Efficient forecast tests for conditional policy forecasts

Central Banks regularly make forecasts, such as the Fed’s Greenbook forecast, that are conditioned on hypothetical paths for the policy interest rate. While there are good public policy reasons to evaluate the quality of such forecasts, up until now, the most common approach has been to ignore their conditional nature and apply standard forecast e¢ ciency tests. In this paper we derive tests for the e¢ ciency of conditional forecasts. Intuitively, these tests involve implicit estimates of the degree to which the conditioning path is counterfactual and the magnitude of the policy feedback over the forecast horizon. We apply the tests to the Greenbook forecast and the Bank of England’s in‡ation report forecast, …nding some evidence of forecast ine¢ ciency. Nonetheless, we argue that the conditional nature of the forecasts made by central banks represents a substantial impediment to the econometric analysis of their quality— stronger assumptions are needed and forecast ine¢ ciency may go undetected for longer than would be the case if central banks were instead to report unconditional forecasts. Keywords: Forecasting, monetary policy, weak instruments. JEL Classi…cation: C53, E37, E5. We thank Steven Durlauf, Chris Sims, Ellis Tallman and an anonymous referee for helpful comments and Je¤ Traczinski for valuable research assistance. NOTE: The view in this paper are solely the responsibility of the authors and should not be interpreted as re‡ecting the views of the Board of Governors of the Federal Reserve System or other members of its sta¤. 1. Introduction Forecasts have long played a prominent role in forming policy at central banks. Recently, forecasts have also become an important part of the way many Central Banks communicate with the public about policy. These facts provide many reasons to be interested in the quality of Central Bank (CB) forecasts. Poor forecasts could lead directly to errant policy. Further, from the standpoint of communicating with the public, the quality of the forecast is an important component of the signal-to-noise ratio for the communication scheme. Finally, the relative forecasting precision of the public and CB gives us a measure of the any information advantage of the CB, which is important in some theories of policy (e.g., Canzoneri, 1985). The nature of common CB forecasts is a signi…cant stumbling block to analysis of these forecasts. The Federal Reserve’s Greenbook forecast and the published forecasts of several in‡ation targeting CBs are conditioned on a particular path for the policy interest rate over the forecast horizon. One standard case is conditioning on an unchanged path for the policy interest rate over the forecast horizon. This approach may be adopted because the CB sta¤ do not wish explicitly to forecast the future decisions of policymakers, or because the CB does not wish to publish forecasts of future policy actions. Whatever the reason, the forecasts are conditioned on a path of interest rates that is counterfactual. That is, the path is not meant to be the CBs expectation of the policy rate. We will follow the literature in referring to these forecasts as conditional and contrasting them with unconditional forecasts, which are taken to be the CB’s expectations for the variables in question, conditioned only on the CB’s information at the time of the forecast. There is a long history of evaluating the quality of the Greenbook forecast by simply treating it as an unconditional forecast and applying standard forecast e¢ ciency tests. For example, Romer and Romer (2000) found that the Greenbook in‡ation forecast is e¢ cient and superior to private sector forecasts. These same exercises are also being conducted on the published forecasts of other central banks (e.g., Andersson, et al. 2005; Bank of England, 2004). The merits of the results of this work are unclear, given that the conclusions rest on an explicit or implicit assumption that the e¤ects of