The International Monetary Fund has published its latest report on the UK economy. It is not clear from the report whether the authors thought that our glass is half full or half empty. The report begins with a statement that 'the UK economy is on the mend', and the view is expressed that 'the government's strong and credible multi-year fiscal deficit reduction plan is essential'. That finding should not be too surprising in light of the way these reports are compiled.

However, the report also makes the points that

'fiscal tightening will dampen short-term growth', that

monetary policy should remain expansionary and will 'need to be nimble if risks materialize', and that

'an adverse scenario where major new shocks—arising from either external forces or domestic ones—trigger another extended contraction in output cannot be ruled out.'

This, then, paints a somewhat unclear picture. The suggestion that a tough and credible deficit reduction plan is needed is not exactly news. The real debate is about how fast this should happen.

For many students of economics, an early encounter with the elegant and sometimes magical nature of the subject comes in the form of the 'multiplier'. The idea of the multiplier is that an autonomous increase in spending in an economy can ultimately bring about a change in national income that is greater than the initial stimulus. The increased spending that kicks off the whole process might come from government - either in the form of increased government expenditure, or as a result of cuts in tax that allow consumers to spend more.

The mechanism that underpins the multiplier is simple. Suppose the government increases spending by engaging in more construction projects. Builders are hired, and they earn incomes. They then spend those incomes - and these expenditures become an increase in someone else's income. And these other people spend their increases in income, thus passing added income on to yet more people. And so on. Ultimately, because we tend not to spend all of any increase in our pay, this process fizzles out, but (at least in the simple cases studied in the textbooks) not before national income has increased by more than the initial increase in spend.

People, understandably, tend to be suspicious when conjurers pull rabbits out of hats. Likewise, many are suspicious about the multiplier. It does, after all, have something of a 'money for nothing' feel about it. In many circumstances, the suspicions are well founded. If the economy is working close to capacity, then the idea of people doing more, generating more income, is misleading. You can't do more if you're already at capacity. In this case, the expansionary effect of the extra spending tends to produce not more output, but simply higher prices. This being so, then beneficial effects of the extra spending get wiped out - or at least reduced. Economists like to talk about increases in government spending being 'crowded out', and this is one form of that.

But there are times when the economy is not working close to capacity. Right now is an example. What about the multiplier at times like now? Two recent papers from the National Bureau of Economic Research - one by Alan Auerbach and Yuriy Gorodnichenko, the other by Robert Gordon and Robert Krenn - tackle this question. And both studies find, convincingly, that the multiplier is much larger during recessions than at other times. Indeed, during recessions, the multiplier may be as high as 2.5. In other words, extra government spending of £100m can generate an increase in the national income of as much as £250m. During recessions, the risk of such fiscal expansion having a detrimental effect on inflation is minimal.

All of this means that fiscal expansion is a sensible policy to follow during recessions. In a dynamic world, we have to keep an eye on the implications of the policy for our ability to pay back government debt - of course. But the evidence we now have suggests that fiscal policy is much more effective (at times like these) than sceptics once suggested.

Vince Cable has, somewhat confusingly, now rejected his own graduate tax proposal as unworkable, but still wants to retain an element of progressivity in graduates' repayment of their student loans. The question is: why?

Progressivity is very laudable (now there's a value judgement for you). But surely it's the progressivity of the tax and benefits system as a whole that matters, not the progressivity of one little bit of it.

In his speech to the TUC today, Mervyn King provided a pretty fair assessment of the state of play. Global imbalances led to cavalier behaviour on the part of the financial institutions, which in turn led to the near collapse of the financial system, needing huge fiscal stimulus to avert a major depression - leaving us with the challenge of a large fiscal deficit.

King states that 'there is a perfectly reasonable debate about the precise speed at which to reduce the deficit. Indeed, I supported the extra fiscal stimulus to the economy provided in the immediate wake of the crisis. And there is a further question about how the deficit should be reduced - the balance between raising taxes and cutting spending. That is not for me to say; that is for you and the politicians to debate.'

It is, as King argues, 'vital for any government to set out and commit to a clear and credible plan for reducing the deficit'. The present government appears to be engaged in an exercise designed to manage people's expectations. While government departments have been asked to prepare for 25% cuts in spending, such drastic cuts far exceed what is needed in order to eliminate the structural deficit. Nevertheless, the cuts will be severe. Their phasing over the next 4 years or so is critical. The Bank of England's own forecasts do not rule out the possibility of a double dip, and the Office for Budget Responsibility forecasts are somewhat less sanguine. Given changes in the state of the US economy since these forecasts were produced, the outlook is, if anything, less favourable. So, while the time to start reducing the deficit is indeed coming up soon, caution will be needed in judging the right speed at which to go.

The plan should not only be 'clear and credible', it should be sensible too - and that means that it should not involve all guns in blazing from the off.

The annual meeting of the Trades Union Congress takes place this week. Delegates will hear calls for an attack on the government's agenda for cuts. This attack includes the possibility of 'joint industrial action'.

The phasing of necessary cutbacks is certainly a matter of debate. I have consistently argued that the cuts should kick in around the early part of next year, conditional on the recovery being sustained, and not before (see, for example, my post on 14 February this year). Interviews with Nick Clegg and George Osborne last week suggest that there is still ongoing debate within the governmnet about this phasing. Until we know the outcome of this debate - when the spending review is announced next month - any threat of militancy looks impetuous.

A lot of media coverage has been given today to an interesting study about the effects of using a lottery in the allocation of pupils to secondary schools in the Brighton area. Lotteries have long been proposed as a means of reducing the social segregation that can result from a system of catchment areas.

Unfortunately, much of the media coverage has oversimplified the results. A curious feature of the Brighton scheme is that catchment areas (which have traditionally served to allocate pupils to schools on the basis of where, in relation to the school, they reside) have continued to exist. Alongside the introduction of the lottery scheme, the catchment areas were however redefined. So a lot of things that might affect the allocation of pupils to schools happened at once.

The evidence provided in the research suggests that the lottery scheme has led to some convergence across schools in the characteristics of pupils that they attract. This is as we would expect. The redrawing of catchment areas has, however, meant that this experience is uneven across the city, with outcomes after the reform being worse (than they would otherwise have been) for some pupils who were previously (but who are no longer) in the catchment area of a good school. None of this is terribly surprising - demonstrating that strange things get into the news during the silly season.

(To reinforce the last point, the front page headline of the Times newspaper on each of the last two days has told us the news that... apparently something didn't happen 14 billion years ago!)

Consumer confidence continues to sink, and house prices are now once more on a falling trend. The latter, at least, is not all bad news. The acceleration in house prices up to July had been something of a puzzle since the earlier fall had not been sufficient to burst the bubble. While I have not been amongst those economists predicting a 30% or more fall in house prices from their peak, I did expect the recovery in prices to be sluggish. Initially it wasn't, raising fears of more boom and bust in that market, and in this context the slowing down that we have seen over the summer is something to be welcomed.

The news on consumer confidence is more disturbing, and I await the August figures with interest.

The rate of growth of GDP accelerated sharply in the second quarter of 2010, with output in that quarter being 1.1% higher than in the first three months of the year. This is clearly very encouraging news. If the strength of the recovery is maintained over the remainder of the year, the economy could be better placed to withstand the government's plans for deficit reduction than appeared to be the case only a short time ago.

The world remains an uncertain place, however. Simultaneous fiscal retrenchment in many countries (including some of our important trading partners), a fragile housing market, the threat of renewed ossification in the banking sector (as evidenced by a rising LIBOR) all point to downside risks that remain significant.

It looks as though Vince Cable's graduate tax proposal, on which I commented in my last blog post, has been mercifully short lived. It is attractive to some because of the property that lifetime repayments rise with lifetime income. But, of course, if you want more progressivity, you can let the income tax system alone take care of that without recourse to graduate taxes.

The downside of the proposal would likely have been a cumbersome bureaucracy making controversial decisions on differential financial allocations to universities. And why, when the market could work out the appropriate resource allocations for free? To thrive, the higher education sector needs more freedom from bureaucracy, not another dose of Stalinism.

University funding is back in the limelight. Vince Cable is to speak in favour of replacing the current system of undergraduate tuition fees with a graduate tax. In many respects, this is not a radical change - students' loan repayments are already proportional to their income. In some ways, a move to a graduate tax might even be welcome - it has the rather nice property of being progressive.

In other ways, though, a shift to a graduate tax might pose problems. Like it or not, it is difficult to see how the UK can, in future, fund world class universities without funding them differentially. It would be reasonably straightforward to achieve this with a system of differential fees - where students who attend the best universities pay a premium (which would have to be covered by a loan). Universities could set their own fees according to their perception of where they stand in the market. This is not so easy to achieve with a graduate tax. For sure, the government could fund the best universities more generously than others - but would those students attending universities that are lower down the food chain be happy to see their graduate tax payments used, in effect, to subsidise students attending universities higher up the rankings? Suddenly the tax no longer seems so progressive. It might, of course, be possible to set differential rates of graduate tax - a lower rate for students attending institutions that offer two year degrees perhaps (such degrees being another proposal doing the rounds) - but that seems dreadfully clunky. And does the government really know better than the market which are the best providers?

As ever with these mechanisms, the devil is in the detail.

It is curious that any government minister should have chosen to preempt the outcome of the Browne review at this stage. That, in itself, suggests that there is a long way still to go on the politics of this issue.

The latest consumer confidence figures from the Nationwide do not make pleasant reading. Consumer confidence has been falling since February, and the worsening state of the index on expectations is particularly striking.

In February, some 39% of respondents expected that, within 6 months, the economic situation in the UK would have improved; only 15% expected the situation to worsen. But the corresponding figures for June are 27% and 24% respectively.

These prospective indicators have a track record of predicting actual fluctuations in the economy rather well. A downturn in confidence and expectations does not necessarily foreshadow a downturn in the real economy. But these figures should give us plenty of reason to be cautious about the sustainability of the present recovery.

Olivier Blanchard and Carlo Cottarelli have published their 'ten commandments for fiscal adjustment'. These are instructive. Commandment 2, which counsels against front-loading the fiscal adjustment, is particularly pertinent to the current debate in Britain.

The G20 summit in Toronto has finished. The limited extent of agreement achieved at the meeting is well encapsulated by the rather novel concept of a 'growth friendly fiscal consolidation plan'. If for nothing else, the authors of the document are to be congratulated on creating the illusion of consensus.

They claim, with some justification that 'efforts to date have borne good results'. The world economy is recovering. But there may be troubles ahead in the form of the dampening impact that is sure to come from simultaneous fiscal consolidation across many countries. Indeed, the International Monetary Fund's report on the summit paints a downside picture that is far from rosy. The markets today reflect some of this gloom. Coordination of policy across countries has never been more important.

Yesterday I wrote about the phasing of the fiscal retrenchment announced in the budget. Today I shall write about the extent of the retrenchment. For sure, a severe correction is needed - nobody questions that. Much of the debate centres around the size of the structural deficit - the bigger that deficit, the greater the consolidation has to be.

The Office for Budgetary Responsibility (OBR) has estimated the size of the structural deficit by, first, estimating the output gap (how far output is from what it would be if the economy were operating at full capacity), and then working out what the balance of government spending would be if the economy were at full capacity. Its estimate of the output gap depends in part on estimates of how much premature scrapping of capital equipment has been going on during the recession. If its estimate of this is too high (and it may well be), its estimate of the structural deficit and of the extent of fiscal consolidation that is needed will also be too high. Until we see how fast the budget deficit shrinks as the economy recovers, we will not know for sure how big is the structural deficit. This provides another reason to think that the phasing of the consolidation needs to be carefully constructed.

Yesterday's budget effectively put off a lot of the real decisions until the autumn statement on spending. But it is clear that the government is looking for 25% cuts over the next 4 years. The public sector pay freeze will go some way towards achieving this, but there will be much ground left to be recovered. There are some quick wins - why, for example, do well-off parents receive child benefit? We shall see in the autumn how economics and politics mix in determining where the cuts fall.

A week ago, the Office for Budgetary Responsibility (OBR) reckoned there was less than a 10% chance of Britain falling back into recession. Today's new estimates suggest that there is about a 20% chance of this happening by 2015. At the same time, the central growth forecast has been downgraded from 2.6% to 2.3%. This is all in the course of a week. The change is, of course, the result of the new measures announced in today's budget.

The deflationary nature of the budget has come as no surprise - expectations were well managed in advance of the event. If the OBR's forecasts are in the right ballpark, then the policies announced in the budget make a great deal of sense. By 2014-15, the government is planning to have phased in a reduction of the deficit amounting to £113 billion per year - half as much again as was planned by the previous government. In itself that may or may not be inappropriate; of course it makes sense to for the government to spend when times are tough, but rein in that spending as the economy improves. Whatever the merits of the extent of retrenchment, the way that it is phased is a matter of great debate.

The plan set by both this government and its predecessor has been to introduce the consolidation gradually, so that about one third of the total deficit reduction (that is, one third of £73 billion in Labour's case, one third of £113 billion in the case of the current government) comes in over the next two years. This means that the cuts announced by the present government over the next couple of years amount to taking £15 billion more out of the economy in 2011-12 (and £8.1 billion - most of which had already been announced) in the current financial year. That is tough medicine for an economy that is still in a fragile state.

To use Donald Rumsfeld's famous terminology, there are 'known unknowns' and 'unknown unknowns'. While one may not wish to argue too much with the central forecast, the risks from the unknowns that do not feature in the OBR model - or in the pretty fan charts - appear to be on the down side. While any budget has to be built on a forecast of how many chickens will hatch, in this particular case the risks of getting it wrong are greater than usual.

An interesting feature of the Office for Budgetary Responsibility's Pre-Budget Forecast concerns the calculation of the 'output gap'. This is the difference between actual output in the economy and the output that would be possible if spare capacity were fully utilised. During a recession, the output gap tends to rise - some firms reduce hours of work so that capital equipment is underutilised, some firms close down leaving premises and other resources unused. At the same time, pulling in the other direction, some capital might be scrapped. It is difficult to get a handle on how much capital scrapping takes place.

In trying to evaluate how the balance of demand and supply factors has affected the output gap over the course of the recent recession, the OBR has had to come to a judgement about (amongst other things) the reduction in capacity. This leads it to estimate that the output gap is currently around 4% of Gross Domestic Product.

This looks like an underestimate. According to the OBR's own figures, that would make the output gap smaller than it was in the 1980s recession.

Does that matter? The smaller the output gap is believed to be, the less potential is there for expansionary monetary and fiscal policies to promote economic growth without resulting in inflation. And the smaller the output gap is believed to be, the higher the proportion of the government budget deficit that is labelled 'structural' rather than 'cyclical'. Both of these are contentious issues.

In general in its report, the OBR has done an admirable job of documenting the uncertainty that attaches to its forecasts. Its estimate of the current output gap is subject to some uncertainty too, is highly policy-relevant, and - as it feeds into next week's budget - carries some danger.

The newly created Office for Budget Responsibility (OBR) has produced its estimates of growth for next year. In the Budget earlier this year, the then Chancellor of the Exchequer predicted that the economy would grow by at least 3% in 2011. The forecasts released today by the OBR suggest that that was too high an estimate. Indeed the OBR expects growth of just 2.6% - well below the previous 3% estimate, albeit higher than some observers had expected.

Whether this correction reflects the fact that the forecasters were subject to political influence before the election or the possibility that they are still (whatever the rhetoric) subject to such influence now is moot. But conjecture on that issue should not hide the fact that, in many respects, the economic picture is not rosy. The austerity measures introduced in other European countries (needed though they are) do little to encourage confidence in growth over the next couple of years.

The good news (inasmuch as there is any) is that the last government did not run up as large a deficit over the last year as had been expected. To some extent this will cancel out the detrimental impact on the public finances of the slower than expected growth over the next 18 months.

A double dip should be avoidable. But the guardians of our public finances are walking a difficult tightrope. They need to be careful not to believe too much of their own political rhetoric.

In a presentation given in London today, John Philpott of the Chartered Institute of Personnel and Development (CIPD) predicts that unemployment will rise close to 3 million by the end of 2012, and that it will stay at roughly that level for a further three years. This represents a marked increase in the CIPD forecast of unemployment, following the announcement of the government's fiscal deficit reduction plans.

An optimistic outlook for the next few years is for slow growth - certainly below the rate required to maintain unemployment at a steady level - so Philpott's forecasts have the ring of truth about them.

If there were to be a double dip, would this be caused by fiscal retrenchment or fiscal profligacy? Curiously, a mix of both. For some countries - Greece has been the most prominent - debt is a serious issue and there have been real concerns about the prospect of those countries honouring that debt. In consequence interest rates on their debt have risen, and there has been nervousness about their ability to raise further borrowing - thereby setting in motion a viscious spiral of concern. If these countries default, their creditors in other countries will lose out. If they do not default, substantial support is nevertheless likely to be needed from other countries. Either way, the sovreign debt problems of certain countries will have an impact on the public finances of other countries, most notably on the engine rooms of the European economy. This will almost inevitably dampen growth in the major European economies over the next couple of years. Those countries that have themselves engaged in significant fiscal retrenchment may find that they are tipped back into recession by the double whammy of tight tax and spend policies alongside the fallout from the sovreign debt problems of other countries.

Where does the UK fit into this? We sit uncomfortably somewhere in the middle. Fiscal retrenchment is needed, but since government borrowing in the UK has been longer term than in some other countries, the need is not quite so immediate, and premature contractionary fiscal policy might still cause a lot of damage. We clearly cannot rely too heavily on growth in Europe helping us out. Yet if a double dip were to happen, we would be hopelessly bereft of policy options - interest rates are virtually zero, quantitative easing would do little but generate inflation, and there would be no further scope for fiscal relaxation. Better to manage a long, slow recovery - but therein lies a real tightrope walk.

Studying time series of a single variable can be a hazardous activity - as indeed can any forecasting exercise. But a reasonable forecast of the 2008 recession could have been made using a neural network analysis of the index of industrial production. (I tried with 24 lags of the dependent variable, 2 neurodes in the hidden layer, and a hyperbolic tangent squasher, using monthly data that go back to 1968 - just in case you wanted to know.) This same model predicted the recovery quite well too. The same model shows the recovery in industrial output stalling somewhat from now onwards, staying at just above zero growth over the next 15 months. But then the forecast indicates a nasty dive in the last quarter of 2011.

One should not place too much confidence in long range forecasts that come out of such a simple model. But we know enough about the general macroeconomic environment to know that we are far from being out of the woods just yet. The growth rate of the Eurozone economies is likely to be severely dampened by the need to address fiscal deficits of the southern states - and the UK trades a lot with (and so its fortunes depend a lot on) the Eurozone. At the same time, the deficit reduction policies being implemented at home will themselves have a deleterious impact on growth. On balance, I would still expect the next few years to be characterised by a long, slow recovery. But a double dip cannot be ruled out, and is, if anything, getting to look more rather than less likely.