Non-linearities and persistence in US long-run interest rates

Figures & data

Figure 1. 10-year US Bond yield (.USGG10Y index). Source: Bloomberg.

Figure 2. 10-Yr US Bond yield (average of monthly observations). Source: ECB.

Table 1. Estimates of the Non-linear I(d) Model

Time Series	d	θ0	θ1	θ2	θ3
Bloomberg monthly 10-year bond yield data (1962–2020)	0.84 (0.76, 0.95)	5.7635 (3.18)	1.7422 (1.66)	−1.9333 (−3.03)	−1.0016 (−2.20)
ECB monthly 10-year bond yield data (1900–2020)	0.83 (0.78, 0.89)	2.9648 (2.08)	−1.0753 (−1.28)	−0.6461 (−1.27)	1.741 (4.80)

In bold, significant coefficients at the 5% level. In parentheses, in columns 3–6, the associated t-values.

Table 2. Sub-sample analysis (white noise errors)

Bloomberg series
Subsamples	No terms	Intercept	Intercept and Trend
January 1962/September 1981	1.05 (0.96, 1.16)	0.99 (0.91, 1.11)	0.99 (0.90, 1.11)
October 1981/September 1987	0.97 (0.83, 1.16)	1.05 (0.90, 1.27)	1.05 (0.90, 1.26)
October 1987/August 2020	0.99 (0.92, 1.08)	1.00 (0.91, 1.11)	1.00 (0.91, 1.11)
ECB series
Subsamples	No terms	Intercept	Time trend
January 1900/December 1920	1.02 (0.93, 1.13)	1.05 (0.96, 1.17)	1.05 (0.96, 1.17)
January 1921/November 1945	0.98 (0.90, 1.08)	1.11 (0.99, 1.24)	1.10 (0.99, 1.24)
December 1945/September 1981	1.17 (1.09, 1.28)	1.16 (1.07, 1.29)	1.16 (1.07, 1.29)
October 1981/August 2020	0.94 (0.88, 1.02)	1.20 (1.10, 1.32)	1.19 (1.09, 1.32)

In bold significant coefficients at the 5% level. In parentheses, the 5% confidence intervals.