$800 billion = $800 billion. Coincidence?

Scott Sumner thinks it's just a coincidence that the increase in excess bank reserves in the US is almost exactly the same as the amount of the government's discretionary fiscal stimulus - $800 billion.

And yet, the increase in the Bank of England's balance sheet through quantitative easing so far - £180 billion or so - is also the same as the UK government's budget deficit this year. Doesn't it make you wonder?

Now it's true that there is no necessary link between the two. In "normal" times, government borrowing and central bank easing are not necessarily correlated - quite the reverse, in many cases. Public borrowing is generally inflationary; so a monetary authority with a constant inflation target is likely to counteract that by raising interest rates or otherwise reducing the money supply.

However, now is different. Inflation and growth are exactly what we need, and the fiscal and monetary authorities are acting together to try to create them.

You could look at these numbers as being simply a fair division of labour: the central bank is doing half the job, and the government the other half. But there is no reason why they should divide this job 50-50. There's something missing in this explanation.

And, as it happens, there's a perfectly good reason why they should be the same.

The fact is that, despite the assumptions many people make about capital markets, most real investors do not move their money around very fast. There is a lot of inertia in most markets. Investors who were long on gilts or Treasuries in 2007 are still long now. Mutual fund investors who held equities are likely to - mostly - still hold them now. It isn't that easy for governments to create $1 trillion of new demand for bonds; and equally, it isn't that easy for a central bank to find $1 trillion of unwanted assets to buy - without taking big risks on buying up risky "toxic" assets.

This makes it very natural that, to avoid too much disruption in markets, central banks would print just about enough money to buy the unexpected surge of government bonds. There needn't be any overt coordination to make this work: price signals are enough. As governments borrow more, long-term rates go up, risking a collapse in business investment; the central bank buys long-term debt to counter this and reduce the chance of deflation.

In the longer run, markets can absorb these greater amounts of debt. Commercial banks may issue their own paper to buy some of it, pension funds will buy it as more people retire, and if not then its price will fall until somebody is willing to take it off the central banks' hands. But it all takes time, because behaviour has inertia.

This is also why all that extra money is not finding its way into business lending. Net lending to business in both the US and UK continues to fall. No doubt it's falling more slowly than before, but there's all sorts of inertia both in the infrastructure of the commercial banking sector and within businesses which leads to slow uptake of the funds that are available.

Nick Rowe's theory of loan officers is one way to explain this; another is the Austrian "recalculation" model, in which it takes time to redeploy resources from one sector to another.

My preferred view is that it's about information and uncertainty. Two years ago, banks and investors "knew" what was a good way to lend money and make a relatively high and safe return. Loans to build buy-to-let properties, loans to private equity companies to buy retailers and utilities, property-secured loans to individuals of low credit quality. Those are no longer regarded as good prospects, so lenders are cautious about making new loans until they have discovered what's worth investing in.

Thus bank reserves stay in reserve and the increased household savings rate goes into government bonds. Maybe, as Scott suggests, a penalty interest rate or expected inflation would encourage lending, but I suspect it will take more than that. The real shortage now is information - information about which businesses banks can lend to and still expect to get their money back.

But information is powerful for one key reason: it has huge positive externalities. A successful investment has a powerful side-effect: it adds to the stock of reliable knowledge about which types of business are a good investment. This extra knowledge can be used by anyone in the economy to make a similar investment, multiplying the impact on the economy many-fold.

The conclusion: government should sponsor loans to a diverse range of businesses, on a randomised basis, with a commitment to publish the results. Industries whose loans produce a return will attract private lending or investment. We don't yet know what the next decade's dotcom or buy-to-let opportunity will be. But if we discover it, a wave of new investment will be unleashed, providing a destination for savings and more importantly a new long-term income stream for the economy.

Unfortunately these "experimental investments" will take time, and we won't know definitively for some time which ones are successful. But the investments in themselves will contribute to fiscal stimulus, data will start to accumulate immediately, and even within a few months those externalities will start to materialise.

Could this be part of the Bank of England's mysterious "Plan B"?

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