The amplifier/divider mechanism of the financial cycle

Abstract

The financial cycle can play a decisive role in the transmission of monetary policy decisions. The impact of these decisions is amplified when the financial cycle is booming, and it is compressed when this cycle is busting. Considering this amplifier/divider mechanism in a semi-structural NKM, estimated for the US economy using Bayesian techniques, confirms this conclusion and improves the decision of raising or lowering the interest rate.

Appendices

Appendix 1 Used data

The model is estimated on quarterly data of the US economy over the period 1970–2018. The variables used are:

• 1. Real GDP

  • Source: U.S. Bureau of Economic Analysis.

  • Unit: US Dollars.

  • Methodological Details: Chained 2012 prices and seasonally adjusted.

• 2. Consumer Price index

  • Source: Organization for Economic Co-operation and Development.

  • Unit: Index (base year 2010).

  • Methodological Details: Global, seasonally adjusted.

• 3. Unemployment rate

  • Source: U.S. Bureau of Labor Statistics.

  • Unit: Percentage.

  • Methodological Details: Quarterly average of the monthly national unemployment rate, seasonally adjusted.

• 4. Nominal interest rate

  • Source: Organization for Economic Co-operation and Development.

  • Unit: Percentage.

  • Methodological details: 3-months interbank rates for the United States.

• 5. Credit and loans granted by commercial banks

  • Source: Board of Governors of the Federal Reserve System (US).

  • Unit: US Dollars.

  • Methodological details: Seasonally adjusted level at the end of the quarter.

• 6. Residential Property Prices Index

  • Source: Bank for International Settlements.

  • Unit: Index (base year 2010).

  • Methodological Details: Covers all types of existing housing throughout the country. The series is deflated by the CPI.

• 7. Consumer confidence Index

  • Source: Organization for Economic Co-operation and Development.

  • Unit: Index (Amplitude adjusted, Long-term average = 100).

  • Methodological Details: Quarterly average of the monthly data.

Appendix 2: Composite Index of Financial Dynamics

In the absence of a variable allowing to describe the financial cycle in an aggregated way, several researchers have proposed composite indexes to describe in a synthetic way this cycle. The principle of these indices is globally the same (see for example Illing and Liu (2006), Lall et al. (2009), Osorio et al. (2011), Hollo et al. (2012), Islami and Kurz-Kim (2014), Duprey et al. (2017)). In terms of financial variables, these indices are often based on the volume of credit and the price of real estate. Information from the stock market, interbank or bond may also be included if it is considered determinative for a country.

Fig. 6

Composite index of financial dynamics calculated quarterly for the US between 1970 and 2018. Source: Author

In this paper, we calculate a composite financial index denoted FI (Financial Index) using three variables: the credit level, the real estate price index (REPI) and the consumer confidence index (CCI). As mentioned by Borio (2014), the combination between credit and real estate prices appears to be the most parsimonious way of describing the financial cycle and its link with the business cycle and financial crises. However, we think that that credit and leverage constraints are a result of the financial cycle dynamics which are mainly determined by the optimism and the pessimism of the agents. Consequently, this paper suggests capturing the financial dynamic through a composite indicator that considers also information about consumer confidence (Fig. 6).

The FI index is the average of the individual financial series divided by their respective standard deviations and re-scaled to ensure that all the individual components lie between 0 and 1. In practice, the construction of the FI index is done in 3 steps. By adopting the notation X_i,j with i for the series and j for the time, the construction of the index is done as follows:

• 1. The indexed series are divided by their respective variances:

$$ {Y}_{i,j}={X}_{i,j}/ VAR\left[{X}_i\right] $$

This transformation is done to avoid overweighting highly volatile variables. It can be interpreted as a weighting that is equal to the variance (see Illing and Liu (2006) and Nelson and Perli (2007)).

• 2. To ensure that all individual observations are between 0 and 1, the minimum value of these observations is subtracted from each of them and the series obtained is divided by its maximum over the period:

$$ {\overset{\sim }{Y}}_{i,j}=\left({Y}_{i,j}-\underset{j}{\min }{Y}_{i,j}\right)/\underset{j}{\max}\left({Y}_{i,j}-\underset{j}{\min }{Y}_{i,j}\right) $$

Thus, each of the individual components of the index will show 0 for the quietest period and 1 for the most disturbed period. This re-scaling avoids the aggregation bias of the individual components into a single composite index without considering different individual scales.

• 3. The sum of the individual components (with equal weight) is divided by the number of series included in the index, 2 in our case, so that the value of the FI index is between 0 and 1:

$$ {FCI}_j=\sum \limits_{i=1}^2{\overset{\sim }{Y}}_{i,j}/2. $$

Appendix 3: Bayesian estimation results of model parameters for the US economy

Parameters	Prior	Low. Bound	Up. Bound	Distribution	Posteriors
α	0.700	0.200	0.900	Beta	0.233
β	0.700	0.050	3.000		0.834
φ 1	0.900	0.100	0.900		0.118
φ 2	0.900	0.300	0.900		0.300
φ 3	0.500	0.100	0.500		0.474
φ 4	0.900	0.100	0.500		0.278
θ	0.500	0.010	0.900		0.811
τ1	0.100	0.050	0.900		0.078
τ2	0.100	0.050	0.900		0.377
τ3	0.300	0.050	0.900		0.050
τ4	0.300	0.050	0.900		0.458
ρ1	0.100	0.100	0.800		0.620
ρ2	0.500	0.300	0.900		0.300
ρ3	0.600	0.300	0.900		0.658
μ1	0.600	0.050	0.900		0.900
μ 2	0.600	0.050	0.900		0.900
f 1	0.900	0.010	0.900		0.900
f 2	0.400	0.100	0.900		0.390
f 3	0.800	0.300	0.900		0.900
f 4	0.600	0.300	0.900		0.476
SD (${\varepsilon}^{\overline{Y}}$)	0.300	0.005	3.000	Inverse Gamma	0.010
SD (εG)	0.800	0.005	3.000		0.557
SD (εy)	0.010	0.005	3.000		0.034
SD (επ)	0.010	0.005	3.000		0.322
SD (εu)	0.100	0.005	3.000		0.023
SD (${\varepsilon}^{\overline{U}}$)	0.200	0.005	3.000		0.010
SD (${\varepsilon}^{g\overline{U}}$)	0.200	0.005	3.000		0.124
SD (εrn)	0.010	0.005	3.000		0.174
SD (${\varepsilon}^{\pi^{target}}$)	0.100	0.005	3.000		0.096
SD (${\varepsilon}^{rr^{neutral}}$)	0.200	0.005	3.000		0.203
SD (${\varepsilon}^{\overline{FI}}$)	0.100	0.005	3.000		0.056
SD (εfi)	0.200	0.005	3.000		0.019