In the olden days, as Peter Dorman notes, macro models would contain variables like M (or r), G, and T (or t) for monetary and fiscal policy. Nowadays they usually contain a monetary policy rule, and sometimes a fiscal policy rule too. Like a Taylor Rule, for example. [Update: but see my old post on fiscal policy rules.] We don't talk about policy; we talk about the policy rule. We don't choose the best policy; we choose the best policy rule. Why?
The short answer is that in most macro models what happens today depends not just on policy today but also on today's expectations of future policy. And if expected future policy matters today, policy is nearly always better if it follows a rule rather than discretion (Kydland and Prescott 1977 pdf). And since we want to use models to learn the best policy, we assume that policy follows a rule. Unless we think the policymaker can't make credible commitments, in which case we assume discretion.
But that also raises a puzzle. Why do real people and real policymakers vary the amount of rules vs discretion over time? (I blogged about this once before, and JW Mason raises a related puzzle in comments.)
Here's a simple "model":
Assume that every day I can: choose what I do today; choose whether to make a promise telling people what I will do tomorrow.
That sounds as if I have two choices every day. But if yesterday I made a promise, I no longer have any choice about what I will do today. Because if I don't do what I promised to do, people won't believe my promises, so I won't really be able to promise.
If I have to keep my promises, there are four types of day:
1. Days where I choose what to do today, and promise what I will do tomorrow. I use two degrees of freedom on days like that.
2. Days where I choose what I will do today, and make no promise about what I will do tomorrow. I use one degree of freedom on days like that.
3. Days where I do what I promised yesterday to do, and make a promise about what I will do tomorrow. I use one degree of freedom on days like that.
4. Days where I do what I promised yesterday to do, and make no promise about what I will do tomorrow. I use zero degrees of freedom on days like that.
So on any given day, I can either use two degrees of freedom, one degree of freedom, or zero degrees of freedom. But on average, I only have one degree of freedom per day. I can borrow one degree of freedom from the future, and so spend two degrees of freedom on one day, but that's my credit limit in this example. If I borrow one degree of freedom from the future, I can either roll over that debt, and continue to spend one degree of freedom per day, or I can repay the debt by spending zero degrees of freedom one day, so I can again spend two degrees of freedom at some future day.
I think you get the idea from that simple example. We could extend that example by assuming I could also make a promise today about what I will do the day after tomorrow. In which case my credit limit is two degrees of freedom. And so on.
There are only two steady states, where all days are the same, and I only use one degree of freedom each day. In the first steady state, all days are like the second type, where I never make a promise. That's "discretion". In the second steady state, all days are like the third type, where I always make a promise. That's "rules".
It is easy to prove that the second steady state ("rules") is almost always better (and never worse) for me than the first steady state ("discretion"), provided contingent promises are possible. The intuition is that my utility depends on others' actions, which depend on others' expectation of my future actions, and by making promises I can influence their expectations of my future actions, and thus influence their actions. [Math appendix, based on Kydland and Prescott 1977: If my utility is U(M,Y(M)), where M is my action and Y is your action, and where your action depends on your expectation of my future action, then choosing M by setting U1 + U2.Y' = 0 ("rules") is almost always better for me (and never worse) than choosing M by setting U1 = 0 ("discretion"). But if I make no promises, then you have already chosen your action when I choose mine, so choosing M by setting U1 = 0 is all I can do.]
That is why most macroeconomic models describe monetary policy in terms of policy rules which the policymaker has promised to follow. Because policy is better under rules than under discretion. Unless the macroeconomic modeller thinks that the policymaker's promises won't be credible, in which case the modeller assumes discretion, which is a steady state with no promises.
But that raises a puzzle. Why in the real world, both for policymakers and for regular folk, do we sometimes see the number of degrees of freedom we spend varying from day to day? Some days we increase our outstanding stock of promises-to-be-fulfilled and other days we reduce our outstanding stock of promises-to-be-fulfilled. Why?
Intuitively, just as we go deeper into debt on some days, and pay down that debt or go into credit on other days, it would seem to make sense to borrow and lend varying numbers of degrees of freedom too. Use more forward guidance in bad times, when you really need it, and less in good times, when you don't need it as much. But the math says we should always be borrowing degrees of freedom right up to our credit limits, or until extra degrees of freedom provide no marginal benefits.
Why don't we do this? Some possible answers:
1. Some sort of uncertainty that we can't get around by making contingent promises.
2. It would take too long to figure out all the contingencies and make an optimal contingent promise. Our brains are the scarce resource.
3. We are always borrowing up to our maximum credit limit of degrees of freedom, but that credit (credibility) limit varies over time.
4. There is some sort of counterpart to a rate of interest charged on the outstanding stock of promises-to-be-fulfilled.