Bicycle Disequilibrium Theory

Suppose you need a bicycle to get to work. Suppose bicycles are a common property resource, because bike locks don't work. Every night the workers deposit their bicycles in the bike bank, and in the morning it's first come first served. And suppose that sometimes there aren't enough bicycles to go around. So sometimes the level of employment is determined by the number of bicycles, and not by all the usual stuff.

Any individual can always get a bicycle in the morning, simply by getting up early enough. But in aggregate they can't. Fallacy of composition. A theory of when workers wake up might be interesting, and useful for microeconomists wanting to understand the distribution of employment, but it won't help us understand what determines the aggregate level of employment.

Bicycle disequilibrium theory helps us understand what determines the level of employment and output. It also helps us understand other puzzling phenomena, like why workers sometimes wake up and go to work so ridiculously early.

Making the quantity of bicycles endogenous does not invalidate the theory. It just makes it more complicated, because a very simple supply function gets replaced with a more complicated supply function. The level of employment will sometimes be determined by the parameters of that more complicated bicycle supply function, just like in the simple case where the supply function has only one parameter.

Does bicycle disequilibrium theory tell us exactly how many bicycles the government should produce? No. That will depend on lots of things, like how the demand for bicycles varies over time, and the cost of having unused bicycles. It does not tell us what the best bicycle supply function would be. You need a lot more information to figure that out. But I would still call it a useful theory, if it helps us understand the world, and think more clearly about why the bicycle supply function matters, and the costs and benefits of changing that supply function.

Paradoxically, the bicycle disequilibrium theory would be at its most useful, empirically, if the government had a really stupid bicycle supply function. Like tossing a coin to decide how many bicycles to supply. The coin toss would predict employment. If the government made the supply of bicycles depend on things the government thought might affect the supply and demand for workers, and how many bicycles were needed, it would be much harder to test the theory, even if the government's model were wrong. You can't identify bicycle shocks because you can't distinguish them from regular labour supply and demand shocks.

This post is my response to Scott Sumner's post explaining why he thinks "monetary disequilibrium" is not a useful concept. My bicycle metaphor is a close cousin to Scott's own musical chairs metaphor, except that any individual can always get a chair by choosing to get up a bit earlier. Internecine wars are always the best. But I agree with Scott that it is not at all obvious how one would measure empirically the shortage of bicycles. Perhaps the workers got up earlier because it was a fine sunny morning.

I think there may be some times and places in the real world where many workers do in fact use a bicycle to get to work, so bicycle disequilibrium theory may in fact have some limited applicability in the real world. But the use of money is more common.

Comments

[George Selgin]

Very good, Nick. Suppose, to extend the analogy, we allow that sometimes workers decide to keep bicycles overnight, and perhaps longer, instead of returning them to the bike bank. And suppose we call the number of bicycles (or workers) reporting to work every morning "NBP" (for Nominal Bicycle Product). If B is the number of bicycles then V = NBP/B is bicycle velocity. It seems to me a small step to conclude that a sensible supply function would allow M to adjust at least enough to keep NBP stable. Of course that may not be quite adequate: as Scott's own analogy suggests, there may be growth in the number of workers etc., warranting changes in B independent of V. But one can in principle work out a B supply f'n that takes account of these issues as well.. Indeed, that seems to me just what Scott and other NGDP-stability proponents have at least implicitly endeavored to do. Whether one chooses to refer to a state in which B- (or M) supply fails to adhere to such an ideal "monetary disequilibrium" is perhaps ultimately a matter of semantics. But It seems to me that the notion of monetary disequilibrium, or something equivalent, whatever one chooses to call it, goes hand-in-hand w/ any attempt to argue for an ideal or optimal money-supply pattern.

[Market Fiscalist]

Suppose there were competing theories to explain the link between bicycles and employment.
- You get unemployment when the demand for bicycles for non-work use increases
- You get unemployment when the demand for workers increases faster than the supply of bicycles

And different branches of each theory had different policy suggestions
- Vary the bicycle supply to stabilize the wage level
- Vary the bicycle supply to stabilize a worker-shortage index based on surveying employers.

As both theories and their recommended polices are based on the assumption that there is an optimal level of bicycle supply they may be grouped together as bicycle disequilibrium theories. However one can see why one might still conclude that bicycle disequilibrium theory is not particularly useful for anything beyond grouping disparate theories.

As George Selgin says - its probably mostly semantics.

[Nick Rowe]

George: thanks!. I think I agree with everything you say there.

[Henry Rech]

Nick,

You have described a vertical supply and demand curve for bicycles (heaven knows what's on the vertical scale). There is permanent disequilibrium and bicycle usage is given by supply. There is no means of adjustment to bring supply into equality with demand. Rationing is effected by first come first served. So how is this like the market for money?

Or have I missed the point as usual with your analogies?

[Nick Rowe]

Henry: you haven't really missed the point. But you are maybe pushing the analogy farther than it can go.

Once you add in the costs of getting up earlier than everyone else to grab a bike, the demand curve for bikes is sloped, so you could say the wake up time adjusts to equilibrate the demand and supply of bikes. Or you could say that employment adjusts to equilibrate the demand and supply of bikes (you don't need a bike if you choose not to work because you don't like getting up at 2.00am to get a bike). But none of this affects the level of employment.

In the long run it's different, because the price level might adjust to equilibrate the demand and supply of money, and that can't happen with bikes, in my example. But I'm thinking short run sticky prices anyway.

[Scott Sumner]

Nick, Thanks for this post. I'm going to have to think about this a bit more--particularly your analogy. But my initial reaction is there are two ways of thinking about this sort of issue:

Monetary disequilibrium causes labor market instability.

Monetary instability causes labor market disequilibrium.

Does it make any difference? Perhaps not, as you and I (and George Selgin) have similar views on many of the implications of monetary economics.

As I said in my post, however, I worry that the monetary disequilibrium perspective might lull people into thinking there was a quick fix for the problem; that it did not require hard thinking. Think of how "removing price controls on gasoline" really was a quick fix for the gasoline market disequilibrium in 1981. But if monetary disequilibrium shows up (and is identified) by there being more or less disequilibrium in lots of goods, services, assets, and labor markets, then there is no obvious clearcut state of "monetary equilibrium". One will always be involved in tradeoffs. What's best for the labor market might not be identical to what's best for product markets where firms are monopolistic competitors. That's why I prefer the formulation that involves monetary instability leading to nominal aggregate shocks which leads to labor market disequilibrium.

But again, perhaps this is all just semantics. And I do need to take account of the fact that almost all the monetary economists I respect the most disagree with me on this.

[Nick Rowe]

Thanks Scott.
"But my initial reaction is there are two ways of thinking about this sort of issue:

Monetary disequilibrium causes labor market instability.

Monetary instability causes labor market disequilibrium."

Hmm. I will have to think about that. Third option: monetary disequilibrium causes disequilibrium in labour and/or other markets.

"As I said in my post, however, I worry that the monetary disequilibrium perspective might lull people into thinking there was a quick fix for the problem; that it did not require hard thinking."

Fair. We agree that conclusion would be wrong.

Not sure how much is semantics, and how much methodological, what counts as a "useful" theory.

[Pete Bias]

Hi Nick,

Too partial equilibriumy for me.
Given its functions, money disequilibrium distorts everything, including the money market finding its own equilibrium. All markets have to practically start over to find proper pricing and outputs with only partial benefit of using the relative values they had established before. Now the markets don't know how to easily respond to the disequilibria. Reals and nominals are intertwined. And all simultaneously. No wonder it takes years to recover from financial shocks.

Don't get in the way of a fluttering veil of bicycles.

Pete

[George Selgin]

Scott says, "I worry that the monetary disequilibrium perspective might lull people into thinking there was a quick fix for the problem." Perhaps. But I worry more that the perspective claiming that there's no such thing as monetary disequilibrium might lull people into thinking that there's no problem in need of a solution!

That was precisely Leland Yeager's concern. His essay on "The Significance of Monetary Disequilibrium" and others defending the notion of monetary disequilibrium were, let's recall, mainly directed against New Classical and ("old-fashioned"0 Keynesian theorists. The former group, let's recall, appealed to what Yeager called "equilibrium always" thinking to deny that business cycles had anything to do with monetary shocks or monetary policy errors. The second embraced it implicitly in treating the interest rate as the "price" of money, and in suggesting that monetary policy had no bearing on the price level or inflation.

All thing considered, I think the idea that there can be such a thing as "monetary disequilibrium" is a lot safer than its opposite, which is only safe in the right hands (like Scott's!).

[Nick Rowe]

Pete: fair point. Every market is a "money market". Bicycles can't capture that.

[Frances Woolley]

Nick, extending/modifying George's point (and because I'm taking your metaphor super-literally) what some percentage of people use bikes for one way journeys, and it's costly to retrieve them? E.g. ride the bike to work in the morning, but don't ride the bike back to the bike bank in the afternoon.

NYC has a dockless bike share program. It charges negative prices on some routes - i.e. if you pick up a bike at a time/place where there are bike surpluses (the World Trade Center at 9 a.m. on a weekday) and take it to a place where there are bike deficits (Williamsburg at 9 a.m. on a weekday) you get a positive credit on your bike share account. (I have heard of one enterprising Canadian living in NYC - no relation - who works out on the weekends by cycling bikes from surplus to deficit locations and then walking/jogging back. He's now using the bike share system for free).

The other solution to the one way journey problem is to have the bike provider drive around with a truck and move bikes from one location to another.

Are either of these useful in extending your analogy?

[Scott Sumner]

Nick, When there's a 100 to 1 Mexican currency reform, the price level immediately falls by 99%. If nominal wages were sticky, this would immediately cause a depression. But currency reforms are the one time that nominal wages are flexible, and respond immediately to the monetary shock. No excess unemployment.

Now how can all this be explained in the bicycle analogy? In my view, the key macro problem is not a shortage of money, it's a shortage of money combined with sticky wages and prices. In the bicycle example, is there a way where wage flexibility would prevent a sudden bicycle shortage from resulting in less employment? If not, is the analogy missing something important?

[Henry Rech]

" If not, is the analogy missing something important?"

The analogy is missing a price based means of adjustment. To some extent, as Nick has mentioned, the costs of getting up earlier to get bikes is the defacto adjustment mechanism. The earlier you get up, the less sleep you have. The less sleep you have the worse you perform. Or you can go to bed earlier but still miss out in recreation which again has performance effects. Rather than the utility of the wage being the adjustment factor, the disutility of earlier rising is the adjustment mechanism.

I would forget the analogy - they are useful to a point but eventually become counterproductive as more is demanded of them.

[Nick Rowe]

Frances: that's probably pushing the bike metaphore a bit further than it wants to go. But I think I see your point. It reminds me of my old post about the circular flow of money; the slowest car determines the speed of all cars on the Wicksellian roundabout. https://worthwhile.typepad.com/worthwhile_canadian_initi/2018/08/the-1-vs-3-model-of-recessions-vs-recoveries.html

Scott: yes, it can't. Because it's the real, not the nominal stock of bicycles, that's fixed. But I think that's also true of musical chairs. Think it was Swift who said "Metaphors run on 3 legs" (which is itself a metaphor).