Monetary policy rules with model and data uncertainty.

• Author: Ghysels, Eric

1. Introduction

   In academic circles, model and data uncertainty are rarely discussed, even when the task at hand involves the construction of real-time forecasts and forecast model selection. By model uncertainty, we mean that the specification and/or parameters of a model are no longer assumed to be fixed and known. While ignoring this type of uncertainty often leads to tractable models that are easily analyzed, it may also paint a picture of the world that is oversimplified. By data uncertainty, we mean that first-released data are often noisy in the sense that incomplete and/or erroneous initial information has been used in their construction. Indeed, it may take many years of revisions before data are considered final.

   From the perspective of monetary policy rules, which we here use as a vehicle to discuss model and data uncertainty, it is worth stressing that actual policy decisions are made in a real-time setting using preliminary and/or partially revised data. Thus, questions relating not only to which variables should be used but also to which data releases should be used make the process of policymaking much more complex than it is typically assumed to be in abstract models of monetary policy. In this paper, we build real-time data sets and simulate a real-time policy-setting environment in which we assume that policy is captured by movements in the actual federal funds rate, and we then assess what sorts of policy rule models and what sorts of data best explain what the Federal Reserve Board (Fed) actually did. (1) This approach allows us not only to track the performance of alternative rules over time (hence facilitating a type of model selection among competing rules), but also to more generally assess the importanc e of the data revision process in the formation of macroeconomic time series models.

   The class of rules we consider are commonly referred to as Taylor's rules (see Taylor 1979, 1993a) and are motivated by the apparent existence of tradeoffs between inflation and output variability. Versions of these rules have been incorporated in and/or arise in a variety of different macroeconomic models. For example, Rotemberg and Woodford (1997, 1998) developed a rational-expectations model with intertemporally optimizing agents in which various interest rate-targeting rules arise as optimal responses of the monetary authority. This series of papers is important not only because monetary policy rules are shown to arise naturally when expected utility in a representative household is maximized, but also because the model allows for the computation of welfare measures for representative households under different monetary policy rule implementations. On the basis of their theoretical model, as well as a thorough empirical evaluation, Rotemberg and Woodford (1998) find that low and stable inflation together with stable interest rates can be achieved when Taylor's rules of the type we examine are augmented by the inclusion of lagged federal funds rates. Many other extensions and variations of Taylor's rule have been proposed in recent years. For example, policy rules that focus on exchange rates or the money supply are alternatives to rules that focus on interest rates. Indeed, the recent literature on policy rules is extensive. A partial list of relevant papers includes work by Bryant, Hooper, and Mann (1993), Henderson and McKibbin (1993), McCallum (1993, 2001), Taylor (1993b), Frankel and Chinn (1995), Fuhrer and Moore (1995), King and Wolman (1996), Fuhrer (1997), and Orphanides (2001). We take our policy rules as given and do not rationalize them with respect to any particular macroeconomic model. Thus, we do not attempt to offer new insights into the usefulness of policy rules per se (see, e.g., Taylor 1993a, b; Sargent 1999). Moreover, unlike Hansen and Sargent (2000), we do not examine the deeper issue of the effect of model uncertainty on the design of policy rules, as we do not concern ourselves with the specification of a theoretical model. Rather, our approach is to emphasize two related but different issues, namely, (i) model uncertainty viewed through the lens of parameter uncertainty and model specification and (ii) the availability and timing of data with which to examine and implement rules. Uncertainty in policy models is an issue that has recently received some attention in the literature, both from the perspective of model misspecification and from the perspective of learning. Examples of papers in this area include those of Granger and Deutsch (1992), Sargent (1999), Anderson, Hansen, and Sargent (2000), and Hansen and Sargent (2000). Related papers in the area of learning include those of Bray (1982), Marcet and Sargent (1989a, b), Woodford (1990), and Kuan and White (1994), and a review of the learning literature can be found in Marimon (1997).

   With regard to data uncertainty, the importance of the timing and availability of the data that are used in the empirical evaluation of policy rules is crucial. In order to address this important issue, we use real-time data sets to replicate the information available to private agents and policymakers at any given point in time in the day-to-day process of policy setting. In this sense, we simulate a real-time policy-setting environment. Our real-time data collection strategy ensures that "future information" due to the use of information that is temporally antecedent to the date under consideration is not (accidentally) incorporated into the data set at the wrong point in time. This is particularly important for seasonally adjusted data, for example, since two-sided filters are generally used in the construction of such data, and the reestimation of the filters after date t using, say, data from t + 1 and t + 2 results in a revised seasonally adjusted figure for t that actually contains information that was available beyond period t.

   Before discussing the relative merits of the use of real-time data sets, however, it is worth pointing out that within the context of timing (or availability), economic data can easily be classified into three types: (i) preliminary data, consisting of the first reported datum for each variable at each point in time; (ii) partially revised, or real-time, data, which are much more difficult to collect than preliminary data because they are made up of a full vector of observations at each point in time for each variable; and (iii) fully revised, or final, data, data which have been successively revised and to which no further revisions will be made. These are the types of data that academics often have in mind when conducting economic time series studies, perhaps simply because they are data that are not subject to revision, and it is felt that if one could adequately forecast a fully revised figure, then there would be no need for further modeling. It is quite possible, however, that true final data will never be available for many economic series. (2) Interestingly, most data sets constructed by applied economists clearly consist of a mixture of preliminary data, partially revised data, and final revised data but are clearly not real-time data sets. This poses a number of serious problems for any empirical analysis that is meant to be real-time in nature. Many of the problems associated with not using the "correct" data in the context of monetary policy rules are outlined in Orphanides (2001). Orphanides reconstructs Taylor's rule along the lines of Taylor (1993a) but for real-time data, and he demonstrates that real-time policy recommendations made on the basis of real-time data differ markedly from recommendations made on the basis of partially and fully revised data. In addition, Orphanides (2001) shows that estimated policy reaction functions based on fully revised data are very different from those based on real-time data. Although similar in many respects, our paper differs from that of Orphanides (2001) in a number of ways. For example, we use monthly data over a period of more than 20 years, examine parameter as well as model specification uncertainty, and also consider the effects of the use of seasonally adjusted versus unadjusted data. Orphanides (2001) instead uses quarterly data over the period 1987-1993 for comparison with the results of Taylor (1993a). In addition, we evaluate a large number of alternative policy rules and ascertain which one best mimics the historical record in a real-time setting in which rules are updated regularly as new information becomes available. Orphanides (2001), on the other hand, is more concerned with real-time policy recommendations that are made using Taylor's rule.

   In related work, Maravall and Pierce (1983, 1986), Trivellato and Rettore (1986), Ghysels (1987), Sargent (1989), and Swanson, Ghysels, and Callan (1999) examine revision process errors, while Fair and Shiller (1990), Diebold and Rudebusch (1991), Swanson and White (1995, 1997), and Croushore and Stark (2001) point out that the comparison of econometric forecasts based on data from CITIBASE, for example, with forecasts made in real time by professional forecasters (see, e.g., Croushore 1993) is invalid, strictly speaking, because real-time data are not used in the estimation of the econometric models.

   Our findings can broadly be summarized as a set of prescriptions and diagnoses that are useful not only in the context of monetary policy rule forecast model selection, but also in the context of the application of real-time data to macroeconomics in general. A partial list of our prescriptions and diagnoses is as follows.

   Vintage matters. For example, it is clear that the use of only "final" data does not yield optimal forecasting models. Thus, prediction precision, and hence monetary authority credibility, is affected by the vintage (or release) of data used. Adaptive least-squares learning yields improved results. In particular, while "calibration" is better than naive estimation...