Some Simple Deficit Reduction Arithmetic

Here’s a short lesson about something that every policy-maker should have learned in Macro 101, but apparently has been forgotten by many of them.

Suppose we are in a country that is running a large budget deficit but, for whatever reason, decides that it needs to dramatically reduce it. Take your pick of examples, because there are plenty to choose from: Greece, the UK, the US...

Suppose that the country – let’s call it Austerityland – has a GDP of $100/year, and a budget deficit of $10/yr, or 10% of GDP. And suppose that the government decides it wants to get the deficit down to 5% of GDP. How can it get there?

No, the answer is not “cut spending by $5/yr”. Nor is it “raise taxes by $5/yr”. And last but not least, it is also not “enact a combination of tax increases and spending cuts that total $5/yr”. To see why, let’s do just a bit of arithmetic.

To keep things simple (and to make it particularly relevant to the three examples mentioned above), let’s focus on the strategy of trying to halve the budget deficit primarily through spending cuts. So the government of Austerityland decides to cut spending by $5/yr. What happens?

Recall that GDP is the sum of spending on final goods and services by domestic consumers, domestic businesses, and the government, along with net exports:
GDP = C + I + G + (X – M) = Y. Recall as well that GDP is, for our purposes, the same thing as income (Y).

If G is reduced by $5 in Austerityland, the first thing that happens is that GDP falls by $5. But then a bunch of secondary effects kick in, including:

• C falls, since individuals in the economy have seen their income drop by $5. This makes GDP fall even further. This is called the “multiplier effect”, and it means that the total fall in GDP is likely to be substantially greater than $5. (Empirical research seems to usually show that the government spending multiplier is in the neighborhood of 1.5, implying that the net fall in GDP will be around $7 or $8.)
  
• If interest rates are positive, they will tend to fall as demand diminishes, which could boost spending by businesses. But if interest rates are already at zero (as they are effectively are in the US), they will not fall, and we get no boost to private investment.
  
• Tax revenues fall as income falls. If the effective marginal tax rate on income is 25% and income falls by $4, for example, then tax collections will fall by $1.

So, what is the budget deficit in Austerityland after a $5 reduction in government spending? If we assume a relatively modest multiplier of 1.5, and a tax rate of 25%, then we get:

ΔG = -$5
ΔY = -$7.5
ΔT = -$1.875

And the new deficit is now $6.875, which is 7.4% of the new level of GDP. Wait, I thought we were trying to get the deficit down to 5% of GDP? What happened?

What happened is that we’ve missed our target, by quite a bit, due to the multiplier effect and the fall in tax revenues that resulted from the shrinking economy. In fact, just a bit of simple algebra allows us to figure out that government spending in Austerityland will have to be cut by about $9 in order to reach a budget deficit target of 5% of GDP. In other words, the government will have to cut spending by almost twice as much as it initially thought it would in order to reach its deficit target.

(When that happens, by the way, GDP will fall from $100 to around $86. Yes, that’s a 14% drop in output. But hey, at least we’ve hit our deficit reduction target!)

Somehow, this simple exercise in macroeconomic math seems beyond the reach of policymakers around the world.

• Many Republicans (and some Democrats) in Washington continue to believe that they can close a $1 trillion deficit by simply cutting $1 trillion in spending, and are apparently hoping to use the debt ceiling vote to do exactly that.
  
  
• The Cameron government in the UK embarked on an austerity program last year to try to reduce its budget deficit, and now mysteriously keeps missing its deficit reduction targets as the UK economy shrinks.
  
  
• The Greek government was forced into enacting a number of austerity measures last year, and... surprise, surprise... is now missing its deficit targets.

Why do people keep getting surprised that austerity doesn't work as well as hoped to reach budget deficit targets? I know, I know, there are people who argue that basic Macro 101 has it all wrong. Even people who know better (ahem, Douglas Holtz-Eakin) somehow allow ideology to get them to make the bizaare claim that when income goes down, people will actually increase spending. Confidence fairies and all that.

But when basic Macro 101 both makes good theoretical sense and also fits what we actually observe, it's really time to start looking for your handy Occam's Razor. I wish I could take more satisfaction from the fact that mainstream macroeconomics, as it has been taught to first-year college and university students around the world for decades, does such a good job explaining what we see happening across the globe today...


UPDATE (May 27): To see an alternative, much less destructive way to get a deficit and debt problem under control, see this post: Two Approaches Toward Deficit Reduction.

UPDATE (May 25): New data from the UK continues to show that the British austerity program is having exactly the effects predicted by this model. From the Financial Times today:

On the brink of a British double-dip

Dramatic, we know. But the ONS has confirmed the economy grew only 0.5 per cent in 2011′s first quarter after its 0.5 per cent fall in 2010′s last three months... confirming a double-dip in GDP in absolute terms over the period...

More worrying is the fact that sectors which previously pushed recovery forward are now definitely double-dipping.

Here’s Howard Archer of IHS Global Insight:

On the expenditure side of the economy, there was a very worrying drop of 0.6% in consumer spending in the first quarter, which reflected the pressure on spending power coming from elevated inflation and muted wage growth. Consumers also faced high unemployment, elevated debt levels, and a weak housing market.

Also worryingly, business investment plunged 7.1% quarter-on-quarter, which hardly fuels hopes that it can be a major growth driver going forward.

But the thing with re-balancing is — the Treasury wants private investment to fill the hole that will be left by government cuts to spending. It’s not happening.

No, it's not happening. But it's not really surprising that private spending isn't filling the gap left by reduced government spending, given that income is falling...