## Multiplying money

The financial crisis seems to have devolved into a debate about whether stimulus packages are a good idea or not, or possibly whether debt-financed ones are.

Really, the stimulus debate seems pretty irrelevant to me — the treasury estimates put Australia’s economic growth as declining by 1.3% without the stimulus package, which barely makes a change in comparison to other countries — only moving us a couple of places down. And those other countries almost uniformly had stimulus packages of their own anyway. So if stimulus doesn’t explain most of the difference between 1% growth and 5% decline, something else must, but the question of “what?” doesn’t seem to get all that much attention.

Personally my best guess is it’s some combination of either a less unstable financial system (ie, less of a loss in down times, less of a gain in boom times) or a less affected mix of products/services in the economy (ie, we’re selling things to China who’s still buying, rather than selling to the US who isn’t), and if the government has anything to do with it, I guess less debt and waste might have made some difference; but otherwise, I’m with Treasury Secretary Ken Henry: who the heck knows?

Anyway, apart from the details of exactly where it’s spent, the debate about stimulus spending seems to be about “multipliers”, where spending a dollar one way has a larger effect on the economy than spending it a different way. Richard Posner writes a good introduction in his article How I Became Keynesian:

And here is the tricky part: the increase in income brought about by an investment is greater the higher the percentage of income that is spent rather than saved. Spending increases the incomes of the people who are on the receiving end of the spending. […] If everyone spends 90 cents of an additional dollar that he receives, then a $1 increase in a person’s income generates$9 of additional consumption ($.90 +$.81 [.9 x $.90] +$.729 [.9 x $.81], etc. =$9), all of which is income to the suppliers of consumer goods. If only 70 cents of an additional $1 in income is spent, […] the total increase in consumption as a result of the successive waves of spending is only$1.54, and so the investment that got the cycle going will have been much less productive. In the first example, the investment multiplier–the effect of investment on income–was 10. In the second example it is only 2.5. The difference is caused by the difference in the propensity to consume income rather than save it.

In essence the conclusion is that the less “thrifty” people are (the more they spend money immediately, rather than saving it for a later day), the more productive people are, which is to say people create, use and enjoy more stuff, and the happier everyone is. So transactions with larger multipliers — ie, money that will be quickly respent — are better, and transactions with lower multipliers — money that will just be sat on — are worse.

Mathematically, that’s all fair enough — if you increase the multiplier, more stuff happens and people are happier. But changing one transaction (spending millions on schools, eg) only changes one step, it doesn’t necessarily change the whole economy. And the “multiplier” for saved money isn’t really zero either — that money usually gets invested, which is to say given to someone else to spend on the basis that they’ll give you more money back later. The reason investment has a lower multiplier than consumption is that while people might spend their fortnightly pay immediately, they’re not likely to be quite as spendthrift which a large loan.

To me though, the “speed” aspect there is what’s crucial there, not the “thrift” versus “saving” dichotomy — and that in turn seems better understood via the exchane equation: MV = PQ where M is the total amount of money in circulation ($), V is the average rate at which a dollar changes hands (Hz), P is the price of value ($/value) and Q is the rate at which value is produced. That’s also pretty much a tautology: pick a period — a day, a minute, a second — that’s short enough that no one has time to spend the money they receive; then the amount of money in circulation, M is just the sum of all the transactions, V is the inverse of the period (1/day, 1/hour, 1Hz), Q’ is the number of goods that changed hands in that time (so Q=VQ’), and the average price of goods is just M/Q’, or MV/Q.

A popular corollary of that relationship is that, assuming you hold V and Q constant, then inflation (overall changes in price) is exactly proportional to changes in the money supply — so in so far as central banks can control the money supply, they can also control inflation. Of course V and Q aren’t constant — V changes if you can access your money more quickly, which is definitely happening, and Q changes if people are more or less productive which also happens.

That has some simple implications for government spending — for instance, higher velocity is better, so stimulus programs that don’t actually get money out promptly are probably not such a great idea. Likewise, it’s probably true that focussing stimulus payments on the poor is more likely to be effective because the money will get passed on quicker (whether spent or used to pay off debt). It may also mean lots of small stimulus payments are better than a small number of larger ones, since, again, they’ll be more likely to be spent quickly.

On the other hand, given the Reserve Bank largely has control over both the money supply (M) and modifies that in order to keep prices (P) stable, that only leaves two free variables for the government to try to influence — overall velocity, which isn’t really easy to manipulate, and GDP which is even harder. So outside of the Reserve Bank’s domain, as far as I can see there’s not actually a lot of either blame or credit left to be assigned. So maybe that’s why pundits and governments are focussed on the stimulus stuff, minor though that actually seems to be in the overall scheme of things.

However when you don’t ignore the Reserve Bank (or the US Fed), there’s a bit more to say… So: to be continued.