Thursday, 14 November 2013

New Keynesians and Interest Rate Effects

John Cochrane's recent blog post on the differences between New Keynesians and Old Keynesians prompted some good responses.  I particularly liked that of Simon Wren-Lewis.

There are two assumptions in the simple NK model that I find particularly troublesome.  The first is that agents have an infinite time horizon.  The second is that agents are homogenous, or that capital markets are perfect, so that everyone can borrow at the risk-free rate.  There are certainly versions of the model where these assumptions are relaxed, but I'm not convinced how well  the whole NK architecture copes with this.

I was thinking about this, whilst reading some recent posts on Brian Romanchuk's excellent blog, where he talks about interest rate effects (especially here).

The NK assumptions described above are quite important to the impact of interest rates in that world.  Taking a very simple model, where GDP (y) is made up of only consumer spending (c) and government spending (g), we have:

y = c + g

all in real terms.

In the long run, there is assumed to be no output gap, so GDP is at its natural level (y*), so we can determine equilibrium consumption (c*) as:

c* = y* - g*

The assumption of consumers maximising utility over an infinite time period, then implies that the relationship between consumption today and consumption tomorrow is a function of the interest rate.  The exact form depends on the assumed utility function, but might be something like this:

ct = ct+1 - α . log [(1+r)/(1+β)]

where r is the real interest rate and α and β are preference parameters.  Current consumption is then given by working backwards from the long run equilibrium level using expected future interest rates.  Higher interest rates will imply less consumption today.

In this model, therefore, interest rates have a substitution effect but no income effect.  Changes in interest rates change how households allocate spending between periods, but don't make households feel any better off overall.  This is because households look at long run income and long run income is simply determined by equilibrium output less what the government spends. 

This conclusion on interest rates however stands in sharp contrast with that of many Post Keynesians, who see an important income effect from rate changes .  In PK models, this arises as a result of the additional interest income of households due to higher interest paid on government debt.  For most, PK economists, this effect tends to override any substitution effect.

In the basic NK model, it's basically Ricardian Equivalence that is eliminating this income effect.  Interest paid on government debt is just a form of transfer income, comparable to a negative tax, so an increase has no effect because agents know they will just pick up the cost later.

And this is really where the assumption about time horizons matters.  Agents maximising over infinite lives might indeed be Ricardian (perhaps given other conditions as well).  But this is a strong assumption, and not in my opinion a very realistic one.  Once we assume agents with a shorter time perspective, the dynamics become somewhat different.

Rather than consider a world with infinitely lived agents, a good way of looking at this is to think of a world with agents who live and die, with agents at all different stages of the lifecycle.  Now, a rise in interest rates redistributes future purchasing power from those without assets to those that do.  To a significant extent, this actually means a redistribution away from agents that have not yet been born, or at least are not yet active consumers.  The potential negative impact on their spending does not therefore materialise currently. 

In effect, we are inducing today's consumers to spend more by promising them a bigger share of tomorrow's resources at the expense of people who have no impact on current demand.
The impact of interest rate changes is a complicated one.  There are different effects working in different directions.  To my mind, the simple NK model assumes away some of the more interesting aspects of what might be going on.


  1. Yes, the consumer behaviour in these models seems highly questionable, particularly for welfare state programs. I doubt that most people who are unemployed are in a good position to smooth over lifetime income. People do save a greater portion of tax cuts, but even then, it was a fairly high proportion.

    The Ricardian equivalence results seem particularly weak. In a growing economy, a lot of variables tend towards infinity as time goes to infinity. It's not clear whether summations will converge as they assume.

    1. That's an interesting point about the summation with a growing economy. I've not come across that before, but it makes sense.

    2. Yeah I think Tobin has made such observations about paradoxes of people thinking into infinite future, although I don't recall which paper of his was this.

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  4. If we could measure Y in purely physical terms, we would have y = c + g as you suggest. Then we could further divide y to assign value to long term investment to separate long term value from strictly short term consumption.

    A major computational complication occurs when we use money to measure physical consumption; money obviously can be created by government, and, money can be held by the private sector from period to period. Both newly-created money and private-draw-from-savings will increase Y during during the period of spending.

    With this background, how could we conclude, as NK's do,

    "In the long run, there is assumed to be no output gap, so GDP is at its natural level (y*), so we can determine equilibrium consumption (c*) as:

    c* = y* - g*" ?

    This is the equivalent to saying "If I turn on the water faucet, and leave it on long enough, the amount of water running out is the natural rate of water delivery". What both statements fail to address is the degree to which the economy is stimulated or the faucet is opened.

    Money-printing and draw-down-of-savings are both stimulative.

    I would agree that a constant rate of stimulation can be achieved by government through the printing of money process. I would disagree that a constant rate of stimulation can be achieved by government borrowing money from the private sector; the private sector can only refresh money-lent-to-government by working for government to recover what has been lent. Once recovered, the money can be re-lent to government, thereby increasing government debt, increasing the debt holdings of lenders, and continuing a stable but no-longer-stimulative cycle.

    So, like you, I find the NK architecture not-at-all satisfying.

    I much prefer to treat a change in money supply or draw-down-of-savings as discrete events with predictable short term and long term effects.

    1. Roger,

      In the NK model, prices are assumed to be fully flexible in the long run, so real quantities hold. In the example with your faucet, we might fix the nominal flow of water, but the real value of the flow in the long run will be the natural rate (I might be stretching the analogy a bit). Anyway, there can be no long-run stimulus in the NK model, because the economy is assumed to be at the natural level of output. The only issue, in the case of increased government spending, is how consumption is reduced to the requisite level.

      However, I don't want to get drawn into defending the NK model. I think it has its uses, but it's not my preferred approach.

  5. It is well known that Ricardian equivalence does not hold when there are liquidity constrained households. And empirical work has shown a high proportion (sometimes as high as 50%) of liquidity constrained consumers. (

    So, these supposed problems in NK results go away once you assume enough liquidity constrained consumers.

    Also note that the economists definition of consumption excludes durable goods (only the current flow of services out of durables are considered). So, you are already skewing the results toward PIH/LFC away from the Keynesian consumption function because durables are the most sensitive to transitory changes. On a side note, the BEA data on services, at least in the US NIPA, are heavily imputed (such as rent on owner occupied homes) and smoothed.

    I think it is fun to have these theoretical discussions and I find the discomfort caused to NKers quite delectable. The NKers seek legitimacy from the RBC types, which they will never get. Yet the NKers sneer at the PKers and do not condescend to acknowledge them--you just need to look at the blogroll of Economistsview .

    The problems of the NK model illustrate what happens when you "fight the battle on other person's turf." Basically, the NKers come from a conclusion that is Oker but want to show the RBC types that it can be derived from their models, using their assumptions, and satisfying the Lucas Critique. In reality, if you had a world that satisfied RBC conditions (barring minor tweaks), there would have been no Keynes!! BTW, the NK models of frictions--such as efficiency wages, menu costs, etc--produce unemployment and output gaps only for small deviations--that is moderate recessions. Large deviations would create enough incentives to reoptimize.

    1. I agree. The issue I talk about in this post, time horizons of agents, is also well-known. Even Barro, in the paper "Are Government Bonds Net wealth?", talks about the results being dependent on an the assumption that there exists an "operative chain of inter-generational transfers" which allows households to be treated as infinite lived.

      I'm perhaps a little more sympathetic to the idea of fighting on the other's turf. It sometimes looks to me that the different schools of economics are just shouting out their own views without paying any attention to what the others are saying. I think that's a pity, because I think most of them have something useful to offer and close examination of those areas that appear to produce conflicting results can be quite illuminating. That sometimes involves couching one set of ideas in the language of the other.

      But I agree that NK seems to have shed most of the things that are interesting about Keynes.

    2. In the French edition of the GT, the translator Jean de Largetaye had an interesting way to say this: that the authority of the General Theory was invoked in favour of views directly contrary to its essential teaching by its opponents.

  6. "There are two assumptions in the simple NK model that I find particularly troublesome. The first is that agents have an infinite time horizon. The second is that agents are homogenous, or that capital markets are perfect, so that everyone can borrow at the risk-free rate."

    The model also assumes that real interest rates go down when inflation expectations go up. But in reality interest rates go up also when inflation expectations increase. The model seems to assume that everyone borrows directly off the central bank or that inflation has no effect on interest rates.

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  8. In "Horizontalists, verticalists, and structuralists: The theory of endogenous money reassessed", Thomas I. Palley gives an sweeping overview of Keysenian and Monetarists theories of money supply. The paper in PDF format can be found at

    The paper is the best review and comparison of four main schools of thought that I have seen. Wish I had read it earlier.