The Predictive Space, or, If x predicts y, what does y tell us about x?
A predictive regression for y(t) and a time series representation of the predictors, x(t), together imply a univariate reduced form for y(t). In this paper we work backwards, and ask: if we observe y(t), what do its univariate properties tell us about any x(t) in the "predictive space" consistent with those properties? We provide a mathematical characterisation of the predictive space and certain of its derived properties. We derive both a lower and an upper bound for the R^2 for any predictive regression for y(t). We also show that for some empirically relevant univariate properties of y(t), the entire predictive space can be very tightly constrained. We illustrate using Stock and Watson's (2007) univariate representation of inflation.
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- Campbell, John Y & Mankiw, N Gregory, 1987.
"Are Output Fluctuations Transitory?,"
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MIT Press, vol. 102(4), pages 857-80, November.
- John Y. Campbell & N. Gregory Mankiw, 1986. "Are Output Fluctuations Transitory?," NBER Working Papers 1916, National Bureau of Economic Research, Inc.
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- Marc P. Giannoni & Jean Boivin, 2005.
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431, Society for Computational Economics.
- Jean Boivin & Marc Giannoni, 2006. "DSGE Models in a Data-Rich Environment," NBER Technical Working Papers 0332, National Bureau of Economic Research, Inc.
- Boivin, J. & Giannoni, M., 2007. "DSGE Models in a Data-Rich Environment," Working papers 162, Banque de France.
- Jean Boivin & Marc Giannoni, 2006. "DSGE Models in a Data-Rich Environment," NBER Working Papers 12772, National Bureau of Economic Research, Inc.
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