Will Deficit Spending in fact be Money-Financed?

It's easy to say that money-financed increases in government spending should be used as a weapon of last resort, if the central bank runs out of ammunition as nominal interest rates fall to zero. But would government deficits in fact be money-financed?

If the central bank targets the monetary base, the answer is trivial: if the bank wants to increase base money to pay for the deficit (printing money and giving it to the government to spend) then deficits will be money-financed; otherwise they won't. But the Bank of Canada (like others) is not targeting base money; it uses a nominal interest rate instrument to target inflation. So if the Bank of Canada keeps the same target rate of inflation, will increased government deficits in fact be money-financed?

I started thinking about this question after reading Willem Buiter on the subject, but my answer is a bit different http://blogs.ft.com/maverecon/2008/11/monetise-public-debt-and-deficits/

The answer matters for two reasons. First, if deficit spending were bond-financed rather than money-financed, future taxes would have to be higher (or future spending lower), to pay the extra interest on the higher future debt. Anticipating higher taxes in future, some people might cut consumption today in response. This offsets some of the effect of increased government spending (and in the extreme case of Ricardian Equivalence, offsets it completely, so an extra $1 of government spending crowds out $1 of private spending). Second, even ignoring any effect on current spending, a higher future government debt is a Bad Thing (bad for future taxpayers, bad for the government's credit rating, bad for its ability to fight future emergencies, etc.).

In simple models where the central bank uses an interest rate instrument, the stock of money is demand-determined, and the demand for money is determined by three things: the price level (positive relation); real income (positive relation); and the nominal rate of interest (negative relation). The stock of money is, well, a stock. And the flow of government spending is, well, a flow. So if a temporary increase in the flow of government spending has a cumulative cost of (say) $100, we can say that it is 100% money-financed if it causes a permanent increase of $100 in the stock of money.

In normal economic times, if the government increases spending, so aggregate demand increases, the central bank will need to offset that increased aggregate demand completely to keep inflation on target. In a closed economy, the central bank raises the rate of interest to do this. This increase in the nominal rate of interest reduces the demand for money, so the money stock falls. The central bank is forced to sell interest-paying bonds to buy back non-interest-paying money. So the government debt in public hands (i.e. not owned by the bank, because since the bank is owned by the government anyway that doesn't matter) actually increases by more than the $100 the government borrowed to finance its spending. The extent to which increased deficits are money-financed is actually temporarily negative in normal times. But when the temporary increase in government spending comes to an end, the interest rate returns to where it was before, so does the stock of money, and so the government spending was 0% money-financed, 100% bond-financed.

In an open economy it's a little more complicated, because the exchange rate appreciates, and so the central bank won't need to raise the interest rate as much to keep inflation on target, but the result is qualitatively the same. (Trust me, or work it out for yourself.)

In normal times, the only effect of government spending on the demand for money is via its effect on the rate of interest. The central bank makes sure it doesn't affect real income or inflation. But in abnormal times, when the central bank has lowered interest rate down to zero, and it's still not enough to prevent a recession, or prevent inflation falling below target, the result is very different.

To keep things simple, assume that a cumulative increased government expenditure of $100 will work very quickly to bring back normal times. And assume that the alternative scenario is to wait for a deus ex machina to bring the economy back to normal in 10 years. Let's focus on money demand after those 10 years have passed, so the economy is back to normal under either scenario.

The price level after 10 years will be higher if the government increased spending than if it waited for the deus ex machina. It's higher because inflation has been at the 2% target for those 10 years, rather than in a deflationary spiral. This will mean money demand is higher. (Note that if the central bank had been targeting the price level, rather than inflation, the price level by definition would be exactly the same under the two scenarios when the economy returned to normal.)

Real income after 10 years will be higher if the government increased spending than if it waited for the deus ex machina. A 10 year recession would have caused lower investment and hence a lower capital stock, so less output and income. This will also mean that money demand is higher. (Note that in an AK growth model real output would never catch up, and this effect would be permanent, but in a Solow growth model it would eventually disappear).

Nominal interest rates after 10 years would probably be about the same under either scenario, so this won't affect money demand. (This assumes the inflation target stays the same, and ignores any effect of lower investment during the recession on real interest rates when the economy gets back to normal.)

So with higher price level and real income, money demand and hence the stock of base money will be higher after 10 years if government spending increases than if we wait for the deus ex machina. So the increased government spending will be, at least in part, permanently money-financed. Could it be 100% money-financed, or even more than 100% money-financed?

Lets do some math. Suppose a cumulative expenditure of 10% of annual GDP is enough to rescue the economy. Suppose the money base is also 10% of GDP. That means the money base would have to double (comparing the two scenarios) to make the government expenditure 100% money-financed. That means money demand would have to double, which could only happen if nominal income were also double after 10 years (comparing the two scenarios). By the Rule of 70, that would require nominal income growth to be 7 percentage points higher for 10 years under the first scenario than under the second. Yep, that's in the right ballpark: 2% inflation vs (say) 3% deflation gives us 5% difference in inflation; and 2% real growth vs (say) 0% real growth gives us 2% difference in real income growth; 5% + 2% = 7% difference in nominal income growth, which would make it 100% money-financed.

So yes, if increased deficit spending were used as a policy of last resort to prevent a deflationary recession, a significant chunk of that spending, perhaps all of it, perhaps even more than all of it, would in fact be money-financed.

Comments

[Tom Grey]

If this means the Fed / Treasury should be sending out checks of USD to taxpayers, I agree with you.

I'm pretty sure that with the house price and stock price bubbles popping, some $60 tr of paper wealth has disappeared. So there are, today, far too many bankers. More banks need to fail.

The bailout so far is mostly to save the top elite bankers from the discipline of failing so badly.

Your deflation definition was also fine. Welcome (I'm new here, too.)

[JKH]

Very interesting – preventing an economic recession also prevents a recession in the normal path of central bank balance sheet growth. The deficit required to prevent economic recession gets funded by the desired outcome for the central bank balance sheet.

[Andrew]

Out of curiosity (and pardon my ignorance), what actually forces the BoC to not decrease the overnight rate below 0%? The effect of course being that money would flow in the opposite diection. In this case, the BoC would not be able to 'run out of bullets' if it could pay banks to borrow from it.

Is there some problem with this that I'm not seeing?

[Nick Rowe]

Tom Grey: money-financed transfers, or tax cuts, should work, but then people might save it. Money-financed government expenditure, by definition, gets spent. Though the UK temporary cut in VAT (their version of GST) could also give an incentive to buy now. And welcome!

JKH: Yep, that's a good way of looking at it.

Andrew: Since we can always earn zero nominal interest just by holding cash, and keeping it under the mattress (or in a safety deposit box), the BoC cannot force interest rates below zero (if it tried, the demand for cash would be infinite). Actually, this is not exactly true, because of the risk of theft if you keep it under the mattress, or the cost of a safety deposit box. And a few days ago, the interest rate on some US T-bills did go briefly negative by a tiny amount. But it's close enough to true. The only way to really get negative nominal interest rates is to put some sort of tax on holding paper money, or have the notes expire after a certain date. But these are just too inconvenient for everybody.

[kevin quinn]

Nick: RE does not imply that consumption would fall as much as g increases! The higher taxes in the future shift the intertemporal budget constraint in; the present value of lifetime consumption must fall by the amount of the g increase. So consumption falls some in every period - with the usual preference for smoothing. Making consumption fall today by as much as G rose puts all the burden of the reduction in the present value of lifetime income on today's consumption alone. So demand rises today. That's why Barro looks for increases in G to raise interest rates, however it is financed.

[Nick Rowe]

kevin: yes, you are right; I was being a bit sloppy. Under RE, a bond-financed increase in G is equivalent to a tax-financed increase in G (the balanced budget multiplier is still there). But the standard balanced budget multiplier does (implicitly) assume zero substitutability between government and private expenditure. At the other extreme, if we assume perfect substitutability (the government buys us stuff we would have bought for ourselves anyway), then the balance budget multiplier disappears too.