Title: Essays on monetary policy with informational frictions
Description: This dissertation contains three essays on monetary policy under informational frictions. All three chapters study the situation in which the private sector has imperfect information about the underlying economy and extracts information about the unobserved shocks from the central bank's interest rate decisions. In this situation, monetary policy has an informational effect, in addition to its direct effect on the nominal budget of the household. Chapter 1 studies how the equilibrium interest rate of an optimizing discretionary central bank is changed when the interest rate has an informational effect. I build a New Keynesian model in which firms are subject to both nominal frictions and informational frictions. There are two types of aggregate shocks in the private sector: the natural-rate shock, which is mapped from the aggregate component of technology shocks, and the cost-push shock, which is mapped from the aggregate component of wage-markup shocks. The central bank has perfect information on the realization of shocks, and has only one policy instrument which is the nominal interest rate.

Private agents do not observe the realization of shocks, and use the interest rate as a public signal to extract information about the shocks. I show that the equilibrium discretionary monetary policy reacts more aggressively to natural-rate shocks and less aggressively to cost-push shocks, relative to the optimal response under perfect information. Chapter 2 analyzes the how the informational effect of interest rates leads to the gains from commitment, and its implications on optimal direct communication strategy. Built upon the model in the previous chapter, I show how commitment to a state-contingent policy rule can change the sensitivity of expected shocks to the interest rate. The key mechanism that yields the gains from commitment is analyzed through the lens of the Phillips curve, which shows the output gap versus inflation trade-off becomes endogenous to the central bank's interest-rate decisions. In addition to optimally control the beliefs in the private sector through policy commitment, this chapter also studies the optimal direct communication strategy which interacts with the informational effect through policy rates.

Finally, Chapter 3 explores the optimal strategy for the central bank to conduct monetary policy when both the private sector and the central bank face imperfect information. Forward guidance is modeled as the central bank providing its expectations on monetary policy, conditional on its own imperfect information. I compare three strategies of forward guidance. The first strategy is called instrument-based forward guidance, in which case the central bank announces and commits to its estimate of future policy actions conditional on its information which is currently noisy. The second strategy is called Delphic forward guidance, in which case the central bank only reveals its noisy information, and waits to decide the actual monetary policy when perfect information becomes available. I show that the optimal Delphic forward guidance involves the central bank doing backward induction, where it takes into account the change in the beliefs in the private sector due to its re-optimization in later periods.

Lastly, I show the optimal monetary policy is rule-based Odyssean forward guidance, which is a state-contingent commitment that specifies how the central bank reacts to both the actual shock and the noise in its own information.