Tuesday, October 01, 2013

Modeling Policy When Policy Is Inside the Model

Without much comment, a very strange thing has happened to economic theory in the past two decades or so: models of the macroeconomy incorporate monetary policy as just another component of “the economy”, along with the behavior of households and firms.  I don’t mean that these models include central bank decisions on interest rates, the way they include the fiscal choices of government; that’s unavoidable.  No, they go even further and include the reaction functions of monetary authorities as determinate behavioral foundations of how the economy works; there is no corresponding behavioral rule on this fiscal side.

Here’s what I mean: Once upon a time, we had models over here (hand sweeps to the left) and policy choices over there (hand sweeps to the right).  Back in the days of IS-LM with a fixed money supply (fixed for some unmentioned reason by an almighty central bank), the model consisted of behavioral responses in the money and goods markets, leading to a predicted outcome, equilibrium levels of national income and interest rates.  In principle, monetary authorities could run this model on various money supply choices to see what economic results to expect.

OK, the model had some flaws, but in a very general way it corresponded to what we all thought models should do.  They were prediction devices: you plugged in a policy choice and it told you how the economy was supposed to respond.

Now it’s different, at least on the monetary side.  In the new versions of IS-LM and AS-AD, as well as the more elaborate models in the professional literature, monetary policy is inside the model.  The choices of central bankers are built in.  You may have interest rate targeting, inflation targeting or some version of a Taylor Rule, but in all of them the monetary choices themselves are predetermined.  The most you can do is alter a targeting parameter, like “what if monetary authorities panic when inflation hits 3% rather than 2%?”  In other words, the only choices the model can inform are those the model itself doesn’t build in.  When you build in a central bank reaction function, policy space is seriously constrained.

Now, we don’t see this on the fiscal side.  The only thing the models assume is that there is some fiscal policy: the government sets tax rates on various activities and makes various spending commitments.  Actual revenues and spending levels may fluctuate with national income in a more fully specified model, but government discretion over fiscal policy is not constrained at all.  That is, pretty much all the fiscal policy choice is outside the model, which means you can run the model with just about any hypothetical choices you care to make.  This is the way models used to be for monetary policy too.

So why on earth has this happened?  Why do the economists who create, propagate, use and teach these models want to limit monetary policy freedom, and the range of usefulness of the models themselves, by putting so much policy inside?

I don’t have a single answer, and I’m not sure there is one.  But I do have a couple of hypotheses, one or both of which might be true.

First, there is an internal, logical reason, which is that earlier generations of macro models rested on untenable assumptions about how monetary aggregates are determined.  After the brief monetarist experiment in the US and the UK in the late 70s–early 80s, it was clear that (a) there is no single measure of “the money supply” that captures the full economic effect of monetary policy and (b) in any case the central bank can’t control it. Trying to do so in a single-minded way would be a recipe for causing massive economic damage.  Models that were based on a fixed money supply, set by the central bank in the short run, lost credibility.  (You can still find them popping up in introductory textbooks, which says something about the textbook business.)

So there needed to be other equations in the model that took the place of money supply setting.  The only alternative economists could come up with was fixed central bank reaction functions.  Maybe this is not perfect either, but it’s what we’ve got.

I suspect there is a measure of truth to this, but it doesn’t explain why such a dramatic change in modeling strategy, one that tinkers with the fundamental purpose of modeling itself, was swallowed wholesale without comment or debate.

Here’s a second hypothesis: modern macro is based on intellectual predispositions that crave fixed policy rules.  I can think of two of them.  First, the shift to built-in monetary policy coincided with the microfoundations revolution.  But these were not any old microfoundations; they were formulations based on optimizing behavior by everyone, with the result that outcomes could be evaluated according to whether they were optimal for society as a whole.  The purpose of macro was no longer to simply connect policy inputs to economic outcomes and leave it to “decision-makers” to make the pick, like those Old Keynesian models used to do.  No, the point is to identify the optimal policy and the corresponding optimal outcomes.  You solve for that.  Throw in some assumptions about the natural rate and utility maps for income and inflation and, behold, you can specify exactly what policy should be.  If that’s what it’s all about, you don’t need to run a model across multiple policies—you’ve already got the policy set you’re looking for.

A second bias is related to the first but is more obviously political.  According to this mindset, economics is technical and has the capability, or should, to generate correct answers to policy questions.  Politics is at best haphazard, however, and at worst is subject to shameless pandering.  Politicians compete by one-upping each other on populist irresponsibility, promising short run boosts to interest groups or even the economy as a whole, whatever the long run costs.  Economics, by showing everyone what policies are truly best over a long time horizon, is a weapon against populism.

If economists think this way, it makes sense that they would be predisposed to fixed rules that eliminate the very possibility of political interference in policy-making.  If you know what’s optimal, why mess with it?  Putting monetary policy inside the model not only closes it, it also represents how the world ought to work.

Ah, you ask, but what then about fiscal policy?  If hypothesis #2 is correct and economists insert central bank reaction functions into their models because they believe in a policy world that is rule-based and predictable, why don’t they do this on the fiscal side?  My answer would be, they don’t need to because there shouldn’t be any discretionary fiscal policy at all.  In the ideal world inhabited by modern macro, automatic stabilizers would be allowed to stabilize, and that’s pretty much it.  All the heavy lifting would come from the monetary side, and that is where fixed rules matter.

In addition, there is no structural need for inserting fiscal policy reaction functions, since existing behavioral equations for households and firms take care of the goods markets just fine, thank you.

Up to now, my only purpose has been to describe and understand what has happened in the world of macro modeling.  I haven’t taken sides, although it’s probably because I don’t like this trend that I am noticing it in the first place.  To close, I just want to mention a few problems.  First, estimated central bank reactions functions, like Taylor Rules, rely on just a few years of data.  It is a huge leap to assume that regularities established over a decade or so are fixed in stone.  Second, even this thin evidence base does not support the presumption that central banks predictably follow fixed rules.  Third, any pretense of rule-based policy was jettisoned in response to the economic crisis that struck in 2008, and rightly so.  Fourth, the supposed anti-political bias of economics is itself very political and has dangerous implications.

But my point is not to get you to agree that this revolution in modeling methodology is bad, but simply to see that it has happened.


  1. This is really interesting. I realize that "hey look at my model" stuff tends to get ignored (for good reason), but hey look at my model ... what you are describing is actually incredibly and fundamentally important in it.

    The "microfoundations" are that aggregate demand is transferring information to the money supply and the signals from the demand are detected by the price level (or interest rates). There are two possibilities at this point and they depend on if the central bank adjusts to the information. Does the central bank use market indicators as targets or does it peg interest rates (or monetary aggregate growth rates)? (In the model it basically comes down to a choice of whether the monetary base is an independent variable in a differential equation or not.)

    In the former case you get liquidity traps:

    In the latter case you get accelerating inflation:

    You need both kinds of regimes to describe the US price level with the monetary base (basically market-based before and after WWII and market-insensitive during the period when the Fed pegged interest rates):

    1. Here's my extended take if anyone is interested:


  2. Anonymous7:14 PM

    This is the model
    That the economy expected
    To predict
    That the economy will expect
    The economy to expand
    If expectations collapse
    Unless they increase
    And cause the economy to shrink
    According to the model
    That Jack built.

  3. Anonymous9:37 PM

    Nick Rowe needs to answer this question. I haven't asked him this question as explicitly, but it's been on my mind numerous times.

    I did once get him to contemplate incorporating a fiscal rule, but I think his response was that fiscal policy has many degrees of freedom and should be applied to optimize along various micro issues while monetary policy with its single degree of freedom is best modeled as a rule.

    1. Rob Rawlings11:24 PM

      Nick Rowe defines monetary policy as policy that affect the money supply and fiscal policy as policy the affects the distribution of real income.

      I think this is one of the reasons why monetarists leave fiscal policy out of their models - defined this way fiscal policy is only distributional.

    2. Funny you ask! I had just read this, and was thinking of responding.

      Short answer: assume AD today is a function of: M today; expected M tomorrow; F today; expected F tomorrow.

      (Most macro models will look something like that, except that expected M the day after tomorrow etc will also matter, etc.)

      Now if you look at that equation, it seems to give the government 4 policy levers: M and F today, and promises about M and F tomorrow. But when tomorrow arrives, will the government actually do what it promised to do? Will people expect it to do what it says it will do?

      The government only has 4 policy levers per period if people are really credulous and always believe government promises even if the government always ignores its past promises. Which isn't very plausible.

      One way to model this is to assume the government sticks to a rule for M and F, and people expect it to stick to a rule. The government then chooses the rule for M and the rule for F.

      A different way to model this is to assume government can only choose today's M and today's F, but cannot precommit to tomorrow's M and F.

      You get very different optimal policies for M and F depending on which way you do it. But you get better policies if you do it the first way.

      Bob Rawlings: "Nick Rowe defines monetary policy as policy that affect the money supply and fiscal policy as policy the affects the distribution of real income."

      No I don't. Fiscal policy includes government spending and total taxes, as well as distributional policies.

    3. Right: you want an AD curve, and you need to fold policy into the model to get it. Also, it's OK to make assumptions that blot out policy discretion, since the policies you get by making the government stick to fixed rules are "better". Those were my two hypotheses.

  4. The central bank should directly target broader measures of money such as M1 directly becuase most of the money is broad in which the economy transacts. Narrow money is mostly confined to the banking system. Monetary policy needs to be more balanced by being less focused on banks and more focused on the overall economy.

  5. A related question: you often get mainstream macroeconomists saying things like "well, we *could* do more stimulus but who knows what the Fed might do?" I've never seen why "why not ask it?" shouldn't be a valid question. If the central bank is a rules-based targeter, there should be no policy uncertainty; we can plug in a budget balance of $xbn and see what change in interest rates it spits out.

    But if there is a deterministic policy rule, then being the central bank is suddenly a lot less fun, as it means you have no latitude of discretion and hence no power. The locus of responsibility shifts to whoever defines the rule, and monetarists in particular tend to go all shifty at this point - Milton Friedman thought it should be a computer. Programmed by who? He didn't say.

    If you think that other actors in the economy are meant to adjust their decisions in the light of the central bank's actions to keep inflation (or whatever) at a target, the rules they apply to achieve this are as important, possibly more, than the target itself. Unless you have some idea of how the system reacts to inputs, you can't close the control loop.

    Lucas believers imagine that the rule is internalised by all representative-agents, but how can this be if the rule is not public or more to the point, isn't actually defined? The Bank of England, for example, has a target of 2% CPI, but its policy rule is "have a meeting and decide".

  6. Anonymous9:35 AM

    Question: isn't this just because we need some sort of monetary policy rule to be able to work out the expectations for future inflation and close the model? I.e., it's a modeling necessity?

  7. Peter: Kydland and Prescott 1977: rules rather than discretion.

  8. Nick is giving a good summary of the modern consensus. But there is something very strange about it, when you think about it.

    When we are making models of the economy, it is perfectly logical to say: "What if the central bank followed a certain monetary policy rule, and stuck with it forever? How about if they followed this other monetary policy rule, and stuck with that one forever? How are the two cases different?"

    But this cannot describe a choice facing any policymaker in the real world. Because no one ever gets to make a choice outside of time in this way. Every existing central bank or fiscal authority has already existed in the past, and so has some rule that it is already following. So if we apply Nick's reasoning to any concrete policy question, we find it does not have two dergees of freedom. it has zero degrees of freedom. The best we can say is, "If you'd done things differently since the beginning of time, you might be better off now." That is what it means to put policy inside the model.

    If policymakers have a choice now, then they could not make a binding commitment in the past. But if they could not make a binding commitment in the past, they cannot make a binding commitment now. The consensus framework is coherent (if not necessarily useful) if we are only interested in a descriptive account of how policymakers do act. But it is logically incoherent when it is applied to the question of how they should act.

    1. Alexander11:59 AM

      Another way of making this point, I think, it to ask the question "When is time t=0?"

      Just because a policymaker has the ability to make a binding commitment to a policy rule does not by itself imply that it cannot have a choice today. Perhaps it simply had not made such a commitment in the past. But typically there are welfare gains from commitment, so the question becomes "If the policymaker wants to commit to a rule at time t=0, why did it not commit to the rule at time t = -1? Or t = -2? Or . . ."

      I guess the reason is "Because you have to start the analysis somewhere."

      In any event, it is also worth pointing out that it is not necessary to assume that the policymaker has the ability to make binding commitments. Plenty of papers assume that the policymaker sets its policy instruments according to discretion each period without being bound by any prior commitments. Nick made this point in his comment above. Other agents in the model are still able to make rational forecasts of policy because they know what is in the policymaker's interest.

    2. JW: I have just been writing a post on that very same puzzle!!

      But I would pose it this way. At the beginning of time, we have one zillion degrees of freedom, and we spend them all on the very first day. For every other of the one zillion minus one days, we spend zero degrees of freedom.

      But real people don't act like that. Some days we spend more than one degrees of freedom, and other days we spend none. Why?

    3. scepticus5:41 PM

      The above describes the beginning of the universe. Maximal degrees of freedom, big bang, minimal entropy.

      The universe couldn't irreversibly spend all those degrees of freedom instantaneously because it took (takes) time to explore and exhaust them. In order to irreversibly dissipate a degree of freedom requires that some complexity be built up which takes time.

      The concept of irreversibility must bear upon the issues discussed in this post and in this particular comment thread.

    4. Wow, I never thought this thread would get into the nature of time, whether we (or the Fed) has free will, or, on the other side, the existentialist dictum that we are "condemned to freedom". I can see how you get there though.

      As a practical matter, what's a model for? To inform policy, right? But isn't it a bit weird to employ a model that works only because it assumes the lack of most policy discretion?

    5. scepticus5:00 AM

      A model is equally well (arguably, better) employed to justify policy or indeed justify any opinion.

      In which case, not modelling policy makes a lot of sense.

  9. Just for kicks I shall throw in a deeper concern that basically has no real resolution, although my doing so is really to point out how arbitrary and ad hoc all this is, even though many who have been doing this stuff are very proud of themselves for their supposed non-ad-hockery.

    The problem is that once you have a policy model inside the model, if that model involves allowing the policymakers to respond to percevied expectations and behaviors of agents in the economy, who in turn are supposedly forming expectations based on what they think policymakers are doing, and once both are aware that the other is looking at what they are doing, one is set up for a possible infinite regress of determining what the behavior of either will be.

    There are various arbitrary ways out. Both parties can be assumed to play game theory and flip coins so as to come to some sort of Nash equilibrium and cut short the infinite regress, or some sort of arbitrary assumptions are made about convergence and uniqueness of a ratex solution and one gets to some sort of policy-agent solution that way. But it should be understood that such devices are indeed ad hoc and arbitrary, if not the sorts of things most macroeconomists want to bother their pretty little heads with.

    Barkley Rosser

  10. Anonymous6:19 PM

    This seems slightly confused to me, and related to how you model money. Both a cash-in-advance model and a money-in-the-utility type of model would say that the sequence (or process) of money supply determines the equilibrium (at least in the short run). Only the cashless economy has the type of property you describe. But this is really the cashless limit, and as we know we're not there yet, so I'm not sure why people obsess so much about it.

  11. Anonymous12:31 AM

    This makes as much sense as only vaccinating 50% of the population against whooping cough, providing postal service only to odd numbered zip codes or defending only half of our counties against enemy invasion. The whole point is that the value of certain goods increases dramatically when almost everyone has them. It's a system effect. Such goods include things like education, health care, defense, law enforcement, network membership and so on.

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