Empirical Economics

, Volume 52, Issue 1, pp 229–254 | Cite as

Forecast combination for discrete choice models: predicting FOMC monetary policy decisions

  • Laurent L. Pauwels
  • Andrey L. Vasnev


This paper provides a methodology for combining forecasts based on several discrete choice models. This is achieved primarily by combining one-step-ahead probability forecasts associated with each model. The paper applies well-established scoring rules for qualitative response models in the context of forecast combination. Log scores, quadratic scores and Epstein scores are used to evaluate the forecasting accuracy of each model and to combine the probability forecasts. In addition to producing point forecasts, the effect of sampling variation is also assessed. This methodology is applied to forecast US Federal Open Market Committee (FOMC) decisions regarding changes in the federal funds target rate. Several of the economic fundamentals influencing the FOMC’s decisions are integrated, or I(1), and are modeled in a similar fashion to Hu and Phillips (J Appl Econom 19(7):851– 867, 2004). The empirical results show that combining forecasted probabilities using scores generally outperforms both equal weight combination and forecasts based on multivariate models.


Forecast combination Probability forecast Discrete choice models Monetary policy decisions Real-time data 



The authors express their sincere thanks and gratitude for the constructive comments of Jan Magnus, Eddie Andersen, Heather Anderson, Rob Hyndman, Gael Martin, Tommaso Proietti, and Farshid Vahid as well as participants at the 4th International Conference on Computational and Financial Econometrics (CFE’10), 7th International Symposium on Econometric Theory and Applications (SETA), and seminar participants at Monash University, the University of Sydney, Macquarie University and Tilburg University.


  1. Anderson H, Vahid F (2001) Predicting the probability of a recession with nonlinear autoregressive leading indicator models. Macroecon Dyn 5:482–505Google Scholar
  2. Bates JM, Granger CWJ (1969) The combination of forecasts. Oper Res Q 20:451–468CrossRefGoogle Scholar
  3. Boero G, Smith J, Wallis KF (2011) Scoring rules and survey density forecasts. Int J Forecast 27:379–393CrossRefGoogle Scholar
  4. Braun SN (1990) Estimation of current-quarter gross national product by pooling preliminary labor-market data. J Bus Econ Stat 8(3):293–304Google Scholar
  5. Brier GW (1950) Verification of forecasts expressed in terms of probability. Mon Weather Rev 78:1–3CrossRefGoogle Scholar
  6. Capistrán C, Timmermann A (2009) Forecast combination with entry and exit of experts. J Bus Econ Stat 27(4):428–440CrossRefGoogle Scholar
  7. Claeskens G, Magnus JR, Vasnev A, Wang W (2016) The forecast combination puzzle: a simple theoretical explanation. Int J Forecast (forthcoming)Google Scholar
  8. Clemen RT (1989) Combining forecasts: a review and annotated bibliography. Int J Forecast 5:559–583CrossRefGoogle Scholar
  9. Clemen RT, Winkler RL (1999) Combining probability distributions from experts in risk analysis. Risk Anal 19:187–203Google Scholar
  10. Clements MP, Harvey DI (2011) Combining probability forecasts. Int J Forecast 27(2):208–223CrossRefGoogle Scholar
  11. Dawid AP (1986) Probability forecasting. In: Kotz S, Johnson NL, Read CB (eds) Encyclopedia of statistical sciences, vol 7. Wiley, New York, pp 210–218Google Scholar
  12. Diebold FX, Lopez JA (1996) Forecast evaluation and combination. In: Maddala GS, Rao CR (eds) Handbook of statistics. North-Holland, AmsterdamGoogle Scholar
  13. Diebold FX, Rudebusch GD (1989) Scoring the leading indicators. J Bus 62:369–391CrossRefGoogle Scholar
  14. Dueker M (1999) Measuring monetary policy inertia in target fed funds rate changes. Fed Reserve Bank St. Louis Rev 81(5):3–9Google Scholar
  15. Epstein ES (1969) A scoring system for probability forecasts of ranked categories. J Appl Meteorol 8:985–987CrossRefGoogle Scholar
  16. Feather PM, Kaylen MS (1989) Conditional qualitative forecasting. Am J Agric Econ 71(1):195–201CrossRefGoogle Scholar
  17. Genest C, Zidek JV (1986) Combining probability distributions: a critique and an annotated bibliography. Stat Sci 1:114–148CrossRefGoogle Scholar
  18. Geweke J, Amisano G (2011) Optimal prediction pools. J Econom 164(1):130–141CrossRefGoogle Scholar
  19. Ghysels (1993) On scoring asymmetric periodic probability models of turning-point forecasts. J Forecast 12:227–238CrossRefGoogle Scholar
  20. Good I (1952) Rational decisions. J R Stat Soc Ser B 14(1):107–114Google Scholar
  21. Hall SG, Mitchell J (2007) Combining density forecasts. Int J Forecast 23:1–13CrossRefGoogle Scholar
  22. Hamilton JD, Jorda O (2002) A model of the federal funds rate target. J Polit Econ 110(5):1135–1167CrossRefGoogle Scholar
  23. Hendry DF, Clements MP (2004) Pooling of forecasts. Econom J 7:1–31CrossRefGoogle Scholar
  24. Hendry DF, Hubrich K (2011) Combining disaggregate forecasts or combining disaggregate information to forecast an aggregate. J Bus Econ Stat 29(2):216–227CrossRefGoogle Scholar
  25. Hoeting JA, Madigan D, Raftery AE, Volinsky CT (1999) Bayesian model averaging: a tutorial. Stat Sci 14:382–401CrossRefGoogle Scholar
  26. Hu L, Phillips PCB (2004a) Dynamics of the federal funds target rate: a nonstationary discrete choice approach. J Appl Econom 19(7):851–867CrossRefGoogle Scholar
  27. Hu L, Phillips PCB (2004b) Nonstationary discrete choice. J Econom 120(1):103–138CrossRefGoogle Scholar
  28. Kamstra M, Kennedy P (1998) Combining qualitative forecasts using logit. Int J Forecast 14:83–93CrossRefGoogle Scholar
  29. Kauppi H (2012) Predicting the direction of the fed’s target rate. J Forecast 31(1):47–67CrossRefGoogle Scholar
  30. Kim H, Jackson J, Saba R (2009) Forecasting the fomc’s interest rate setting behavior: a further analysis. J Forecast 28:145–165CrossRefGoogle Scholar
  31. Lancaster T (2004) An introduction to modern Bayesian econometrics. Blackwell Publishing, MaldenGoogle Scholar
  32. Lichtendahl KC Jr, Winkler RL (2007) Probability elicitation, scoring rules, and competition among forecasters. Manag Sci 53(11):1745–1755CrossRefGoogle Scholar
  33. McCabe BP, Martin GM, Harris D (2011) Efficient probabilistic forecasts for counts. J R Stat Soc Ser B 73(3):1–20Google Scholar
  34. Monokroussos G (2011) Dynamic limited dependent variable modeling and U.S. monetary policy. J Money Credit Bank 43(2–3):519–534CrossRefGoogle Scholar
  35. Murphy AH, Daan H (1985) Forecast evaluation. In: Murphy AH, Katz RW (eds) Probability, statistics and decision making in the atmospheric sciences. Westview Press, Boulder, pp 379–437Google Scholar
  36. Ng J, Forbes CS, Martin GM, McCabe BP (2010) Non-parametric estimation of forecast distributions in non-Gaussian state space models. Monash University, MimeoGoogle Scholar
  37. Orphanides A (2001) Monetary policy rules based on real-time data. Am Econ Rev 91(4):964–985CrossRefGoogle Scholar
  38. Pauwels LL, Vasnev AL (2016) A note on the estimation of optimal weights for density forecast combinations. Int J Forecast 32(2):391–397CrossRefGoogle Scholar
  39. Pesaran MH, Pick A (2011) Forecast combination across estimation windows. J Bus Econ Stat 29(2):307–318CrossRefGoogle Scholar
  40. Raftery AE, Madigan D, Hoeting JA (1997) Bayesian model averaging for linear regression models. J Am Stat Assoc 92:179–191CrossRefGoogle Scholar
  41. Rodebusch G (2002) Term structure evidence on interest rate smoothing and monetary policy inertia. J Monet Econ 49:1161–1187CrossRefGoogle Scholar
  42. Rodebusch G (2006) Monetary policy inertia: Fact or fiction? Int J Central Bank 49:85–135Google Scholar
  43. Smith J, Wallis KF (2009) A simple explanation of the forecast combination puzzle. Oxf Bull Econ Stat 71:331–355CrossRefGoogle Scholar
  44. Taylor JB (1993) Discretion versus policy rules in practice. Carnegie-Rochester Conf Ser Public Policy 39(1):195–214CrossRefGoogle Scholar
  45. Timmermann A (2006) Forecast combinations. In: Elliott G, Granger C, Timmermann A (eds) Handbook of economic forecasting, vol 1. Handbook of economics 24. Elsevier, Horth-Holland, pp 135–196Google Scholar
  46. Vasnev AL, Skirtun M, Pauwels LL (2013) Forecasting monetary policy decisions in Australia: a forecast combination approach. J Forecast 32(2):151–166CrossRefGoogle Scholar
  47. Wallis KF (2005) Combining density and interval forecasts: a modest proposal. Oxf Bull Econ Stat 67:983–994CrossRefGoogle Scholar
  48. Wallis KF (2011) Combining forecasts—forty years later. Appl Financ Econ 21:33–41CrossRefGoogle Scholar
  49. Winkler RL (1993) Evaluating probabilities: asymmetric scoring. Manag Sci 4:1395–1405Google Scholar
  50. Winkler RL (1996) Scoring rules and the evaluation of probabilities (with discussion). Test 5(1):1–60CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.The University of Sydney Business School Abercrombie Building (H70)DarlingtonAustralia

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