A Multiplier of One: Mission Accomplished?

Karl Smith very clearly explains what stimulative multipliers really mean:

A multiplier of zero implies complete crowding out of the private sector by government. The government spends more and the private sector offsets this exactly by spending less.

A multiplier between zero and one means that there is some crowding out by the private sector. The government spends more, the private sector spends less but not enough to offset government spending.

A multiplier of 1 would suggest no crowding out. The government spends more and private spending is unaffected on net.

A multiplier above one would suggest crowding-in. The government spends more and this increases private as well as public spending.

He then takes issue with Russ Roberts’ claim that a multiplier of 1 means there is no stimulative effect:

As for the total cost, it depends in large part on whether you place any value on those expenditures. So if we are buying roads and schools, you may not believe that are as useful as private construction spending might be, but are they 100% useless? If they are even only 50% useless then you have come out ahead.

Being unschooled in these matters my question is this: If the roads and schools were useful wouldn’t they increase (multiply) private spending? That is, isn’t the usefulness of the commodities produced by government spending already “baked in” to the multiplier? The fact that the multiplier is 1 or less seems like evidence that on net extra roads don’t create extra private production or investment. I’d like a better definition of “useful” from Prof. Smith. Is he arguing that the roads and schools stimulate the economy by creating something else? Subjective well-being perhaps? I get that they create jobs but he also seems to be arguing that new roads and schools have value even when they don’t increase overall production, when all they do is transfer money from taxpayer to unemployed worker, without further benefit (or cost). This is the digging and filling holes examples that Keynesians often stubbornly subscribe to. Why, after all, do we want to invest in infrastructure if we are fairly certain it won’t increase growth and productivity?

Smith goes on to sweeten the deal. The government won’t even have to pay the bonds back:

…note that the government does not ever have to pay the bonds back and in general does not even have to tax the population in order to service them.

I don’t really care what explanation you follow that with it is patently false if you stop and think about what you’re saying. There’s no such thing as a free lunch. I’m not sure I understand how Smith explains this fantasy (I think by presupposing a recovery) but as Bob Murphy points out in the comments: “In principle then, a government could eliminate all taxes and slash its budget, but still maintain a constant level of spending…that it never has to finance in any way?” Call this the Greek Gambit it is true until it is horribly, disastrously false.

There is a cost to investment in roads and schools. They consume real resources not just idle labor resources. They bid up the price or or reduce the quantity of those resources. This is bad for the private sector even if the net effect isn’t negative on private production because it perturbs the valuation of those resources in ways that mislead everyone. When the government bids up house prices or the price of education it might seem like a relatively way to advantage obviously beneficial industries. But lost in the fray are real demand price signals from the private sector, both for resources and laborers. Resources that go to schools and roads are necessarily diverted from somewhere else. Workers too, train and gain experience in the wrong lines of work. Resources and workers should go to their first best use and discovering what that is is an extraordinarily difficult task. Stimulus spending only makes that job harder.


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