Annex B: Graphs
B.2. Spectral analysis of equilibrium real interest rate
This annex contains estimates of the frequency domain indicators.
B.2.1. Australia Spectral density estimates: Australia1
In logarithm Graph B.2.1.1
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2 Real interest rate
Financial development index3 Real housing price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Spectral density, or power spectrum, is estimated using Welch’s method. It records the contribution of the component(s) belonging to a specific frequency or frequency band to the total variance of a stochastic process. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–20
Cospectral density estimates: Australia1
In logarithm, with real interest rate Graph B.2.1.2
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real housing price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Cospectral density, also known as cross power spectral density or cospectrum, is estimated using Welch’s averaged, modified periodogram method. It represents the covariance between the in-phase components of two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–12
Squared coherence estimates: Australia1
With real interest rate Graph B.2.1.3
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real housing price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Squared coherence, known as coherency, is estimated using Welch’s averaged periodogram method. It is similar to the coefficient of determination , and measures the strength of linear association between two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
0.0
Frequency-specific correlation coefficient estimates: Australia1
With real interest rate Graph B.2.1.4
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real housing price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 The frequency-specific coefficient of correlation measures the strength of correlation between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–0.2
Frequency-specific regression coefficient estimates: Australia1
Real interest rate as regressand Graph B.2.1.5
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real housing price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 The frequency-specific coefficient of regression indicates the degree of linear association between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
4
B.2.2. China
Spectral density estimates: China1
In logarithm Graph B.2.2.1
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2 Real interest rate
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Spectral density, or power spectrum, is estimated using Welch’s method. It records the contribution of the component(s) belonging to a specific frequency or frequency band to the total variance of a stochastic process. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–18
Cospectral density estimates: China1
In logarithm, with real interest rate Graph B.2.2.2
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Cospectral density, also known as cross power spectral density or cospectrum, is estimated using Welch’s averaged, modified periodogram method. It represents the covariance between the in-phase components of two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–12
Squared coherence estimates: China1
With real interest rate Graph B.2.2.3
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Squared coherence, known as coherency, is estimated using Welch’s averaged periodogram method. It is similar to the coefficient of determination , and measures the strength of linear association between two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
0.0
Frequency-specific correlation coefficient estimates: China1
With real interest rate Graph B.2.2.4
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The dashed lines indicate 95% confidence intervals. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”).
The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 The frequency-specific coefficient of correlation measures the strength of correlation between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–0.4
Frequency-specific regression coefficient estimates: China1
Real interest rate as regressand Graph B.2.2.5
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The dashed lines indicate 95% confidence intervals. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”).
The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 The frequency-specific coefficient of regression indicates the degree of linear association between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–5.0
B.2.3. India Spectral density estimates: India1
In logarithm Graph B.2.3.1
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2 Real interest rate
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Spectral density, or power spectrum, is estimated using Welch’s method. It records the contribution of the component(s) belonging to a specific frequency or frequency band to the total variance of a stochastic process. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–20
Cospectral density estimates: India1
In logarithm, with real interest rate Graph B.2.3.2
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Cospectral density, also known as cross power spectral density or cospectrum, is estimated using Welch’s averaged, modified periodogram method. It represents the covariance between the in-phase components of two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–12
Squared coherence estimates: India1
With real interest rate Graph B.2.3.3
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Squared coherence, known as coherency, is estimated using Welch’s averaged periodogram method. It is similar to the coefficient of determination , and measures the strength of linear association between two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
0.0
Frequency-specific correlation coefficient estimates: India1
With real interest rate Graph B.2.3.4
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The dashed lines indicate 95% confidence intervals. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”).
The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 The frequency-specific coefficient of correlation measures the strength of correlation between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–0.6
Frequency-specific regression coefficient estimates: India1
Real interest rate as regressand Graph B.2.3.5
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The dashed lines indicate 95% confidence intervals. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”).
The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 The frequency-specific coefficient of regression indicates the degree of linear association between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–1
B.2.4. Indonesia
Spectral density estimates: Indonesia1
In logarithm Graph B.2.4.1
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2 Real interest rate
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Spectral density, or power spectrum, is estimated using Welch’s method. It records the contribution of the component(s) belonging to a specific frequency or frequency band to the total variance of a stochastic process. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–20
Cospectral density estimates: Indonesia1
In logarithm, with real interest rate Graph B.2.4.2
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Cospectral density, also known as cross power spectral density or cospectrum, is estimated using Welch’s averaged, modified periodogram method. It represents the covariance between the in-phase components of two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
–12
Squared coherence estimates: Indonesia1
With real interest rate Graph B.2.4.3
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”). The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 Squared coherence, known as coherency, is estimated using Welch’s averaged periodogram method. It is similar to the coefficient of determination , and measures the strength of linear association between two stochastic processes at a specific frequency or frequency band. 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
Source: author’s calculations.
0.00
Frequency-specific correlation coefficient estimates: Indonesia1
With real interest rate Graph B.2.4.4
Share of population aged 39-64 Old age dependency ratio Working age population growth
KOF globalisation index2 KOF globalisation index (Economics)2
Financial development index3 Real equity price growth (YoY) Credit-to-GDP ratio
Real GDP growth (YoY) Saving rate Investment ratio
Horizontal axis indicates frequency ranging from 0 to ; vertical axis indicates spectral density. The dashed lines indicate 95% confidence intervals. The shaded area indicates the business-cycle frequency, ranging from six quarters (marked by “H”) to 32 quarters (marked by “L”).
The area between 0 and L corresponds to the low frequency range which contains the trend component.
1 The frequency-specific coefficient of correlation measures the strength of correlation between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).
1 The frequency-specific coefficient of correlation measures the strength of correlation between two stochastic processes at a specific frequency or frequency band. See Zhu (2005). 2 The overall KOF Index of Globalisation covers the economic, social and political dimensions of globalisation. For details on the Index and the Economics sub-index, see Dreher (2006) and Dreher, Gaston and Martens (2008). 3 For details on the financial development index, see Sahay et al (2015).