Program Update, total spending in 2008 was 73 billion. Spending in 2009 was estimated to be 72 billion. Given deflation of 4.4% (CPI), this represents an increase in spending in real terms…

One thing I notice about from the Stability Program Update is that the structural deficit needs to be narrowed to 10% of GDP, so it doesn’t take account of interest on the national debt. This is a small crumb of comfort, but it makes me wonder why the government is talking about needing an extra 1.5 bn in savings to pay interest on the promissory notes…

What I know about simultaneous equations is that they produce unique answers. That is exactly what your model produces. The only equilibrium answers for Y and D are the ones which are currently in equilibrium, according to this linear model.


I take it then that you are serious.

But I’m afraid its back to the point about simultaneous equations. In terms of your partial derivatives: dY/dD captures the impact of the deficit on GDP; dD/dY capture the impact of GDP on the deficit. There is absolutely no reason why one of these impacts has to be the inverse of the other; they capture completely different causal phenomena.

I generally find your comments thought provoking, particularly on banking, but I think you should raise the knowlege bar a bit before commenting, or at least not do it with such misplaced confidence.

@ John

I general I respect your views, otherwise I would not have looked at your attachment. Maybe partial dY/dD is not the inverse of partial dD/dY. But certainly the linear model breaks down badly over the full range. Maybe it is a good approximation over the short range, in which case your conclusions would be valid.

But what I absolutely stand over, from by O-level math without having a clue about economics, is that the sign of d(D/Y)/dD is the same as that of Y/D – dY/dD. And that is what this thread is all about. Is d(D/Y)/dD positive or negative. The mathematical truism shows this to be equivalent to asking “is dY/dD less than or equal than Y/D”? Y/D is a bit over 7 so this translates to a fairly tractable question. Is the elasticity of GDP to the deficit greater than or less than 7. I would guess that any empirical studies would support one’s instinct that it is less.

In short, reducing the deficit almost certainly reduces the deficit/GDP ratio, a conclusion which your model supports, but it also reduces GDP. There is a trade off.

I don’t see we have any choice now but to pursue tough deficit reduction measures. It is not going to be pleasant.

People in the public service who believe in ‘full on’ austerity should be consistent and resign their positions and accept they will see some of their pension at 65. It really is that simple.

Ireland under Ahern, McCreevy and Cowen spent too much on public service and now the books don’t balance. Reducing every public service official’s pay is not very sensible since it will leave a large rump of passive-aggressive agitators in place. Reducing the deficit in reality as opposed to fiction entails firing (making redundant) several thousand public sector workers and amalgamating jobs and institutions. On the other hand if deficit reduction is just a titbit for salon discussion, just trundle on Ireland. The IMF will hopefully straighten things out.

@ John McHale

Your equation (1) reads:

1) Y = Y0 + mD, rearranging this is

1a) D = -Y0/m + Y/m

your equation (2) reads:

2) D = D0 – bY

Now (2) and (1a) can only be true across a range of Y if -b = m
and D0 = -Y0/m; and with these values your formula for Y* becomes the indeterminate 0/0

What you are missing is a third independent variable and I will address that in my next post.

@ All

A model to help answer the question.

Let Y0 and D0 by the GDP and Deficit before budgetary adjustment.

Let B be the budgetary adjustment (were positive means an increase in the deficit)


1) Y = Y0 + mB

2) D = D0 + B – bmB

where m is the multipler effect of the adjustment and b is the stabiliser effect of a change in GDP.

Then after a bit of algebra we get:

Sign (dR/dB) = Sign [(1 – bm)/m – R0]

where R is the Deficit/GDP ratio.

The answer to the question then is that a negative budgetary adjustment will reduce the ratio if (1-bm)/m > R0

We can make a number of observations:

It is not at all clear a priori that the answer is yes.

If R0 is high, as it is, a yes answer is less likely

If m is high again yes is less likely.

If bm is greater than 1 then there is no way the answer is yes.

A plausible set of values which would leave the question right on the cusp would be m=1.6, b = .5 and R0 = .125

@ Michael Hennigan
“Politics is the art of the possible”
There are choices but now we have to look at what we do post-IMF intervention.
And that requires looking at whether or not Euro membership is still possible.
But the quality of debate in this crisis has been truly dreadful. So the IMF will make the decisions for us. Don’t be surprised if the ideas you dismissed as pubstool economics – i.e. debt restructuring and leaving the common currency area become reality then.
These were choices we had all along but too many people in this country enjoy stoking up feelings of national guilt an inadequacy to debate issues effectively.


Thanks again forthe time taken. I actually think the differences between us are far greater than you believe, not least because ofthe inherent flaws of equilibrium models (including DSGE models). But that is a far larger topic and less pressing than the one at hand.

Re point 1. I have seen the assertion many times that the collapse in taxation revenues in 2009 was uniquely related to the bursting of a tax-rich property bubble. But I have yet to see it in evidence.

Construction collapsed by €3.9bn in 2009 while GNP fell by €16.5bn (real terms)- the fall in transport and services sectors combined exceed the building and construction slump. In terms of expenditures, imports fell by €13bn and personal consumption by €6.7bn. The total decline in GFCF far exceeded the construction slump, €12.3bn to €3.9bn and brought in not only transport equipment of all knds but also machinery and business equipment.

This is reflected in the tax heads, where VAT is the main contributor to the slump in taxation, not stamps or CGT, and is followed by income tax.

2. The cobweb pattern is not convincing, even within the limits of equilbrium based models without a multi-year dynamic, which I’ll come back to below. The cobweb reminds me of Soros’ ‘reflexivity’, although he places himself rather than government spending at the epicentre of economic activity.

In advanced economies, where social safety nets exist, the automatic stabilisers tend to shelter private consumption from the worst of the recession, and indeed become a factor in shortening it. When Keynes wrote the General Theory he used employment and consumption almost interchangeably, as, absent a safety net, they pretty much were. In the OECD database, household consumption was just 21% of the Great Recession as those stabilisers set to work, and the recession has long ended, if not its effects.

By contrast, policy here was to shut down the stabilisers by cutting PS pay and welfare payments. On the same OECD data, the fall in household consumption here is equivalent to 53% of the Irish Depression, which is ongoing. We cannot know the impact of that consumption slump on factors such as investment, but it is hardly likely to be a positive one, in my view.

In essence, therefore we agree that there is a web or interrelationships between the components of GDP. However, in your construction, the sign magically changes direction after first-round effects. That is, to take a concrete example, a PS pay cut of €N bn somehow becomes less than half of that as private agents do what, exactly? Maybe run down their savings rates and consumer prices fall? Perhaps, and yet the fall in private consumption was €6.7bn.

In Daniel Leigh’s research for the IMF, highlighted here, he estimated that the typical multiplier from govt. spending is 1: 0.5. But the offsetting factors typically arose from lower interest rates, a weaker currency and a greater share of buoyant overseas demand. In the atypical conditions which apply currently, he argues that the inability to lower either rates or the currency doubles the multiplier to 1:1 and that the simultaneous fiscal retrenchment elsewhere double it again to 1:2.

That alone ought to be sobering enough for advocates of further spending cuts.

But a neglected aspect of the research, and a common failing in discussions here, is to ignore entirely the dynamic, multi-year effect of a one-off cut in government spending. When both adverse conditions apply on rates & generalised austerity, there is a cumulative effect over 5 years where the multiplier aggregates to 1:6.

He further says that year 6 represents a ‘beak-even’ point for austerity and in year 7 onwards there are positive growth effects. Perhaps. But given the current economic and fiscal crisis we need that output curve to be sloping upwards now, and downwards only in 7 years’ time. That would only be possible by increased governent spending.


Sorry for being snipy last night.

Could I ask you to take another look at Figure 1 in the note I link to?

The whole point of an equiilibrium is that it is a combination of D and Y that satisfy both equations. This equilibrium is unique in this linear model (and stable provided m is greater than -1/b).

You are trying to make two equations coincide. Instead, we look for values that satisfy the two distinctive equations.


you confuse cause and effect.

Cuts have been made, but no savings were made. Dissavings occurred.

Either that, or the capex spendinn cuts, cuts to PS pay, levies, cuts to jobseekers’ allowance and single parents all pased you by. Surely you remember the cut the allowance for the blind, though? Certainly stuck in my mind.

Here’s a reminder, before we start to go down the road of ‘mac the kife is a myth’ mythology.

@John McHale

Many thanks for this note and for your willingness to engage on the issues it raises. This is precisely the kind of input that makes this blog so valuable. It progresses the debate on a solid basis, but I expect it is far from settling it. I sometimes wonder if consideration of these multipliers is often an attempt to estimate a post hoc quantification of the impact of Keynes’s ‘animal spirits’. And it becomes even more difficult when these animal spirits have been crushed. In addition, the nature of many of these macroeconomic statistics – being aggregates of the quantifiable elements of millions of individual decisions – means that we’re often not very sure where we’ve been, are even less sure about where we are and probably don’t have an earthly about where we’ll be in a year’s time. What we do know is that certain decisions will have certain unambiguous impacts – even if they cannot be quantified precisely.

The focus on fiscal adjustment serves this ‘one hurdle at a time’ Government very well. All public, media and commenting attention is directed at one place and the Government spin-machine can get to work. All the sound and fury of the coming weeks will reveal some of the vested interests protecting their patches – though those who will be most successful will not reveal their pitches in public. But most of it will be without effect as the 15 members of government are a committee of pro-consuls implementing the dictates of the EC/ECB. They, and their advisers, will decide on the allocation of fiscal pain within the parameters set externally. The civil service will provide the number-crunching services and put a gloss on the output to convey some residual semblance of sovereignty. The Oireachtas will be totally irrelevant while the Government is able to maintain backbench discipline. The threat of total loss of sovereignty should be enough to achieve this. But the Government is stretching its constitutional legitimacy to the limits by devoting public resources in a court action to postpone effecting the full representation of electors in three constituencies.

And the EC/ECB is taking a huge gamble that the scale of the fiscal adjustment it is imposing will allow the NTMA to re-enter the market early next year. It is possible that some of the larger EU banks and financial institutions, which could suffer serious losses if Ireland were to be pushed into default, are being ‘squared’ to enter into a syndicate to allow the NTMA to get away a largish, longish-dated issue early next year. This could prove to be a ‘damn close run thing’.

Meanwhile the real economy, in terms of output, jobs, investment, productivity, efficiency – the things that really matter – is languishing between the current focus on fiscal adjustment and the BS on innovation hubs, cloud computing ecosystems and competition and better regulation. Property prices and rents are being prevented from adjusting to market clearing levels as this would put more mortgage holders and more of the banks’ dodgy property loans under water. Public sector unions seem to have accepted implicitly cuts in services to protect existing levels of employment and pay. The semi-states are subject to the scrutiny of the State Asset Review Group which won’t report until the end of the year. What it will recommend is unknown and how the Government will respond is an even bigger unknown. But significant privatizations that could be used to pay down the national debt over time might be enforced by the EC/ECB – even if the opposition of the Green Party, keen to impose additional deadweight costs on the economy in pursuit of its pet policies, will have to be overcome. And continued profit-gouging in the private sheltered sectors is not being addressed.

The focus should be on deep-seated reform of the political process and of the real economy, but deflecting attention from these is in the interests of those who exercise power and influence – and of those who aspire to do so.


No problem. This is not a handbags occasion. I think the algebra is fairly important. Your algebra points to it being very unlikely that a deficit would be self defeating, mine points to it being not at all clear cut.

I will as you say look again at your workings. Meanwhile consider the following thought.

My very first simultaneous equation went as follows: Jack is 2 years older than Jill; Jill is half Jack’s age. Answer Jack is 4 and Jill is 2. I think, but I will take a closer look, that in you stating two simultaneous functional relationships it is like saying Jack is always 2 years older than Jill (of course that is possible) and Jill is always half Jack’s age – which is impossible.

@Michael Burke
“Here’s a reminder, before we start to go down the road of ‘mac the kife is a myth’ mythology.”
I don’t doubt for a moment that changes have been made to where the government spends it money. The wrong changes, in my view. But that is neither here nor there when we are talking about aggregates.

In aggregate, the government is spending more in real terms in 2009 than it was in 2008. As it is raising less in tax, in real terms, it is taking a reducing amount of tax out of the economy.

I say that both of these are a result of the collapse of the asset bubble and the effects that has had on growth and economic activity. You reckon that the decline in economic activity is due to the government cutting spending and raising taxes to the tune of 10.4 bn.

I don’t see evidence for this. I don’t think we are in that situation yet, though I believe it is coming. I also believe the wrong choices will be made – cutting welfare absolute amounts, property tax, water charges. For me, the cuts have to come from tax rebates, particularly those on deferred spending (pensions and savings), the administrative levels of the PS (with redundancy paid over a number of years to ease the cost to the exchequer) in particular the quangos, and large capex projects that are not labour intensive. All income should be taxed, including benefits (that’s where the ‘cut’ comes in), with a cap on total benefit and a sliding scale of income earning to reduce benefit traps. Social security contributions must cover the cost of the social security system. Capital taxes must be increased (there’s no justification that I can see for capital tax offsets either). And so on.

And this is just to get us to the point where we can reform how the health system is paid for, pensions, overall welfare etc.

@ John McHale

Okay, I looked at the Figure and I admit it was a struggle. The following is my take, please correct if I have got this all *ssways.

The upward sloping line represents the relationship between the economy and the net government deficit. I note that the independent variable in this statement is the net government deficit and not the discretionary element of that deficit.

The downward sloping solid line represents the situation if the government just sat on its hands and left all existing tax rules, social welfare rules, capital spend etc. as is. The deficit would then be solely at the mercy of the economy and plausibly is a straight line with negative slope b.

Now the government changes the rules creating a discretionary shock. It is assumed that this does not change the upward sloping line.

It does change the downward sloping line. It is assumed that the slope is still the same. It is also assumed that if the government then left the rules unchanged and let the economy run its course that if the economy fell to zero the deficit would be precisely equal to the earlier Y0 deficit less the discretionary shock.

In summary there are three key assumptions in the model:

1) The upward sloping line is unaffected by the discretionary shock.

2) The slope of the downward sloping line is unaffected by the shock.

3) The Y intercept of the downward sloping line moves precisely in line with the shock.

I can’t get my head around what these assumptions mean in economic behavioural terms, whether they are reasonable or heroic.

I have posited a slightly different model above which appears more natural, at least to me. What is worrying is that two similar approaches produce quite widely differing answers to the question put by your opener.

@Brian Woods II
@J McHale

The above exchange is interesting if a bit tetchy!

Could I respectfully suggest you consider those arguments in the context of the US throughout the thirties and fourties.

The public debt vs public debt/GDP split — where they go in opposite directions is key and a fact that is generally politically unpopular with many.

This is more or less the position which bond investors suspect may apply in Ireland, at the point they decide the target or loading doesn’t matter. That is when the bond market closes.

wrt another point (possibly Smpleton) above about whether it is possible for the bond market to accept a different target and open to the Irish State next year – the answer is yes, of course it is, if that provides a more likely eventual non-default outcome. But they would need persuading.


wrt the bond market accepting another target, presumably involving a longer adjustment period. There is another actor in this drama, namely the EU. It would have to sign off on a longer adjustment period as well.

I submit that if there was a dispute between Ireland and the EU over the path of adjustment or indeed the modalities of the adjustment then the bond market would stay shut.

Michael B,

I fear you are right that we are not going to reach agreement.

In attemting to respond to your previous comment, I over-complicated things by bringing up the cobweb pattern.

I actually think the issue is quite straightforward: if you believe the multiplier effect is positive and the automatic stabiliser effect is negaative — which I believe you do — then as a matter of logic the actuall deficit and the discretionbary deficit move in the same direction.

This result does not depend on the sizes of m and b.

I am happy to let you have the last word.

@ John McHale

Apologies. Totally agree with your math. There are in fact three variables D0, Y and D. D0 is in the role of the independent variable and Y and D satisfy different simultaneous equations as D0 varies. I mistakenly thought D0 was a constant (coz it looks like one!).

My model above is exactly the same as yours except my m is the multiplier with respect to D0 (or B) while yours (M) is in respect to D. They are related by the formula M = m/(1-bm).

Why then do the conclusions seem so different? The answer is in your final formula. You find that the sign of dR/dB is that of (1+mb)Y0. I agree but this deceives because we think of Y0 as being positive. But Y0 is a mere mathematical fallout from the model and it can be evaluated from:

Y1 = Y0 +mD1, where Y1 and D1 are the current values of Y and D.

Thus Y0 = Y1 – mD1 and can be negative as a purely mathematical aspect of the model since clearly Y0 in practice must be positive.

After further manipulation it transpires that your sign test is the exact same as the one I developed above viz.

Sign (dR/dB) = Sign [(1 – bm)/m – R0] = Sign(1/M – R0)

The apparent diference (and it is only apparent) is that your original conceals the fact that the current Ratio is part of the criterion.


If bond market participants were to begin think that the EU insisting on plan A, is a bad idea, preferring plan B – then the situation is roughly this:

For plan B to open up the market, the perceived advantages would have to be so clear that they would more than make up for the additional risk to holders from an EU less likely to offer a bail-out subsequently. This is unlikely unless plan A was clearly a non-runner.

However, if the bond market was signalling a preference for plan B over plan A, it is highly unlikely that the EU could easily ignore this “advice”. Pressure from the market would probably force a different view from the EU, hence plan B would become available.

Currently there is an element of defining a line, in order to see if Ireland is willing, generally, to tow lines. That is why there is waffle from the government about starting on a target and then, maybe, it might get turned into something else at some point down that line, in the future, going kind of forward-ish.

@grumpy (& tull),

I think it is more than an element of “defining a line”. The Government obviously wants to keep Ireland out of the treatment room, i.e., the EFSF. The EC/ECB wants this too, but for different reasons. Both sides are throwing shapes about the extent and duration of fiscal pain Ireland will have to/be able to bear. The Government wants to see what trade-offs might be on offer before it commits – and needs to get some assurance that the effort will achieve the desired result.

@ JMcH. Will do.

If additional credit or existing savings are brought in, and used appropriately – this might increase added value output? Would additional debt creation be a factor? In what direction?

Brian P.

@grumpy. I am kind of interested in the actual processes of these Multipliers – they do have a measurable effect – but what is the mechanism? You can use biological analogies for economic activity – they share all sorts of interesting parallels!

Brian P

This goverments national emergency strategy should not focus on monetory matters – its focus should be on the physical world provided by fiscal means – to hell with deficits – people did nothing when there was huge monetory deficits – fiscal deficits are needed now to reorient the economy back to the physical world.
The banking sector cannot govern – they really no nothing about making wealth although they seem to now every trick with regard to taking it.
Monetary matters should be let to the ECB and they should be completly ignored and if not supportive the goverment should declare that the ECB is mounting a war against the Irish people to take back money that their clients created.
Gormleys focus on water meters and a goverments efforts to raise money privatly is pathetic beyond belief.
They should refocus towards a platform that renationalises utilities whose capital has been run down to create false profits – not trying to get credit to obtain more credit but making the system work.
Goverment now does not know how to think or how to govern – the extremely funny but toxic ideas of Yes Minister has resulted in nearly all critical goverment functions being outsourced to buccaneers who care little for structure but only a false efficiency of reducing redundancy withen systems and expressing these as profits.


you’re the soul of courtesy.

I actually think the multipliers from both government spending and the automatic stabilisers are positive, just that the former are much higher (and that it was disastrous to block the latter via welfare cuts).

I even think the values of, say, 2, for government spending in the first year alone and 1.2 for the stabilisers would provide a satisfactory explanation of the course of the economy and government finances in 2009, maybe even using your model.

That would also fit with this IMF research, which I think is the most authoritative of all recent model-based analysis

Thanks again for the willingness to engage.

This is quite a simple problem it all depends on the overall level of projected debt at the end of the 2010 and the GDP multiplier effect of government expenditure. There are also leakages back to government in terms of taxation revenue on the expenditure and reduced taxation revenue due to falling GDP. There is also the drag due to increased interest payments weather this coupon is paid or not.

Obviously different government expenditure will cause different multipliers. For example payment to Anglo senior bondholders is probably pretty close to 1 as the cash will nearly all go to large entities abroad or very wealthy individuals who will bank it. I suspect expenditure on people on social has a multiplier effect pretty close to 2.5 in the year as they spend a lot of their cash on locally sourced food, alcohol and services and bank very little.

The critical parameters in the longer run are not the underlying deficit as a % of GDP, which is a short term transient. The most important is the % government debt as a % GDP (or probably GNP in Irelands case). Why are so hooked on deficit as a % of GDP when thats not what tripped up Greece last year It was the other much more important parameter of debt/gdp which caught them.

This overemphasis on the % deficit is illusory. It is like calling a family bankrupt because they had a income deficit of 200% the year they got their mortgage. Important parameter that this is not what the bond markets will see as important when we visit them in again in March. What will engage them more is the debt/GDP ratio and prospects of growth and or recession in the economy.

My model is showing that because of the large debt already run up and the multiplier effect you basically have a parabolic effect on end year debt/GDP ratio with a minimum at about 2 bn expenditure cuts.
The game has already been lost. Further reductions in government expenditure will only further increase in the debt/GDP ratio.
The government needs to concentrate on putting whatever is left in our credit line into job creation and building up employment in the economy. It also needs to urgently examine other ways of reducing the deficit other than cuts by increasing taxation on the higher earners urgently and introducing a flat simple property tax of €1000 per dwelling immediately. More equitable property tax can be phased in later when the department of finance gets around to working it out.

Tell the Anglo bond holders INBS that we are keeping their paper on the books but suspend all payments. Similarly suspend all % dividends on the NAMA bonds.

It is only a matter of time before we hit the wall and we need to get as well prepared as we can.

“For example payment to Anglo senior bondholders is probably pretty close to 1 as the cash will nearly all go to large entities abroad or very wealthy individuals who will bank it. I suspect expenditure on people on social has a multiplier effect pretty close to 2.5 in the year as they spend a lot of their cash on locally sourced food, alcohol and services and bank very little.”
Well, in the first case, money that flows abroad is probably 0 or maybe even negative?

In the second case, what locally sourced food? Heinz beanz? Noodles? Rice? Pasta? Pasta sauce? By value, more food is imported than is produced locally. The figures are worse for alcohol. Then who owns the companies that do this?
So I’d say the multiplier there is at best 0.5 and probably lower.

This is not to say that you are wrong in your assertion that welfare recipients are more likely to spend some of their welfare in a positive multiplier way, but I don’t think it is at all clearcut that it is a high value. Some of the spending may indeed be at very low positive values or zeroes, for example, clothes, shoes, books, music.

“This overemphasis on the % deficit is illusory. It is like calling a family bankrupt because they had a income deficit of 200% the year they got their mortgage.”
This is just not the case; you are mixing up debt and cash flow. If the family couldn’t pay the monthly payment without borrowing it, would you call them bust? That is the position we are in. The state’s cash-flow is deeply negative. It can’t afford the debt it has, because it is spending too much. If it wasn’t spending so much, the debt wouldn’t be a problem.

Yes, our problem is different from Greece, but only this year. Add up all the years until the deficit is roughly balanced and we are in the same situation as Greece.


I agree with what you say. I just used a multiple of 1 as the baseline as I assumed the first payment to the bondholders or the social welfare recipents would count as a 1 in the national accounts, probably wrongly. I am engineer and not a national accountant. I seem to remember something about social transfer payments being not counted.

In reference to social welfare payments I am also including the fact that the shop, pub would spend a portion of the cash they get again to come up with higher estimate of 2.5 but your point about a lot of the payment going on foreign sources is very relevant, one of the problems of a highly open economy is that state expenditure rapidly disappears.

However all this just changes the point of the minima, depending on the accontancy conventions used and the overall multiplier.

The point i am trying to make is that there is an optinum point in deficit reduction. If we go the whole hog and do away with the deficit in one shoot we will kill the economy and the debt/gdp ratio will shoot up to 200% +, literally shooting ourselves in the foot

@John Mc
Having wandered in the park earlier, when it wasn’t the middle of the night, I realised that my attempted complication of your equation was on a path towards impossible overcomplication, so while I’m sure we’d all love to have a grand unified equation I’ve reverted to your neat and minimal outline.

Been doing more math on this. I get that for each budgetary adjustment of 1% of GDP the Deficit/GDP ratio moves by (1 – mb – mR)%. Where m is the multiplier in relation to the adjustment rather than in relation to the net deficit; b is the stabilizer and R is the current Deficit/GDP ratio.

This is a pure mathematical identity arising from differentiating a ratio with respect to its numerator and is quite independent of any theory of economic behaviour. It is also in agreement with above findings regarding the sign of the change but is more informative as it actually quantifies it.

R is currently about .13. To get m and b does need an economic theory or at least empirical observation. But plausible candidates produce quite scary results. Let m be 1.6 and b be .5 then the effect of a budgetary downward adjustment is marginally negative on the ratio (in the sense that it increases it).

The choice of budgetary adjustment can of course influence the relevant m. Broadening the tax base and cutting social welfare would suggest a relatively high m, maybe as high as 2. The choice of adjustment has less influence on b. How can one guess at b. Well assume someone loses their job for 50k and goes on the dole. Loss of direct and indirect taxes together with the social welfare payments could well amount to 30k i.e. a value for b of .6.

So let us slot these figures into the formula. Let’s say the budgetary adjustment is -3% then the effect on the deficit/GDP ratio will be c. +1.5% i.e. seriously counterproductive.

We need some external stimulus big big time!!

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