be seen that macro factors track quite closely to the actual data and the fitting of the bond yields are reasonably good across maturities. This demonstrates that ATSM is adequate to jointly model the dynamics in bond yields and macro factors. Nevertheless, it is noted that the model-implied bond yields often bleach the zero lower bound and become negative during the sample periods after late 1995. This generates notable degree of pricing errors when the actual short-term bond yields are effectively zero. Figure 1 (c) depicts actual and estimated yields curve at specified four points including both of non-zero and zero interest rate policy periods. This graph indicates goodness of fit in terms of cross section aspect of time series of term structure of panel (b). Table 2 and Figure 2 report the corresponding results for the QTSM which imposes a quadratic mapping in between bond yields and macro factors. The filtered output and inflation factors as shown in Figure 2 (a) and (b) also track closely to the actual data, however, there is a substantial deviation of the monetary stance factor. The latter case indicates that the enforced quadratic mapping in the macro-finance QTSM can be potentially misspecified. In contrast to the ATSM, the model-implied bond yields of QTSM are guaranteed to be positive. Hence, the QTSM is able to produce a much better fit to the actual short-term bond yields near the zero lower bound. Figure 2 (c) draws a counterpart of the QTSM for the yields curve of the ATSM in Figure 1 (c).

## [ Insert Figures 1 and 2 around here ]

To understand how the term structure model predicts the responses of bond yields to shocks in the underlying macro variables (i.e., impulse response), it is important to take a closer look at the estimated factor loadings. Figure 3 reports the factor loadings of the estimated Gaussian ATSM using the recursive relationship (7) and the posterior means under Q-measure in Table 1. Because the short-term interest rate is taken as one of the state variables, we can impose the initial loading of the inflation and output factors: $ \delta_{1,2} $ and $ \delta_{1,3} $ at Eq.(5), to be zero as in Ang et al. (2011). For the ATSM, we see that the output and inflation loadings: $ b_{2} $ and $ b_{3} $ , are positive for all maturities, which is consistent with the Taylor rule specification. For example, a positive shock to output gap induces an upward shift and a steepening of the yield curve, which is consistent with the view that the slope of yield curve is highly related to economic outlook (Diebold and Rudebusch, 2013). As expected, the loading to the monetary stance: $ b_{1} $ , is less than one and hence the transmission effect of the short-term interest rate to the long-end of the yield curve is imperfect as can be seen from Figure 3.

Figure 4 reports the factor loadings of the estimated QTSM using the recursive relationship (12) and the posterior means under Q-measure in Table2. In contrast to the ATSM which only has 4 factor loadings, the QTSM provides in total 10 loading combinations to the three macroeconomic factors, including 4 loadings through the linear terms: $ a, b_{1}, b_{2}, b_{3} $ , and 6 loadings.