December 9 2004 | John H. Cochrane and Monika Piazzesi
The appendix to the paper "Bond Risk Premia" by John H. Cochrane and Monika Piazzesi provides additional results and robustness checks. It includes:
1. **Unrestricted Forecasts**: Table A1 reports the point estimates, standard errors, and test statistics for the unrestricted regression of 1-year excess returns on forward rates. The regression coefficients are plotted in Figure 1, and the $R^2$ and other statistics are reported in Table 1B. The individual-bond regressions show high significance, similar to the regression of average excess returns on forward rates.
2. **Fama-Bliss Regressions**: Table A2 presents the estimates and statistics for the Fama-Bliss regressions, including confidence intervals for $R^2$ and small-sample distributions. The Fama-Bliss $R^2$ is just above the confidence interval where the $0.35 \ R^2$ values are significantly higher. Small-sample standard errors and $\chi^2$ statistics are also provided, showing that the small-sample statistics still reject the null hypothesis.
3. **Comparison with Fama-Bliss**: Table A3 compares the performance of the return-forecasting factor with the Fama-Bliss forward spread. The return-forecasting factor subsumes all the predictability of bond returns captured by the Fama-Bliss spread, as indicated by the unchanged coefficients and significance of the return-forecasting factor in the presence of the Fama-Bliss forward spread.
4. **Forecasting Short Rate Changes**: Table A4 shows that the Fama-Bliss regression does not capture the forecastability of short-term interest rate changes. The return-forecasting factor, however, successfully forecasts changes in 1-year yields, indicating that it subsumes the predictability of bond returns.
5. **Additional Lags**: Table A5 reports the results of including additional lags in the regression model. The $R^2$ for individual regressions mirrors the $R^2$ for the forecasts of bond average returns, and the restricted regressions are almost as effective as the unrestricted regressions.
6. **Eigenvalue Factor Models**: The appendix discusses the eigenvalue decomposition of yield curves and the factor structure of expected excess returns. The first factor captures almost all of the variation in expected excess returns, with a standard deviation of 5.16 percentage points.
7. **Robustness Checks**: The paper investigates robustness by comparing results across different datasets, subsamples, and real-time forecasts. It shows that the results are stable and consistent, suggesting a premium for real rather than nominal interest rate risk.
8. **GMM Estimates and Tests**: The appendix provides detailed calculations for the GMM estimates and tests, including the moment conditions, standard errors, and test statistics for the restricted and unrestricted models.
9. **Affine Model**: The appendix derives an affineThe appendix to the paper "Bond Risk Premia" by John H. Cochrane and Monika Piazzesi provides additional results and robustness checks. It includes:
1. **Unrestricted Forecasts**: Table A1 reports the point estimates, standard errors, and test statistics for the unrestricted regression of 1-year excess returns on forward rates. The regression coefficients are plotted in Figure 1, and the $R^2$ and other statistics are reported in Table 1B. The individual-bond regressions show high significance, similar to the regression of average excess returns on forward rates.
2. **Fama-Bliss Regressions**: Table A2 presents the estimates and statistics for the Fama-Bliss regressions, including confidence intervals for $R^2$ and small-sample distributions. The Fama-Bliss $R^2$ is just above the confidence interval where the $0.35 \ R^2$ values are significantly higher. Small-sample standard errors and $\chi^2$ statistics are also provided, showing that the small-sample statistics still reject the null hypothesis.
3. **Comparison with Fama-Bliss**: Table A3 compares the performance of the return-forecasting factor with the Fama-Bliss forward spread. The return-forecasting factor subsumes all the predictability of bond returns captured by the Fama-Bliss spread, as indicated by the unchanged coefficients and significance of the return-forecasting factor in the presence of the Fama-Bliss forward spread.
4. **Forecasting Short Rate Changes**: Table A4 shows that the Fama-Bliss regression does not capture the forecastability of short-term interest rate changes. The return-forecasting factor, however, successfully forecasts changes in 1-year yields, indicating that it subsumes the predictability of bond returns.
5. **Additional Lags**: Table A5 reports the results of including additional lags in the regression model. The $R^2$ for individual regressions mirrors the $R^2$ for the forecasts of bond average returns, and the restricted regressions are almost as effective as the unrestricted regressions.
6. **Eigenvalue Factor Models**: The appendix discusses the eigenvalue decomposition of yield curves and the factor structure of expected excess returns. The first factor captures almost all of the variation in expected excess returns, with a standard deviation of 5.16 percentage points.
7. **Robustness Checks**: The paper investigates robustness by comparing results across different datasets, subsamples, and real-time forecasts. It shows that the results are stable and consistent, suggesting a premium for real rather than nominal interest rate risk.
8. **GMM Estimates and Tests**: The appendix provides detailed calculations for the GMM estimates and tests, including the moment conditions, standard errors, and test statistics for the restricted and unrestricted models.
9. **Affine Model**: The appendix derives an affine