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Aside: "suppose money is both the medium of exchange and medium of account" seems like a strange thing to say.

Sorry -- I posted that prematurely.

Maybe I'm missing something simple, but I don't understand what money is fixed "to" in your hypothetical. You say it is fixed to one; one what?

Do rent controls cause recession?


Bill: I thought/hoped you would answer that. And it's not just they don't, but that they can't? And it's because money is the medium of exchange, and apartments aren't? There's an excess demand for apartments, but the markets for each of the other n-2 non-money goods clears.

Let's see if there are any Keynesians (or that subset of Keynesians who downplay the role of money) who answer differently.

dlr: with n goods, there are only n-1 relative prices. So there's a convention to set the price of one good, the numeraire, at 1, so that the prices of the n-1 other goods are expressed relative to the numeraire.

Okay, thank you. I thought you were introducing some kind of price level constraint.

My answers is yes, there could be clearing for all other n-2 goods. Excess rent demanders would give up and demand something else, and that something else would include an exchange of money (1) and n-x good or service. They wouldn't have the option of merely reducing spending to procure more rental space, as in the case of money. Although there would be a permanent excess supply of everything else in relation to rental space, prices would otherwise adjust and there would not be an excess supply of everything else in relation to the medium of exchange or unit of account. This doesn't answer whether there would be a recession, but there should not be a monetary recession caused by a fall in nominal spending amid imperfect price flexibility. There could be a recession (decline in real GDP) for other reasons, such as if price controls and rental shelter were together important enough to constitute a meaningful productive capacity shock, but that's not what you're getting at.

I haven't figured out how you're going to spring the unit of account versus medium of exchange distinction into this.

Suppose we have rent controls and thus a 'waiting-list' of demand. Do people idling hoard cash waiting out their turn? No. They expand their remaining income in other ways consistent with their indifference curves. So I have trouble with this illustration still. Something is missing from your narrative.

Nick, you write: "So if there is an excess demand for rental apartments, there must be an equal excess supply of...."

I do not think this is a statement of Walras's law. You've interchanged demand and supply going from the antecedent to the consequent. Walras states that if there is not an excess (positive) demand of any good, there is not an excess (negative) demand of any good either (and vice-versa).

Did Walras also believe that if there is an excess positive demand of and good that there is also an excess negative demand? I think this is a different statement than Walras made, but lets play it forward:

Suppose for instance that were in fact an excess demand for rentals, it seems to me that if money is hoarded for those unrealized rentals then indeed there is a negative excess demand for other goods and a general recession. But this scenario is unphysical for the reason I outlined above.

I think you are basically right that recessions arise from 'excess constraints' on relative prices--but in particular excess constraints that are inconsistent. i.e., a preference of cash balances over all quantities offered by others and a preference of all quantities offered by you over cash.

Thought problem: can a barter economy have a 'recession' if all agents price pairs of goods inconsistently (i.e., such that one defector could profit from arbitrage trade)? I think yes.

"Suppose money is both medium of exchange and medium of account; its price is fixed at 1. Suppose the prices of all other goods are perfectly flexible, with one exception. Apartment rents are controlled by law. And the authorities set the rent below the market equilibrium. So the price of rental apartments is just as sticky as the price of money."

One what? One hour of rental of a studio apartment? That would make the price of rental apartments (in terms of money) just as sticky as the price of money (in terms of rental). Otherwise, how do you get that one is as sticky as the other?

Ah! Are you assuming that, during the period of time in question, the authorities do not reset rental prices?

It is not money's role as a medium of exchange that is the key, it is money's role as a store of value that is the key. Recessions come about because of intertemporal allocation of demand. If everybody wants to earn today, but consume tomorrow, you have a problem.

P.S. Actually of course in the current circumstances, it is more that everybody wanted to consume yesterday but earn today.


Yes, I realize that the point is to show why price controls on housing (and the resulting shortage) cannot cause a general glut of everything else, while a shortage of the medium of account, with its fixed by definition price, can cause a general glut.

In barter, I think not, and I sent you an email with some puzzles about that situation.

With a medium of account defined in terms of its own units and a separate fiat currency defined in its own units, the supply and demand for the medium of account generates monetary disequilibrium.

And with a credit money, it generates monetary disequilibrium in a more obvious way. That, I think, is the situation with a gold standard where the money is all redeemable paper currency and deposits.

dlr: your thinking is the same as mine.

On your very last point ("I haven't figured out how you're going to spring the unit of account versus medium of exchange distinction into this.") my thinking was that a good being a medium of account has macro implications because its price is fixed, but by fixing rents, apartments should be on a par with money, if the fixed price of a medium of account were all that matters.

Jon: I'm not sure whether or not the excess demand for apartments would affect the demand for money. But I'm not sure it matters, if all other goods' prices are flexible. If people do hoard cash, for instance, because they want to immediately place a downpayment if they spot an empty apartment, the only effect would be that other goods' prices need to fall further to increase the real money supply.

I always understood Walras Law as saying the sum of the excess demands = 0. So the statement "if n-1 excess demands are 0, the nth must be 0 too" was just a corollary.

I would say there is an excess supply of money matching that excess demand for apartments in the apartment market. But there is zero excess demand/supply for money in all the other n-2 markets. There is no such thing as *the* excess demand for money. There are n-1 excess demands for money, matching the n-1 markets in a monetary exchange economy. That's what Walras' Law misses.

"Thought problem: can a barter economy have a 'recession' if all agents price pairs of goods inconsistently (i.e., such that one defector could profit from arbitrage trade)? I think yes." I have tried to think about that. But it's so damn hard when you have so many markets, with all sorts of indirect barter allowed. I'm not sure about "inconsistent" prices, but with consistent (no arbitrage) prices, fixed arbitrarily, a hypothetical frictionless barter economy could nearly always do better than a monetary exchange economy. Unemployed workers could barter directly with sales-constrained firms, for example.

Min: setting the price of money at one is a weird theorist's construct. What indeed are the units? Better just to say that all goods are priced in terms of money, and the price of apartments in terms of money is fixed.

reason: what about land? For apartments, substitute land. And assume the price of land is fixed by law, so there's an excess demand for land. Can that cause a recession, if all other prices are flexible? I say no.

Bill: I haven't got your email yet. NickunderscoreRoweatCarletondotca. I look forward to seeing it.

Nick, My first thought was "what about non-price competition for apartments?" Does that provide a sort of equilibrium? If there is queuing, then a sort of equilibrium is reached. If there is no queuing (say apartments are allocated based on the last two digits of social security numbers) then there would seem to be no business cycle problem. Money not spent on apartments is spent on other goods.

My second thought is an empirical one. We normally assume that sectoral shocks (at least in the US) are rarely strong enough to create a recession. So if rent controls cause excess demand for apartments and excess supply of all other goods, it could theoretically cause lower output without creating a full-blown recession. I say this because our intuition is that there would be no recession, but does our intuition come from theory, or an instinctive belief that the shock simply wouldn't be big enough?

My last comment is that if there are rent controls, and the demand for apartments changes, you don't see the real price of apartments change. Instead the queue gets shorter or longer. But money is traded in a free market, so if the demand for money changes its real value does change, which means all other prices must change. I suppose this means I don't look at recessions from an excess supply perspective, but rather from a sticky-wage perspective. I.e. prices getting out of synch because the value of money needed to change and other prices are often sticky.

I have no idea if any of this makes any sense, just hoping for one out of three.

Scott: I agree. That's what I was trying to get at but failed.

If people don't commit to queuing, then the purchasing goes elsewhere and drives up prices of other goods.

Hi Scott: I think you get your one out of three!

Your first thought: when there is excess demand, there is always some sort of rationing mechanism, be it queues or lotteries, or whatever. And some people realise they won't be able to buy any (or everyone realises they won't be able to buy as much as they want). They then revise their decisions about how much to buy and sell of other goods, taking those constraints into account. So the notional excess supply of other goods disappears. But they still want those apartments, even if they know they are at the back of the queue, or lost the lottery. What you are doing here is fleshing out my own analysis, by making the rationing mechanism explicit.

Your third thought: "But money is traded in a free market". Nope. In my example, money is traded in n-2 free markets and 1 non-free market (the market for apartments). There is no "money market"; or rather, every market is a money market, in a monetary exchange economy.

Your second thought. This is what gave me pause. Suppose for example I replaced "rent controls on apartments" with "minimum wage laws". Minimum wage laws, that were high enough, and binding enough, could definitely create a recession. So maybe I am slipping in some hidden empirical judgments into a theoretical analysis. (And of course rent controls might create a mini-recession in the apartment construction industry, which is part of what dlr was saying above.)

But: *minimum* wage laws could create an excess *supply* of labour; *maximum* rent laws could create an excess *demand* for apartments. If we invoke Walras' Law, there should be an excess demand for other goods when there's an excess supply of labour. Now if money wages were fixed, and all other prices were flexible in terms of money as the medium of account and exchange, would there really be an excess demand for other goods? I say "no". In the labour market, there's an excess supply of labour matched by an excess demand for money (but the unemployed workers don't want to *hold* that money of course, they want to spend it, or most of it). In all other n-2 markets there is zero excess demand for the good or for money.

Again; the key point is that with n goods, including money, there are n-1 excess demands/supplies for money, one for each market. Walras' Law assumes there's only 1. There's no such thing as *the* excess demand/supply for money.

Nick: "with consistent prices, fixed arbitrarily, a hypothetical frictionless barter economy could nearly always do better than a monetary exchange economy"

This is the heart of this whole debate: you aren't comparing like with like. Certainly a frictionless barter economy could do better than a frictional monetary economy. But surely "frictionless" is incompatible with "fixed prices"?

In reality of course, no barter economy could possibly be frictionless. Money is the main technology that lets us immensely reduce economic friction; it doesn't do so perfectly (because of sticky prices, illiquid futures markets and their joint corollary, the desire to hoard money). Therefore we still have recessions.

In a frictional barter economy output would be much lower than today (I'm not sure if you'd call this a recession, but it may as well be one). In this scenario there is no money, so it has no special role.

Our imperfect monetary economy goes a long way to removing frictions, so output is higher and increases most of the time, but recessions can still happen. Thus the effect of money is not to cause recessions and reduce economic growth, but to increase it.

In an ideal frictionless economy, whether barter or monetary, everything would clear and recessions would not happen. In this case the role of money is no longer special.

So yes, we can have recessions in a monetary economy. But in a real non-monetary economy, we would not avoid recessions. Instead, we would be stuck in (effectively) a permanent recession.

Have I understood your point correctly, or do you think that in a frictionless monetary economy we would still get recessions, while in a frictionless barter economy we would not? I know your hypothesis is an automated auctioneer which clears all bartered goods instantly, but if you are considering this case, surely you should allow for some equivalent in the monetary economy?

But they still want those apartments, even if they know they are at the back of the queue, or lost the lottery.
I don't think this is meaningful. Again, the concept of an indifference curve applies. This is true in all supply/demand situations. A price-control is really a constraint on the shape of the supply curve. Given that supply curve per-se, everything else that we might say about a free market applies--which is to say that we don't claim that there is 'excess demand'. Rather we claim that the markets reach an equilibrium consistent with the supply and demand schedules of all goods.

However, counterfactually, we can claim that a price control is inefficient. i.e., there are unrealized gains from trade based on the true supply/demand schedules (preferences). This is really not the subject of 'recessions' at all. But rather simply that at best the price-control does nothing and at worst it leaves unrealized gains from trade.

Again; the key point is that with n goods, including money, there are n-1 excess demands/supplies for money, one for each market. Walras' Law assumes there's only 1. There's no such thing as *the* excess demand/supply for money.

I finally basically agree with your claim, but I really think you should rephrase it. In particular, in a recessionless economy, there is only '1' constraint. This is because all preferences are consistent and hence the additional supports are not independent--they collapse to Walras's one. What you've been striving at, and what I've been suggesting in other words is that a recession arises from inconsistent supports. Once the supports are inconsistent, they must necessarily not be independent and, so, do not collapse into 1.

As I mentioned previously, a barter economy can experience a recession for the same reason. It isn't fundamentally different.

What's important, as Scott suggests, are stick-prices which ultimately create the inconsistencies.

Nick Rowe: "Min: setting the price of money at one is a weird theorist's construct. What indeed are the units? Better just to say that all goods are priced in terms of money, and the price of apartments in terms of money is fixed."

Many thanks. :)

BTW, if you had said, "normalize", I would have gotten it. :)

Nick, Here is what I am wondering. You spoke of n-2 free markets. Let's suppose n is very large, so that money is traded in an approximately free market. In other words suppose almost all prices do freely adjust. All except apartments. Then it seems to me that we are back to the debate about whether recessions are caused by sticky wages (i.e. real wage movements as prices change unexpectedly) or by the excess supply of goods. So I agree that if your transmission mechanism is correct, my point 3 about money trading in a relatively free market is misleading. But what if my transmission mechanism is correct? Assume it's all about real wage changes. Then I think my third point might have some validity. Does that make sense?

I sort of agree with you.
But first I want to distinguish 2 sorts of frictions. There are fixed prices, and there are transactions costs.

In a zero transactions cost world, we wouldn't use money anyway.

I am indeed comparing a zero transactions cost monetary economy with a zero transactions cost barter economy. So when I say "a barter economy does better than a monetary economy when prices are fixed", I really mean " the transactions costs that prevent us using barter mean we do worse than if there were zero transactions costs on barter". Really, I am criticising people who implicitly assume zero transactions costs, when they implicitly assume barter.

Of course, there are still transactions costs in a monetary economy. But the assumption that transactions costs are zero for monetary exchange and infinite for barter seems better than assuming zero transactions costs for barter.

Min: yes, I should have said "normalise". There's a distinction between what good the economist uses to normalise, and what good economic agents in the real world use to normalise. If prices are all flexible, and we have enough calculators, it doesn't matter which good anyone uses. But if some prices are fixed, it does matter. Because they are fixed relative to the normalised good.

Scott: I'm not sure. This is how my mind thinks about it:

Suppose some fraction f of the n-1 other goods have fixed prices. As f goes to 1, we get a pure monetary disequilibrium. As f goes to zero, we get a pure relative price disequilibrium. It also seems to matter if the goods with fixed prices are newly-produced (which includes labour services) or if they are in inelastic supply (land, used furniture). If we fix the prices of newly-produced goods too high, and f is large, we get excess supply of newly-produced goods and a recession at the aggregate level.

If we fix the price of non-produced goods too high, we would get an excess supply of those goods, but no recession.

But some people (Keynes, and some Keynesians) argue that if we fix the price of non-produced goods too LOW, we get an excess demand for those goods, and an excess supply of newly-produced goods, and a recession. This seems to me to be wrong.

I actually dreamed about this post and thread last night.

Unit of account, medium of exchange, store of value.

For the "fixed" rent control price to be meaningful, it has to be fixed as a relative price, not just a nominal price, doesn't it?

If the Walrasian auctioneer supplies "money" exclusively as a unit of account -- imagine the auctioneer beginning tatonnement with an arbitrary assignment of credits, based on a first guess at prices for what is being offered -- then the nominal rent control price becomes the numeraire, and equilibrium can be achieved in n-1 markets, including the controlled rentals.

If the Walrasian auctioneer treats money as a medium of exchange, with a fixed stock, then the nominal rent control price, is fixed in relative terms, by the fixing of the stock of money. The unit of account is constrained in nominal terms to be such that the total stock of money, measured in nominal units, is just sufficient to clear all markets.

Constraining the rental price to some nominal amount is equivalent to constraining it to some fraction of the total stock of money, and, therefore, fixing it relative to the prices of all other goods.

Notice, in this second case, as in the first, money is not a store-of-value. No one has any money before the auction begins, and no one has any money after the auction has ended. Or, at least, no one wants to have any money after the auction has ended -- since money has no intrinsic value.

It seems to me, that in this second case, with a fixed "stock" of money constraining the units of account, that general equilibrium unravels completely, and the auction must fail. It cannot be that people wanting apartments at the fixed rent-control price, and failing to be assigned their desired good, simply spend the money elsewhere. If they try to spend their unused money credits on other goods, the prices of those other goods must be affected.

If one market -- the market for rent-controlled apartments -- is out of equilibrium -- then, through a process of recursive unraveling as the excess of unwanted money rolls through the auction, every market must be put into disequilibrium.

If money has a store-of-value function -- if people have money as well as goods at the beginning of the auction and may want money as well as goods at the end of the auction -- and the auctioneer must make use of units of account that correspond to units of that money, then we have some possibility for disequilibrium in one goods market only, offset by a disequilibrium in the nth market, the money market, where "money market" is an exchange of promises for money.

Of course, if there can be an exchange of money for promises of money, then there can be an exchange of oranges for promises of apples, and . . . I woke from my nightmare.

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