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Appendix: Description of Data
John Bluedorn, David Harvey, Ayhan Kose, Grace Li, Tara Sinclair, Herman Stekler and seminar audiences at George Washington University, and Goldman Sachs provided valuable comments that improved this work. At the time of writing this paper, the second author was with the Monetary and Capital Markets Department of the IMF.
Conference Board (2001), Section II describes the methodology. The criteria include concepts such as conformity (the series must conform well to the business cycle), consistent timing (the series must exhibit a consistent timing pattern over time as a leading, coincident or lagging indicator), and economic significance (cyclical timing must be economically logical), among others.
The indices are the Conference Board Coincident and Leading Indicators (CBCI and CBLI, respectively), OECD Leading Indicator for the U.S. (OECD-LI), and Chicago Fed’s National Activity Index (CFNAI).
In the application, we also experimented with a single regression using a moving average of an indicator variable, i.e.
See Galbraith and van Norden (2011) for a new approach where probability forecasts are evaluated using kernel estimators, instead of binary or other discrete groupings.
Clements and Harvey offer three alternative tests, and note that there is little to suggest the use of one formulation over another in the literature. We choose to use the Harvey et al. version, which is FE(2) in their notation, as it is most commonly used in recent empirical studies in the literature.
Note that the encompassing tests are based on estimated probit models but do not account for the parameter estimation uncertainty.
One can use alternative encompassing tests and different loss functions, The current version of the algorithm is based on QPS only.
Forecasts are called ‘pseudo’ out-of-sample as we use revised data, as opposed to real time. In that sense, the analysis here differs from a complete real-time out-of-sample forecasting exercise.
Note that we do not exactly calculate a coincident index as doing that would require using in-sample encompassing tests, as opposed to forecast encompassing tests. Yet, the difference between one-month-ahead versus current estimates of a recession should not be very significant.