Three questions on the transmission of business cycles

I've been mulling this over for the last couple of weeks. I haven't really come up with a clear answer. So I thought I would just throw it out there.

I've got three questions. The most important question is the third question.

1. Assume I am an individual household or small firm, and that I have perfectly flexible prices. How am I affected if all the other households and firms around me have sticky prices, and there is a monetary shock that causes a recession? To what extent can my adjusting my own prices optimally insulate me from the recession around me?

2. Assume my country is a small open economy with sticky prices, and an independent monetary policy with flexible exchange rates. How is my country affected if all the other countries around mine also have sticky prices, and there is a global monetary shock that causes a global recession? To what extent can my country's adjusting its own monetary policy optimally insulate my country from the recession around it?

3. Do questions 1 and 2 have essentially the same answer?

My hunch is that the answer to question 3 is "yes". But I'm not sure. What is the difference between questions 1 and 2?

Update: to be a little more specific, my hunch is that the answers to both 1 and 2 are: "Even if I respond optimally, I will be worse off, because my terms of trade will deteriorate." But I'm not sure if I'm missing something, and if those standard answers are correct. My focus is on 3, not on 1 and 2 per se.

Comments

[Neil]

#3 seems to be 'yes,' though the human behaviour factor - changes in expectations - that economics has a hard time quantifying may be a bit different.

It seems clear that by adjusting prices (of currency or products) we may keep ourselves working, but will have less money with which to buy the sticky-priced things from other households/firms/countries. We were presumably importing them in the first place because it's less efficient at producing them ourselves, so we'll be worse off.

[Bill Woolsey]

Yes, but only if you have no debts and all input providers are in on the plan. If some input prices are sticky, you have problems.

For a small country, devaluation means that the problem is foreign debts.

Suppose your target nominal GDP, so the exchange rate falls enough to keep spending on domestic output the same. When you import inputs, domestic GDP is dometic value added. The value added by imported materials don't count anyway. And so you expand nominal demand for domestic final product so domestic value added is on target. So, it looks like you have sticky imported inputs beat.

It is like all the producers of domestic inputs (wages too, of course) take cuts enough so that prices of exports (and other output) fall enough, to maintain full employment.

[david]

Goals are different; conventionally we write that households maximize utility and central banks maximize some inflation-unemployment objective function, don't we?

Which does not affect "my optimal action holding everyone else's constant" but of course everyone else's need not be constant if you change your own position. Some of the New Keynesians emphasize that the demand externality of Q1 is individually irresolvable because there are millions of households; coordination is implausible even if you eat the losses as first mover. But there are only so many countries. Most countries have major trade partners that can be count on a hand.

[anon]

The global recession acts as a supply shock on #2, due to decreasing global output. This is true even though #2 can mantain full resource utilization in its economy.

Similarly, #1 may only be able to e.g. find work at very low wages, because firms' demand for labor is low and inelastic. If #1 is a firm, it is affected by low (present and future) demand for its output. Although some input prices may fall, the dearth of business investment may also make other inputs potentially more costly than they otherwise would be.

In short, the answers are broadly similar, although #2 will of course benefit by pursuing full resource utilization.

[Becky Hargrove]

Ideally the answer to 3 would be yes, but the household or firm has advantages not (presently) available to the communities in a national open economy. 'In house' solutions can suffice for the first to meet obligations, which the actors can control at least to a degree with flexible prices. However, in the national economy, local communities cannot compensate as readily for sticky prices, because local actors have little control over the various inputs in the process. While the community can observe the flows that happen between actors, they do not have the same rationale for balance or equilibrium that exist in the first example. The challenge is to create such equilibriums in a spontaneous way.

[Scott Sumner]

Nick, I've tried to make similar arguments, and I basically agree.

But you make a bit too strong a claim. The situations are similar, but not "essentially" the same. Even small countries have huge non-traded goods sectors. So most small open economies wouldn't be able to completely avoid the recession, but wage and price flexibility would help them more than it would help an individual.

Maybe they are "essentially" the same--depends how you define "essentially."

[Ken]

I have a simpler question that I've been trying to get an answer to. Any help is appreciated!

In a standard New Keynesian model, are sticky prices/wages the only source of cyclical unemployment? In other words, if it weren't for sticky prices/wages, would the New Keynesian model suggest zero cyclical unemployment?

[Nick Rowe]

While I'm still mulling over my questions, and the responses in comments, I will take Ken's question:

1. There may still be real (supply-side) shocks in a NK model, so that if monetary policy were perfect it would still have cyclical fluctuations like a perfectly flexible price RBC model.

2. All other cyclical fluctuations in a sticky price NK model come from imperfect monetary policy responses to shocks.

2a. If prices and wages were perfectly flexible, the standard NK model, in which the central bank sets a nominal rate of interest, would explode into hyperinflation or hyperdeflation if monetary policy were imperfect. The central bank cannot set a nominal interest rate if prices and wages are perfectly flexible. So the question cannot be answered at the limit.

2b. As the speed of price and wage adjustment increases (but stays finite) the size of the cyclical fluctuations might either increase or decrease. It depends on the particular monetary policy rule being followed. So your question can be answered in the limit, but I think the answer is that it depends on the monetary policy rule, and the particular way in which it is imperfect.

[Costard]

The difference is that #1 is a reaction to circumstances, while #2 is the introduction of an entirely new circumstance. A monetary shock and a monetary infusion do not cancel each other out any more than burning your feet warms your hands. You are talking about the difference between price discovery and price obfuscation... any similarity is superficial, or perhaps, "aggregate".

[Nick Rowe]

Scott: (This post was inspired by my reading of some of your recent posts.)

Individual households have a "non-traded sector" too, called "home production. But yes, there is a (big?) difference in degree. Individual households are typically more open than even a small country. The more we aggregate, the less open is the economy.

Neil and anon: that is my thinking too. Imagine an economy composed of lots of yeoman farmers, each specialising in one type of fruit, that sell their output to other farms and buy consumption goods from other farms. If all other farms hold their prices fixed, and there's a fall in the money supply, I can only keep full employment at my farm by lowering my real price. I am better off than if I kept my real price the same, but still worse off than before the shock. And we can presumably think of the answer to 2 in exactly the same way, except that the central bank lowers the real exchange rate for us.

Bill: "Yes, but only if you have no debts and all input providers are in on the plan. If some input prices are sticky, you have problems."

I'm not sure what question your "yes" is an answer to.

Is your "yes" an answer to the question in 1 and 2 "can each individual household/country keep its utility/welfare the same if all others go into recession?"?

Or is it: can you keep RGDP the same? I think that even if you could keep to full employment RGDP, you would still be worse off, because your terms of trade would suffer.

david: "Goals are different; conventionally we write that households maximize utility and central banks maximize some inflation-unemployment objective function, don't we?"

Not always. Some macro models have the central bank maximise the welfare of the representative agent. Let's assume that here.

"Which does not affect "my optimal action holding everyone else's constant" but of course everyone else's need not be constant if you change your own position."

I wanted to keep questions 1 and 2 the same in this respect, so that both the individual household and the individual country really are *small* open economies, so that everyone plays Nash. That may be a little less realistic for many countries. But, on the other hand, most households and firms do a lot of interaction with a small number of other households and firms, either as trading partners or as competitors.

Becky: but (I think) the individual central bank can coordinate responses within its own economy to other economies in much the same way that an individual household/firms can coordinate its response to other household/firms.

[Nick Rowe]

Costard: you lost me. Suppose all the other countries in the world tighten monetary policy, and go into recession. How should my country's central bank react to that circumstance, and how well can it insulate my country from that circumstance?

[Alex Godofsky]

2a. If prices and wages were perfectly flexible, the standard NK model, in which the central bank sets a nominal rate of interest, would explode into hyperinflation or hyperdeflation if monetary policy were imperfect. The central bank cannot set a nominal interest rate if prices and wages are perfectly flexible. So the question cannot be answered at the limit.

This is related to something I've been trying to figure out for a while. In a liquidity trap, with the natural nominal rate below zero, shouldn't it be impossible for the central bank to raise rates through monetary contraction? If the natural rate is below zero shouldn't rates stay at zero even if the central bank sells its entire stock of government debt?

Can you explain how it is that sticky prices, and sticky prices alone, give the central bank the ability to target interest rates? Does that also imply that without sticky prices the central bank would be unable to target any asset price at all?

[Nick Rowe]

Alex: (We will blame Ken, and me for answering him, for allowing this to go so totally off-topic!)

"Can you explain how it is that sticky prices, and sticky prices alone, give the central bank the ability to target interest rates? Does that also imply that without sticky prices the central bank would be unable to target any asset price at all?"

Suppose there is a well-defined money demand function. By changing the nominal stock of money, M, the central bank can target the nominal price of any real asset even if prices are perfectly flexible. For example, it could target the price of gold, or land, or the S&P stock price index, etc. But it would not be able to target the nominal price of nominal assets, like bonds (well, that's not quite right, because it it wanted to lower the price of bonds and raise nominal interest rates it could create higher inflation and expected inflation and use the Fisher equation, i=r+expected inflation, to indirectly target bond prices).

"If the natural rate is below zero shouldn't rates stay at zero even if the central bank sells its entire stock of government debt?"

No. The standard liquidity trap story is that the money demand function becomes perfectly interest-elastic once the stock of money increases past a certain point. Simply reduce the money supply below that point, and the nominal interest rate will be forced up above 0%.

[Greg Ransom]

Hayek takes up most aspects of these questions in his _Monetary Nationalism and International Stability_.

The country in question 2 is Britain in the 1920s and 1930s.

[Lord]

I would have to say there is much more opportunity for input substitution in the second case. Individually we do that to some extent (eg, cook our own meals instead of going out), but there is more possibility of some level of specialization in the second case, and more flexibility with exports of outputs based on domestic inputs (natural resources). It is easier to cut back on imports than on everything, or commonly, expensive luxuries, durables, and debt. A country that imported most of its consumables would be in a much more difficult position as would one with foreign denominated debt. The terms of trade would change, but so would the items traded.

[david]

david: "Goals are different; conventionally we write that households maximize utility and central banks maximize some inflation-unemployment objective function, don't we?"

Not always. Some macro models have the central bank maximise the welfare of the representative agent. Let's assume that here.

Fair enough, but I do maintain that this is not conventional (presumably for a reason).

"Which does not affect "my optimal action holding everyone else's constant" but of course everyone else's need not be constant if you change your own position."

I wanted to keep questions 1 and 2 the same in this respect, so that both the individual household and the individual country really are *small* open economies, so that everyone plays Nash. That may be a little less realistic for many countries. But, on the other hand, most households and firms do a lot of interaction with a small number of other households and firms, either as trading partners or as competitors.

Is there any country plausibly small enough that the actions of their central bank are literally don't matter and are wholly ignored by their (also small) trading partners?

But take your assumption re #1. We know what the Nash outcome is, with Mundell-Fleming and a bank that pursues the welfare of its representative agent: devalue first and externalize your own unemployment. Domestic inflation is mitigated to the extent your money flows overseas, as expected. Contrast the small-individual analysis where adjustment reduces your own profit/utility. The difference is because unemployment enters into the welfare of the representative household and therefore central bank objective but does not enter in into the welfare of the representative price-setting agent: unemployment is, by necessity, internalized for the domestic central bank.

If every individual were partially underemployed, instead of some individuals being fully employed and some individuals fully unemployed, unemployment in the New Keynesian nominal-rigidity sense would be a lot easier to resolve.

[Ken]

Thanks Nick! I greatly appreciate you response, although it shows me that I have years of studying to do!

[Costard]

How should my country's central bank react to that circumstance, and how well can it insulate my country from that circumstance?

Is "insulate" the right word? In the individual example, prices are only relevant with respect to other households or other firms. You can maintain prices to the detriment of sales, or you can reduce prices and clear inventory, but in neither case are you insulated. Even if all prices economy-wide were to adjust instantaneously, you would still have the knock-on effects of outstanding debt vs. reduced income. In the national example, the impact of global tightening will be felt in prices specifically more so than in prices generally. Some goods, ie housing and raw materials, will collapse, while others will fall less, and others still will be almost unaffected.

The argument I was trying (ineffectively) to make, is that a national monetary policy will not be capable of reversing, or insulating against an international collapse. Capital injections must find their way somewhere, but not into those industries hit hardest, for the simple reason that investors have been burnt and bad investments/flawed paradigms have been unmasked; and capital goods tend to be global goods. Perhaps you could force this reinvestment, but not with monetary policy. So housing will continue to fall, materials might stabilize, and something else - stocks? bonds? stamps? toothbrushes? - will experience an ephemeral boom. For the individual in example #1, this makes the job of predicting future demand, future prices of inputs and capital goods, and alternative business plans, much more difficult. This is why I said of your two examples, that one is (necessary) price discovery, while the other is a monkey wrench.

Yes you can maintain employment, or production, or some other holy aggregate by cutting rates and easing. However adding one imbalance to counter another, is a bit like dealing with the monster under your child's bed by telling him there's another one in the closet. You might keep him in bed this way, but....

[Nick Rowe]

Costard: "insulate" is the traditional word to use in this context. I agree with you that insulation will be partial -- less than 100%, even if the monetary policy/price response is optimal.