Title page
Contents
Abstract 2
Non-technical summary 3
1. Introduction 5
2. Data 8
2.1. Inflation-linked swap rates 9
2.2. Inflation survey forecasts 11
3. Stylised facts on ILS rates and inflation trend proxies 12
3.1. Observed π∗t proxies 12
3.2. Cointegration and common trend in ILS rates 13
3.3. Spanning tests 15
4. Model 18
4.1. A term structure model with a shifting endpoint 18
4.2. Accounting for inflation survey forecasts 20
5. Main results 21
5.1. Estimated π∗t 21
5.2. Expectations components and inflation risk premia 25
6. Breaking down the main results 28
7. Robustness tests 33
7.1. Regime shifts in the volatility of π∗t 34
7.2. Parameter restriction tests 35
8. Conclusion 36
Appendix A. Additional results from the preliminary analysis 38
Appendix B. An affine term structure model with fixed endpoint 43
Appendix C. Details of the Bauer and Rudebusch (2020) model 45
References 47
Table 1. Cointegration regressions and tests based on 10y ILS rates 14
Table 2. Spanning tests as in Joslin et al. (2014) 15
Table 3. Spanning tests based on one-period realised quarterly excess returns regressions 17
Table 4. ILS rates fitting errors 35
Table 5. Exclusion restriction tests 36
Figure 1. ILS rates and inflation survey forecasts 11
Figure 2. Inflation trend proxies and cointegration residuals 13
Figure 3. π∗t and observed proxies 22
Figure 4. Trend and cyclical components in ILS rates 24
Figure 5. ILS rates loadings on π∗t 25
Figure 6. Inflation expectations components and inflation risk premia 27
Figure 7. Expectations components 29
Figure 8. Average log-likelihoods as a function of ση 30
Figure 9. Fit of Consensus Economics survey forecasts 32
Figure 10. Fit of SPF forecasts 33
Figure 11. Estimated π∗t with regime shifts 35
Table A.1. Cointegration regressions and tests based on 2y ILS rates 40
Table A.2. Cointegration regressions and tests based on 5y ILS rates 41
Table A.3. Spanning tests based on one-period realised monthly excess returns regressions 42
Table A.4. Spanning tests based on one-period realised annual excess returns regressions 43
Figure A.1. Core inflation mean squared errors for different gain parameters ν and φ 39