A friend pointed me to this paper:

Svensson, Lars E. O. and Michael Woodford. “Indicator Variables For Optimal Policy,” Journal of Monetary Economics, 2003, v50(3,Apr), 691-720.

You can get the NBER working paper (w8255) here. The abstract:

The optimal weights on indicators in models with partial information about the state of the economy and forward-looking variables are derived and interpreted, both for equilibria under discretion and under commitment.

The private sector is assumed to have information about the state of the economy that the policymaker does not possess.Certainty-equivalence is shown to apply, in the sense that optimal policy reactions to optimally estimated states of the economy are independent of the degree of uncertainty. The usual separation principle does not hold, since the estimation of the state of the economy is not independent of optimization and is in general quite complex. We present a general characterization of optimal filtering and control in settings of this kind, and discuss an application of our methods to the problem of the optimal use of ‘real-time’ macroeconomic data in the conduct of monetary policy. [Emphasis added by John Barrdear]

The sentence I’ve highlighted is interesting. As written in the abstract, it’s probably true. Here’s a paragraph from page two that expands the thought:

One may or may not believe that central banks typically possess less information about the state of the economy than does the private sector. However, there is at least one important argument for the appeal of this assumption. This is that it is the only case in which it is intellectually coherent to assume a common information set for all members of the private sector, so that the model’s equations can be expressed in terms of aggregative equations that refer to only a single “private sector information set,” while at the same time these model equations are treated as structural, and hence invariant under the alternative policies that are considered in the central bank’s optimization problem. It does not make sense that any state variables should matter for the determination of economically relevant quantities (that is, relevant to the central bank’s objectives), if they are not known to anyone in the private sector. But if all private agents are to have a common information set, they must then have full information about the relevant state variables. It does not follow from this reasoning, of course, that it is more accurate to assume that all private agents have superior information to that of the central bank; it follows only that this case is one in which the complications resulting from partial information are especially tractable. The development of methods for characterizing optimal policy when different private agents have different information sets remains an important topic for further research.

Here’s my attempt as paraphrasing Svensson and Woodford in point form:

- The real economy is the sum of private agents (plus the government, but ignore that)
- Complete information is thus, by definition, knowledge of every individual agent
- If we assume that everybody knows about themselves (at least), then the union of all private information sets must equal complete information
- The Central Bank observes only a sample of private agents
- That is, the Central Bank information set is a subset of the union of all private information sets. The Central Bank’s information cannot be greater than the union of all private information sets.
- One strategy in simplifying the Central Bank’s problem is to assume that private agents are symmetric in information (i.e. they have a common information set). In that case, we’d say that the Central Bank cannot have more information than the representative private sector agent. [See note 1 below]
- Important future research will involve relaxing the assumption in (f) and instead allowing asymmetric information across different private agents. In that world, the Central Bank might have more information than any given private agent, but still less than the union of all private agents.

Svensson and Woodford then go on to consider a world where the Central Bank’s information set is smaller than (i.e. is a subset of) the Private Sector’s common information set.

But that doesn’t really make sense to me.

If private agents share a common information set, it seems silly to suppose that the Central Bank has less information than the Private Sector, for the simple reason that the mechanism of *creating* the common information set – commonly observable prices that are sufficient statistics of private signals – is also available to the Central Bank.

In that situation, it seems more plausible to me to argue that the CB has *more* information than the Private Sector, provided that their staff aren’t quietly acting on the information on the side. It also would result in observed history: the Private Sector pays ridiculous amounts of attention to every word uttered by the Central Bank (because the Central Bank has the one private signal that isn’t assimilated into the price).

**Note 1:** To arrive at all private agents sharing a common information set, you require something like the EMH (in fact, I can’t think how you could get there *without* the EMH). A common information set emerges from a commonly observable sufficient statistic of all private information. Prices are that statistic.