A dynamic Nelson-Siegel yield curve model with Markov switching

Recent events have highlighted the potential importance of nonlinear efiects of flscal variables (notably debt and deflcits) on interest rates: While in times when government solvency is not a concern the standard crowding-out efiects are of moderate magnitude, in times when default risk becomes an issue the interest rate efiects can become very large. This paper provides new evidence on the magnitude of these efiects. For the case when default risk is not a concern, it uses an arbitrage-free term structure model to estimate the dynamic efiects of flscal policy shocks on interest rates along the entire maturity spectrum. For the case when default risk becomes a concern (thereby violating a central assumption of the term structure model), I present evidence based on EMU government bond spread regressions on time-varying efiects of national flscal policies on spreads as well as the time-varying sensitivity of yield spreads to international risk aversion as a function of the state of flscal policy. JEL classiflcation: E6, H6.

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

Dai and Singleton (2002) and Duffee (2002) show that there is a tension in affine term structure models between matching the mean and the volatility of interest rates. This article examines whether this tension can be solved by an alternative parametrization of the price of risk. The empirical evidence suggests that, first, the examined parametrization is not sufficient to solve the mean-volatility tension. Second, the usual result in the estimation of affine models, indicating that some of the state variables are extremely persistent, may have been caused by the lack of flexibility in the parametrization of the price of risk. Term structure models have several uses, including pricing fixed-income derivatives, managing the risk of fixed-income portfolios, and detecting relationships between the term structure of interest rates and macrovariables such as inflation and consumption. To perform well in these tasks, term structure models must be numerically and econometrically tractable while matching the empirical properties of the term structure movements. At least two empirical properties of the term structure of interest rates have been well established by financial economists over the years [see Dai and Singleton (2003) for a survey]. First, the term premium, or the expected excess return of Treasury bonds, has a high time variability. Second, the volatility of interest rates is time varying. These two properties are so prominent in the data that they will be referred to as stylized facts. While these two stylized facts are very well established in the empirical literature, affine term structure models are thoroughly discussed in the theoretical literature. Affine models are those in which the yield of zero coupon bonds are affine functions of the model state variables. Classic

Inflation Expectations and Monetary Policy in Thailand

Recent empirical research shows that a reasonable characterization of federal-funds-rate targeting behavior is that the change in the target rate depends on the maturity structure of interest rates and exhibits little dependence on lagged target rates. See, for example, Cochrane and Piazzesi (2002). The result echoes the policy rule used by (1994) to rationalize the empirical failure of the `expectations hypothesis' applied to the term- structure of interest rates. That is, rather than forward rates acting as unbiased predictors of future short rates, the historical evidence suggests that the correlation between forward rates and future short rates is surprisingly low. showed that a desire by the monetary authority to adjust short rates in response to exogenous shocks to the term premiums imbedded in long rates (i.e. yield-curve smoothing), along with a desire for smoothing interest rates across time, can generate term structures that account for the puzzling regression results of Fama and Bliss (1987). also clearly pointed out that this reduced-form approach to the policy rule, although naturally forward looking, needed to be studied further in the context of other response functions such as the now standard Taylor (1993) rule. We explore both the robustness of McCallum's result to endogenous models of the term premium and also its connections to the Taylor Rule. We model the term premium endogenously using two different models in the class of affine term structure models studied in Duffie and Kan (1996): a stochastic volatility model and a stochastic price-of- risk model. We then solve for equilibrium term structures in environments in which interest rate targeting follows a rule such as the one suggested by (i.e., the McCallum Rule). We demonstrate that McCallum's original result generalizes in a natural way to this broader class of models. To understand the connection to the Taylor Rule, we then consider two structural macroeconomic models which have reduced forms that correspond to the two affine models and provide a macroeconomic interpretation of abstract state variables (as in Ang and Piazzesi (2003)). Moreover, such structural models allow us to interpret the parameters of the term-structure model in terms of the parameters governing preferences, technologies, and policy rules. We show how a monetary policy rule will manifest itself in the equilibrium asset-pricing kernel and, hence, the equilibrium term structure. We then show how this policy can be implemented with an interest-rate targeting rule. This provides us with a set of restrictions under which the Taylor and Rules are equivalent in the sense if implementing the same monetary policy. We conclude with some numerical examples that explore the quantitative link between these two models of monetary policy.

The term structure of interest rates, i.e., yield curve, has long been of interest to monetary policymakers and their advisers. The transmission of monetary is conventionally viewed as running from shortterm interest rates managed by central banks to longer-term rates that influence aggregate demand. A central bank's leverage over longer-term rates comes from fact that market determines these as average expected level of short rates over relevant horizon (abstracting from a term premium and default risk). Working in other direction, long bond rate contains a premium for expected and, thus, serves as an indicator of credibility of a central bank's commitment to low inflation.1 Different theoretical perspectives support two above-mentioned uses of term structure for monetary policy: John Hicks's (1939) expectations theory of term structure supports first, and Irving Fisher's (1896) decomposition of nominal bond rates into expected and an expected real return supports second.2 The two views are compatible in principle, although reconciling them creates difficulties of interpretation in practice. For example, does a steepening yield curve indicate a loss of confidence in central bank's commitment to low inflation, or does it indicate that markets expect tighter in form of a higher path of short rates pursued by central bank? The yield curve contains information of use to monetary policymakers, but it needs to be interpreted in light of judicious subsidiary identifying conditions, together with other data on economy. Some circumstances lend themselves to clearer interpretations than others, and there are many pitfalls. Whether or not one regards longer-term interest rates as economic indicators or as part of transmission mechanism for policy, or both, term structure plays a potentially important role in policymaking process. In spite of its complexity, term structure cannot be ignored. This article addresses some issues involved in using term structure to conduct monetary policy. I begin by discussing long bond rate as an indicator of expectations. Second, I comment on role that bond rates have played in recent U.S. monetary history. Third, I explain how information in yield curve can be used to overcome what I call policy in pipeline problem. Fourth, I review recent empirical evidence supporting two theoretical views underlying our understanding of term structure. I explain how peso problems associated with inflation scares in bond market may help to account for a serious empirical failure of expectations theory of term structure. I also discuss evidence supporting view that significant movements in long-term interest rates are largely driven by expected inflation. Finally, I point out some pitfalls of using term structure to make tactical decisions. 1. PURSUING LOW INFLATION The Chairman of Federal Reserve Board, Alan Greenspan, supports a longrun goal for price stability such that the expected rate of change of general level of prices ceases to be a factor in individual and business decisionmaking.3 The long bond rate is particularly well suited to help a central bank assess degree to which it has achieved low defined in that way. One could compare behavior of yield on a long-term nominal bond to its behavior in a past period in which was very low and public was reasonably confident that it would stay low. For instance, in United States 30-year nominal bond rate ranged from around 3 percent to a little over 4 percent from mid-1950s until mid-1960s, a period in which averaged around 1 to 2 percent, and presumably, long-term expectations were no more than that.4 One would think that if Federal Reserve (the Fed) were to achieve full credibility for low inflation, long bond rate would once again move down to 3 to 4 percent range. …

Modeling the Term Structure of Interest Rates: Where Do We Stand?

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of square-integrable functions, and is characterised by the Fisher-Rao metric. In the nonparametric case the relevant geometry is determined by the spherical distance function of Bhattacharyya. In the context of term structure modelling, we show that minus the derivative of the discount function with respect to the maturity date gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that the general arbitrage-free yield curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that the theory of interest rate dynamics can be represented by a class of processes in Hilbert space. We also derive the dynamics for the central moments associated with the distribution determined by the yield curve.

A market based approach to inflation expectations, risk premia and real interest rates

Inflation expectation is an important indicator for policy makers and financial investors. To capture a more accurate real-time estimate of inflation expectation on the basis of financial markets, we propose an arbitrage-free term structure model across dierent countries. We first estimate inflation expectation by modeling the nominal and the inflation-indexed bond yields jointly for each country. The joint dy- namic model for inflation expectation is a cross sectional state space model combined with a GeoCopula model, which accounts for the default risk and the non Gaussian dependency structure over countries. We discover that the extracted common trend for inflation expectation is an important driver for each country of interest. More- over, the model extracts informative estimates of inflation expectations and will provide good implications for monetary policies.

Central banks pay close attention to inflation expectations. In standard models, however, inflation expectations are tied down by the assumption of rational expectations and should be of little independent interest to policy makers. In this paper, we relax the assumption of rational expectations with perfect knowledge and reexamine the role of inflation expectations in the economy and in the conduct of monetary policy. Agents are assumed to have imperfect knowledge of the precise structure of the economy and the policymakers' preferences. Expectations are governed by a perpetual learning technology. With learning, disturbances can give rise to endogenous inflation scares, that is, significant and persistent deviations of inflation expectations from those implied by rational expectations. The presence of learning increases the sensitivity of inflation expectations and the term structure of interest rates to economic shocks, in line with the empirical evidence. We also explore the role of private inflation expectations for the conduct of efficient monetary policy. Under rational expectations, inflation expectations equal a linear combination of macroeconomic variables and as such provide no additional information to the policy maker. In contrast, under learning, private inflation expectations follow a time-varying process and provide useful information for the conduct of monetary policy.

Nominal Interest Rates and the News

Short‐term interest rate processes determine the term structure of interest rates in an arbitrage‐free market and are central to the valuation of interest rate derivatives. We obtain parameter estimates and compare the empirical fit of alternative one‐factor continuous‐time processes for the South African short‐term interest rate (and hence of arbitrage‐free term structure models) using Gaussian estimation methods. We find support only for diffusions where the interest rate volatility is moderately sensitive to the level of the interest rate. Other common models with restrictions that either preclude this effect, or restrict it to be too high, do not fit the data. Differences in the specification of the drift function have no evident effect on model performance.

Modifying Gaussian Term Structure Models When Interest Rates are Near the Zero Lower Bound

Can monetary policy stimulate consumption through inflation expectations? We study how US consumers revise inflation expectations and readiness to spend in response to monetary policy shocks using a structural vector-autoregressive model, where we identify exogenous policy shocks with interest rate surprises around FOMC announcements. Based on survey data, we construct measures of changes in consumers’ readiness to spend conditional on how consumers update their inflation expectations. Expansionary policy shocks tend to increase readiness to spend conditional on higher expected inflation outside the zero lower bound (ZLB), but the effect is small. At the ZLB, consumers increasingly reduce their readiness to spend if they expect higher inflation. Overall, we find only limited evidence suggesting that policy-induced variations in inflation expectations are associated with adjustments that are in line with the predictions of standard macroeconomic models.