Strategy spaces and monetary policy

Posted on by

Over at Worthwhile Canadian Initiative, Nick Rowe suggests that central banks should find something else to discuss instead of interest rates.  The analogy provided is that of oligopoly competition: namely how the Cournot-Nash and Bertrand games have exceedingly different outcomes, even though the only superficial difference is that one game involves choosing output and the other game involves choosing price.

However, in the same way I don’t believe the difference in these games is just the product of “framing”, I am not sure if the call to arms against using interest rates as a focal point is necessarily that compelling.

On quantity and price competition

Back in the 19th century some economists called Cournot and Bertrand came up with separate models of firm oligopoly behaviour.  In the Cournot model firms picked quantities, and they kept some market power – albeit less than in the monopoly case.  In the Bertrand model firms picked prices – and we got this crazy result that merely having two firms in a market provided perfect competition.

As a result, economists became concerned.  We had two models, one which seemed to fit data better (Cournot) and one which had assumptions we felt were more realistic (Bertrand).  A multitude of ex-post imperfections could be introduced to a Bertrand game to create “supernormal profits”, such as heterogeneous goods, transaction costs, and imperfect information – but there was still the problem that, if we had only two firms competing and they decided to “play” in prices instead of quantities we had a different outcome.  Given that the demand curve is the thing along which both price and quantity were picked, and given that the firms in both cases were seen as equivalent, this didn’t seem consistent.

Eventually economists realised that there was something else at play here.  The Cournot and Bertrand firms were not equivalent at all.

In the Cournot game the question is:  if I LIMIT myself to producing a quantity how will other firms react – and given that reaction what level of quantity would I want to limit myself to.

In the Bertrand game the question is:  I have an unlimited ability to produce.  As a result, if I set a price how will other firms react – and given that reaction what price would I charge for the produce I will be able to make.

So in the Cournot game you build things first, set the price later.  In the Bertrand game you set your price and immediately satisfy this demand.  As a result, economists realised that the Cournot game was simply a Bertrand game with capacity constraints.

What in the hell does this have to do with the point on monetary policy!

I was getting there.  Fundamentally, in the same way that Cournot and Bertrand games were discovered to only give different results because they were fundamentally different, I believe that any difference between an interest rate target and other targets only differs if “effective policy” is different – I don’t believe in a framing issue persee (although framing explanations can be funky).

Now I don’t disagree with the idea that just talking about the nominal interest rate would be silly.  But central banks don’t just talk about a nominal interest rate – they also discuss an inflation target, which anchors inflation expectations.  In essence the current “focal point” for policy is the real interest rate.

Furthermore, since they control a real interest rate, and have anchored inflation expectations, they can print money which in turn increases demand for goods and services.  As Nick states:

And most of the power of a central bank comes from its ability to influence people’s expectations of the future. Like governments, police, armies, and referees, most of central banks’ power comes from belief in their power

The fact that inflation expectations are anchored implies that people believe they know the future price level, given that a significant portion of any nominal increase in income will be confused for real income – leading to extra spending activity.  That is the very power of an inflation target – an inflation target that is easy to communicate and explain to the public by discussing interest rates.

Targeting arbitrary variables that are positively related to an economic recovery, but not appropriately related to “monetary policy” seems both sort of aimless and potentially dangerous.  A central bank can keep discussing interest rates and its inflation target, and even at a “zero bound” it could stimulate activity by printing, printing, and printing.

Finally, I think it is important to note that this subject only really matters in the rare occasion that it really matters ;-) .  Outside of zero interest rates and a steep, depression like, drop in demand the interest rate (or some indicator of “monetary/financial” conditions) is an amazingly effective tool for communication.

However, my belief is that this effectiveness continues even in the extreme conditions.

  • http://worthwhile.typepad.com/worthwhile_canadian_initi/ Nick Rowe

    Matt: thanks for your thoughts on my post!

    Sure, economists are unhappy with the Cournot/Bertrand result (that the equilibrium can depend on something as ephemeral as the strategy space). And applying some more structure to the game can seem to resolve this problem (suppose that firms *really do* have to produce output in advance, or *really do* have to advertise prices in advance). But what determines the equilibrium is not whether forms *really do* set q or p in advance, but whether the other firms *think* they do.

    From my cursory reading, this strategy space problem is pervasive in game theory.

    Back to monetary policy. I wrote in some earlier post, something like “We always knew that setting interest rates couldn’t work in theory, but it seemed to work in practice, so eventually we stopped worrying about the theoretical problem”. *Provided* that inflation expectations remain well-anchored, I think we can understand that interest rate policy can work. But what happens if people lose faith in central banks’ ability to keep inflation on target? (And over the last year, that loss of faith was a very real danger). If inflation expectations become unanchored will framing policy in terms of interest rates still work? And what about the US Fed, which doesn’t really have an inflation target?

    Here’s where I really disagree with you though: “Targeting arbitrary variables that are positively related to an economic recovery, but not appropriately related to “monetary policy” seems both sort of aimless and potentially dangerous.”

    Why aren’t things like share prices or commodity prices “appropriately related to “monetary policy””? Go back 100 years, when “monetary policy *meant* fixing the price of gold (a commodity price)! You have been so captured by the current way of framing monetary policy that you can’t see that it is just one of many possible framings! Escape The Matrix!

  • http://worthwhile.typepad.com/worthwhile_canadian_initi/ Nick Rowe

    Yep. The neutrality of money tells us that it is (real) interest rates that aren’t appropriately related to monetary policy. And the Quantity Theory tells us that nominal variables like share and commodity prices ARE appropriately related to monetary policy!

  • http://www.tvhe.co.nz Matt Nolan

    Hi Nick,

    Thanks for the insightful comments – I will have a quick go at listing down a couple of my thoughts with regards to them.

    @Nick Rowe

    “But what determines the equilibrium is not whether forms *really do* set q or p in advance, but whether the other firms *think* they do.

    From my cursory reading, this strategy space problem is pervasive in game theory.”

    Agreed, as far as I understand it the folk theorem and the strategy space issue are two of the biggest methodological issues in game theory. However, we have to ask what we do when faced with a methodological quandary – do we ignore it, or do we try to take a step back and see if we can endogenise the process that gets us there.

    The solution to the Cournot-Nash vs Bertrand game was to take an extra step back – and make the strategy space endogenous.

    Now in the case of monetary policy we do hit a dilemma, because the choice of instrument is exogenous. However, before we state that there is a framing problem we need to ask whether changing policy really matters.

    “If inflation expectations become unanchored will framing policy in terms of interest rates still work? And what about the US Fed, which doesn’t really have an inflation target?”

    I agree here that inflation expectations ARE the central issue. Ultimately, best policy involves a central bank blatantly targeting inflation expectations.

    If we do reach a situation where “inflation expectations are unanchored” this means that when the bank prints money (which it can still do when the interest rate hits a zero bound – and it can still communicate, by saying it is going for inflation) it just turns into inflation, and we get no recovery in output.

    However, here the real issue is that inflation expectations are become unanchored. In this case we need to ask how the hell that happened – and how prices became so much more responsive to contemporaneous changes in the money supply.

    I do agree with you that, if banks only mentioned nominal interest rates, and they hit zero, and as a result this managed to unhinge inflation expectations then we have a problem – however, I was under the impression that inflation expectations were still anchored, and that if there is an issue it is a lack of printing action from central banks.

    “Why aren’t things like share prices or commodity prices “appropriately related to “monetary policy””?”

    @Nick Rowe

    The key term for me here is “appropriately”.

    Inflation expectations, the money supply, nominal interest rates – these are all factors that are determined on the basis of monetary policy directly. The idea of using these variables is to ensure so type of nominal change. As a result, they seem appropriate.

    Commodity prices, the stock market, both strongly influenced by monetary policy for sure. However, they are also separate – supply shocks should have a direct influence on these variables. Do we want the public to view changes in commodity prices and the stock market as an effective lead on monetary policy?

    Say we have a drought (negative supply shock), commodity prices rise, the public looks at this as a defacto signal of tighter monetary policy as well as a normal supply shock – this leads to downward pressure on the price level exacerbating the problem. New Zealand has the occasional issue with drought, and so this sort of issue concerns me.