Tag Archive for 'Information'

Who has more information, the Central Bank or the Private Sector?

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 di fferent private agents have di fferent information sets remains an important topic for further research.

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

  1. The real economy is the sum of private agents (plus the government, but ignore that)
  2. Complete information is thus, by definition, knowledge of every individual agent
  3. If we assume that everybody knows about themselves (at least), then the union of all private information sets must equal complete information
  4. The Central Bank observes only a sample of private agents
  5. 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.
  6. 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]
  7. 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.

    The Baltic Dry Index and the information value of markets

    I have some questions about on the Baltic Dry Index (a rough guide to the price of moving dry goods by sea – more detail available here):

    Low-information advertising

    Go here to read a wonderful question from Richard Posner.  It’s much too long to post here, but here is his topic:

    At the same time that sellers forgo much product disclosure that would seem advantageous both to them and to their customers, they make disclosures that have no information value and should not persuade any rational consumer, such as implausible, self-serving, and empty claims that their product is better, or super; and these claims are often wrapped in clever, funny pictures or anecdotes that are designed to seize the attention of the viewer, but that convey no information.

    Posner’s question is a simple one:  why?  In their typical conversational posting style, Gary Becker posted his opinion.  It’s again too long to post in it’s entirety, but two paragraphs of note are:

    Economists have generally not been friendly toward persuasive advertising since it is much easier with the usual economic analysis to discuss advertisements that provide information or misinformation. Yet tools are also available for considering the persuasive formation of attitudes and preferences with rational consumer behavior – see my book of essays, Accounting for Tastes, 1996. Although such an analysis of preference formation is dependent on some underlying psychological mechanisms that are not well understood, the process appears to be quite rational.

    That said, challenging puzzles remain in using economic analysis to explain the types of information used and not used in advertisements, whether or not there are comparisons to the products of rivals. However, given all the professional time and thought that goes into advertisements, I am reluctant to claim that advertisers are not rational in what they do, for we do not understand all the relevant considerations that enter into the determination of the types of persuasion and information that are highlighted.

    I have been fascinated by this for a while.  I think a good example lies in product packaging.  A year or two ago I was shopping for a new web-camera.  At the time, a major producer of webcams offered a “Webcam Live!” and a “Webcam Live! Pro”, with the latter 20% more expensive, in a noticeably larger box (despite housing a product of the same volume) and with insufficient information printed on either box to allow a potential customer to identify the functional difference between the two.

    More than simple vertical product differentiation, this seems to me to also be a form of “information discrimination”.  By denying the consumer the details of the differences between the two options and offering only general, suggestive signals of their respective quality, the producer seems to ensure that wealthier consumers will purchase the more expensive option and that poorer individuals will choose the cheaper option, irrespective of their functional or qualitative differences.  Armed with complete information, the wealthy consumer might recognise that they only require the functionality of the cheaper option, or the poorer consumer – who cannot afford the more expensive option – might consider the cheaper option insufficient for their needs and so not buy either.

    Of course, such a tactic on the part of the manufacturer would necessarily rely on two social norms: (a) that people generally accept the information presented to them and make their decision on that basis without seeking more; and (b) that people generally believe that information presented to them, if not entirely accurate, is at least indicative of the truth.

    We can expand this by considering the retail outlet that sells the webcams. The retailer would be capable of circumventing the producer’s packaging strategy by, for example, putting information cards beside the two boxes or employing highly knowledgeable retail staff. However, assuming that the retailer shares in the profit from the product sales and not just the revenue, it is in their best interest to collude with the producer and provide no additional information.  Without naming names, I can assure readers that this is exactly the scenario that I encountered (the no extra information, that is, not the collusion).

    Of course, the two companies would carry a risk of reputation damage as a result of their discrimination.  If, as seems intuitively reasonable to me, there is also a third social norm of tending to allot blame to the most visible perpetrator, the retailer carries the bulk of this risk.  How can they offset this?  By having an advertising campaign emphasise how helpful and informative their staff are …