The Bickerstaffe Record

The world beyond West Lancashire

Optional algebra, German protectionism dressed up as fiscal rectitude, the collective action problem, and what it all might possibly mean

12.17.08 | 2 Comments

Here’s a very interesting post from Paul Krugman, that clever Keynesian bloke, about  Germany’s ‘interesting’ and mixed reaction to the fiscal stimulus ideas being promoted by Gordon Brown. A big hat tip to Next Left for pushing it my way.

Krugman starts from the proposition that Europe is, or soon will be, in a position where interest rates are low enough to mean both that fiscal policy is the only substantial means left for stimulation of the economy, and then moves on to examine how additional public spending from borrowing works it’s way through additional consumer spend, taxation revenue associated with bolstered government purchasing and then vitally – the factoring in of imports from outside the trading area in question. 

He compares the outcomes when the trading area in question is the nation state with outcomes when it is the EU as a whole, and finds that the ‘multiplier effect’ of increasing public spending is exponentially higher for everyone if it is done ‘en bloc’ across the EU (including in Germany).

The algebra

The following algebraic formulations make it all absolutely crystal clear. I’ve filled it out quite a bit from Krugman’s own post, as he is a bit elliptic with the notation and the workings, clever bloke that he is. 

If this stuff isn’t really your bag, just skip to the conclusion a bit further down, but you’ll have to trust our Kruger’s workings (and in fact there’s a typo error in his original post, naughty nobel prize winner that he is).

 Notation used in the workings

1) c = the marginal propensity to consume i.e. Krugman below uses an assumpton of half (0.5) additional money coming into the ecoomy through increased public spending will be spent rather than saved.

2) m = the share of  ‘marginal’ ‘consumption that is spent on imports — initially for individual county, then for the EU as a whole.

3)  t = the share of an increase in GDP that accrues to the government in increased taxes or reduced transfers.

4) Y=GDP, dY=change in GDP,

5) D=Deficit, dD=change in deificit,

6) G=Government purchases and dG=change in Government purchases.

The workings

If government purchases (dG) increase through public spending, this will raise GDP directly, to the extent that domestic goods and services are bought, and indirectly, as the rise in GDP induces a rise in consumer spending. We have then in algebraic terms:

dY = (1-m)dG + (1-m)(1-t)c dY

or, fiddling around with both side of the equations, we can have:

dY/dG = (1-m)/[1 – (1-m)(1-t)c]

That is, the ratio of the increase in GDP (the country/EU ‘wealth’) to the additional deficit incurred is calculated from the marginal amount not spent on imports divided by the increased taxation level staying in the system multiplied by the amount of money not spend on imports then factoredto take acocunts of what’s really spent and not saved.  Sort of.

He then factors in how much the budget deficit is increased by an increase in government spending. This is not one-for-one, because higher spending leads to higher GDP and hence higher tax revenue.

This is written as:

dD = dG – tdY

The ratio of the increase in GDP to the increase in the deficit is dY/dD. Taking the above into account, the first equation above can be filled out to:

dY/dD = (1-m)/[1 – (1-t)(1-m)c – t(1-m)]

According to Krugman, the average EU country spends about 40 percent of GDP on imports, and collects about 40 percent of GDP in taxes. (Krugman assumes for convenience that the marginal rates will be are the same as the average). That sounds about right overall.  

He also assumes, as noted above that the marginal propensity to consume is 0.5.

So, in algebraic terms for an average EU country m = 0.4, t= 0.4, c = 0.5.

He then represents a coordinated fiscal policy by looking at the numbers for the EU as a whole. The only difference is that m falls to 0.13 (ie. one third of m = 0.4), because about two-thirds of the imports of EU members are from other EU members.

And he gets the following results:

FISCAL EXPANSION IF ONLY ONE COUNTRY DOES IT (and imports therefore make up 40% of additional spend)

dY/dD = (1-m)/[1 – (1-t)(1-m)c – t(1-m)]

dY/dD = (1-0.4)/[1 – (1-0.4)(1-0.4)0.5 – 0.4(1-0.4)]

dY/dD = 0.6/[1 – (0.6)(0.6)0.5 – (0.24)]

dY/dD = 0.6/[1 – 0.18 – 0.24]

dY/dD = 0.6/0.58

dY/dD = 1.03

Ratio of the increase in GDP to the increase in the deficit = 1.03

COORDINATED EXPANSION ACROSS EU (and imports reduced by two thirds)

dY/dD = (1-m)/[1 – (1-t)(1-m)c – t(1-m)]

dY/dD = (1-0.13)/[1 – (1-0.4)(1-0.13)0.5 – 0.4(1-0.13)]

dY/dD = 0.87/[1 – (0.6)(0.87)0.5 – (0.348)]

dY/dD = 0.87/[1 – 0.261 – 0.348]

dY/dD = 0.87/0.391

dY/dD = 2.23

That is, the ratio of the increase in GDP to the increase in the deficit = 2.23

 Conclusion to the algebra

The respective ratios of the increase in GDP to the increase in the deficit show that the trade-off between increased debt and effective stimulus to the economy is much better for the EU as a whole than it is for any one country.

 An interpretation of the German stance

Economist commenters on Paul Krugman’s blog have run some other assumptions on the marginal propensity to consume etc., using models and software I don’t pretend to understand, and they suggest the analysis is correct even with changed variables.

More interesting, though, is one of the comments that relate specifically to Germany’s current position.  Her/his thesis is that their lack of willingess to increase borrowing is that, as the largest economy in the EU and the biggest exports, they actually stand to gain, at least in the short term, from everyone else’s co-ordinated fiscal stimulus without actually having to go through the pain of increasing their own debt (which, as Neil has pointed out, is a much higher percentage of its GDP than the UK has, for example, meaning that borrowing might be all the harder to ‘sell’ to the electorate).

This would make sense of why a pro-European unity Chancellor like Angela Merkel appears to be backing a co-ordinated stimulus package, while a Finance Minister backed by the mass ranks of macro-economists is saying ‘Hold on, Angela, we can get something for nothing here if we use our sheer size of economy to its best effect’, only in German.  I dare say other Finance Ministers might do the same in his shoes, though possibly not in German.

It is, in short, the classic collective action /free-rider problem in action – the problem neo-liberal ideologues have never quite got the hang of asking, never mind answering.

And the meaning of all this?

First of all, regular readers of mine – all three of you – may find it strange that I’m venturing into macro-economic number crunching territory here, with an apparent willingness to go to the algabreic dark side.  

Certainly it all feels a bit strange, and I stand by my broad views, expressed at some length towards the end of this seemingly unrelated post, about the need to cultivate a society (and the social economy that Mil wants to see develop), which is based on an ideological commitment to social justice and all that stuff, rather than an economy which needs ‘macro-managing’ without much regard to human cost, and where capital still gets to use the banking and ‘money supply’ rules that it ‘invented’ in 1844 exclusively to its own ends.

And yes, I think that an overwhelming reliance on current macro-economic theory, however ‘liberal’, is the thin end of the wedge to an acceptance that the only thing we can really do is to work out the best way to sort out a failed capitalist economy so that the capitalists can then have another go at failing, only with less strong unions to worry about, because the cleverer capitalist ‘took them down’ during the recession.

But with these caveats, the kind of stuff Krugman gives us here is a useful heuristic tool for assessing how we can make the best of the people’s downtrodden lot for the moment, even though I know this continues to maintain the essential paradox of social democracy – uphold the capitalism we kind of know is bad for people, because letting it collapse completely may be even worse for them as we have no ready alternative.

It’s a useful tool not so much because it’s accurate – or ‘realist’ in the epistemological sense of the word – but because macro-economists DO hold sway over public policy, so it’s important to understand how and why they react the way they do.  It’s important in the same way as Colin Hay has showed how the whole neo-liberal notion, that low tax economies are needed to remain/become economically competitive, is not based on ‘reality’ , but on a self-fulfilling narrative of what the reality might be, according to those same neo-liberally trained economists.

To this extent then, and within social democratic parameters, Paul Krugman’s analysis (and that of his clever commenters) is very useful.  What he shows us, without stating it himself, is that international co-operation is good for the international economy.

Of course, that’s exactly the same message that the neo-liberals gave us during their ‘good times’, when they said international trade barriers must be torn down through WTO agreements (except the ones that they like having). 

But that’s a message which all of a sudden some of them – especially in the US – don’t seem too keen on hearing.


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