Against the Paradox of toil

In a recent post Paul Krugman raises the “paradox of toil” to explain why tax cuts are silly and government spending is good during a recession:

So what’s the paradox of toil? If you cut taxes on labor income, this expands labor supply — which puts downward pressure on wages and leads to expectations of deflation, which increases the real interest rate, which leads to lower output and employment.

However, this is completely misleading.  Cutting a tax doesn’t really “shift the supply curve” (which is what expanding the labour supply means) in this way.  Lets have a little think about wages and what cutting the tax probably does.

Lets start with the idea that wages are perfectly flexible – which is rubbish but is a nice starting point.  In that case, lets look at how the tax would influence the equilibrium in the labour market:

Point C is where we would be sitting with no tax.  Point B is the after tax wage received by the supplier (our aggregate employee) and Point A is the cost to the consumer (our aggregate employer).  With fully flexible wages a reduction in the tax makes this wedge between points B and A smaller – implying that we “move” up the supply curve and “move” down the demand curve.

As a result, the lower tax leads to higher employment, higher net wages, and lower gross costs for businesses.

Now assume that the net wage is fixed.  Why would it be fixed, hell I have no idea, but for now lets assume that businesses take ALL of any tax cut IMMEDIATELY.  In that case there is no “downward pressure on wages” for workers, as they are fixed.

Now assume that the gross wage is fixed.  If this is the case a lower tax will lead to higher net wages.

We have three situations here:

1. Wages are flexible.
2. Net wages are fixed
3. Gross wages are fixed.

In all three case net wages did not fall.  As it is falling net wages that will “feed into expectations of deflation” when Krugman says “If you cut taxes on labor income, this expands labor supply — which puts downward pressure on wages and leads to expectations of deflation” he appears to be talking crack.

But there is something in this right.

Of course the is an argument that leads down these roads.  And it stems from an issue I ignored in my viciously partial equilibrium discussion above (one I merely made to rebut what sounded like a very partial eqm analysis on the other side).

The paper Krugman links to makes a slightly different argument for why tax cuts lead to lower output.  Namely when the central bank is unable (or is at least unwilling to) react to deflationary pressure, then a tax cut could lead to lower GOODS prices.

In this case the direct impact of the tax cut on the labour market (an increase in real net wages leading to a temporary increase in the quantity of labour supplied) is dwarfed by the increase in the real interest rate (as a sudden drop in goods prices leads to a reduction in inflation expectations).

Given the assumptions of:

1. A central bank that can’t commit to future inflation,
2. Some adaptive nature (at least from a one-off shift in goods prices) in the formation of inflation expectations,
3. Complete Ricardian equivalence (so that the tax cuts have no impact on aggregate demand)

This is reasonable enough.  However, then we have to ask if we find those assumptions reasonable, and whether they translate into the current situation that we are in.

I’m not sure, but I was under the impression the the Fed had pushed up inflation expectations and that typically credit constraints (which are heightened during a credit driven recession) made Ricardian equivalence a relatively poor approximation of short term behaviour in the face of a temporary tax cut.