The Optimal Interest Rate Rules: General Theory And Applications

Interest-rate rules theory, which views short-term interest rate as monetary policy instrument, reflects the new ideas and efforts of monetarists engaged in monetary policy. Two problems have to be resolved in this theory, that is, "what effects does an interest rate policy shock have on non-policy variables?" and "what is characteristic of a good interest-rate rule?" A typical interest-rate rule means that short-term interest rate is an endogenous feedback function of non-policy variables, so that the problems can be analyzed in the framework of general equilibrium models. However, the results of discussion do not satisfy the criterion of robustness and science, because of interest rate rules being predetermined by individual preferences of monetarists. As a result, the reliability of the conclusions deduced from the assumption that interest rate is an endogenous feedback function of non-policy variables is impaired. In a sense, until endogenous interest-rate rules find out a firmer micro-foundation for themselves, 'art of science' does not fall on the shoulders of interest-rate rules theory.This paper, in the case of an improved general linear rational-expectations model and under full time consistency criterion, gives a new explanation to the optimal interest-rules theory developed by Giannoni and Woodford (2002) . The optimal interest-rules theory is the breakthrough and development of the traditional one. Not only does it succeed to the same way as the latter strives for being 'an art of science', but also bases macroeconomic analysis of monetary policy on a firmer, more normative and more scientific micro-foundation. As a consequence, the dreams of making interest-rate rules theory evolve into a true 'art of science' maybe come true, and then the optimal interest-rules theory developed here does be the kernel of this whole 'art of science'. Three core questions are raised and answered in turn in this thesis, namely intrinsic properties, alternative forms and extrinsic aspects of full time consistent optimal interest-rate rules, which offer an outline for the new theory. The first question leads us to bringing forward three criteria used to define essentially an optimal interest-rate rule. The second question provides an opportunity for us to distinguish between Taylor rules (or instrument rules) and non-Taylor targeting rules. And the third question guides logically our attention to seeking what is characteristic of a full time consistent robustly optimal instrument rule or full time consistent a robustly optimal targeting rule.Specifically, besides the introduction and summary, the text divides naturally into four chapters.Chapter 2 gives a survey to interest-rate rules theory. In this chapter, relevant empirical literatures, theoretical literatures and policy evaluation literatures are all touched on in a systematic logical way. The important facts and conclusions laid out here either are quantitative descriptions or are qualitative definitions of optimal interest-rate rules. However, these descriptions and definitions undoubtedly result in indeterminate equilibriums or non-robust interest-rate rules, or even if neither is the case, the disadvantage that interest-rate rules are simply came up with by preferences of monetary analysts is unavoidable. Thus, following the significations of 'art of science' and the criteria of optimality, traditional interest-rate rules are not scientific and not optimal. It is the inferiority that lays a foundation for the following chapters.Chapter 3～4 constitute improvement on a general theory of optimal interest-rate rules. In chapter 3, we propose three criteria of optimality that are full time consistency criterion, determinacy criterion and robustness criterion. These three criteria amount to different equations or inequalities, corresponding to non-economic restrictions as a part of the general linear rational-expectations model constructed in next chapter. Therefore, criteria of optimality characteristic of a good interest-rate rule serve as an additional filter and more efficient an approach to identification of optimal forms of policy rules.Improvement on the general linear rational-expectations model is presented in chapter 3. Also, characterization of full time consistent dynamics of optimal equilibrium and proof of existence of full time consistent optimal interest-rate rules are accomplished in this chapter. Furthermore, in the framework of the linear rational-expectations model, we discuss general forms of full time consistent robustly optimal instrument rules and full time consistent robustly optimal targeting rules. We find that whatever alternative forms optimal policy rules take, they conform to three criteria of optimality, and some extrinsic aspects such as rational expectation, inertia and minimal inertia are always characteristic of them. As far as inertia is concerned, a full time consistent robustly optimal targeting rule is inertial to a lower degree than a full time consistent robustly optimal instrument rule, but hardly can we make certain that one policy rule is superior to the other. As a matter of fact, each policy rule has its strong point, for example, instrument rules have the advantage of 'flexibility' and targeting rules gain from 'operationality'. A full time consistent robustly optimal instrument rule can be interpreted equivalently as a full time consistent robustly optimal targeting rule, which indicates that full time consistent robustly optimal interest-rate rules combination containing both policy rules is optimal.Chapter 5 constitute applications of optimal interest-rate rules theory. In the chapter, we improved four cases brought forward by Giannoni and Woodford (2002)。Under the circumstances, besides inertia, other apparent features such as super-inertia, directness, minimal inertia, implicitness and limited mean distance of expectation are characteristic of a full time consistent robustly optimal instrument rule, while the features such as limited mean distance of expectation, inflation-forecast target bias and trade-off are characteristic of a full time consistent robustly optimal targeting rule. Additionally, the locus of the numerical values of mean distance of expectation is reviewed, and we come to a conclusion that mean distance of expectation is no more than five quarters. Thus we find little justification for a policy that give primary attention to the targeting variables forecast at a horizon five quarters longer in the future, the mean future horizon of inflation forecast is equal to two years for instance, as is true of the inflation-forecast targeting currently practiced at the Bank of England.