Neither Gullible Nor Unteachable Be: Signal Extraction and the Optimal Speed of Learning from Uncertain News

Abstract

In the development of modern thinking about policy measures that extend to entire economies, the question of what the private sector knows or undertakes to find out about the policymakers and their plans has loomed ever larger. Whether officials proclaim their programs of action boldly, keep them discreetly hidden, or even camouflage them with extra injections of indistinct (“white”) noise during execution, the private sector has to decide what to believe about the future to make its own best possible plans. Its beliefs will be formed on the basis of convictions gained about the modus operandi, steadfastness, and credibility of the authorities in view of their past record and current actions. If the private sector had a fixed set of objectives and knew about the data generating process through which signals of public policy action could be received, it would be straightforward to derive the optimal rate of learning that is conditioned on that process. However, if the data generating process cannot be extrapolated because it is unstable or at least time-varying or subject to abrupt discretionary change in some dimensions, optimal learning cannot be defined objectively and without appealing to prior conviction. Rather, learning can be recognized as optimal only to the extent the strength of prior convictions turns out to be just right for avoiding systematic errors during the learning process about the entire variety of situations that may be encountered with defined subjective probabilities. Hence if strings of one-sided errors keep being committed, the strength of prior convictions should be adjusted. These convictions would need to be strengthened if recent data proved not nearly as revealing as the gullible were inclined to think; on the other hand, convictions should be weakened if recent data revealed more about underlying changes than those who are unteachable were prepared to accept. This chapter tries to explain why and how economists have come to concern themselves with such matters of “faith” which bring them into close contact with other disciplines.