مدل های اقتصاد کلان و منحنی بازده:یک ارزیابی مناسب

Many have questioned the empirical relevance of the Calvo–Yun model. This paper adds a term structure to three widely studied macroeconomic models (Calvo–Yun, hybrid and Svensson). We back out from observations on the yield curve the underlying macroeconomic model that most closely matches the level, slope and curvature of the yield curve. With each model we trace the response of the yield curve to macroeconomic shocks. We assess the fit of each model against the observed behaviour of interest rates and find limited support for the Calvo–Yun model in terms of fit with the observed yield curve, we find some support for the hybrid model but the Svensson model performs best.

Many have questioned the empirical relevance of the Calvo–Yun optimising model (see, for example, Rudd and Whelan, 2005). This paper examines the relationship between the yield curve and the macroeconomy using three models that have been widely used to study problems of optimal monetary policy. These models can be derived from intertemporal optimisation by households and firms with imperfect competition in goods markets, nominal rigidities arising from sticky prices and timing conventions. We use these models to solve for the yield curve (see, for example, Ellingsen and Söderström, 2001) and examine their ability to replicate three features of the curve—the level, slope and curvature—calculated from historical data.1 Our main results suggest that a model that is backward looking in prices and output does best. A model which is entirely forward looking does particularly badly.2 The term structure is an important conduit for the transmission of monetary policy to output and inflation. Understanding the yield curve is helpful for both market participants and the monetary authorities since yield curves can provide useful information about underlying expectations of inflation and output over a number of different horizons. Financial economists typically make use of factor models. For example, Knez et al. (1994), Duffie and Kan (1996), and Dai and Singleton (2000) all consider models in which a handful of unobserved factors explain the entire set of yields. By contrast monetary economists attempt to proxy these unobservable factors by macroeconomic conditions (Ang and Piazzesi, 2003, Piazzesi, 2005 and Wu, 2006). For example, Diebold et al. (2006) and Hordahl et al. (2008) argue that a joint macro-finance research strategy is likely to provide the most comprehensive understanding of the term structure. Macroeconomists see the short term interest rate as a policy instrument that the Central Bank uses to pursue objectives concerning the price level and output. Financial economists in turn will see the policy rate as a crucial building block for the whole term structure since each yield at a different maturity will be a risk adjusted average of future expected short term rates. Macroeconomics can contribute by providing the basis upon which the Central Bank sets interest rates. We add to this literature by examining how three stylised macroeconomic models, widely used in macroeconomic theory, can replicate key features of the term structure.3 We assess the fit of each model in terms of the behaviour of the model-consistent yield curve implied by each of the three macroeconomic models and the actual behaviour of the yield curve. As there is a literature that draws attention to the extent to which the yield curve can be informative about future output and inflation movements (Estrella and Hardouvelis, 1991 and Estrella and Mishkin, 1997) we also examine the ability of the artificial (or model consistent) yield curve to predict output and inflation dynamics. In this paper, we show that the predictive capabilities of the yield curve seem to stem from the markets’ forward-looking expectations of how the monetary authority will use the short term interest rate to stabilise incipient, or pipeline, inflation and output. The relationship between the volatility of the short and long term interest rates has also been of continuing interest to economists. In a seminal paper, Shiller (1979) drew attention to an important implication of the expectations model of the term structure, where the long term interest rate is the average of a stream of future expected short rates, the smoothing that this implies should provide limits on the volatility of the long rate. However, Shiller pointed out there appears to be excess volatility in long rates when the data is examined. To some extent, this problem persists in our analysis, as it looks quite difficult to replicate the term structure of volatility with completely forward-looking behaviour. By using a model in which shocks are amplified by an endogenous persistence mechanism the problem appears somewhat less intractable and in this regard we echo a solution offered by Turnovsky (1989, p. 323), who suggested that increasing the relative importance of persistence shocks would help explain ‘the apparent excess volatility of long term rates’. Building on the previous two points, this paper also contributes to the literature on persistence of macroeconomic variables and the need to develop models in which amplification and persistence occur (see, Kocherlakota, 2000). To match the observed mean and volatility of the yield curve, the paper suggests that we need models that generate their own persistence.4 The mechanism is as follows: with little or no internal propagation of shocks future output and inflation can be stabilised without recourse to persistent interest rate responses and hence future interest rates should display limited volatility. As the propagation mechanism becomes more persistent, a shock will create momentum for future pressure on output and on inflation and hence will require some response and volatility in future interest rates. The paper is organised as follows. In Section 2 we set out the models we will analyse and the term structure recursion, Section 3 outlines the key stylised facts on macroeconomic data and the yield curve, Section 4 outlines the results, and Section 5 draws some conclusions.

The recent macro-finance literature has attempted to exploit the implications of macroeconomics for the behaviour of the yield curve (see, for example, Piazzesi, 2005 and Rudebusch and Wu, 2008). This paper's clear result is that macroeconomic models need to build in substantially more endogenous persistence if a good mapping to yield curve behaviour is to be found. The results point to the difficulty a purely forward-looking macroeconomic model has in explaining the persistence in the term structure, the lead–lag relationships between interest rates, both short and long, and output and inflation and in the term structure of volatility. When endogenous persistence is incorporated, in a relatively simple manner, we find a marked improvement but also suggest that there is much work to be done in order to amplify model-consistent interest rates and fit a satisfactory macroeconomic model to the data. A promising route has been proposed by Kozicki and Tinsley (2001) who suggest some elements of learning to amplify interest rate responses. Both Gurkaynak et al. (2003) and Rudebusch and Wu (2008) attach an important role to persistent shocks in implicit inflation targets as a mechanism for providing a macro mapping, in a two factor model, back to the yield curve. In our paper, to some extent the persistence that is introduced into the dynamic process for inflation, by incorporating lagged effects seems to mimic this device. Our results show that a relatively close mapping to real world term structure data can be generated by reducing the forward-looking element in the determination of inflation.