What do we do about it? Some people might note that we live in a market economy, where prices carry information. High lumber prices tell mills to boost capacity and train up more skilled labor, and builders to look for methods that use less wood. Isn't that what prices are for?
Others might say that market adjustment isn't so quick or smooth, so it might be wise to speed the process along. We could, I don't know, offer cheap credit to lumber companies looking to expand capacity? or look for regulations that would favor less wood-intensive construction?
Of course another thing we *could* do is look for other costs of construction, and jack those up too, to the point that so little building takes place that available lumber supplies are enough. Not the most obvious choice, but it would probably get wood prices down.
Now, what about if instead of lumber prices rising, it was health care costs, or college tuition, or rents in in major cities. Would jacking up the cost of home building be a good answer to those problems as well?
When you put it that way, most people would probably say no. Discouraging the construction of new housing does not seem like a sensible response to the problem of rising rents.
But - and you probably guess this is where I was going - that is exactly the solution we turn to under the current policy orthodoxy. It's the only solution to rising prices that is even considered.
When prices, of anything, begin rising more quickly, for any reason, the answer is always the same: the Fed should raise interest rates. Higher interest rates don't directly reduce inflation, tho; they reduce spending in interest-sensitive sectors, most importantly housing.
Less construction means less income of workers and business owners in that sector, which reduces their spending. Eventually the lower spending filters through to lower demand throughout the economy, bringing down prices - tho not necessarily the prices that were rising at first.
In the original example of lumber, there was a certain crude logic to this response. But for most forms of rising prices, it's bizarrely roundabout and poorly targeted. It's only accepted as reasonable, I think, because the possibility of alternatives is never even discussed.
It's one of the ironies of modern macroeconomics that a field that prides itself on "microfoundations" has a vision of inflation that only makes sense if output is a single homogenous substance, so that inflation is just a rising price of stuff in general. In reality it never is.
In a real world inflation, a rise in the price index means a rise in the prices of some things in particular. A change in inflation is always also a change in relative prices. You can't have one theory and policy for relative prices and a whole different one for the price level.
(The arbitrary separation and inconsistency between theories of relative prices and theories of the price level is, incidentally, one of the main defects of the orthodox economics of his time that Keynes pointed to as a motivation for writing The General Theory.)
It gets worse when we recall that the link from interest rates to the price level is supposed to operate via wages. Now we are not only assuming a single homogenous output, but that all wage changes are passed through one for one to prices.
One hopes that by the time we next have to deal with a serious inflation, we will have at least considered some other responses to it beside "have the Fed hit the housing market on the head until it falls down."
Altho it must be admitted, not every alternative would be an improvement. https://twitter.com/Econ_Marshall/status/1391821572999028738?s=20
So what are the better alternatives? Four broad categories:

1. Do nothing, because inflation is likely transitory, due to bottlenecks that will be resolved thru normal market adjustments, and temporarily higher inflation is ok or positively desirable.
2. Do nothing, because higher inflation, while costly, is less costly than the effects of higher interest rates - not only lower income across the board, but a fall in relative income for interest-sensitive sectors and inelastic-supply factors, especially labor.
Deciding whether 2 is reasonable or not would require a better worked out account of the costs of inflation than anyone currently seems to have. But in its absence, I do not think "any amount of inflation over 2% is infinitely costly" is a reasonable first approximation. Do you?
Then we have 3. Focus on supply constraints that are driving up prices in whatever areas they are rising. Specifics will depend on what areas those are, but in general will call for easier credit rather than tighter.
4. (oops, there will be five total). Directly limit price increases. This has become verboten in polite company and I expect to hear I have the blood of 100,000 starving Ukrainian kulaks on my hands for even mentioning it. But, maybe?
By definition, the prices that rise fastest in a context of overall rising demand are those of things in most inelastic supply. But precisely because supply is inelastic, price controls will not impose the costs we would usually expect them to have.
If inflation takes, say, the form of rapidly rising rents in major cities, rent control would be one way of limiting it. Won't that reduce new housing supply? But the fact that rents are rising so fast is itself a sign that supply is already fixed, so controls can't do much harm.
Conversely, if you think that rising rents will eventually translate into more housing production if we give markets time to work, then to extent that rents are driving inflation that's an argument *against* raising rates to tamp down demand, i.e. for option 1.
Landlords might not like rent control. But the conventional approach, which deals with rising rents by making renters too poor to afford them, does not make renters *or* landlords better off. (This is a literal description of how present-day monetary policy works.)
Finally there's 5. Yes, reduce demand, but through channels other than an across-the-board increase in interest rates. There are several variations here. Closest to current practice is to limit new lending, but via quantity rather than price.
This would probably still hit housing hardest. But the big advantage of lending constraints over interest rate hikes is that they don't also raise debt-service burdens across the economy, for the public sector as well as the private sector.
If we move away from conventional policy that controls inflation via a single overnight interest rate, I think effect on debt service will be big reason why. Some people have noticed this and think the alternative is uncontrolled inflation, but my point is there are other tools.
5b is across the board income reduction outside of the credit system. Consumption taxes are the obvious tool here, and were used for exactly this purpose by US and UK during World War II. Bad distributional effects, obvs, but at least impact is broader than with interest hikes.
If we had something like Fed accounts they could also be used for this purpose. I suspect this would give more fine-grained control over demand than rate hikes, which in practice don't seem to do much until they're high enough to tip economy into recession.
5c is policies to reduce demand specifically in sectors suffering from price increases. Like directly dealing with supply constraints, will be opposed on grounds that it distorts markets. But conventional policy does too, favoring sectors are less interest sensitive.
As @TheStalwart points out, you could reasonably say that the reason lumber prices are so high is not that demand is too high now, but that it was too low a decade ago, with a lasting effect on the industry's capacity. https://www.bloomberg.com/news/articles/2021-05-10/every-discussion-of-the-economy-keeps-coming-back-to-the-same-keynes-quote?sref=P8BMJPMy
If we treat the price increases that accompany any acceleration of demand as a crisis that has to be met with interest rate hikes until we are poor enough to buy no more than the economy can currently produce, we'll never see the rising capacity that could have met that demand.
@M_C_Klein made similar point recently, that lumber and chip shortages are both result of diminished capacity following long period of weak demand. Conclusion is the same: rising prices aren't argument for cutting the boom off, but for keeping it going. https://www.barrons.com/articles/the-lumber-and-chip-shortages-have-the-same-root-cause-underinvestment-51619540757
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