The IMF multipliers: some maths, and Labour’s chance to get it right
Hurrah! Fiscal multipliers are back in the news.
The IMF has, as Duncan points out in his excellent post, revised its assumptions about the impact on GDP of austerity measures:
[T]he Fund initially thought that the multiplier was around 0.5 (i.e. £10bn of spending cuts will reduce GDP by around £5bn) whilst it now thinks they are between 0.9 and 1.7 (i.e. £10bn of spending cuts will reduce GDP by between £9bn and £17bn).
The really interesting bit for the UK, Duncan concludes, is whether the OBR will do the decent thing and revise its own projections, given that its earlier ones were based on the very assumption the IMF has now accepted was wrong. If the OBR does do the decent thing, then the government’s Plan A pig-headedness will be even further exposed. It won’t do anything to change government policy, but honesty from the OBR might make for a further nail in its electoral coffin. And if the OBR obfuscate (and I think that’s very likely), that will look and feel like political maniplation of a body set up with the express promise of independence.
So Duncan having done the job I planned to do (and much better than I would have done), I’ll content myself with rehearsing the maths behind the concept of the fiscal multiplier, and especially how it works best when several countries at once adopt sensible Keynesian policies when recession hits.
To do so I cut and paste shamelessy from a post I wrote 3 years ago, in which I filled out Paul Krugman’s rather elliptic analysis (in fact Krugman comes out with a possible 2.23 multiplier if EU countries adopt a co-ordinated fiscal package).
So if you’re sitting comfortably….
1) c = the marginal propensity to consume i.e. Krugman uses an assumption of half (0.5) additional money coming into the economy 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.
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 factored to take account 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 FISCAL 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
Of course, there are countervaling views, like this:
Proponents of discretionary fiscal stimulus hope for a Keynesian multiplier effect. It follows from the national accounts spending identity when combined with the textbook Keynesian consumption function. The latter has current income as the main driver of consumption spending. A government-induced increase in total spending then raises income and boosts private consumption, which in turn raises total spending further.
Does the multiplier work? The recent debate in the US indicates quite some disagreement even among Keynesian economists. President Obama’s advisers Christina Romer and Jared Bernstein estimate that 1% of government spending would generate a 1.6% increase in GDP……………
Our analysis suggests government spending quickly crowds out private consumption and investment, because forward-looking households and firms will consider eventual increases in future taxes, government debt, and interest rates.
In a recent paper, Tobias Cwik and I assess the magnitude of Eurozone stimulus and construct a range of impact estimates……..
Our findings confirm the earlier analysis with models of the US economy. Once you allow for a significant role of forward-looking behaviour by households and firms, there is no multiplier. The expectation of future tax increases, or rising government debt and future interest rate increases leads to a reduction in private consumption and investment spending…………
Leaving aside the difference between the 1.6x multiplier effect on the US economy suggested by Obama’s economists and Krugman’s 2.23x effect (in Europe), the essential thing to note here is that the Keynesian algebraic formulations are called into question on the basis of a missing independent variable – the ‘forward-looking behaviour by households and firms’ and’ the expectation of future tax increases, or rising government debt and future interest rate increases.
This is the core of the matter – the Keynesian stimulus works best if there is a wider Keynesian environment in which it can operate; in circumstances where households and firms are uncertain about the effects of national debt and interest rates, it doesn’t work (I’ll leave aside the notion that tax rises damp down investment, save to note that I have spent time disputing that here).
Conversely, surely goes the argument, if households and firms are sanguine about government debt, on the basis that it’s not that big really, and sanguine about interest rates, then investment will take place, and growth will occur.
It seems to me that this is a classic example of the importance of political context for economic policy making and implementation, which I set out in this post, and in which I quoted Massimo de Angelis:
Keynesianism is defined in terms of an expansionary strategy of growth. Embedded within a social and institutional framework that enables the different interests in society to remain on a dynamic balance within a regime of capitalist accumulation…..Keynesianism was never just an economic theory, it was also a form of social practice – it needed institutions that allowed the theory to work, and it implied a vision of power relations amongst classes in society.
In other words, the success or failure of economic policies depends upon who has political power, and who has the dominant ideological narrative. To date, the neoliberal discourse of the need to balance national debt holds has held sway.
Maybe, just maybe, the IMF’s revisions are starting to change that. It is, as noted earlier, too much to expect that the Conservatives will be able to reverse out of the economic cul-de-sac they drove into three years ago; Cameron’s conference speech today, in which he delivers the same tired old rhetoric about Labour and borrowing, is confirmation enough of that.
But the IMF’s revised stance may come at a time when Labour can still distance itself from the all too persuasive urgings of its own financial illiterates, and instead engage confidently in planning for an investment-led recovery from 2015, by which time the country really will be in a mess.