Date of Degree


Document Type


Degree Name





Thom Thurston

Committee Members

Temisan Agbeyegbe

Wim Vijverberg

Subject Categories

Economics | Economic Theory | Macroeconomics


Taylor principle, optimal Taylor rules, combination policy, unobservable shock, money signal


The dissertation consists of three Chapters. I consider New Keynesian models which involve tradeoffs between output gap and inflation variances. Such policy strategy is often referred to as flexible inflation targeting rules (e.g., Lars Svensson 2011, pp.1238-95). Taylor rules, in general, have the symbolic expression 𝑖t=πœ‘xπ‘₯t+πœ‘πœ‹πœ‹t+πœ‘g𝑔t, where 𝑖t is the nominal interest rate at period t, π‘₯t is the target variable output gap at period t, πœ‹t is the target variable inflation rate at period t, 𝑔t is realized shock to output gap at period t, and πœ‘x, πœ‘πœ‹ and πœ‘π‘” are coefficients. This three-term Taylor rule is the most efficient Taylor rule in terms of the social welfare loss measurement (i.e., the minimized social welfare loss involved with the three-term Taylor rule is the smallest value when we compare it with the minimized social welfare loss involved with a one-term Taylor rule (𝑖𝑑=πœ‘πœ‹πœ‹π‘‘) or a two-term Taylor rule (𝑖𝑑=πœ‘π‘₯π‘₯𝑑+πœ‘πœ‹πœ‹π‘‘).) Thus, the three-term Taylor rule is used as the benchmark for comparing the performance of Taylor rules in the dissertation.

Chapter 1 argues that the dynamic interpretation most authors have put on the β€œstability and uniqueness” (determinacy) condition of the new Keynesian monetary policy model is inappropriate. Literatures authors maintain a belief when monetary policy is operating through a Taylor rule, the model stability and uniqueness requires the real interest rate move in the same direction as inflation (Taylor Principle). This chapter shows the determinacy condition does not necessarily require the Taylor Principle to hold. The Taylor Principle and the determinacy condition are two different kettles of fish.

Although the three-term Taylor rule is applied in Chapter 1, some people may object or think that it is impractical or β€œunrealistic” to expect the central bank (β€œthe Fed”) bases a rule on a shock term (πœ‘π‘”π‘”π‘‘). Thus, in Chapter 2 and Chapter 3, I examine two-term (β€œsimple”) Taylor rules which do not have πœ‘π‘”π‘”π‘‘ termβ€”i.e., 𝑖𝑑=πœ‘π‘₯π‘₯𝑑+πœ‘πœ‹πœ‹π‘‘.

Chapter 2 is a study of the linear relationship of the coefficients πœ‘π‘₯ and πœ‘πœ‹ in Taylor rules, which πœ‘π‘₯ is the coefficient to the target variable output gap (π‘₯𝑑) and πœ‘πœ‹ is the coefficient to the target variable inflation rate (πœ‹π‘‘). Furthermore, since I use only π‘₯𝑑 and πœ‹π‘‘ in Taylor rules instead of using π‘₯𝑑 and π‘π‘‘βˆ’π‘π‘‘βˆ’1 (i.e., the difference between price levels in two periods) in Taylor rules, the Taylor rules do not cause optimal inertia. In other words, the Fed has once-and-for-all response to the new development in either π‘₯𝑑 or πœ‹π‘‘, or both. Such new developments are either from realized output gap shocks or inflation rate shocks or both. The monetary policy objective function is then treated as a period quadratic social welfare loss function for two target variables and their coefficients because the solution expectation for all periods is the same as the solution for period t. The optimal policy implies that, especially, the coefficients πœ‘π‘₯ and πœ‘πœ‹ must produce minimum social welfare loss to the economy when the Fed’s monetary policy target is based on the tradeoffs between two target variables inflation rate πœ‹π‘‘ (not price levels) and output gap π‘₯𝑑. For those policy-rate paths (expressed by Taylor rules) which the minimum social welfare losses are guaranteed, I use the term optimal Taylor rules, and for those coefficient vi values satisfied this purpose, I called them optimal coefficients or optimal linear relationship among those coefficients. The natural optimum Taylor rule, as pointed out by Woodford (2001), would have the πœ‘π‘” term (=𝜎), but for the reason in the previous paragraph, I only examine the case of a simpler Taylor rule, 𝑖𝑑=πœ‘π‘₯π‘₯t+πœ‘πœ‹πœ‹π‘‘ (hereafter this Taylor rule is called the simple Taylor rule or the simple TR), when the rule is specified as the optimal interest rate rule for governing the optimal paths of output gap and inflation rate. The global-type solutions with β€œoptimal inertia” will not be considered in all chapters.

The first part of Chapter 2 develops an approach to obtain the linear relationship of πœ‘π‘₯ and πœ‘πœ‹ which is the first order condition for minimum social welfare loss, 𝐿=1/2*[πœ‹π‘‘2+𝛀π‘₯𝑑2], where L denotes social welfare loss, E is the expectational operator and 𝛀 is the weights on output gap.

The second part of Chapter 2 is the discussion of two properties of the linear relationship of πœ‘π‘₯ and πœ‘πœ‹ that are observed by comparing with the three-term Taylor: (a) the linear relationship is the same for governing the optimal paths of π‘₯𝑑 and πœ‹π‘‘ whether g-shocks are nullified by containing πœ‘g=𝜎 in the baseline new Keynesian model or not; (b) the limit of the social welfare loss containing the simple Taylor rule (𝑖𝑑=πœ‘π‘₯π‘₯𝑑+πœ‘πœ‹πœ‹π‘‘) is at the minimum when the values of πœ‘π‘₯ and πœ‘πœ‹ are very big (or approaching infinity), and such minimum is the same as the social welfare loss containing the three-term Taylor rule. This implies the three-term Taylor rule with πœ‘π‘”(=𝜎) suggested by Woodford (2001), whose model has different setup but it works out with the same result, is more efficient than the simple (two-term) Taylor rule.

In Chapter 3, using the method developed from and the two properties discovered in Chapter 2, I propose a combination monetary policy rule when the Fed sets the interest rate before observing current variables of output gap (π‘₯𝑑) and inflation (πœ‹π‘‘). The missing information is πœ€π‘‘ in π‘₯𝑑 equationβ€”i.e., 𝑔𝑑=πœ†π‘”π‘‘βˆ’1+πœ€π‘‘ where πœ€π‘‘~𝑖𝑖d 𝑁 (0,πœ€2), and πœ‚π‘‘ in πœ‹π‘‘ equationβ€”i.e., 𝑒𝑑=πœŒπ‘’π‘‘-1+πœ‚π‘‘ where πœ‚t~𝑖𝑖d 𝑁 (0,πœŽπœ‚2). Thus, the Fed cannot adjust their interest rate for those shocks because the Fed cannot observe πœ€π‘‘ and πœ‚π‘‘. On the other hand, the information of money is immediately available to the Fed when I use a model as abstract representation of the Fed’s observation of money surprise, so the Fed can use signals about money to adjust their interest rate. My model of the Fed’s operation on how they observe money surprise is a simplified model for making a theoretical point, not for the purpose of improving what the Fed is actually doing. The combination policy of a Taylor rule and money signal can improve the social welfare loss when the Fed sets their monetary policy with unobservable shocks. Chapter 3 uses an inverted version of Poole’s (1970) combination policy analysis and shows that the social welfare loss is improved from the money signals.