Increasing public spending levels is not necessarily a boon to the poor. The money often ends up lining the pockets of the wealthier classes
Comprehensive Spending Review 2000: special report

A mystery at the heart of the third way is how much a progressive, fairness-minded government should actually be spending. Is the UK's 39.5% of GDP the right amount; would 10% more - pushing us up to French and German levels - be better? It is not a question Gordon Brown is going to answer this week when, despite the size and shape of his rabbit having been plain for a long while, the prestidigitator of the public finances performs.

On present evidence, Labour is wedded to 40% as a kind of norm. If the economy continues broadly on track, by 2005 public spending will have risen to only 40.5% of GDP, which is still less than in John Major's last year. Edging it up in a continental direction would be, says Peter Robinson of the Institute for Public Policy Research "a perfectly feasible option". Provided taxes rose to pay for it. And that is one explanation for the arbitrary limit with which the Blair government works - closure on the fiscal front.

There is another, troubling reason. Government is not sure what effect public spending has. Interest groups clamour for it, for tanks or prisons, but their effect is not exactly uncontroversial. Relating given levels of spending with "big picture" questions such as prosperity, wellbeing or even, God forbid, public happiness is so difficult it is rarely attempted.

But Gordon Brown dresses to the left. His acolytes like to present him as the least neo of Labour's neo-socialists. They expect the chancellor's spending plans to address inequality - there are signs it has continued growing under Labour. So he shall. Education spending, tipped to rise at the same rate as health, is now accepted as the most direct if the most long-term way of addressing social exclusion and low income. In a new book the Nobel prize-winning economic historian Robert Fogel says whatever else governments do or don't do, they must bump the share of GDP spent on schooling up to unprecedented levels, from about 7% to 12% of GDP*.

But Gordon Brown will also be judged in the short term. Will his tenure leave the distribution of income fairer? A key indicator this week will be what the Treasury allows for spending by the Home Office, Department of Trade and so on and what it projects for social security, disability and pensions. This is the difference between increases under departmental spending limits and "annually managed expenditure". On present evidence the former will get 4.7% a year in real terms over the planning period 2001-2004 against 1.7% for welfare.

Such figures may look ideologically suspect for a would-be egalitarian but they do accord with an emerging Anglo-Saxon consensus about big government. It is the argument made by American academics that the best explanation for declining public trust in the state has to do with the dramatic growth in what are called transfer payments. The chart shows how significant an element in state activity welfare cash has become. In the UK total spending has fallen from the watershed of the mid-70s - Peter Shore turns out to have been right in saying the party was over - but transfers have risen. They have been financed, notes Carl Emmerson of the Institute for Fiscal Studies, by large decreases in investment spending by the state. That has resulted partly from privatisation but also the large reduction in council house building. But (the Americans argue) the more government redistributes the more it generates winners and losers. Everyone benefits from spending on hospitals or roads. But payments to pensioners or asylum seekers are perceived as looting one person's pocket to fill another's, and resented.

Gordon Brown's question (though he is unlikely to pose it) is whether such transfer spending "works". Does big government make for a fairer society? Economists of an Anglo-American stamp, the kind whose thinking informs the analyses of the OECD, are dubious. Vito Tanzi and Ludger Schuknecht* have collected together a great array of measures of the effectiveness of public spending across the western world, noting how it has been since 1960 that public spending has anywhere risen from its previous maximum of about a third of GDP.

The growth area has been welfare transfers, which rose from an average of 5% of GDP in the 30s - when the means test was mean - to 23% now. This constitutes excessive "churning", they say: government taking from and giving to broadly the same people. These economists tend to a narrow view of government purposes and probably miss the ways in which state spending can provide a frame and inspiration for civil society and private economy.

None the less it is hard to reject their empirical finding that big-spending governments turn out to be not much more successful than small ones in counteracting inequality. That is because even in social democratic Scandinavia, transfers end up in the pockets of people who already have considerable resources. Across the west, in the mid-80s 57% of transfers went to the middle 60% of the income distribution, 16% to top fifth and only 27% to the bottom fifth. Sweden is a more egalitarian society than the United States, yes, but not by the margin you might think.

Gordon Brown will say his new public service agreements target spending better. But he is unlikely to offer a reason for why this total of spending, no more, no less.

*The Fourth Great Awakening by Robert Fogel, University of Chicago Press.

*Vito Tanzi, Ludger Schuknecht: Public Spending in the 20th Century, CUP £13.95 (pub August 24).