Tim Worstall reminds us that there's something of a problem with the Keynesian multiplier:
And if we look closer at this, and we find that the relationship is actually only one to one, then we’ve a disproof of the central Keynesian contention. Which is that a rise in government spending (when in recession, when there’s unused assets lying around) increases GDP by more than the increase in government spending. We were certainly in recession, government spending certainly changed, but if GDP only changed by the amount of spending change then that’s a disproof, not a proof, of the central Keynesian claim.
But the myth is widespread - if you look at the work of many in the field of local and regional economics, the idea of the multiplier is absolutely central to the presumed effectiveness of the policies they propose. Now I appreciate that Worstall is making a different point (essentially the arithmetic is just arithmetic never scientific proof - the biggest problem with much of macroeconomics) but we still need to remind ourselves that the multiplier is something of a myth. It's a myth when it's observed that government spending increases GDP by the amount of government spending (i.e. there is no multiplier) and just as much a myth when it's used to justify some sort of localist quasi-protectionism or that government procurement contributes to economic growth.
My concern is that this approach to public spending results in more expensive local services (the only reason for the quasi-protectionism is that non-local supplier may be cheaper) without any real evidence - other than arithmetic - that there is any economic benefit to deliberately making prices higher. Indeed, most of the time in economics we'd rather prefer prices to be stable and not determined by the arbitrary (or protectionist) choices of government.
The same applies for the local high street. Because supermarkets are more efficient, their prices are (mostly) lower than the prices in the precious independents on the high street. If we regulate and tax so as to penalise supermarkets for being more efficient all we do is to make prices higher for the consumer. And because such price rises fall most painfully on the poorest, such regulation and taxation is highly regressive (rather like duty on booze and fags - but that's another story). All those trendy folk talking about 'resilience' and 'sustainable high streets' are, when you boil it down, calling for the prices of basic everyday goods to be higher so the greengrocer on the high street isn't undercut by the supermarket.
Thus, to return to the multiplier, any benefits that might come from money circulating more in the local community are more than absorbed by the higher prices. And this is before we consider the opportunity costs of government spending. We simply can't presume that simply spending the money has more economic impact than either lower borrowing or lower taxes (or both). As has been observed:
"From where to people find the means to purchase consumption goods, other than production?"
Even if we accept that there is some local impact, it is limited by several factors (ones that NEF ignore in their LM3 model). Since the biggest cost for most businesses is wages, we have to start by noting that around 40% of that cost go straight back to the government in tax. And, after this, other significant costs - utilities, fuel, transport - aren't retained within the local community either. If our assessment is on consumers then we should note that their biggest costs (tax, rent or mortgage, utilities and transport) aren't retained locally. What the advocates of local multipliers are arguing is that the economy will be transformed by the redirection of part of the cost of groceries - in reality this is an utterly insignificant effect even assuming inefficiencies haven't wiped out any gain.
At the heart of all this work is a keen urge for the public sector to feel it is contributing - by its very existence - to economic growth and not just on a pound for pound basis (which isn't really growth) but as a stimulus to the economy. The problem is that, between protectionism and opportunity cost, any benefits that might arise from the multiplier are lost - and this assumes there are such benefits in the first place.