"Some Simple Deficit Reduction Arithmetic"

Kash Mansori notes that it takes more than a $100 cut in government spending to cut the deficit by $100. The reason is fairly simple. A cut in government spending causes output and income to fall, and the resulting fall in tax revenue increases the deficit offsetting some of the gain from the cut in spending:

Some Simple Deficit Reduction Arithmetic, by Kash Mansori: 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? ...

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? ...

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 ...[list of effects]

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 ... 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. ...

When the policies they want to pursue have large negative effect on the deficit, the economy, employment etc. Republicans invent a story where the pain goes away. Somehow, the deficit actually falls, output goes up, and employment is stimulated even if it runs counter to obvious intuition. When tax cuts are the goal, we are told that tax cuts lead to so much additional effort that revenues actually go up and this reduces the deficit. We can cut taxes, and reduce the deficit! This magical answer is, of course, nonsense, but Republicans were able to hoodwink quite a few people into believing this.

When it comes to cuts in government spending, the main worry is that output and employment will fall, a very bad outcome when the economy is trying to recover from a recession. A secondary worry is that the cut in the deficit won't be as large as advertised. Not to worry, just invoke the invisible confidence fairy and make the claim that reducing the deficit will make people so jubilant about the prospects for the future, they'll go out and purchase or build lots of stuff, and output will actually go up! This too is nonsense (just ask the Europeans who bought into this and are now paying the price), but no matter -- they have again hoodwinked enough people into believing it.

Apparently some people just want to believe, enough to make these policies politically viable, but it's really frustrating to see people fooled like this again and again.