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Introducing a composite indicator of cyclical systemic risk in Croatia: possibilities and limitations*
Tihana Škrinjarić 
Article | Year: 2023 | Pages: 1 - 39 | Volume: 47 | Issue: 1 Received: June 1, 2022 | Accepted: November 3, 2022 | Published online: March 6, 2023
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FULL ARTICLE
FIGURES & DATA
REFERENCES
CROSSMARK POLICY
METRICS
LICENCING
PDF
Source: Author’s adjustment based on OECD (2012).
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Full name
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Risk category covered
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Unit measure
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New bank loans to households
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Credit developments
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Q sum of monthly new loans
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New bank loans to nonfinancial corporations
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Property prices
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Potential overvaluation of property prices
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Year-on-year change
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Household debt and gross disposable income
ratio
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Private sector debt burden
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Year-on-year growth rate
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Nonfinancial corporations debt and gross
operating surplus ratio
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Spread between rate on new loans to households
and 3M PRIBOR (multiplied with -1)
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Potential mispricing of risk
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% annually
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Spread between rate on new loans to
nonfinancial corporations and 3M PRIBOR (multiplied with -1)
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PX 50 stock index
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Three-month average
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Adjusted current account deficit and GDP ratio
(multiplied with -1)
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External imbalances
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% annually
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Note: All variables in the table in the described form indicate that the greater the value, the greater the risk accumulation is. Source: Plašil et al. (2015).
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Risk category
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Variables
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Transformation
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Cyclogram
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Cyclogram+
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Lending market
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Credit-to-GDP gap HH
Credit growth HH
Credit growth NFC
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Credit-to-GDP gap HH
Credit-to-GDP gap NFC
Credit growth HH
Credit growth NFC
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HP gaps
Differences
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Risk appetite
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NPL values
Default rates of NFC
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NPL values HH
NPL values NFC
Default rates of NFC
Interest rate margin HH
Interest rate margin NFC
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Everything in levels
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Indebtedness
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Indebtedness of HH
Indebtedness of NFC
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Both in HP gaps and levels
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Property market
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Residential property price
Price to income ratio
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Residential property price
Residential property price in main city
Price to income ratio
Price to rent ratio
Flat to house price ratio
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Growth rate and levels
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Macroeconomy
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ESIŽUnemployment rate
Output gap
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ESI
Unemployment rate
Output gap
Revenue gap
Current account deficit to GDP ratio
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HP gaps and levels
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Note: The gap denotes the HP gap, NPL denotes nonperforming loans, HH and NFC are households and nonfinancial corporations, y-o-y is the year-on-year change or growth rate, ESI is the economic sentiment indicator. All variables in the table in the described form indicate that the greater the value, the greater the risk accumulation is. Source: Rychtarik (2014, 2018).
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Indicator
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Transformation
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Method of data aggregation
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Data selection criteria
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Advantages
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Shortfalls
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FCI
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Order statistics
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Nonlinear function (like portfolio variance)
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Financial cycle theory, previous literature, without
empirical evaluation of the variable characteristics before the crisis.
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Takes correlation into consideration, graphical
representation, no problems with statistical filters regarding data
transformation, robustness due to scaling variables.
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Lack of objective data selection criteria, variable
selection affects the dynamics of the indicator, harder to communicate, hart
to evaluate the results
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Cyclogram
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Max min or based on percentiles of distribution
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Average, weighted average
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Previous experience with variable dynamics tracking.
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Graphical representation, no problems with
statistical filters regarding data transformation, easy aggregation and
interpretation
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d-SRI
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Normalization, standardization or max min
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Early warning models of signaling crisis.
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Data selection criteria, simple aggregation and
interpretation, robust9
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Correlations not observed, biased results for one
country analysis
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PCA
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Normalization, standardization
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Weighted average based on loadings on the first
principal component
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Any of the previous three main approaches
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Simple aggregation
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Assumptions of PCA analysis, changing correlations,
bad predictive power of the first principal component.
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Geometric average
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Normalization, standardization
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Geometric average formula
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Hard to interpret results in economic way,
correlations not observed, depends on the main method of aggregation,
negative values in data.
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RMS
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Normalization, standardization
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Root mean square formula
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Hard to interpret results in economic way,
correlations not observed, depends on the main method of aggregation,
negative values in data, lack of risk accumulation in one category is
substituted with high risk in other.
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OI
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Binary variable depending on EWM results
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Average or weighted average
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If based on d-SRI approach, advantages as there
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Hard to interpret results in economic way,
correlations not observed, depends on the main method of aggregation,
negative values in data.
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Abbreviation
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Transformation
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Variable
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Risk category
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FCI variant
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ΔICSN
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Yearly growth rate
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House price index
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Potential overvaluation of property prices
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(1)
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A. 2ΔICSN
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Annualized two-year growth rate
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(2)
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ΔKK
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Yearly growth rate
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Bank loans to households
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Credit dynamics
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(1)
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A. 2ΔKK
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Annualized two-year growth rate
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(2)
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ΔKNFP
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Yearly growth rate
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Bank loans to nonfinancial corporations
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(1)
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A. 2ΔKNFP
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Annualized two-year growth rate
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(2)
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Δ(LR)
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Yearly change
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Leverage ratio
(multiplied with -1)
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Strength of bank balance sheets
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(1)
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A. 2Δ(LR)
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Annualized two-year change
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(2)
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Δ(LTD)
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Yearly change
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Credit to deposit ratio
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(1)
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A. 2Δ(LTD)
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Annualized two-year change
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(2)
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Δ(K/Y)
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Yearly growth rate
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Debt (households) to disposable income ratio
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Private sector debt burden
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(1)
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A. 2Δ(K/Y)
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Annualized two-year growth rate
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(2)
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Δ(NFP/BOV)
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Yearly growth rate
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Debt (nonfinancial corporations) to gross operating
surplus ratio
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(1)
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A. 2 Δ(NFP/BOV)
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Annualized two-year growth rate
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(2)
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ΔCROBEX
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Yearly growth rate
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CROBEX, stock market index
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Mispricing of risk
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(1)
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A. 2 ΔCROBEX
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Annualized two-year growth rate
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(2)
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Δ margin K
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Yearly change
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Household credits interest rate margin (difference
between average new credits interest rate to households and 3 month EURIBOR
interest rate)
(multiplied with -1)
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(1)
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A. 2 Δ margin K
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Annualized two-year change
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(2)
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Δ margin NFP
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Yearly change
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Nonfinancial corporations credits interest rate
margin (difference between average new credits interest rate to nonfinancial
corporations and 3 month EURIBOR interest rate)
(multiplied with -1)
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(1)
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A. 2 Δ margin NFP
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Annualized two-year change
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(2)
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ΔRN
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Yearly change
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Current account to GDP ratio (multiplied with -1)
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External imbalances
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(1)
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A. 2 ΔRN
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Annualized two-year change
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(2)
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Source: CNB, author’s calculation.
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Variant (1)
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Variant (2)
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Combination of variables that are transformed to
annualized two-year changes or growth rates, and HP gaps, 125.000 value of
the smoothing parameterr14.
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Variant with GDP and unemployment dynamics.
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Source: CNB, author’s calculation.
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Risk
categories
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Indicator
description
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Credit dynamics measures
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HP gap for the broad
definition of credit to households, smoothing parameter of 125,000
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HP gap for the broad
definition of credit to non-financial corporations, smoothing parameter of
125,000
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HP gap for the ratio of
narrow definition of credit and the sum of GDP of the current quarter and the
preceding three quarters, smoothing parameter of 125,000
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Measures of credit
institution financing risk
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Annualized two-year change
in the negative ratio between credit institutions’ equity and assets
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Annualized two-year change
in the negative ratio between private sector deposits and credit
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Measures of potential real
estate price overvaluation
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Annualized two-year growth
rate in the residential real-estate price index
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Annualized two-year growth
rate in the residential real-estate price-to-disposable income ratio
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Annualized two-year growth
rate in the volume index of construction works
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Measures of private sector
debt burden
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HP gap for the ratio
between corporate debt and gross operating surplus, smoothing parameter of
125,000
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HP gap for the ratio
between household debt and disposable income, smoothing parameter of 125,000
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HP gap of debt service
measures – households, smoothing parameter of 125,000
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HP gap of debt service
measures – corporations, smoothing parameter of 125,000
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Measures of external
imbalances
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Annualized two-year change
in the negative share of net exports of goods and services in GDP
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Annualized two-year change
in the negative share of current account balance in GDP
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Measures of potential
mispricing of risk
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Annualized two-year growth
rate in CROBEX
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Annualized two-year change
in the negative interest margin on new loans to households relative to the
3-month EURIBOR
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Annualized two-year change
in the negative interest margin on new corporate loans relative to the
3-month EURIBOR
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Source: CNB, author’s calculation.
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Variant
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Description
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Variant (1)
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Variables from table 6, normalization via median and
standard deviation of each variable.
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Variant (2)
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Variables from table 6, normalization via max-min
approach of each variable.
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Source: CNB, author’s calculation.
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Indicator
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error T1
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error T2
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Sum
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Weight (%)
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HP gap,
household credit
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0,08
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0,08
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0,16
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8,84
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HP gap,
nonfinancial corporations credit
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0,08
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0,21
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0,29
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4,47
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HP gap,
narrow definition of credit
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0,00
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0,41
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0,41
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2,84
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2y change,
equity to assets ratio
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0,50
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0,00
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0,50
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2,15
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2y change,
deposit to credit ratio
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0,00
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0,09
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0,09
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15,82
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2y growth
rate, house price index
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0,00
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0,13
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0,13
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11,09
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2y growth
rate, house price to income ratio
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0,00
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0,09
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0,09
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17,14
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2y growth
rate, volume index of construction works
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0,00
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0,00
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0,00
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8,00
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HP gap,
ratio debt to gross operating surplus
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0,00
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0,22
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0,22
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6,10
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HP gap,
ratio debt to disposable income
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0,00
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0,49
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0,49
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2,24
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HP gap,
debt service ratio, households
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0,00
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0,49
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0,49
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2,24
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HP gap,
debt service ratio, nonfinancial corporations
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0,00
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0,33
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0,33
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3,73
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2y growth
rate, net exports to GDP ratio
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0,00
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0,61
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0,61
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1,57
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2y growth
rate, current account to GDP ratio
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0,08
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0,45
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0,53
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1,95
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2y growth
rate, CROBEX
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0,00
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0,00
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0,00
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8,00
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2y change,
interest margin, households
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0,33
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0,16
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0,49
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2,22
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2y change,
interest margin, nonfinancial corporations
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0,25
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0,19
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0,44
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2,60
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Note: Abbreviations refer to variables from table 6, the following the sequence from first to last one as in the mentioned table. Source: CNB, author's calculation.
Source: CNB, author’s calculation.
Source: CNB, author’s calculation.
Source: CNB, author’s calculation.
Source: CNB, author’s calculation.
Figure 1Composite indicator construction steps DISPLAY Figure
Table 1Variables used in Plašil et al. (2015) for FCI indicator DISPLAY Table
Table 2List of variables used in the cyclogram (and +) DISPLAY Table
Table 3Summary of the three main approaches for composite indicator construction DISPLAY Table
Table 4Summary of two FCI variants DISPLAY Table
Figure 2Selected FCI indicators and their dynamics DISPLAY Figure
Table 5Cyclogram variants for Croatian case DISPLAY Table
Figure 3Cyclogram variants from table 5 DISPLAY Figure
Table 6Best indicators chosen for d-SRI calculation DISPLAY Table
Figure 4d-SRI indicator variants DISPLAY Figure
Table 7Variants of PCA aggregation DISPLAY Table
Figure 5Composite indicators based on PCA aggregation DISPLAY Figure
Table 8Weights assignment based on errors type 1 and 2 DISPLAY Table
Figure 6OI indicator, based on weights in table 8, and equal weights DISPLAY Figure
Figure 7Structure of OI indicator, number of variables exceeding referent value, equal weights DISPLAY Figure
Figure 8OI indicator, weights from table 8 and equal weights, median value for thresholds DISPLAY Figure
Figure 9Geometric mean and RMS approaches of aggregating data DISPLAY Figure
* The views presented in this paper are those of the author and do not necessarily represent the institution the author works at. I would like to thank two anonymous referees for their useful comments and suggestions.
1 CCyB is a macroprudential instrument used to mitigate the pro-cyclical nature of bank lending and reduce risks to the financial system's stability. This buffer is used for absorbing possible losses when the crisis hits. It could help limit excessive credit growth when the optimism rises during the upward phase of the cycle, the risk appetite is higher, and risks are undervalued. In that way, the CCyB is used for mitigating the fluctuations of the financial cycle. Some evidence in favour of this is found in both theoretical (the DSGE model in Brzoza-Brzezina, Kolasa and Makarski,  2015 shows that CCyB mitigates credit imbalances in the upward phase of the cycle; and something similar is shown in Gersbach and Rochet, 2017; and Tayler and Zilberman, 2016) and empirical research (Chen and Friedrich, 2021, show that tightening the cycle of CCyB in other countries has reduced lending in Canada; Basten, 2020, shows that the CCyB activation has resulted in raising mortgage pricing in bank's pricing offers; and Couallier et al., 2022, found that capital relief measures (including CCyB) were successful in supporting credit supply).
2 The HP filter has various other problems, which are listed as follows. First, the HP filter is a statistical method in the application of which the author must decide in advance on the value of the smoothing parameter. This affects the filtering result and the gap evaluation. Following the original article by Hodrick and Prescott ( 1997), when calculating the long-term business cycle trend the authors most often use lambda 1600 (100) for quarterly (annual) data. However, there are also examples of alternative proposals in the literature. In research dealing with the credit gap, lambda 400.000 is most often used because it is assumed that the financial cycle lasts longer than the business one. Another common problem is the short time series, such as those for Croatian data. The values of the obtained gaps vary significantly depending on the length of the filtered series, because they depend on the dynamics of the series the trend of which is being evaluated. Related to this are the problems of the last point and the first point, discussed in Jokipii et al. ( 2021) and Drehmann and Tsatsaronis ( 2014 ). The value of the gaps also depends on the period of the systemic risk accumulation phase that is included in the filtering itself; the result depends on whether we start to filter the series at the top or at the bottom of the credit cycle. For the series observed here, the evaluation of the long-term trend and the filtering process also includes the period of credit expansion before the global financial crisis. After that there is a prolonged period of reduction in the value of the gap (see Lang et al., 2019; Galán, 2019). Also, the HP filter creates apparent cycles (Cogley and Nason, 1995), has poor real-time properties (Kamber, Morley, and Wong, 2018), and is imprecise at the ends of the time series (Hamilton, 2018). Finally, the credit to GDP ratio is based on a stock variable in the numerator and a flow variable in the denominator, which makes it sensitive to sudden shocks in GDP. It could therefore result in signals misleading for macroprudential policy, e.g., leading to further tightening after the onset of a recession (Gross, 2022). See Škrinjarić and Bukovšak ( 2022), which deals with all of these issues in the case of Croatia.<
3 Before the transformation, it should be noted that the interpretation of the variable is such that greater values indicate whether risks are high or not. This applies to all composite indices. Those variables whose greater values indicate lower risks are multiplied with -1 value so that everything is comparable. In this research, credit spreads are multiplied by -1 to obtain the interpretation that higher value means more risk for the composite indicators. Due to those spreads falling before a bust occurs, lower spreads imply more risk. Thus, the multiplication by -1 results in the interpretation of “more risk” for the sake of the composite indicator value. As Croatian data are such that the credit spreads are falling in the entire period, not exhibiting cyclical dynamics, the one- or two-year changes were calculated in the first step, but to obtain the same interpretation of greater value of the variable means more risk, those changes are multiplied by -1.
4 The order statistics approach does not change the shape of the original data distribution. It rather rescales the data to an interval such that different individual variables can be comparable if they have different measurement units. On the opposite side, data normalization assumes that original data follow a normal distribution, that the first two moments of the distribution are enough to explain the distribution itself, and the distribution is symmetric. Suppose this is not the case for the original data. In that case, the interpretations about how many standard deviations an observation is above or below the mean do not have any meaning if this mean is not representative of the sample.
5 To ensure better comparability among countries, the variable selection process should be as objective as possible. Although the rationale for the risk categories used in the original FCI paper is given, the specific variable selection is not based on a literature review in terms of theory and practice. Tölö, Laakkonen and Kalatie ( 2018) and Lang et al. ( 2019) provide good examples of how the whole variable process selection should be based.
6 Although some of these transformations lead to similar dynamics and conclusions, when dealing with data without normal distributions, such as the data in this study, one cannot use any transformation. This is important for, e.g., the mentioned CCyB calibration, as it often depends on the distribution of the indicator on which the calibration is based. Thus, wrong assumptions about a distribution could lead to potential misleading results regarding this buffer.
7 Details about the ROC curve, AUROC values, and other relevant indicators and mathematical background can be found in Candelon, Dumitrescu and Hurlin ( 2012) and references within.
8 The authors do not explain why they choose this approach. One parallel that can be made from microeconomic theory is the interpretation of the constant elasticity of production factor substitution. The ratio of marginal contributions of each sub-indicator between two sub-indicators is always the same when the ratio increases by 1%. This is a fairly restrictive assumption.
10 However, working with methods that do not rely on EWM has the advantage of being informative and feasible when looking at a country that did not experience notable crises in its own past, i.e., for which a LHS crisis indicator would not be quite informative/moving.
11 Total number of correlation coefficients used in the estimation and FCI construction is a binomial coefficient, where n is over k, n being the number of variables entering the indicator, and k = 2.
12 The full graphical representation is available in Škrinjarić ( 2022), on request.
13 Berti, Engelen and Vašiček ( 2017) find that its dynamics for the euro area are more related to the business cycle.
14 Since it is not known how long the financial cycle lasts in Croatia, the value of 125.000 is chosen based on the assumption that the financial cycle lasts three times as long as the business cycle. This means that the financial cycle lasts approximately 22.5 years. Issues with HP gaps closing too late based on the value of 400.000 is well documented in the literature, please see Valinskyte and Rupeika ( 2015) or Galán ( 2019).
15 In the pre-GFC period, we had credit growth of 20-40% year on year for several years. The property price growth also had the highest growth rates. In the last couple of years, we do not experience this at all. Credit activity was somewhat subdued in the Covid period due to uncertainty when this crisis hit. The housing activity is not nearly as vigorous as it was in the pre-GFC period, as the index of house construction is not increasing that much, the number of building permits is smaller, and almost half of the transactions are in cash. Moreover, the banking system is more capitalized now. All of this leads to the conclusion that the economy at present is not at the same level of risk as it was in the pre-GFC period.
16 To save space, we do not report all of the values, but the results are available upon request. Details on which dates were chosen for the formal analysis are given in appendix.
17 It is hard to communicate the correlation due to calculating N over 2 (binomial coefficient) different values of correlation coefficients. If we look at 15 indicators that enter the composite one, it means that 105 different coefficients of correlation need to be tracked, alongside variances and the total value of the indicator. If a value of the total indicator increases from one period to another, we would need to look at all of these values to see the most significant contributors to this rise in risk. Due to total risk being based on individual risks and their interaction, it is hard to communicate, e.g., several dozen correlation coefficients contributing to risk increase or decrease. The correlation contribution of the FCI indicator in the figures is a simple average that remains after we account for individual variances. It is not representative of all 105 individual correlation coefficients.
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March, 2023
I/2023
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