Modeling the yield curve with macro factors.

Among a myriad of existing financial assets, a zero-coupon bond stands out for its simplicity. This fixed-income instrument is a promise to pay one unit of money on a specified date. Its price today is a function of the expected level of future short-term interest rates plus an adjustment for risk. As a consequence, it contains valuable information regarding the expected development of the economy. The same information contained in bond prices can be expressed in terms of interest rates or yields to maturity. The cross-section of all yields to maturity at a certain point in time is called the term structure of interest rates or yield curve. The yield curve is therefore a concise representation of the forward-looking decisions taken by market participants expressed as equilibrium bond yields. There are a number of reasons to study what moves the yield curve over time. As mentioned before, one of these reasons is forecasting. A second reason is derivative pricing. The yield curve can, for example, be used to value coupon bonds since these can be considered as a portfolio of zero-coupon bonds. Debt policy is a third reason. When the government issues new debt it has to decide on the maturity of the new bonds. This choice might affect the shape of the yield curve since it depends on the supply of bonds with different maturities. Finally, a good understanding of the term structure dynamics is also crucial for the implementation of monetary policy. Although central banks have a direct control over short-term interest rates, these institutions are also concerned about the effects on long-term yields, which have an important effect, for example, on aggregate demand. In short, the importance of the term structure of interest rates can hardly be overstated. Modeling the yield curve dynamics has proven difficult. The price of a bond depends on two components that seem hard to model: the market's expectation regarding the future path of the economy, and the investors' attitude towards risk. As a result, despite the efforts made in the last thirty years, no definite model seems in sight. Nevertheless, among the many approaches developed in this field, one looks specially promising. Affine term structure models have provided an accurate fit of the yield curve, while being econometrically and numerically tractable. The previous literature on such models has, however, been based on latent factors without any macroeconomic interpretation. This thesis contributes to the field by proposing and estimating affine term structure models making use of macroeconomic aggregates. In Chapter 1, we introduce a no-arbitrage, continuous-time model of the term structure of interest rates making use of observed and unobserved factors with a macroeconomic interpretation. The model is applied to the U.S. economy. The results show that one is indeed able to explain in a satisfactory way the dynamics of the yield curve based on macroeconomic factors. The long-run expectations of macroeconomic variables play an important role in the description of the monetary policy rule applied by the central bank and in the explanation of long-term yield movements. The average one- and ten-year ahead inflation forecast implied by our model is in line with survey data provided by the Federal Reserve Bank of Philadelphia. The model also shows some forecasting power when compared to a simple random walk model, to an AR(1) and a VAR(1) representation, and to a standard three-factor latent model. The results also show that both observed and unobserved factors influence the risk premium of a bond. Chapter 2 uses a framework similar to the one presented in the previous chapter. The goal is to provide a much needed benchmark to assess the monetary policy implemented by the European Central Bank. We first estimate an affine term structure model applied to the German economy for the pre-EMU period (1987-1998). As before, the state space is composed of macroeconomic factors. We then apply the estimated Bundesbank monetary policy onto the EMU period (1999-2004). The results indicate that the observed nominal and real interest rates in Germany are significantly lower than they would have been in case the Bundesbank were still in charge of the monetary policy. Moreover, ECB spreads are on average larger than they would have been under the Bundesbank regime. In Chapter 3, we make use of an affine term structure model to filter in a consistent way the market's long-run inflation expectations. For this, we assume that such factor follows a martingale process. The main objective is to find a satisfactory explanation for the variation in long-term yields. The plausibility of the filtered long-run inflation expectation is assessed in two ways. We first show that it is in line with survey data provided by the Federal Reserve Bank of Philadelphia. We also provide evidence that such series is consistent with a model in which market expectations are an average of heterogeneous, agent-specific, inflation expectations. The model is also used to provide a macroeconomic interpretation to the standard "level", "slope" and "curvature" factors found in standard latent factor models. As expected, the "level" factor is mainly explained by the agent's long-run inflation expectation. The "slope" factor appears to reflect business cycle conditions, while the "curvature" factor seems to be related to the monetary policy stance of the central bank. Overall, the long-run inflation expectation is the predominant factor in explaining movements at the long end of the yield curve. Observed inflation and unobserved real interest rate have similar influences on the term structure -- a strong effect on short-term yields, decreasing with maturity. The output gap exerts a minor influence throughout the maturity spectrum. Both observed and unobserved variables also play an important role in the determination of the central bank monetary policy. A standard Taylor rule, based solely on observed inflation and output gap, is therefore too restrictive. Market prices of risk are clearly time-varying and also a function of the whole state vector. The estimation of the models without restricting the dynamics of the state space also proves important. This dissertation contributes to the affine term structure literature. We show that one is able to model jointly the dynamics of the yield curve and the macroeconomy in an accurate way. It improves therefore our understanding of the economic forces driving movements in the yield curve. This might be relevant to the design of monetary and debt policies, to the valuation of interest rate derivatives, and to the forecasting of the future path of the economy. The proposed model can also be used to assess the behavior of the ECB, a topic frequently discussed in the press without reference to an objective benchmark.