How Seriously Should We Take the New Keynesian Model?

Calvo pricing Google Search

Nick Rowe continues his long twilight struggle to try to take the New Keynesian-DSGE seriously, to understand what the model says, and to explain what is really going on in the New Keynesian DSGE model to the world. I said that I think this is a Sisyphean task. Let me expand on that here:

Now there is a long–and very successful–tradition in the natural sciences of taking the model that produces the right numbers seriously. Max Planck introduced a mathematical fudge in order to fit the cavity-radiation spectrum. Taking that fudge seriously produced quantum mechanics. Maxwell’s equations produced equivalent effects via two very different physical processes from moving a wire near a magnet and moving a magnet near a wire. Taking that equivalence seriously produced relativity theory.

And economists think they ought to be engaged in the same business of taking what their models say seriously. They shouldn’t. For one thing, their models don’t capture what is going on in the real world with any precision. For another, their models’ fudge factors lack hooks into possible underlying processes.

Now to business:

In the basic New Keynesian model, you see, the central bank “sets the nominal interest rate” and that, combined with the inflation rate, produces the real interest rate that people face when they use their Euler equation to decide how much less (or more) than their income they should spend. When the interest rate high, saving to spend later is expensive and so people do less of it and spend more now. When the interest rate is low, saving to spend later is cheap and so people do more of it and spend less now.

But how does the central bank “set the nominal interest rate” in practice? What does it physically (or, rather, financially) do?

¯_(ツ)_/¯

In a normal IS-LM model, there are three commodities:

  1. currently-produced goods and services,
  2. bonds, and
  3. money.

In a normal IS-LM model, the central bank raises the interest rate by selling some of the bonds it has in its portfolio for cash and burns the cash it thus collects (for cash is, remember, nothing but a nominal liability of the central bank). It thus creates an excess supply (at the previous interest rate) for bonds and an excess demand (at the previous interest rate) for cash. Those wanting to hold more cash slow down their purchases of currently-produced goods and services (thus creating an excess supply of currently produced goods and services) and sell some of their bonds (thus decreasing the excess supply of bonds). Those wanting to hold fewer bonds sell bonds for cash. Thus the interest rate rises, the flow quantity of currently-produced goods and services falls, and the sticky price of currently-produced goods and services stays where it is. Adjustment continues until supply equals demand for both money and bonds at the new equilibrium interest rate and at a new flow quantity of currently produced goods and services.

In the New Keynesian model?…

Nick Rowe: Cheshire Cats and New Keynesian Central Banks:

How can money disappear from a New Keynesian model, but the Central Bank still set a nominal rate of interest and create a recession by setting it too high?…

Ignore what New Keynesians say about their own New Keynesian models and listen to me instead. I will tell you how it is possible…. The Cheshire Cat has disappeared, but its smile remains. And its smile (or frown) has real effects. The New Keynesian model is a model of a monetary exchange economy, not a barter economy. The rate of interest is the rate of interest paid on central bank money, not on bonds. Raising the interest rate paid on money creates an excess demand for money which creates a recession. Or it makes no sense at all.

I will take “it makes no sense at all” for $2000, Alex…

Either there is a normal money-supply money-demand sector behind the model, which is brought out whenever it is wanted but suppressed whenever it raises issues that the model builders want ignored, or it makes no sense at all…

Must-Read: Nick Rowe: Adding More Periods to Diamond-Dybvig: Fear of Illiquidity, Not Insolvency

Must-Read: Nick Rowe: Adding More Periods to Diamond-Dybvig: Fear of Illiquidity, Not Insolvency: “We simply add an extra time period…. It’s a friendly amendment…

…Agents are ex ante identical. Each agent has an endowment of apples. There is a costless storage technology for apples. There is also an investment technology (planting apples in the ground) which gives a strictly positive rate of return at maturity, but a negative rate of return if you cancel the investment before maturity. Each agent has a 10% probability of becoming impatient (getting the munchies) and wanting to eat all his apples this period. Those probabilities are independent across agents, and there is a large number of agents, so exactly 10% of agents will become impatient each period. Getting the munchies is private information….

Standard Diamond-Dybvig… has… an initial period where agents lend their apples to the bank; a second period where 10% of agents get the munchies and ask for their apples back; and a third period when the investment matures. Banks exist to provide insurance against risk of munchies by pooling assets; normal insurance won’t work because the information is private…. Make it a 4 period model:

  1. An initial period where agents lend their apples to the bank;
  2. A second period where 10% of agents get the munchies and ask for their apples back;
  3. A third period where another 10% of agents get the munchies and ask for their apples back; and
  4. A fourth period when the investment matures….

The bank credibly commits that it will never cancel an investment before maturity, and stores 20% of apples in reserve. In the good equilibrium… only agents who get the munchies ask for their apples back. Now suppose there is a… run on the bank in the second period…. An agent who does not have the munchies in the second period will rationally join that run on the bank, falsely claiming that he does have the munchies… [because] he might get the munchies in the third period, and if the bank suspends redemptions he will be unable to satisfy his future cravings, so he wants to join the line before the bank runs out of stored apples, so he can store apples at home…. Even if people are 100% confident that the bank is solvent, there can still be bank runs if people cannot predict their own future needs for liquidity, and fear that the bank might become illiquid…. Having a deposit in an illiquid bank is functionally not the same as having a deposit in a liquid bank, even if both are solvent…

Must-read: Nick Rowe et al.: The Leijonhufvud Tradition

Must-Read: Nick Rowe et al.: The Leijonhufvud Tradition:

Must-read: Nick Rowe: “Capital Theory and the Distribution of Income”

Must-Read: Nick Rowe provides a very brief masterclass in “capital theory”, which is really the theory of the price system not just at a point in time but over time. (Cf. Christopher Bliss (1975): Capital Theory and the Distribution of Income.) Needless to say, there is no presumption that there is only one equilibrium vector for the intertemporal price system. And there is no presumption that problems of aggregation for commodities called “capital” is any easier than problems of aggregation for commodities called “labor” or “services” or “nondurable goods”. (The question of whether the problems of aggregation for commodities called “capital” is any more difficult than for any other not-completely-unreasonable grouping is left as an exercise):

Nick Rowe: Interest, Capital, MRScc=(1+r)=1+(MPK/MRTci)+(dMRTci/dt)/MRTci: “The slope of the indifference curve [is] the Marginal Rate of Intertemporal Substitution…

…between consumption this year and consumption next year. Call it MRScc…. The slope of the PPF [is] the Marginal Rate of Intertemporal Transformation, between consumption this year and consumption next year. Call it MRTcc. The equilibrium condition is: MRScc = (1+r) = MRTcc…. We don’t need ‘capital’, or its marginal product, to determine the rate of interest…. Where is ‘capital’ in this model? And where is the Marginal Product of Kapital? Does MPK determine r? Does MPK=r? ‘No’, is the answer to both those questions.

The equilibrium condition is MRScc=(1+r)=MRTcc. MPK is one of the things, but not the only thing, that affects MRTcc. And MRTcc is equal to (1+r), but it does not determine (1+r)…. MPK is defined as the extra apples produced per extra existing machine, holding technology and other resources constant, and holding the production of new machines constant. If we move along the PPF between consumption and investment this year, we will have a bigger stock of capital goods next year, which will shift out next year’s PPF. MPK tells us how much it shifts out, per extra machine….

If capital exists, the real rate of interest is equal to, but not determined by, the Marginal Product of Kapital divided by the real price of the machine, plus the capital gains from appreciation of the real price of machines…. Rather than saying ‘MPK determines r’, it would be more true to say ‘MRScc determines r, which determines the prices of capital goods’. And the only thing wrong with saying that is that is that MRScc… depends on the expected growth rate of consumption, which in turn depends on our ability to divert resources to producing extra capital goods instead of consumption goods, and the productivity of those extra capital goods…

Must-read: Nick Rowe: “It’s easier to have a sensible fiscal rule with an NGDP level-path target”

Must-Read: Nick Rowe: It’s easier to have a sensible fiscal rule with an NGDP level-path target: “Even if you are skeptical about the feasibility of a formal fiscal rule…

…it’s a useful thought-experiment to help us be conceptually clear about what we want fiscal policy to look like…. One thing we want… is sustainab[ility] in the long run…. whether we think fiscal policy is or is not needed to help monetary policy stabilise aggregate demand. A sensible fiscal rule would not let the debt/GDP ratio wander off over time towards plus infinity or minus infinity…. We are talking about a ratio of debt to nominal GDP…. A (say) 5% Nominal GDP level-path target… would make it a lot easier to write down a sensible fiscal rule…. If you don’t have an NGDP level-path target, nobody know what NGDP will be be over the coming decades. So nobody knows what average deficit would be sustainable…. Sure, an NGDP level-path target only fixes one problem with getting fiscal policy right. But every little bit helps.

Must-read: Nick Rowe: “Neo-Fisherian Equilibrium with Upper and Lower bounds”

Must-Read: At least this has produced some useful work in how to teach the ignorant today things about convergence to equilibrium that Frank Fisher, Tom Sargent, and many others knew very well back at the end of the 1970s:

Nick Rowe: Neo-Fisherian Equilibrium with Upper and Lower bounds: “Naryana [Kocherlakota]… [thinks] models should have relatively robust predictions….

If what happens in the limit is totally different from what happens at the limit, we have a problem…. If each boy racer had wanted to drive at 90% of the average speed, we get exactly the same Nash equilibrium, where they all drive at 0km/hr and stay in Ottawa, only now it’s a ‘stable’ equilibrium. We do not get multiple equilibria by adding an upper (or negative lower) bound to their speed. Any plausible equilibrium should be like that; it should be robust to minor changes in the boundary conditions. But if each boy racer wants to drive at 110% of the average speed, so driving at 0km/hr becomes an unstable equilibrium, adding boundary conditions creates new equilibria that are more plausible than the original unstable equilibrium, simply because they are stable….

We can see what Narayana is doing, when he considers a finite horizon version of the same game, as being like adding boundary conditions. If the game’s equilibrium is very fragile when you add or subtract or change those boundary conditions, there is something wrong with that equilibrium. We ought to get the same results in the limit as at the limit. If we don’t, we have a problem. Something like the Howitt/Taylor principle (or controlling a monetary aggregate or NGDP rather than a nominal interest rate) can convert an unstable equilibrium into a stable one.