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

## Abstract

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.

## Keywords

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

### Acknowledgments

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.

## References

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