Daylight Savings Time and the non-neutrality of money

I've heard stories about people who set their watches 10 minutes fast, so they won't be late for meetings. It's hard to understand how it could work. Do they forget they set their watches 10 minutes fast? Because if they remember, they should be able to figure out they've got an extra 10 minutes, so there's still plenty of time to grab a quick coffee before the meeting starts. If it works, they must be fooling themselves.

This weekend the government will tell us all to put our watches back one hour. They want us all to do everything one hour later. It's hard to understand how it will work. Do they think we will all forget we've set our watches one hour slow? What's more, they can't even force us to change our watches.

But I know it will work. We will (almost) all set our watches one hour slow, and we will (almost) all start doing (almost) everything one hour later, by the sun, compared to what we would have done if we hadn't changed our watches. But why?

A purely nominal change (whether we say than solar noon is called "12.00" or "13.00") will have a big real effect. Even though we all know that it's just a nominal change. Nobody is fooled by the government changing our watches without us seeing them do it. Nobody suffers from "time illusion". We know it's not really earlier. In fact, it's the people who don't hear that the time has changed who are likely to still get up at the same real time, by the sun.

And the real effects of this nominal change will last, at least until the Spring, when the government will tell us to change our watches forward again.

I'm not the first economist who has drawn the analogy between Daylight Savings Time and money. Milton Friedman used the same analogy to explain why it was easier to adjust the real exchange rate through adjusting the nominal exchange rate than through adjusting millions of nominal prices.

Milton Friedman's analogy is even more apt this time around. The US changed the date at which Daylight Savings Time would end. After some discussion, because the new US date didn't work so well for us up North, Canada decided it was more important to stay in synch with the US than to stay in synch with our own dawn and dusk. Canada and the US may not be an optimal currency area, but it's been decided that we are an optimal time area. No currency union, but we do have a time union. It's the equivalent of fixed exchange rates. When the US devalues its time, we devalue our time too.

Why does money have real effects? It's just bits of paper. It's not real. We are still stuck on David Hume's puzzle. If we double the number of bits of paper each one should be worth half as much. It should be a purely nominal change. Nothing real should change. If we switch from meauring turkeys in pounds to measuring them in kilograms, the price per unit weight should be divided by 2.2, but the same turkey should cost exactly the same in pounds or kilograms, and we should buy exactly the same number of turkeys as before.

Metrification was a nominal change that had negiligible real effects, as far as I know. Daylight Savings Time is a nominal change that has real effects. Some monetary changes, like currency reforms where we knock a couple of zeroes off the old currency and call it the new currency, are like metrification, where nothing real changes. And maybe all monetary changes are like metrification in the long run. But some monetary changes are like Daylight savings Time, and have real effects, at least in the short run.

If we understood Daylight Savings Time better, and how it works, we might understand monetary policy better.

First, let's think about the individual's choice problem. When I choose to do something depends on two things: the sun; and everyone else's chosen time. Let t be the time I choose, let T be the time everybody else chooses, and let S be the time the sun chooses. So my reaction function is t = R(T,S). Assume that dR/dT>0, dR/dS>0, and dR/dT+dR/dS=1. What this means is that if everybody else gets up one hour later, I will get up (say) 45 minutes later. And if the sun gets up one hour later, I will get up (say) 15 minutes later. But if everybody else and the sun all get up one hour later, I will get up one hour later too.

For example, t = 0.75T + 0.25S could be a simple linear reaction function.

Now, assume everyone else has the same reaction function as me. We solve for the symmetric Nash equilibrium, where t = T. The answer is T = S. Everyone follows the sun, and so I'll follow the sun too.

OK. That theory failed miserably. In equilibrium it doesn't matter what our watches say, and so Daylight Savings Time makes no difference to what we do. Which is not what happens. And that theory is the exact counterpart of the individual firm's profit maximising price-setting equation where the price an individual firm sets depends on the prices other firms set and on the money supply. We can't get non-neutrality that way.

We need some sort of discontinuity in the reaction function. If we are one minute late for the meeting, it's almost as bad as being 10 minutes late. Otherwise, if the sun gets up one hour later, and everybody arrives at the meeting one minute after they expect everyone else to arrive, the meeting starts one minute late, and then the next day two minutes late, and when everyone figues out what's happening, and extrapolates to the new Nash Equilibrium, the meeting is an hour late, just like the sun.

What sort of loss function would gives us the linear reaction function like t = 0.75T + 0.25S ? It would have to be a quadratic loss function. Each individual wishes to minimise Loss = a(t-T)^2 + b(t-S)^2. The first order condition for a minimum is dLoss/dt = 2a(t-T) + 2b(t-S) = 0. And we solve for t as t = (a/(a+b))T + (b/(a+b))S.

That loss function was smooth. The indifference curves are roughly circular (ellipsoid?). Suppose we changed the loss function to something that has a kink in it. Something like this: Loss = aABS(t-T) + b(t-S)^2 . The marginal cost of moving away from the sun starts at zero, when you are following the sun exactly, and steadily increases as you move further and further away from the sun. But the marginal cost of moving away from everyone else is a constant. It doesn't start at zero. Being even one minute late for the meeting is costly, and being two minutes late is twice as costly. So, unless everyone else is a long way away from the sun, you will want to show up exactly on time for the meeting. It's only when they hold the meeting well before dawn that you decide to sleep in, forget everybody else, and just follow the sun. The reaction function is discontinuous.

Now we are getting somewhere. If we solve for the symmetric Nash equilibrium we find there's a range of equilibria around the sun. Any time, as long as it's not too far away from the sun, is an equilibrium time to hold the meeting. Everybody shows up when they expect everybody else to show up. And if the government tells, or merely suggests, that we all put our watches back one hour, and if everyone expects that everyone else will follow the government's suggestion, we all go to the meeting one hour later by the sun. Because everyone hears the government's suggestion, and knows that everyone else hears it too, and so on, it acts as a focal point to coordinate our expectations about when meetings will take place. But if the government suggests we all set our watches back two hours, or maybe three or four, we decide to ignore it, and know that everyone else will too.

Back to monetary policy. What we need is some sort of loss function with a kink in it. So the losses to a firm that raises or lowers its price, relative to other firms' prices, are significant even if it raises or lowers its price by just a penny. The marginal costs of having the wrong relative price don't start at zero. So firms won't cut their prices unless they expect other firms to cut theirs too, even if all prices are too high relative to the sun, I mean the money supply. The losses from small deviations of price from the money supply must be second order of smalls, but losses from small deviations of price from everyone else's price must be first order of smalls.

The Beatles.

Comments

[edeast]

What is ABS? absolute value?

[Nick Rowe]

edeast: Yep. (I think that's the standard symbol, unless you type 2 vertical lines, one each side, but I can't find them on the keyboard).

[Jim Rootham]

You mean |a|? Mine's shifted \.

[edeast]

they are to right of the shift key, under the large 'enter'. shift + backslash

[Just visiting from Macleans]

In Canada, Saskatchewan doesn't switch to DST. Apparently, it's "strategic".

[edeast]

Thanks by the way. This post makes sense. But could you solve the nash equilibria? something I don't know how to do. What is too far away from the sun? when b(s-S)^2 > a|t-T|. Taking the derivative wrt t eliminates t.

[edeast]

Nevermind I think I get it. I read the focal point article. Sometimes I type before I think.
But at least I understand this one, unlike that infinite multiplier post.

[Nick Rowe]

Loss = a|(t-T)| + b(t-S)^2 Oooh Yes! Thanks Jim. I didn't see that. Funny thing is, my keyboard actually says something else on the top part of that key. I've got a typo on my keyboard!

I was actually hoping one of the mathematicians here could minimise that loss function for me, and solve for the symmetric Nash Equilibrium. I'm cr*p at math.

Let's see. I think you need that Kuhn- Tucker stuff?

Graphically, the loss from the first part is V-shaped, with T at the bottom of the V. The loss from the second part is U-shaped, with S at the bottom of the U. Add the V on top of the U, and you get a weird-shaped loss function, with a pointy bit above T. If that pointy bit can hold water, go to T. If it can't, go somewhere between S and T. That's the reaction function. Now set t=T to solve for the Nash equilibrium.

Damn. I can't solve it. But any semi-competent mathematician or economics grad student could solve it.

[edeast]

I should say this reminded me a lot of bird flight/ fish school dynamics. And I'm currently looking at swarm intelligence papers. The delta S could be the stochastic process.

[Frances Woolley]

As Just Visiting says, Saskatchewan doesn't switch, neither does the Peace River nor one spot out towards Labrador/Eastern Quebec.

I'd always figured Sask/Peace River didn't switch for a couple of reasons. One is that if you're farming you have to follow the sun (or at least follow your livestock, and they follow the sun). Also with Sask there's not an obvious coordination gain - one way they're synced with Manitoba, the other way they're synced with Alberta. Same with the Peace River - one either gets the gains of being the same time as Alberta or the same time as BC.

[Larry Willmore]

JVFM: Also, in the US Arizona does not participate in Daylight Savings Times. Like Saskatchewan, Arizona participates in a currency union, but not in a time union. I wonder why?

[Nick Rowe]

OK. The math (well, sort of).

Suppose initially T=S. That's one Nash equilibrium. Now suppose the Sun S starts to move away from the meeting T. At which point would one individual choose to miss the start of the meeting? It's where the Marginal Cost of being one second late for the meeting equals the marginal benefit of moving one second closer to the Sun. Which is where a=2b(T-S).

Therefore, any T between S+a/2b and S-a/2b is a Nash equilibrium. (I think that's right, but don't trust me).

Since Daylight Savings Time works in Canada, we know that a/2b is greater than one hour in Canada (except maybe Saskatchewan)

[Nick Rowe]

edeast: yes, it looks very much like fish dynamics. Doesn't every fish want to get just slightly ahead of the centre of the school? If so, that would explain why they keep darting one way then another. It's an unstable equilibrium path. It's just like fashions in clothes, and explains why they change with no apparent reason.

And the trouble with interest rate targeting is there's no nominal anchor, like the sun, to stabilise the system. So the price level is like a school of fish, with the Fed as the shark, trying to make them go in a straight line.

[Nick Rowe]

Hi Larry! Thanks for the nice things you said on your blog! (And it was good seeing those old photos on Arch's blog).

[edeast]

I think it's more a version of the EMH. Public flock knowledge vs private knowledge, once an individual finds something they all do. I don't know how the nominal stuff works out. I was thinking of milling about about, and an individual making a play, what determines how long followers follow before turning back. Canada, following US, cost of leaving the association, greater then leaving the Sun. Cost of leaving competitors vs cost of leaving the price level.

[edeast]

I think what some people are scared of is the swarm jumping to the price level and having a ton of inflation. The fed/Sun pushing over the non-linear cost function. But I guess sooner is better then later though.

[edeast]

Style isn't arbitrary. Achieve real results by looking good. Avant garde vs gaudy. Speculation rewarded, on the leading edge less at the tail.

[Mike Sproul]

Nick:
"Why does money have real effects? It's just bits of paper. It's not real. We are still stuck on David Hume's puzzle. If we double the number of bits of paper each one should be worth half as much."

There are lots of historical episodes where money was introduced into an economy and produced near-miraculous real effects. The playing card money introduced in Quebec in 1685 is the first episode that comes to mind. The thing is that when they doubled the number of bits of paper, they normally doubled the assets backing them, so the bits of paper held their value. But the people who had previously gotten by with barter were now able to trade using those very efficient bits of paper--hence the real effects of paper money.

[Scott Sumner]

Nick, Another great post. Would a (fixed) menu cost create the kink you need? I.e. a lump sum price adjustment cost, no matter how small the change in price.

[Nick Rowe]

Mike: I find it easier to understand why going from zero bits of paper to a positive number of bits of paper would make a real difference. Monetary exchange is much better than barter.

Here's how I would give some role to "backing". If money is expected to depreciate, people will hold lower real money balances, and that has real costs. Not just the textbook "shoe-leather", but also occasional resort to barter. Zimbabwe would be the extreme data point. The *rate of change* of the number of bits of paper matters. Non-superneutrality.

Scott. Yes. That's where the analysis would normally go. Quadratic costs of not following the sun, plus a fixed cost of change. But that model won't work for Daylight Savings Time. Costs of changing our sleep patterns over time are probably quadratic too. It's the costs of missing a meeting, or a train, that are kinked. So my hunch is that it's the same with prices too. But I never followed this post through to its conclusion. Because I don't really have one. Yet.

edeast: "I think it's more a version of the EMH. Public flock knowledge vs private knowledge, once an individual finds something they all do."

Wow! I never thought of that.

[Richard Mason]

I once had a girlfriend who set her clocks ten minutes fast so she wouldn't be late for meetings, and for a while I picked up the habit from her.

I can report that one does, in fact, sometimes forget that the clock is set ten minutes fast.

It may be relevant that one is most in danger of being late when one is under pressure, or barely awake, etc., and thus not perfectly rational.

[Gregory Magarshak]

I think it's a lot more simple than that.

Your commitments are based on the clock usually.
Most people do this independently of daylight savings time. They don't have one set of schedules for the part of the year when daylight savings time is in effect, and a slightly different set of schedules for the other part.

And therefore, during the fall, all your appointments start happening an hour later, and in the spring, they start happening an hour earlier. Simple as that.

Now, why do governments decide to do this? I am sure there is a whole host of problems, such as saving energy (again, which has to do with the business day) and when people come home, etc.

[Nick Rowe]

Gregory: "Your commitments are based on the clock usually.
Most people do this independently of daylight savings time. They don't have one set of schedules for the part of the year when daylight savings time is in effect, and a slightly different set of schedules for the other part."

But that's just assuming the conclusion. *Why* don't people have two sets of schedules?

Richard: "I can report that one does, in fact, sometimes forget that the clock is set ten minutes fast." OK. That makes sense. So you can (at least sometimes) fool yourself.

[Mike Sproul]

Nick:

It depends on how many bits of paper are required for people to conduct their business conveniently. If 500 bits of paper (valued, let's say, at 1 oz. of silver each) would be enough to prevent people from having to resort to barter, then the first 100 bits would have real effects. The next 400 bits, adequately backed by new assets, would also have real effects, without causing inflation. Any bits beyond 500 would have no real effects, but they would also not be issued in the first place, or if they were issued they would reflux to their issuer. The reason is that people would have to want the new bits badly enough to give up equal-valued assets in exchange for the new bits, and by assumption people had no need for those extra bits.

[Rick]

Time operates in a perfect market. The sun is an absolute known, as are time zones.
Money and prices are variable and unknown, market failure is guaranteed.

[Bill Barth]

Nick, I think that part of the issue is that retail and other businesses that deal with the public have opening and closing times. They don't set these to the sun (i.e. open 4 hours before local noon and close 5 hours after, or whatever). They don't work with sun time because our time keeping devices don't work on sun time (or, they certainly didn't do this historically). Recall that trains used to run on the local noon, and that this turned out to be supremely annoying (and thus we have time zones).

Once you decide that it's more convenient to approximate the local noon and fix that for broad bands of land (time zones), you've guaranteed that businesses will open at a particular fixed (w.r.t. the standard time) hour and close at a fixed time as well. Once you've done that, it's a huge hassle to change all your signage and literature and whatnot just to keep your opening time fixed with respect to the local time when switching from winter to summer time. It's considerably less of a hassle to get change your personal schedule a bit, especially if you have an alarm clock that keeps good standard time.

[Greg Ransom]

Hume solved this puzzle -- it matters who gets the new money first.

Imagine honey spread flat on a large floor.

Then imagine twice as much honey spread flat on a large floor.

In both cases you would have a very thin flat layer of honey.

Now.

Imagine thick honey pouring in one spot on the floor.

You would get a never disappearing MOUND of honey.

Flow matters.

A changing flow of money can distort interest rates and the time structure of production (people will NOT choose longer production processes which do not promise greater output).

What is so hard about any of this?

I'm continually shocked that economists are incapable of "getting" something to basic -- and so simple.

[Greg Ransom]

The solution to Hume's puzzle is called The Cantillon Effect".

A gold standard economy has places were new gold is discovered -- the new gold changes prices first where that gold flows, into local land prices, local food prices, local capital goods for gold production, and into the consumer spending od gold workers and gold mine owners.

Again, this isn't rocket science -- and Hume's science fiction thought experiment does help us think soundly about the issue -- it blocks economists from thinking at all.

[Greg Ransom]

Sorry, make that,

"this isn't rocket science -- and Hume's science fiction thought experiment doesn't help us think soundly about the issue -- it blocks economists from thinking at all."

[Declan]

I recall when the Rhinocerus Party used to advocate for switching from driving on the right to driving on the left, cars would switch in the first year, and trucks would switch in the second year.

Interesting post.

[Nick Rowe]

Bill: "Nick, I think that part of the issue is that retail and other businesses that deal with the public have opening and closing times."

Agreed. But to my mind, what matters is that businesses want to coordinate their opening and closing times. Same with trains. "Holding a meeting" is just my metaphor for these same sorts of coordination issues.

Greg: I don't get it. Patinkin, and Archibald and Lipsey, looked at Cantillon effects. All you get is a change in the distribution of income, and the macroeconomic consequences that follow if different people have different spending patters. It's no different from redistributive taxes.

[Nick Rowe]

Increase the money supply by 10% per year, but give it to the A's, and none to the B's. The A's get the seigniorage, and the B's pay the inflation tax. If the A's like apples, and the B's like bananas, the relative price of apples to bananas will be higher.

[edeast]

I was brute force graphing this, the minimum tracks T to the edge defined by the derivative, but no further. Even at extremely large values of T. It doesn't snap back to equal S. Need to vary 'a' as T becomes ridiculous for people to ignore it altogether.

[Greg Ransom]

Nick wrote:

"Greg: I don't get it. Patinkin, and Archibald and Lipsey, looked at Cantillon effects. All you get is a change in the distribution of income, and the macroeconomic consequences that follow if different people have different spending patters. It's no different from redistributive taxes."

This is only true because capital has been removed from "mainstream" macroeconomics -- who gets the money first matters, it changes savings choices, it changes investment choices, it changes leverage, it changes risk assessments, it changes interest rates, it changes the price of goods, it changes the flow of money FIRST AND FOREMOST across the time structure of production and consumption.

One of the most basic facts in ALL of economics is simply missing from the mental world of the macroeconomist -- people will not choose longer production processes which do not promise greater output, and that choice is profoundly influenced by changes in the flow of money in different sectors of the economy, changing the marginal valuation trade-offs involving savings, consumption, interest, risk, leverage, investment, etc.

Consider how changing flows of money, credit, leverage, etc. altered the time structure of production in one of the most long-term production goods in the economy -- housing.

In other words, understanding the Cantillon requires getting your economics right. It's Cantillon acting through banking, finance and capital, i.e. its Cantillon + Minsky + Bohm-Bawerk.

Impoverished economics "models" lacking real world things like heterogeneous production processes taking more or less time simply don't tell us about the real world of the Cantillon effect.

[Greg Ransom]

Increase the money supply by 10% per year, but give it to the A's, and none to the B's.

The A's create even MORE money via mutual arrangements of banking, leverage, etc, and see themselves as having greater wealth and an longer investment time horizon -- they dump there money into housing investments.

.. and the B's build the houses, increase short term consumption, and but savings into the banks of the A's, creating the opportunity for even more money creation.

If the A's like long term investments and leverage, and the B's like short term consumption and long term investments, the relative price of houses will temporarily expand -- until input supply constraints and insolvency issues reveal all of these production plans and finance deals to be untenable.

[Greg Ransom]

Sorry, let me clean the typos:

Increase the money supply by 10% per year, but give it to the A's, and none to the B's.

The A's create even MORE money via mutual arrangements of banking, leverage, etc, and see themselves as having greater wealth and a longer investment time horizon -- they dump their money into housing investments, loans, and securities.

.. and the B's build the houses, increase their short term luxury consumption via borrowing from the A's on their rising housing equity.

If the A's like long term investments and leverage, and the B's like short term consumption and long term investments, the relative price of houses will temporarily expand -- until input supply constraints and insolvency issues reveal all of these production plans and finance deals to be untenable.

[Greg Ransom]

"Increase the money supply by 10% per year" -- to sustain the structure, you'll need to increase the supply by percentages more more, year after year.

[edeast]

Had this paper in mind while reading this thread. Price response difference between technology shocks and monetary shocks.
Also related to I think, the post on optimum monetary response to the past recession. If we consider change in terms of trade a tech shock.