Tuesday, May 01, 2012

Real wages, nominal debt

SRW says that, in a balance sheet recession,
The only way out of a post-Keynesian depression is to increase real wages relative to the real burden of debt. In the post-Keynesian story, inflation is helpful only if real incomes hold steady, or, at very least, fall more slowly than the real value of prior debt.
I'm not sure if this is true.

Debt is nominally denominated, so its real burden goes up in a deflationary environment. This means that, even if real wages remain flat or fall, real debt burdens will fall so long as nominal wages increase regardless.

So, even if my old $100 salary bought two loaves of bread and my new $200 salary buys one loaf, I am still better off carrying the burden of my $1000 debt. Here, my real income is worse, my nominal income is better, but my debt burden is lighter.

If the Government uses its monopoly power as a producer of NFA(e) and writes everyone a check, then the non-Govt sector has more nominal wealth, but real wealth is unchanged (it may be redistributed). If this increase in nominal wealth boosts AD and factories start humming and the unemployment line shortens, then the real wealth of the economy increases as well as there is more sweat and atoms producing real output.

9 Comments:

Blogger JKH said...

ws,

He’s not saying real wages need to increase.

He’s saying real wages need to increase RELATIVE to real debt.

If nominal wages increase, then real wages DO increase relative to real debt.

They are equivalent specifications.

E.g. 5 per cent nominal wage increase

- with 10 per cent inflation, real wages decline by 5 per cent and real debt declines by 10 per cent; that’s an increase in real wages relative to real debt of 5 per cent

- with 10 per cent deflation, real wages increase by 15 per cent and real debt increases by 10 per cent; that’s also an increase in real wages relative to real debt of 5 per cent

In both cases, the relative increase is defined by the increase in (real wage change – real debt change).

Your bread example is the first case of inflation.

And it holds true in that case and in your example that real incomes/wages fall more slowly than real debt – because of the inflation of nominal incomes/wages.

7:16 PM  
Blogger Neil Wilson said...

"with 10 per cent deflation, real wages increase by 15 per cent and real debt increases by 10 per cent; that’s also an increase in real wages relative to real debt of 5 per cent"

But real wage rises in that environment are near impossible.

Isn't this a case of static analysis again, when it is the dynamics of the circulation that matters.

You can say the two are equivalent statically, but dynamically they most certainly are not.

11:20 PM  
Blogger winterspeak said...

For some reason, blogger ate steve's comment. here it is:

WS — We're saying the same thing. In your example, the real burden of the debt has fallen by 3/4 (the $1000 you owe means you have to produce with 5 loaves of bread the not 20 you'd have to bake originally), while your real income has only fallen by half. (You "bake", perhaps indirectly, one loaf of bread a week rather than two.) So real incomes have fallen more slowly than the real burden of the debt.

1:29 PM  
Blogger winterspeak said...

JKH/SRW: You guys are right -- we are saying the same thing. I still prefer my formulation because it is obvious how a Government may increase someone's nominal wealth and not at all clear how they might increase real wealth (politics aside).

So, "increase real wages relative to the real burden of debt" sounds like the economy must become more productive in real terms without taking on additional debt (which sounds hard) while "increase nominal wages relative to the nominal burden of debt" points to a simple solution -- print some money (NFA(e)).

Neil: I actually don't think this is a static/dynamic confusion. They're right.

1:32 PM  
Blogger The Arthurian said...

The key word in the first SRW quote is "prior".

Prior debt.

If debt resumes the rapid growth we had before the crisis, finessing the real and nominal of wages and debt is beside the point.

7:12 PM  
Blogger Ohm (Ώ) said...

This comment has been removed by the author.

1:46 PM  
Blogger Ohm (Ώ) said...

reposting with error correction:

RE: "E.g. 5 per cent nominal wage increase

- with 10 per cent inflation, real wages decline by 5 per cent and real debt declines by 10 per cent; that’s an increase in real wages relative to real debt of 5 per cent."

This can mislead, in that one might conclude from this that the debtor is better off. But he might not be:

say, the current nominal (and real) income of the guy is $100, and he is servicing existing debt @ $30 every income period.

So after debt service, he is left with $70 to consume.

Now, wage increases by 5% but inflation is 10%.
After debt service, he is now left with $105-30 = $75 nominal = $75/1.10 = $68.18 real, which buys him less than what he could buy before.

Therefore, if inflation is @ 10%, for this debtor to be better off, his wage should rise such that he is left with at least $77 nominal = $70 real after servicing the prior debt at $30 nominal. In other words, the nominal wage rise needs to be at least 7% (on the $100 income) to cope with inflation of 10%. As a formula:

w (needs to be) > i*(1-f0)
So, in our example, 10%*(1-0.3) = 7%.

WHERE w = % nominal wage increase
and f0 = proportional of income in the beginning that services the fixed (nominally denominated) debt, i = %inflation rate


In Real terms, in this example, a guy can take a hit of upto ~ 3% wages in real terms (actual calc wld be [3/110]*100) yet stay no worse off than before.

Formula for max fall in real wages that can be absorbed without pinch = i*f0/(1+i).

1:54 PM  
Blogger Ohm (Ώ) said...

In other words, in JKH's inflation example, the debtor suffered the following:

A loss of real wage of 5%, and relative to debt burden, he gained: 10%*0.3 - 5% = -2% (he overshot his max real wage hit tolerance by 2%).

5:16 PM  
Blogger Ohm (Ώ) said...

Got totally Monk'd on this!

New "Real Burden of Debt" (misleading term plain in English, though technically correct in Econ) = W0f0/(1+i)

Original "Real Burden of Debt" = W0f0

=> Fractional fall in RBoD = i/(1+i) ...(1)

BUT max fractional fall in real wages that can be absorbed without pinch = i*f0/(1+i) = (using 1 above) f0*Fractional Fall in RBoD

i.e. Fractional fall in Real Income < f0*Fractional Fall in "RBoD"

=> (Fractional fall in Real Income/Fractional Fall in "RBoD") < f0 (which is the fraction of income that is currently servicing the fixed debt)

i.e. To leave the debtor better off:
***
Not only the real income needs to fall a lower fraction relative to the fractional fall in "Real Burden of Debt" BUT further:
It (Real Income) needs to fall a lower fraction by the factor of the current (Debt Service/Income) ratio or lower.
***

In our example, Real Income can fall upto 10% (fall in "real burden of debt") * 30% (current Debt Service/Income) = 3% without leaving the debtor worse off. But if his real income fell more than 3%, he will hurt.

11:05 PM  

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