Financial system stress: From empirical validity to ... · Financial system stress: From empirical validity to theoretical foundations [Authors Removed] * June 2014 . A review of

Financial system stress: From empirical validity to theoretical foundations

[Authors Removed]*

June 2014

A review of financial system stress measures reveals not only the absence of theory on financial stress, but also the absence of search for theory. This study conducts an empirical analysis of an evolving financial system to construct a concise set of latent factors that condition financial stress. The empirical analysis parses out maximum likelihood factors utilizing longitudinal exploratory factor analysis, highlighting a number of problems with a priori stress construction. The resulting stress measurement model is tested via confirmatory factor analysis and substantiated for convergent, discriminant, and predictive validity. We test the hypotheses of association and causality between the factors, their variables, and financial stress for an evolving financial system using financial market observations and the Financial Accounts of the United States from 1991 to 2014. The analytical insights lead to an extension of financial stress measurement for system agents and instruments. The empirical validity also leads us to posit a new theoretical foundation for a deeper understanding of financial stress—one that can adapt to continual changes in financial system structure and instruments.

Keywords: financial stress, empirical validity, factor analysis, asset pricing JEL classification: C12, E02, G01, G20, H30

* This paper represents the views of the individual authors and is not to be considered as the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System. The authors are grateful to Stephen Ong and Amanda Janosko for their critiques, to the faculty of the Case Western Reserve University, particularly Jagdip Singh, Kalle Lyytinen, James Gaskin, and Toni Somers for research guidance, and to Joseph Haubrich, Edward S. Knotek II, Ben Craig, Manfred Kremer, Marco Lo Duca, Tuomas Peltonen, and Mark Flood for constructive feedback. The authors also thank the participants of the International work-conference on Time Series (Granada, June 25-27, 2014), the IRMC conference on “The Safety of the Financial System - From Idiosyncratic to Systemic Risk” (Warsaw, June 23-24, 2014), the 6th International IFABS Conference on “Alternative Futures for Global Banking: Competition, Regulation and Reform” (Lisbon, June 18-20, 2014), and the 12th INFINITI conference on international finance (Prato, June 9-10, 2014) for helpful comments and suggestions.

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Financial system stress: From empirical validity to theoretical foundations

A review of financial system stress measures reveals not only the absence of theory on financial stress, but also the absence of search for theory. This study conducts an empirical analysis of an evolving financial system to construct a concise set of latent factors that condition financial stress. The empirical analysis parses out maximum likelihood factors utilizing longitudinal exploratory factor analysis, highlighting a number of problems with a priori stress construction. The resulting stress measurement model is tested via confirmatory factor analysis and substantiated for convergent, discriminant, and predictive validity. We test the hypotheses of association and causality between the factors, their variables, and financial stress for an evolving financial system using financial market observations and the Financial Accounts of the United States from 1991 to 2014. The analytical insights lead to an extension of financial stress measurement for system agents and instruments. The empirical validity also leads us to posit a new theoretical foundation for a deeper understanding of financial stress—one that can adapt to continual changes in financial system structure and instruments.

Keywords: financial stress, empirical validity, factor analysis, asset pricing JEL classification: C12, E02, G01, G20, H30

TABLE OF CONTENTS

1. INTRODUCTION .......................................................................................................... 1 2. RESEARCH QUESTIONS ............................................................................................ 1 3. EMPIRICAL BASIS ....................................................................................................... 3

3.1 Empirical Measure of System Stress ........................................................................ 3 3.2 Hypotheses ................................................................................................................ 4 3.3 Empirical Measure of Stress for Agents and Instruments ........................................ 9

4. THEORETICAL FOUNDATION ................................................................................ 11 5. RESULTS ..................................................................................................................... 14 6. DISCUSSION ............................................................................................................... 22 REFERENCES ................................................................................................................. 23 FIGURES .......................................................................................................................... 26 TABLES ........................................................................................................................... 35 APPENDIX: LONGITUDINAL FACTOR ANALYSIS ................................................. 37

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1. INTRODUCTION

A review of financial system stress reveals not only the absence of theory of stress (Gramlich

et al., 2010; Oet et al., 2011, Kliesen et al., 2012), but also the absence of search for theory. This

is a critical problem. Due to this dearth of theory, we possess limited ability to evaluate the

adequacy of a stress indicator (Holló, Kremer, and Lo Duca, 2012) and current measures of

stress do not adapt to structural changes in the system.

In this study, we develop a theory of financial stress from empirical foundations in four steps.

First, we find reliable factor decomposition for the U.S. financial stress and show its convergent,

discriminant, and predictive validity. Second, we extend the empirical measurement model to

construct stress for heterogeneous agents and instruments. Third, based on theory emerging from

empirical observations, we hypothesize and validate a set of latent factors that condition financial

stress for system agents and instruments. Fourth, we advance a new theoretical foundation for a

deeper understanding of financial stress which incorporates and validates the hypothesized

factors and allows stress measurement under continuous change in financial system structure.

The rest of this paper is structured as follows: Section 2 establishes the research questions

and maps this study. Section 3 reviews the empirical basis of financial system stress, tests

hypotheses of stress formation, and extends financial stress measurement to agents and

instruments. Section 4 advances a generalized theoretical framework of financial system stress

measurement. Section 5 provides the study results. Section 6 concludes with a brief discussion of

this study’s research implications.

2. RESEARCH QUESTIONS

What is financial system stress? What are the system factors that identify financial stress?

Are the factors empirically reliable? How can stress be theorized in an adaptive system? Is the

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measurement model sound across heterogeneous agents? Does theoretical stress substantiate

empirical identification? These are the questions we will pursue in this article.

Figure 1 shows the methodological map for this study grounded in literature. To begin

with, financial stress as a real phenomenon is a latent construct. It is unobserved, because

epistemology enabling its measurement is nonexistent, a significant practical barrier. We address

this problem through an empirical construct which replicates the real phenomenon, using data.

The data comes from the Financial Accounts of the United States, as well as financial market

observations from the 3rd quarter 1991 to first quarter 2014, sourced from Bloomberg,

Datastream, Haver Analytics, and Global Financial Data. This set of data—our target of

analysis—exhibits an observable hence known set of relationships. We establish the means to

answer the first research question about factors identifying financial stress through longitudinal

exploratory factor analysis (EFA). The exploration of the factors found in the data lets us test and

modify our a priori views about latent factors in the financial system with respect to construction

of the financial stress measure. We analyze the empirical reliability and validity of EFA factors

and test these factors against a set of alternative measurement models in confirmatory factor

analysis (CFA).

Insert Figure 1 about here

Building upon the EFA and CFA results, we construct a structural equation model (SEM)

to examine across time, across different regimes, and across different agents whether a consistent

measure of system stress can in fact be theorized in a more abstract way despite financial system

heterogeneity and evolution. Having formed an initial set of hypotheses about measuring stress

in an adaptive system of agents and instruments, we then test whether this measurement model is

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sound across the heterogeneous agents and instruments. After analysis, testing, and validation,

our last question is whether theoretical stress substantiates the empirical identification.

3. EMPIRICAL BASIS

3.1 Empirical Measure of System Stress

The topic of financial stress measurement has gained considerable attention since the

early 2000s and particularly since the financial crisis. In this literature, financial stress typically

aims to measure economic forces characterizing relative state of financial system instability (Oet

et al., 2012; Holló et al., 2012). Holló et al., (2012) measure the European financial system stress

using five representative market segments and dynamically weigh them using asset price

correlations.2 Oet et al. (2011) test and empirically support a conjecture that stress is identified

by a function of asset price spreads that are dynamically weighted by transactions in the

economy. Oet et al. (2012) measure U.S. financial system stress with an index construct (the

Cleveland Financial Stress Index—CFSI) consisting of six a priori 𝑓𝑓 factors at time t, where each

represents a distinct financial market:3

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑡𝑡 = ∑ 𝑤𝑤𝑓𝑓𝑡𝑡[∑ 𝑤𝑤𝑗𝑗𝑡𝑡𝐶𝐶𝐶𝐶𝐶𝐶(𝑥𝑥𝑗𝑗𝑡𝑡)]𝑛𝑛𝑗𝑗=1

6𝑓𝑓=1 (1)

where 𝐶𝐶𝐶𝐶𝐶𝐶(𝑥𝑥𝑗𝑗𝑡𝑡) = 𝑅𝑅𝑅𝑅𝑛𝑛𝑅𝑅�𝑥𝑥𝑗𝑗𝑗𝑗�𝑇𝑇

(2),

𝑤𝑤𝑗𝑗𝑡𝑡 = 𝑇𝑇𝑇𝑇𝑅𝑅𝑛𝑛𝑇𝑇𝑅𝑅𝑇𝑇𝑡𝑡𝑇𝑇𝑇𝑇𝑛𝑛𝑇𝑇𝑗𝑗𝑗𝑗∑ 𝑇𝑇𝑇𝑇𝑅𝑅𝑛𝑛𝑇𝑇𝑅𝑅𝑇𝑇𝑡𝑡𝑇𝑇𝑇𝑇𝑛𝑛𝑇𝑇𝑘𝑘𝑗𝑗𝑛𝑛𝑘𝑘=1

(3),

and 𝑤𝑤𝑓𝑓𝑡𝑡 = 𝐹𝐹𝑇𝑇𝐹𝐹𝑓𝑓𝑗𝑗∑ 𝐹𝐹𝑇𝑇𝐹𝐹𝑔𝑔𝑗𝑗6𝑔𝑔=1

(4).

When transaction level data is available, otherwise equal weights are assigned to each

measure. Accordingly, the CFSI stress construct is operationalized as shown in Figure 2, where

2 The CISS (Holló et., 2012) assumes five representative factors: money market, bond market, equity market, financial intermediaries, and foreign exchange market.

3 The CFSI (Oet et al., 2012) utilizes six a priori factors: funding, foreign exchange, credit, equity, real estate, and securitization.

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financial system stress is measured from observations of six a priori market factors and sixteen

financial components 𝑥𝑥𝑗𝑗𝑡𝑡which are dynamically weighted within (𝑤𝑤𝑗𝑗𝑡𝑡) and subsequently across

�𝑤𝑤𝑓𝑓𝑡𝑡� markets. Thus, component and factor loadings of the stress measure are time-varying

according to each component’s and factor’s changing share of the economy. Each of the sixteen

indicators describes a different aspect of one a priori market factors. Eleven components are

asset spreads of characteristic factor assets; two measure the degree by which underlying series

(indexes of equity and foreign exchange markets) have decreased in the past year, and one

measures the covered interest spread. A moving average of relative bid-ask spreads and a

financial beta are also included.


3.2 Hypotheses

A review of selected theoretical and empirical literature strands —monetary policy

transmission, structure of financial intermediation, and financial crises and cycles—provides the

material from which we support hypotheses associating sectoral variables with financial stress.

Monetary policy literature generally recognizes financial stress as a latent condition of the

financial system (Mishkin, 1995; Borio and Zhu, 2012). All three strands are jointly motivated

by understanding the factors affecting system behavior across products and agents and by

studying the factor interactions. Monetary policy transmission studies recognize factors acting in

distinct mechanisms with economic conditions.4 Remarkably, each of the mechanisms includes

information about the prices of reference assets as well as information about aggregate activity

(e.g. volumes and transactions) based on these asset prices. The literature on financial

4 Current literature distinguishes the following mechanisms: monetary channel, interest rate channel, credit channel, exchange rate channel, asset pricing channel, bank lending channel, bank capital channel, and consumer wealth channel (Borio and Zhu, 2012; Mishkin, 1995).

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intermediation (Berger et al. 2004) brings to light the controversial role of concentration as a

factor critical to the structure of economic systems. At the same time, literature on financial

cycles and crises (Schwert, 1989; Stock and Watson, 2003, 2005) emphasizes the extent to which

factors of economic conditions are generally unstable and exhibit volatility across economic

systems. Accordingly, we form the following direct association and interaction hypotheses

concerning asset spread, volume, transaction, concentration, while controlling for volatility

effects.

Direct association hypotheses

Hypothesis 1: Higher Yield spreads between assets and risk-free instruments of similar

investment horizon are associated with higher financial system stress. Prices of financial

instruments5 form an essential component in monetary policy mechanisms (Bernanke, 1986;

Greenwald and Stiglitz, 1993; Bernanke and Gertler, 1995; Obstfeld and Rogoff, 1995; Taylor,

1995; Clerc and Pfister, 2003; Rigobon and Sack, 2003). Empirically, Stock and Watson (1989)

find that “default spreads” formed as the spread between risky and risk-free reference rates

contain forward-looking information about the state of the economy. Bernanke (1990 pg.61)

confirms the finding and suggests that “this spread may be useful because it summarizes

available information about the likelihood of a recession.” Freixas and Rochet (2008) emphasize

that the spread’s key role in various channels of monetary policy transmission results from its

amplification effect on interest rates and generating the financial accelerator effect. Indeed, in a

comprehensive empirical survey of the association of asset prices, output, and inflation, Stock

and Watson (2003) emphasize that the idea that interest rates and asset prices contain forward-

looking information about expectations of future economic developments lies at the heart of

5 E.g., including short-term rates, exchange rates, equity prices, and bank deposits.

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macroeconomics. In particular, the evidence supports the idea that market-clearing spreads

between risky and alternative risk-free instruments embed expectations on the likelihood of

default of the risky instrument. Thus, it is reasonable to expect that yield spreads of this type are

positively associated with financial stress.

Hypothesis 2: Exposure volumes are positively associated with financial system stress.

Exposure volumes describe current valuations of aggregate economic activity of financial agents.

In this sense, financial exposure can be considered an aspect of agent net worth due to a

particular instrument or a set of instruments. While the literature we considered attributes

significant role to aggregate exposure (e.g., net worth, capital, wealth, aggregate loans, etc.), it

differs on the expected relationship. Monetary policy literature generally expects that at times of

distress, “borrower net worth is low” (Bernanke & Gertler, 1989: 14). For example, in the

Bernanke and Gertler (1989 pg. 35) credit channel, the default spread facing a borrower depends

on borrower's financial position: the greater the borrower's net worth, the lower the spread.

Similarly, in Chen (2001), agent’s exposure volume forms a constraint on future activity, e.g.

through borrowing and lending, when current exposure serves as collateral. Greater exposure

volumes enable agents to earn greater returns. However, empirical literature finds a positive

association of exposure with stress. Aizenman and Pasricha (2012) find a consistently positive

association of GDP/person with financial stress during the Great Recession across a sample of

107 countries. For the U.S. bank holding company data from 1991 to 2012, Oet et al. (2013) find

evidence that market capitalization imbalances are consistently positively associated with

financial system stress. The apparent paradox may be resolved by the logic of the following

balancing feedback (Borio and Zhu, 2012 pg. 243):

𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ↗ 𝑑𝑑𝑠𝑠𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑑𝑑𝑑𝑑 ↘ 𝑛𝑛𝑠𝑠𝑠𝑠 𝑤𝑤𝑤𝑤𝑠𝑠𝑠𝑠ℎ ↘ 𝑠𝑠𝑠𝑠𝑤𝑤𝑏𝑏𝑑𝑑𝑏𝑏𝑏𝑏𝑑𝑑𝑏𝑏𝑠𝑠𝑏𝑏 𝑤𝑤𝑓𝑓 𝑑𝑑𝑠𝑠𝑓𝑓𝑑𝑑𝑑𝑑𝑑𝑑𝑠𝑠 ↘ 𝑣𝑣𝑑𝑑𝑑𝑑𝑑𝑑𝑠𝑠 𝑤𝑤𝑓𝑓 𝑑𝑑𝑠𝑠𝑏𝑏𝑠𝑠 ↗ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 (5)

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During times of high market stress, default spread can be expected to increase. Higher

default spread should reduce agent net worth, and in turn lead to higher agent probability of

default. Higher likelihood of agent default will reduce the ability of the agent to borrow and

reduce the value of its outstanding debt. Lower value of debt should in turn reduce the agent

stress. Thus, reduction in net worth should lead to reduction in stress with a positive association.

On the other hand, low stress should lower default spread, increase net worth, lower

probability of default, increase the value of debt, and increase stress. Here, an increase in net

worth leads to an increase in increase, also with a positive association.

The logic of the positive association between exposure and stress also makes sense from

the point of view of the definition of financial stress. Since agent financial stress reflects inherent

economic forces applied, it is reasonable to expect that larger entities, exposures, and positions

involve greater forces, resulting in greater unit financial stress.

Hypothesis 3: An increase in transactions is associated with financial system stress. The

effect of transactions (change in exposure) on financial stress appears to be moderated by the

transaction type. When transactions on the asset side of the balance sheet increase from the

previous period, agents earn more revenue and end up with a higher level of net worth (Chen,

2001; 416), leading to an increase in financial stress—a positive association. However, when

transactions on the liability side of the balance sheet increase (e.g. deposits grow for banks),

financial stress is reduced—a negative association. Greenwald and Stiglitz (1993 pg. 78), argue

that transaction dynamics has large effect on the agent willingness to produce.

Hypothesis 4: Exposure concentration is positively associated with financial system

stress. Cetorelli and Gambera (2001) “explore empirical relevance of banking market structure

on growth.” They find that the effect of banking concentration on growth is generally mixed and

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moderated by its context: positive for sectors that are dependent on external financing and

negative for the banking sector itself. Berger et al. (2004) review similarly mixed results from

theoretical studies on this topic: the “concentration-stability” view (Allen and Gale, 2000) vs. the

“concentration-fragility” view (Boyd and Runkle, 1993; Mishkin, 1999; Boyd and De Nicolo,

2005). Empirical evidence is less ambiguous. Aizenman and Pasricha (2012) find a positive

association of concentration and financial stress in the Great Recession sample of 107 countries.

Similarly, Oet et al. (2013) find a consistent pattern of positive association of exposure

concentrations with financial stress in 1991-2012 sample of the top 33 US bank holding

companies.

Moderation hypotheses: interactions

The preceding discussion of associations of asset characteristics (spreads, exposure

volumes, transactions, concentrations) with financial stress suggests that these variables do not

act independently, but may in fact interact, either reinforcing or diminishing individual effects.

Since all the individual characteristics, except for transactions are hypothesized to have positive

effects on the financial stress, it is reasonable to expect spread-exposure and spread-

concentration interactions would further magnify the positive effects on stress, while

transactions-concentration and transactions-spread interaction would further attenuate the effect

on stress.

Hypothesis 5: Financial stress is amplified by the interaction of asset spread with volume. Hypothesis 6: Financial stress is amplified by the interaction of asset spread with exposure concentration. Hypothesis 7: Financial stress is attenuated by the interaction of transactions with asset spread. Hypothesis 8: Financial stress is attenuated by the interaction of transactions with exposure concentration.

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Figure 4 summarizes the above hypotheses in a schematic diagram.


3.3 Empirical Measure of Stress for Agents and Instruments

The problem of financial stress in an adaptive system is motivated by the evidence of

dramatic transformation of the financial system agents (Figure 4). The figure shows the assets of

several selected US financial system agents from 1952 to 2013, where the relative waxing and

waning of agents suggests the presence of dynamic tipping points that are characteristic of

complex systems. The recent financial crisis evidences one such dynamic shift. Pension funds

and mortgage pools experience a sharper decline in their asset holdings than other financial

institutions. ABS issuers suffer a decline in their assets earlier than most other economic agents

and remain below their pre-crisis holdings. At the same time, the central bank’s balance sheet

expands with the implementation of new monetary policy tools. Examining the relative asset

share of these institutions over time reveals that banks hold a fairly stable 50% of assets until

1980. Then, their share begins to decrease until 1998, when it becomes stable at 20% with

market share recapture by investment funds and pension funds.


Addressing the adaptive context, we extend the measure of financial stress (Oet et al.,

2012) by explicitly considering two dimensions: financial instruments 𝑏𝑏 ∈ 𝐶𝐶 = {1, … ,𝑚𝑚} and

agents 𝑗𝑗 ∈ 𝐽𝐽 = {1, … ,𝑛𝑛}. Let 𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡 and 𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡 represent the assets and liabilities in the instrument 𝑏𝑏 on

the balance sheet of agent 𝑗𝑗 at time 𝑠𝑠. Because we are interested in the impact of each investment

on both sides of the agent’s balance sheet, we define 𝑛𝑛𝑇𝑇𝑗𝑗𝑡𝑡 = �𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡� + �𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡�. Let 𝑠𝑠𝑇𝑇𝑡𝑡 = 𝑠𝑠𝑇𝑇𝑡𝑡 − 𝑠𝑠𝑇𝑇𝑡𝑡𝑇𝑇𝑓𝑓 be

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the spread between the return on risky instrument i and a risk-free product with comparable

investment horizon.6 Then, we define sector stress as:

𝜉𝜉𝑡𝑡 = ∑ ∑ 𝑛𝑛𝑖𝑖𝑗𝑗𝑗𝑗𝑡𝑡𝑇𝑇𝑡𝑡𝑅𝑅𝑙𝑙𝑗𝑗

𝐶𝐶(𝑠𝑠𝑇𝑇𝑡𝑡)𝑗𝑗𝑇𝑇 (6),

where 𝑠𝑠𝑤𝑤𝑠𝑠𝑑𝑑𝑑𝑑𝑡𝑡 = ∑ ∑ 𝑛𝑛𝑇𝑇𝑗𝑗𝑡𝑡𝑗𝑗𝑇𝑇 (7),

and 𝐶𝐶(𝑥𝑥𝑡𝑡) = 1𝑇𝑇𝑅𝑅𝑑𝑑𝑛𝑛𝑅𝑅(𝑥𝑥𝑡𝑡) (8).

Here, 𝐶𝐶(𝑥𝑥𝑡𝑡) is the cumulative distribution function of the observed value of 𝑥𝑥𝑡𝑡. 𝐶𝐶(𝑥𝑥𝑡𝑡)

represents the probability of observing a value less than or equal to 𝑥𝑥𝑡𝑡 using the full time series.

Applying the CDF modification will naturally convert each series 𝑥𝑥𝑡𝑡 so that it is positive,

avoiding a situation when raw spreads may negate each other during aggregation, with

misleading indication of low or nonexistent stress. Finally, we continue constructing sector stress

as the weighted average of the cumulative density function (CDF) of instrument spreads. The

contribution of each agent to total stress depends only on the extent of its position 𝑛𝑛𝑇𝑇𝑗𝑗𝑡𝑡 in each

instrument. Because these weights vary according to agent’s choices over time, as a measure

aggregated over time, agents, and instruments, sector stress extends the empirical identification

of system stress to capture stress in system agents in the presence of continual structural change.

We draw data from the Financial Accounts of the United States to determine the asset

and liabilities of each sector in every instrument. Observations of risky prices and returns as well

as risk-free yields are drawn from Datastream, Global Financial Data, and Haver Analytics at

highest available frequency between Q1 1980 and Q4 2013.

6 Where possible, the spread between expected return (or yield to maturity) of the risky and risk-free instrument is used, allowing us to interpret the spread as the risk premium offered for instrument i. However, it is frequently not possible to access the historical expected rate of return on an instrument. In these cases, we use the spread between the realized return on instrument i and the rate that one could have earned by investing in a risk-free instrument over the same timeframe.

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4. THEORETICAL FOUNDATION

What is the theory underlying stress applied to the adaptive financial system? Among the

many financial system dynamics, new financial instruments are introduced potentially creating

entire markets, laws are changed inciting regulatory arbitrage, and financial agents may radically

change their size, composition, and behavior over time. How can we be sure that a measure

which identifies stress well today will still be good tomorrow? Specifically, other than the useful

finding that a particular set of spreads in various markets seems to capture useful information,

the question of selecting the candidate series is at best an empirical result, at worst it is

theoretically opaque.

Based on EFA analysis, we know how to measure stress for the US, but we do not

understand why these particular latent factors are relevant or why certain time series should be

included and others omitted. In CFSI, the selected series are based upon the seminal and intuitive

empirical study of Illing and Liu (2003, 2006) which also fails to provide a theoretical basis for

their variable selection. We continue to lack a comprehensive theory of why certain series are

selected and why a stress measure should be constructed a certain way. Furthermore, we are

concerned that when the financial system changes our empirical financial stress measure will no

longer be relevant. We desire therefore to establish a theory of financial system stress that

continues to be applicable both for the changing agents and instruments, as well as different

economies. Put differently, we desire a way to measure stress in a changing system—with

heterogeneous evolving agents and heterogeneous evolving instruments.


Consequently, we consider a changing financial system composed in financial products

𝑏𝑏 = {1, … , m} traded by agents 𝑗𝑗 = {1, … ,𝑛𝑛} such that financial instruments can be partitioned

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into markets 𝑏𝑏 ∈ 𝐶𝐶 = {𝐶𝐶1, … . , 𝐶𝐶𝑀𝑀} and agents can be partitioned into various sectors 𝑗𝑗 ∈ 𝐽𝐽 =

{𝐽𝐽1, … , 𝐽𝐽𝑁𝑁} (see figure 5). We define 𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡 = 𝑠𝑠𝑇𝑇𝑡𝑡𝑣𝑣𝑇𝑇𝑗𝑗𝑡𝑡7 to be the wealth invested in instrument i by

agent j at time t which incorporates the choice of the agent to own a volume 𝑣𝑣𝑇𝑇𝑗𝑗𝑡𝑡 and the market

clearing instrument price 𝑠𝑠𝑇𝑇𝑡𝑡. Furthermore, let 𝑠𝑠𝑇𝑇𝑡𝑡 = 𝑠𝑠𝑇𝑇𝑡𝑡 − 𝑠𝑠𝑇𝑇𝑡𝑡𝑇𝑇𝑓𝑓 be the spread between the expected

return on instrument i and a risk-free product of comparable investment horizon. Then we define

the momentum in instrument i experienced by agent j at t as 𝜌𝜌𝑇𝑇𝑗𝑗𝑡𝑡 = 𝑠𝑠𝑇𝑇𝑡𝑡 ∗ 𝑣𝑣𝑇𝑇𝑗𝑗𝑡𝑡 and economic force

becomes

𝐶𝐶𝑇𝑇𝑗𝑗𝑡𝑡 = 𝑑𝑑�𝜌𝜌𝑖𝑖𝑗𝑗𝑗𝑗�𝑑𝑑𝑡𝑡

= 𝑑𝑑𝑑𝑑𝑡𝑡

(𝑠𝑠𝑇𝑇𝑡𝑡)𝑣𝑣𝑇𝑇𝑗𝑗𝑡𝑡 + 𝑠𝑠𝑇𝑇𝑡𝑡𝑑𝑑𝑑𝑑𝑡𝑡�𝑣𝑣𝑇𝑇𝑗𝑗𝑡𝑡� (9)

We propose that the wealth 𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡 of agent j in instrument i at time t may be interpreted as a

form of economic area. Then we define the financial stress experienced by agent j in instrument i

at time t as the economic force divided by the economic area affected

𝜉𝜉𝑇𝑇𝑗𝑗𝑡𝑡 = 𝐹𝐹𝑖𝑖𝑗𝑗𝑗𝑗𝑅𝑅𝑖𝑖𝑗𝑗𝑗𝑗

=𝑑𝑑𝑑𝑑𝑗𝑗(𝑇𝑇𝑖𝑖𝑗𝑗)𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗+𝑇𝑇𝑖𝑖𝑗𝑗

𝑑𝑑𝑑𝑑𝑗𝑗�𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗�

𝑅𝑅𝑖𝑖𝑗𝑗𝑗𝑗 (10)

We expect that an increase in the risky spread on an instrument will correspond to a

realignment of market expectations, while an increase in the volume of an instrument traded may

also reflect changes in the market, both of which are interpreted as positive stress. This granular

measure of financial system stress can then be aggregated by taking a weighted sum as

𝜉𝜉𝑡𝑡 = ∑ ∑ 𝑤𝑤𝑇𝑇𝑗𝑗𝑡𝑡𝜉𝜉𝑇𝑇𝑗𝑗𝑡𝑡𝑛𝑛𝑗𝑗=1

𝑚𝑚𝑇𝑇=1

= ��𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡

∑ ∑ 𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡𝑛𝑛𝑗𝑗=1

𝑚𝑚𝑇𝑇=1

�𝑛𝑛

𝑗𝑗=1

𝑚𝑚

𝑇𝑇=1

𝑑𝑑𝑑𝑑𝑠𝑠 (𝑠𝑠𝑇𝑇𝑡𝑡)𝑣𝑣𝑇𝑇𝑗𝑗𝑡𝑡 + 𝑠𝑠𝑇𝑇𝑡𝑡

𝑑𝑑𝑑𝑑𝑠𝑠 �𝑣𝑣𝑇𝑇𝑗𝑗𝑡𝑡�

𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡

=∑ ∑ 𝑑𝑑

𝑑𝑑𝑗𝑗(𝑇𝑇𝑖𝑖𝑗𝑗)𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗+𝑇𝑇𝑖𝑖𝑗𝑗𝑑𝑑𝑑𝑑𝑗𝑗�𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗�

𝑛𝑛𝑗𝑗=1

𝑚𝑚𝑖𝑖=1

∑ ∑ 𝑅𝑅𝑖𝑖𝑗𝑗𝑗𝑗𝑛𝑛𝑗𝑗=1

𝑚𝑚𝑖𝑖=1

= 𝐹𝐹𝑗𝑗𝐴𝐴𝑗𝑗

(11)

7 For practical considerations we let 𝑑𝑑𝑇𝑇𝑗𝑗𝑡𝑡 = �(𝑑𝑑𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠)𝑇𝑇𝑗𝑗𝑡𝑡� + �(𝑑𝑑𝑏𝑏𝑑𝑑𝑏𝑏𝑏𝑏𝑑𝑑𝑏𝑏𝑠𝑠𝑏𝑏𝑠𝑠𝑠𝑠)𝑇𝑇𝑗𝑗𝑡𝑡� to incorporate the effect of changes to both sides of the balance sheet.

13

This framework can accommodate a changing agent and instrument population over time

as well as potentially dramatic changes in the system. However, this measure has no “memory”

allowing it to consider risk premiums or volumes in a historic context. For this reason we also

propose a definition of relative stress as

𝜉𝜉𝑇𝑇𝑗𝑗𝑡𝑡𝑅𝑅𝑅𝑅𝑙𝑙 =𝐹𝐹𝑖𝑖𝑗𝑗𝑗𝑗𝑅𝑅𝑅𝑅𝑅𝑅

𝑅𝑅𝑖𝑖𝑗𝑗𝑗𝑗𝑅𝑅𝑅𝑅𝑅𝑅 =

𝐶𝐶� 𝑑𝑑𝑑𝑑𝑗𝑗(𝑇𝑇𝑖𝑖𝑗𝑗)�𝐶𝐶�𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗�+𝐶𝐶(𝑇𝑇𝑖𝑖𝑗𝑗)𝐶𝐶� 𝑑𝑑𝑑𝑑𝑗𝑗�𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗��

2�1−�𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗

∑ 𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗𝑖𝑖��

𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗∑ 𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗𝑗𝑗

�� (12)

By applying the CDF to each term in the definition of economic force we not only

compare each term to its historical realizations adding a layer of historic interpretation, we add

several attractive properties. First, relative force is naturally on a scale of [0,1] allowing direct

comparison across instruments. Second, since all terms of relative stress are positive we need not

worry about situations where stress appears small despite significant activity (e.g. high stress due

to large positive spread changes may be neutralized by simultaneous reductions in volume). We

divide the numerator by two to ensure that relative force is on a [0,1] scale. The largest

difference between theoretical stress and relative stress is the definition of relative area which

calculates the relative wealth invested in instrument i by agent j compared to the wealth invested

in instrument i across agents and also compared to the wealth of agent j. Therefore, relative area

will magnify 𝜉𝜉𝑇𝑇𝑗𝑗𝑡𝑡 when 1) the position of agent j in instrument i is a large portion of the agents

net worth or 2) when the agents position in instrument i is a large portion of the total wealth

invested in instrument i (with the largest increase occurring when 1 and 2 both occur).

Effectively, the modifications to force facilitate comparison across time while the new area

definition adds the perspective of the cross-sectional importance. Relative stress can be

aggregated using the same weighted sum methodology as theoretical stress without the

convenient simplifications, namely

14

𝜉𝜉𝑡𝑡𝑅𝑅𝑅𝑅𝑙𝑙 = ∑ ∑ � 𝑅𝑅𝑖𝑖𝑗𝑗𝑗𝑗∑ ∑ 𝑅𝑅𝑖𝑖𝑗𝑗𝑗𝑗𝑛𝑛

𝑗𝑗=1𝑚𝑚𝑖𝑖=1

�𝑛𝑛𝑗𝑗=1

𝑚𝑚𝑇𝑇=1

𝐶𝐶� 𝑑𝑑𝑑𝑑𝑗𝑗(𝑇𝑇𝑖𝑖𝑗𝑗)�𝐶𝐶�𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗�+𝐶𝐶(𝑇𝑇𝑖𝑖𝑗𝑗)𝐶𝐶� 𝑑𝑑𝑑𝑑𝑗𝑗�𝑣𝑣𝑖𝑖𝑗𝑗𝑗𝑗��

2�1−�𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗

∑ 𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗𝑖𝑖��

𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗∑ 𝑎𝑎𝑖𝑖𝑗𝑗𝑗𝑗𝑗𝑗

�� (13)

5. RESULTS

Finding 1: Market factors identify financial system stress. There is strong and consistent

evidence that stress in distinct (possibly correlated) markets can be measured, eventually

affecting the stress level of the overall financial system. This finding is supported by longitudinal

exploratory factor analysis of the components of CFSI as constructed in Oet et al. (2012), results

shown in table 1-2. Three factors explain 82% of the variance, where the credit and securitization

factor explains 42%, funding factor explains 23%, and real estate explains 17% of the variance.

Table 1 shows the three rotated factors with clean loadings. We also find in this process, that two

a priori factors (credit and securitization) behaved as a single combined factor, while two

remaining a priori factors (equity and foreign exchange) were not identified because of

insufficient number of components. We subsequently fix both of the unidentified factors and

rerun the exploratory factor analysis (for full results see Appendix). The revised equity factor

consists of eight components: consumer, energy, financials, health, industrials, information,

materials, and consumer durables. We also fix the foreign exchange factors to include fourteen

components in relative foreign exchange rates (currency crashes) and covered interest spreads,

(two sets of components for Canada, Mexico, Japan, UK, Australia, South Africa, and Europe),8

these updated sectors are shown in Figure 6.

Insert Table 1 about here

8 Inclusion of China in our analysis would be preferred due to the large volume of trade between China and the United States however the regulated nature of the USD-Yuan Renminbi (notably from 1995 through 2010) could compromise its usefulness in a currency crashes or covered interest spread measure and as a result we do not consider this data.

15



The five-sector CFSI (Figure 7) shows the relative contributions of each factor over time

to overall stress in units of stress, where zero is the lowest, and one hundred is the largest

possible. This approach—because the CDFs are used—revalues the history of stress, where a

hundred units of stress always represents the maximum possible stress at a given point in time.

We can see that in historical terms, the largest contribution to stress comes from the equity

market (about 35 units of stress maximum), with four remaining factors contributing roughly

equally to stress (about 18 units of stress maximum each). We can also see that for these four

factors, the financial crisis of 2007 represented a relative historical stress peak. However, for the

equity factor, the 2007 stress (about 28 units of stress) is the second largest period of distress. In

historic terms, the equity factor has been most stressed in the period from the late 1990-s to 2002

recession, encapsulating both the Long-term Capital Management (LTCM) crisis to the Dot-Com

bubble burst.


Finding 2: Factor structure reliability and validity. There is clear and robust evidence

that the empirical factor structure of CFSI is reliable and valid. Following exploratory analysis

(EFA) of the a priori stress measure (CFSI), we find a number of serious problems. Table 1

above shows the findings from the reliability and validity testing of the revised factors, following

EFA; five factors are found. Note in table 2 that Cronbach’s Alpha (CA) is excellent for all

factors. It exceeds in all cases 0.819, which is greater that the recommended threshold of 0.7. We

further look at the correlative validity of the revised factors, to see if the factor structure itself

demonstrates convergent and discriminant validity. In the correlation matrix (table 1 above) the

16

indicators identifying a factor show consistently high cross-correlations (supporting convergent

validity), while the cross-correlations of groups of indicators identifying different factors are low

(supporting discriminant validity). Thus, we show both empirical convergent and discriminant

validity of the factor structure, and the high reliability of the factor components. Convergent

validity: A more formal way to test our measure is to consider its convergent, discriminant, and

predictive validity. Here, convergent validity analysis attempts to formally test the financial

stress measure against alternative measures of systemic conditions that utilize a different

methodology.9 This is accomplished by a comparison of the measure against the frequency of

discussions of financial system conditions in the meetings of the Federal Open Market

Committee (FOMC) that sets US monetary policy. We find that the two alternative measures are

highly correlated (67%) and have bi-directional Granger causality, which suggests that they are

both measuring the same underlying condition and could be taken as proxies for one another.


Discriminant validity: For discriminant validity, we test whether CFSI can discriminate

among a reference set of distress signals from a representative set of financial markets. In order

to test whether the empirical and theoretical financial stress measures and CFSI identify stress,

we test them against volatility based benchmark at a variety of monitoring frequencies (daily,

weekly, bi-weekly, monthly, and quarterly). We test at varying frequencies in order to analyze

whether the stress measure captures the pattern sets of reference distress signals that characterize

the conditions of different financial markets over time. To measure the discriminant ability of the

9 We therefore criticize the validity of competing measures of stress (list) that utilize equity volatility directly in the index construction. It makes convergent validity testing against volatility based distress signals impossible, as one cannot validate volatility by comparing it to volatility!

17

various stress indicators we employ three tools.10 Information value (IV) is calculated by

determining whether the signal generated by our indicator was the same as the benchmark. We

then sort our dataset by the stress indicator and group them into I bins allowing us to define the

information value according to (14).11 The noise-to-signal ratio is defined according to (15) as

the ratio of the proportion of no crisis periods where a crisis was mistakenly signaled (Type 2

error), to one minus the proportion of crisis signals which are false (Type 1 error). Finally,

sampling adequacy is defined according to (16) where 𝑠𝑠𝑗𝑗𝑅𝑅2 are the correlations and 𝑠𝑠𝑗𝑗𝑅𝑅2 are the

partial correlations between j and k.12

𝐶𝐶𝑉𝑉𝑥𝑥 = ∑ (𝑔𝑔𝑤𝑤𝑤𝑤𝑑𝑑𝑇𝑇 − 𝑏𝑏𝑑𝑑𝑑𝑑𝑇𝑇) ln �𝑔𝑔𝑇𝑇𝑇𝑇𝑑𝑑𝑖𝑖𝑏𝑏𝑅𝑅𝑑𝑑𝑖𝑖

�𝑇𝑇 (14)

𝑁𝑁𝑁𝑁𝐶𝐶𝑅𝑅 = 𝑇𝑇21−𝑇𝑇1

(15)

𝑀𝑀𝐶𝐶𝐴𝐴𝑗𝑗 =∑ 𝑇𝑇𝑗𝑗𝑘𝑘

2𝑘𝑘≠𝑗𝑗

∑ 𝑇𝑇𝑗𝑗𝑘𝑘2

𝑘𝑘≠𝑗𝑗 +∑ 𝑝𝑝𝑗𝑗𝑘𝑘2

𝑘𝑘≠𝑗𝑗 (16)

We find that across weekly, monthly, and quarterly frequencies that CFSI, empirical and

theoretical stress are consistently good identifiers. Furthermore, the testing shows that the

financial stress measure is the only measure in our sample that can be consistently relied on to

robustly identify the distress signals at varying frequencies.


Both convergent and discriminant validity tests support the use of empirical CFSI as a

measure of US financial stress. In table 4, we see that CFSI converges with an alternative

10 The number of IV bins chosen for each frequency of analysis attempts to minimize the number of measure for which IV and/or NTSR becomes undefined.

11 If the stress indicator contains no information about the benchmark we would expect to see the same number of good and bad predictions in each bin leading to an information value of zero. Siddiqi (2006) suggests that an IV less than 0.1 is weak, between 0.1 and 0.3 is medium, between 0.3 and 0.5 is strong, and greater than 0.5 may be suspicious.

12 According to Kaiser (1970) an MSA above 0.8 is very good, between 0.6 and 0.8 is middling, and below 0.6 is poor.

18

measure of the state of system through analysis of FOMC discussion; whereas table 5 shows that

CFSI converges with a measure of financial market distress signals across a set of frequencies.

Predictive validity: Finally, we test whether CFSI has predictive validity by testing it in

the context of a monetary policy rule. Since its introduction in 1993, the Taylor rule appears to

explain fairly well how monetary policy action in the US on the fed funds target rate may be

considered as a function of inflation and employment. We supplement this rule by a function

related to the financial stability measure, and we find that across a number of distinct regimes

that are identifiable in the fed funds time series using Bai-Perron structural break test, the model

using a function of financial stress (tri-mandate model) significantly improves the measurement

of short-term rates from a mean 𝑅𝑅𝑇𝑇𝑅𝑅𝑇𝑇𝑙𝑙𝑇𝑇𝑇𝑇2 = 50% to a mean 𝑅𝑅𝑡𝑡𝑇𝑇𝑇𝑇−𝑚𝑚𝑅𝑅𝑛𝑛𝑑𝑑𝑅𝑅𝑡𝑡𝑅𝑅2 = 90% (results shown

in Fig. 11). Thus the CFSI financial stress measure passes not only the convergent and

discriminant validity, but also predictive validity tests.




Furthermore, Gallegati (2014) constructs an early warning indicator for the financial

system selecting financial data such as corporate bond spreads and stock market decline using

wavelet decomposition by analyzing the relationships between these variables and the KCFSI.

The wavelet early warning indicator (𝐸𝐸𝐸𝐸𝐶𝐶𝑊𝑊𝑅𝑅𝑣𝑣) he constructs is strongly correlated with KCFSI,

STLFSI, NFCI, and CFSI with five quarters lead. Gallegati then tests the information that the

wavelet methodology contributes to forecasting KCFSI, STLFSI, and CFSI by constructing a

straightforward VAR model with and without additional wavelet factors (including the EWI^W).

While the RMSE of each VAR model was superior for every financial stress indicator with the

19

addition of the 𝐸𝐸𝐸𝐸𝐶𝐶𝑊𝑊𝑅𝑅𝑣𝑣 as a factor in the model, the information gain CFSI experienced was

smaller at every forecasting horizon than the gain experienced by KCFSI and STLFSI. This

relative lack of improvement may indicate the construction of CFSI is more sensitive to changes

in selected indicators than alternatives.

Finding 3: Empirical stress guides the theoretical basis for stress. There is evidence that

asset spreads, transaction volumes, agent exposures, and financial frictions form a sound

theoretical basis for financial system stress. This finding is supported by CFA of the financial

stress measurement model.

The results are summarized for selected sector agents in Fig. 10 & 11. The adaptive

nature of the financial system is evident in the nonlinearities of structural, functional, and

behavioral patterns exhibited by the economic agents over time. The emergent macro-patterns

stem in large part from the heterogeneous agents’ micro-activities. For example, on the level of

the macroeconomy, financial stress exposures and experiences of US banks, REITs, GSEs, and

funding corporations differ over time (see Fig. 10).

Finding 4: Measurement model is sound across heterogeneous agents and instruments.

There is clear evidence that the financial system stress empirical measurement model is sound

across heterogeneous agents and instruments. This finding is supported by CFA of the financial

stress measurement model. In Table x we test the CFA measurement model for invariance. Panel

A shows configural invariance assessment for the multiple agents. The results show good fit for

all models, supporting configural invariance across the agents. However, metric invariance tests

(panel B) show that not all agents exhibit the same goodness of fit.

Insert Table x about here

20

The empirical stress results for heterogeneous agents are shown in Fig. 15 for US

chartered depository institutions, funding corporations, real estate investment trusts (REITs), and

government-sponsored entities (GSEs). US banks are among the more complex agents covered

by empirical stress, their main sources of stress stems from time deposits, residential real estate,

and GSE backed securities, as well as consistently decreasing stress in checkable deposits and

somewhat sporadic stress in commercial real estate (mainly during the crisis). Funding

corporations have an entirely different structure evidenced by the way they experience stress

which arises from commercial paper (with consistently decreasing importance), followed by

corporate bonds and money market mutual funds shares (each of which steadily rises in

importance). For the REITs, the most massive source of stress comes from bonds, followed by

the commercial real estate, GSE backed securities, and commercial real estate (not normally

concurrently) and after 2002 they pick up minor stress from residential real estate. GSEs

experience stress primarily due to residential real estate and GSE back securities with minor

stress from multi-family residential real estate.


The second part of research question 4 examines whether stress can be quantified across

different financial instruments. Figure 16 shows the stress contributions of different agents to

stress in particular financial instruments. Shown here is a sample selection of GSE backed

securities, interbank activity, residential real estate and corporate bonds. For the GSE securities

the largest participants are GSEs and mortgage pools with life insurance and US banks

participating in a minor capacity, note the growing participation of the rest of the world.

Interbank activity is due mostly to US banks and foreign banking, with steadily decreasing

participation by credit unions and sporadic participation by the rest of the world and the

21

monetary authority. Residential real estate stress is experienced in large part by households with

mortgage pools and US banks as steady minor stakeholders and GSEs entering as participants in

the past 4 years. Corporate bonds have fairly stable participation with corporate businesses, ABS

issuers, and the rest of the world as primary holders while households are a minor but growing

part of the market.


Finding 5: Theoretical stress converges to empirical identification. There is strong

evidence that theoretical stress converges to the empirical identification. This finding is

supported by SEM comparison of the empirical five-factor stress, empirical sectoral stress, and

theoretical stress. In Figure 12 we compare the goodness of fit statistics for the empirical five-

sector system stress based on the EFA results, empirical sectoral stress modified with the

findings of the CFA, and the theoretical stress models based on the formal theoretical conjecture

and hypothesis testing using detailed heterogeneous agent and instrument data. The initial results

are less than adequate for chi-square/df statistic, and good for other goodness of fit statistics. The

results also show convergence between the models. As a side note, both the empirical and the

theoretical stress measurement models, while promising in identification of show several

departures from the overall five-sector stress. Some of these may be welcome, like the

identification of increasingly high stress in 2005 and 2006 by the new sectoral stress models.

Others, like the underestimation of the late 1990s (LTCM) crisis, are disappointing.

Insert Figure 12 about here In order to investigate this closer, we propose an alternative model that recognizes the

potential importance of a common factor that adds a layer of meaning to all asset price and

volume based information. From the point of theory, this common latent factor is the idea of

correction due to market frictions (market imperfections). In the alternative model, we recognize

22

the idea of market friction and test for its significance. We have two alternative models: first the

time-varying liquidity as friction, and second the time-varying factor correlation matrix as

friction. We test both and show the results. In the empirical sectoral model, we investigate the

frictional factor as induced by liquidity, [we also investigate is as the time-varying factor

correlations (Hollo, Kremer, and Lo Duca, 2012), with the standard assumption that frictionless

markets should be perfectly independent. However, the extent to which factor-cross-correlation

is non-zero, the friction in the financial economy can be observed at each point in time.

6. DISCUSSION

A fundamental challenge to researchers and policymakers is that financial stress lacks a

definition which has theoretical basis, requiring that empirical indicators are compared to

volatility series or historical lists of crisis events. This study employed EFA to verify and

improve the design of CFSI which has hitherto relied on a priori assumptions and referenced

against a constructed volatility benchmark. Subsequently, we leverage this validation of a spread

based stress measure and extend the methodology to examine a partitioning of the financial

system into a collection of agents exposed to designated asset categories allowing us to construct

the empirical stress measure. The design of this empirical stress measure, supported as an

extension of the validated CFSI measure, allows us to handle adaptations in the structure of the

financial system by observing stress as it arises due to agent’s wealth allocation choices

(weighting) and market clearing pressure (spread determination).

Drawing upon literature we also support 8 hypotheses which aim to determine the drivers

(rate spreads, transaction volume, agent exposures, ect.) of financial system stress; these are

validated empirically through structural equation modeling. This allows us to construct a new

23

theoretical measure of stress with components and architecture supported conceptually and

quantitatively.

REFERENCES

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26

FIGURES

FIGURE 1: Methodological Map

real phenomenon

RQ1: What are the system factors that

identify financial stress?

RQ2: Are the factors

empirically reliable?

RQ3: How can stress be

theorized in an adaptive system?

What is financial system stress?

Flow of Funds Financial markets'

observations (1991Q1-2013Q4)

EFA EFA CFA SEM

data

known stable

relations

Problem of

practice

target of analysis

empirical construct RQ5: Does theoretical stress

substantiate empirical

identification?

RQ4: Is the measurement

model sound across heterogeneous

agents?

analysis and validation

27

FIGURE 2: A Priori US Financial Stress Measurement Model (CFSI)

Financial system stress

FM share

CM share

EM share

FX share

RE share

SM share

Equity markets (EM) stress SMC

Securitization markets (SM) stress

RMBS CMBS ABS

V- RMBS V-

CMBS V- ABS

Real estate (RE) markets stress

CRE RRE

V- CRE V-

RRE

Foreign exchange (FX) markets stress WDC

Credit markets (CM) stress

CI CP TYC

V- L V-

CI V- CP V-

TYC V- CB

CB L

Funding markets (FM) stress

ICB BB IL

V- FB V-

ICB V- BB V-

IL

FB

28

FIGURE 3: Hypotheses

FIGURE 4: Percentage of total financial assets held by each financial sector (1952-2013)

Note: Vertical bars highlight episodes of change in relative ranking of financial sectors by total assets

29

FIGURE 5: Conceptual Diagram of the Adaptive System Solution

FIGURE 6: Factor Revisions for US Financial Stress (CFSI)

Extended Equity Factor Currency Crashes Indicator for the International Factor

Covered Interest Spreads Indicator for the International Factor

State at time = tState at time = t +1

30

FIGURE 7: Factors of Financial System Stress

5-factor Financial Stress (CFSM) Equity Factor

redit and Securitization Factor Funding Factor

Real Estate Factor International Factor

31

FIGURE 8: Financial Stability Theme vs. US Financial Stress (CFSI)

FIGURE 9: Predictive Validity of Financial Stress A: Taylor Guideline for Monetary Policy B: Tri-mandate model of Monetary Policy

-.01

.00

.01

.02

.03

.04

.05

.06

.07

92 94 96 98 00 02 04 06 08 10 12Effective Fed Funds rateTri-mandate rule rate

Regime 1 Regime 2 Regime 3 Regime 4 Regime 5

-.01

.00

.01

.02

.03

.04

.05

.06

.07

92 94 96 98 00 02 04 06 08 10 12Effective Fed Funds rateTri-mandate rule rate

Regime 1 Regime 2 Regime 3 Regime 4 Regime 5

Measure Regime Tri-mandate rule 𝑅𝑅𝑅𝑅𝑑𝑑𝑗𝑗2 ALL 93.7%

𝑅𝑅𝑅𝑅𝑑𝑑𝑗𝑗2 Regime1 98.7% 𝑅𝑅𝑅𝑅𝑑𝑑𝑗𝑗2 Regime2 94.9% 𝑅𝑅𝑅𝑅𝑑𝑑𝑗𝑗2 Regime3 90.7%

𝑅𝑅𝑅𝑅𝑑𝑑𝑗𝑗2 Regime4 99.1%

𝑅𝑅𝑅𝑅𝑑𝑑𝑗𝑗2 Regime5 97.7% Note: Gap for financial stress measure proxies financial stability in the tri-mandate model (Oet et al., 2014) given by 𝐶𝐶𝑠𝑠𝑑𝑑𝐶𝐶𝑑𝑑𝑛𝑛𝑑𝑑𝑠𝑠 =𝑐𝑐 + 𝛽𝛽1𝐸𝐸 + 𝛽𝛽2𝐸𝐸𝐸𝐸 + 𝛽𝛽3𝐸𝐸𝐸𝐸𝐸𝐸 + 𝛽𝛽4𝐶𝐶 + 𝛽𝛽5𝐶𝐶𝐸𝐸 + 𝛽𝛽6𝐶𝐶𝐶𝐶𝐸𝐸 + 𝛽𝛽7𝐶𝐶 + 𝛽𝛽8𝐶𝐶𝐸𝐸 + 𝛽𝛽9𝐶𝐶𝐶𝐶𝐸𝐸 + 𝛽𝛽10𝑀𝑀𝐶𝐶 + 𝑠𝑠1, where E ≔ employment gap theme; EG ≔ employment gap; I ≔ inflation theme; IG ≔ inflation gap; S ≔ financial stability theme; SG ≔ stability gap; MS ≔ money supply.

-2

-1

0

1

2

3

0.0%

2.5%

5.0%

7.5%

10.0%

12.5%

15.0%O

ct-9

1M

ar-9

2A

ug-9

2Ja

n-93

Jun-

93N

ov-9

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pr-9

4Se

p-94

Feb-

95Ju

l-95

Dec

-95

May

-96

Oct

-96

Mar

-97

Aug

-97

Jan-

98Ju

n-98

Nov

-98

Apr

-99

Sep-

99Fe

b-00

Jul-0

0D

ec-0

0M

ay-0

1O

ct-0

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03N

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pr-0

4Se

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05Ju

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-05

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08Ju

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09Fe

b-10

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2

FINANCI MARKET FINANCI CONDITION EQUITI PRICE FOREIGN EXCHANGVALU OF THE DOLLAR TREASURI SECUR MARKET CONDITION STOCK MARKETCORPOR BOND MORTGAG RATE BALANC SHEET NONFINANCI DEBTCREDIT CONDITION MONEI MARKET COMMERCI PAPER STOCK PRICEFUND MARKET EQUITI MARKET FINANCI INSTITU MORTGAG INTEREST RATETREASURI YIELD MUTUAL FUND MARKET INTEREST RATE MARKET PRICE

Frequency Standard Deviations

-.02

.00

.02

.04

.06

.08

.10

90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13

Effective Fed Funds rateTaylor rule: Fed Funds = f(c, inflation gap, employment gap)

32

FIGURE 10: Empirical Stress for Heterogeneous Agents

Note: These graphs represent stress in a selected group of agents (restricted for the sake of brevity), stress series for all agents available from authors upon request. The charts represents in descending order: US Chartered Depository Inst. (US Banks), Funding Corporation, REITs, and GSEs.

33

FIGURE 11: Empirical Stress for Heterogeneous Instruments

Note: These graphs represent stress in a selected group of instruments (restricted for the sake of brevity), stress series for all instruments is available from authors upon request. The charts represents in descending order: GSE Backed Securities, Net Interbank, Residential Real Estate, and Corporate Bonds

34

FIGURE 12: Convergence of CFSM, Sectoral System Stress, and Theoretical System Stress

Measure CFSI Empirical

sectoral stress Theoretical sectoral

stress Threshold Assessment

Chi-square/df (cmin/df) 26.386 26.386 26.386 < 2 good adequate

CFI 0.985 0.985 0.985 > 0.95 great very good

RMSEA 0.014 0.014 0.014 < 0.05 good good

PCLOSE 1.000 1.000 1.000 > 0.005 very good

SRMR 0.008 0.008 0.008 < 0.08 very good

-2

-1

0

1

2

3

4

Mar

-81

Nov

-81

Jul-8

2M

ar-8

3N

ov-8

3Ju

l-84

Mar

-85

Nov

-85

Jul-8

6M

ar-8

7N

ov-8

7Ju

l-88

Mar

-89

Nov

-89

Jul-9

0M

ar-9

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ov-9

1Ju

l-92

Mar

-93

Nov

-93

Jul-9

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ar-9

5N

ov-9

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l-96

Mar

-97

Nov

-97

Jul-9

8M

ar-9

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l-00

Mar

-01

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-01

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Mar

-13

Z_Empirical_Stress Z_Theoretical_Stress 5-factor stress

35

TABLES

TABLE 1: Rotated Factor Pattern (Standardized Regression Coefficients)

Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 BBS 0.901 CFSI 0.888 CMBSS 0.879 ABSS 0.867 CBS 0.697 LS 0.576 ILS 1.014 CPTBS 0.970 ICB 0.783 RRES 0.921 CRES 0.906 Equity 1 Equity 2 Equity 3 Equity 4 Equity 5 Equity 6 Equity 7 Equity 8 FX 1 FX 2

Note: Normalization of factor rows by rescaling to represent covariances

TABLE 2: Reliability of Five-Factor Financial System Stress Measure (CFSM)

TABLE 3: Correlation and Granger Causality of Financial Stability and CFSI Frequency (t) 1 observation lag / lead (t-1, t+1) 2 observations lag / lead (t-2, t+2)

Observations Correlation Observations F-Statistic Prob. Observations F-Statistic Prob. Financial stability theme → US financial stress (CFSI) 168 0.6704 167

8.82256††† 0.0034 166

5.20859††† 0.0064

US financial stress (CFSI) → Financial stability theme 12.4203††† 0.0006 3.85861††† 0.0231

Note: ††† – indicates Granger causality with 95% or better confidence.

36

TABLE 4: Discriminant validity of the Financial Stress Measures Frequency

(Signaling Threshold) Rank Model Class Indicator IV Noise-Signal MSA

Quarterly (Threshold: 0.77)

- Macro-financial linkages COVAR (5%) 0.58 0.11 0.51 1 Macro-financial linkages KDF 0.58 0.17 0.80 2 Financial stress CFSI 0.54 0.12 0.84 - Early warning Construction Returns 0.50 0.11 0.67 - Macro-financial linkages Delta CoVAR (%1) 0.48 0.10 0.48 - Contagion risk Equity concentration 0.48 0.21 0.42 3 Sector risk Energy volatility 0.41 0.16 0.81 - Asset price Liquidity index 0.39 0.21 0.60 - Macro-financial linkages Delta COVAR (5%) 0.37 0.20 0.54 4 Sector risk Materials volatility 0.35 0.15 0.82 5 Sector risk Industrials Volatility 0.27 0.16 0.89 - Stress testing BankCaR 0.22 0.13 0.37 6 Sector risk Health care volatility 0.20 0.19 0.79 - Contagion risk FX concentration 0.20 0.17 0.58

Monthly (Threshold: 0.99)

1 Sector risk CFNAI: Inventories 0.57 0.04 0.94 2 Financial stress CFSI 0.47 0.00 0.77 - Sector risk Technology volatility 0.37 0.03 0.63 3 Sector risk Materials volatility 0.37 0.06 0.82 - Stress testing SRISK 0.25 0.00 0.54

Weekly (Threshold: 1.00)

- Sector risk Consumer staples volatility 0.55 0.01 0.68 1 Contagion risk CFNFCI leverage 0.46 0.03 0.78 - Sector risk Consumer discr. volatility 0.44 0.02 0.66 - Sector risk Technology volatility 0.28 0.02 0.50 2 Financial stress CFSI 0.23 0.00 0.72 3 Stress testing SRISK 0.21 0.028 0.71

TABLE 5: Bai-Perron Structural Break Test Results Break Test Date F-statistic Scaled F-statistic Critical Value**

Panel A: Effective Fed Funds rate 0 vs. 1 * 2008M02 22.41 44.82 11.47 1 vs. 2 * 2004M07 9.91 19.82 12.95 2 vs. 3 * 2001M01 30.95 61.90 14.03 3 vs. 4 * 1994M01 20.82 41.63 14.85

Panel B: FOMC discussion themes Financial stability theme 0 vs. 1 * 2007M08 9.56 19.12 11.47

1 vs. 2 * 1999M01 7.86 15.73 12.95 Output theme 0 vs. 1 5.70 11.40 11.47 Inflation theme 0 vs. 1 5.33 10.65 11.47 Employment theme 0 vs. 1 3.39 6.78 11.47 Foreign activity theme 0 vs. 1 3.57 7.14 11.47 Fiscal policy theme 0 vs. 1 5.37 10.74 11.47 Money supply theme 0 vs. 1 5.03 10.05 11.47 Panel C: Communications policy rule 0 vs. 1 * 1999M01 66.94 535.48 23.70 1 vs. 2 * 2003M03 23.32 186.54 25.75 2 vs. 3 * 2008M02 36.97 295.75 26.81 3 vs. 4 * 1995M09 13.71 109.68 27.65 Note: * Significant at the 0.05 level. ** Bai-Perron (2003) critical values.

37

APPENDIX: LONGITUDINAL FACTOR ANALYSIS

The Cleveland Financial Stress Index is constructed under the assumption that indicators

can be aggregated to reflect conditions in six underlying markets with conceptual importance to

the financial system. Exploratory Factor Analysis (EFA) is applied to the weighted cumulative

density functions of each indicator used to construct CFSI to test this claim. Since EFA does not

incorporate a priori intuition about how latent factors should be grouped it is appropriate for an

initial investigation of the effect that latent factors such as stress in designated financial sectors

may exert on observable measures. We will first address the suitability of EFA for the analysis of

time series data and then verify our dataset satisfies the properties required.

𝑥𝑥𝑇𝑇(𝑠𝑠) = 𝜆𝜆𝑇𝑇𝑓𝑓𝑇𝑇(𝑠𝑠) + 𝑠𝑠𝑇𝑇(𝑠𝑠) (A1)

The core assumptions of EFA (equation A1) include that factors 𝑓𝑓𝑡𝑡 and idiosyncratic

residuals 𝑠𝑠𝑡𝑡 do not exhibit serial. Referring to the assumption of serial correlation Geweke (2007

pg. 365) raises the point that “if the 𝑥𝑥𝑇𝑇(𝑠𝑠) are time series this assumption is almost always

inappropriate since 𝑥𝑥𝑇𝑇(𝑠𝑠) and 𝑥𝑥𝑇𝑇(𝑠𝑠 + 𝑠𝑠) will in general be correlated.” Stock and Watson (2010

pg. 2) provide the analogy that residuals pick up on issues unique to an individual indicator, like

the impact of a salmonella scare which affects restaurant employment but not the pet store next

door. Anderson (1963 pg. 7) agrees that shocks in the time dimension may persist across

multiple time periods leading to serial correlation issues. However, Anderson concludes that the

“day-to-day correlation may be of no greater disadvantage than if the observations were

independent”.13 Table A1 shows that there is significant serial correlation for several variables

used in the original CFSI construction and that even after two forms of differencing are applied

13 Referring to Principal Component Analysis, a special kind of EFA, Bai and NG (2008) point out that dealing “with cross-sectionally correlated errors, which is a genuine feature of an approximate factor model, remains an unresolved issue.”

38

this serial correlation may not be entirely corrected. However, after conducting EFA on all three

datasets we find that our results are robust in that very similar factors are found from each

dataset.

In order to determine whether the data is suitable for factor analysis, several assumptions

must be tested: 1. whether data is suitable for correlation testing; 2. whether data is normally

distributed; 3. whether the relations between variables are linear; 4. whether data has outliers; 5.

whether data is factorable; and 6. whether the sample size is adequate.

Suitability: The CFSI data is a longitudinal dataset suitable for factor analysis with

variables consisting of metric data with 5436 observations for each of the 24 variables.14

14 One of the variables is a date series.

Table A1: Serial correlation testing of the weighted components of CFSI, the differenced spreads, and the differenced weighted components. Weighted CDFs Differenced Spreads Differenced Weighted CDFs

Variable LM Obs*R-squared (at -1 lag)

H0 ( no serial correlation)

LM Obs*R-squared (at -x lags)


LM Obs*R-squared (at –x lags)


CR_ABS 0.000(ns) cannot reject at *** 6.707(ns-2) cannot reject at *** 3.381 (*-1) cannot reject at ** CR_BBS 0.207(ns) cannot reject at *** 1.908(ns-2) cannot reject at *** 4.727 (**-1) cannot reject at * CR_CBS 0.000(ns) cannot reject at *** 1.953(ns-3) cannot reject at *** 1.038 (ns-3) cannot reject at *** CR_CMBS 2.968* rejected at ** 6.164(ns-4) cannot reject at *** 8.318 (ns-12) cannot reject at *** CR_LIQS 2.329(ns) cannot reject at *** 6.06(**-2) cannot reject at *** 7.376 (ns-12) cannot reject at *** EQ_COND 2.266(ns) cannot reject at *** 6.222(**-2) cannot reject at *** 5.872 (ns-3) cannot reject at *** EQ_CONS 0.000(ns) cannot reject at *** 4.647(ns-7) cannot reject at *** 14.132 (***-1) rejected EQ_ENRS 0.000(ns) cannot reject at *** 6.253(ns-6) cannot reject at *** 13.179 (***-1) rejected EQ_FINL 2.900* rejected at ** 9.820(ns-9) cannot reject at *** 6.101 (**-1) cannot reject at * EQ_HLTH 1.875(ns) cannot reject at *** 6.797(ns-6) cannot reject at *** 5.461 (**-1) cannot reject at * EQ_INDU 12.725*** rejected 4.640(ns-7) cannot reject at *** 7.791 (**-1) cannot reject at * EQ_INFT 16.995*** rejected 0.775(ns-2) cannot reject at *** 6.591 (**-1) cannot reject at * EQ_MATR 1.834(ns) cannot reject at *** 7.012(ns-7) cannot reject at *** 0.059 (ns-1) cannot reject at *** EQ_UTIL 0.000(ns) cannot reject at *** 0.208(ns-1) cannot reject at *** 11.018 (***-1) rejected FD_CPTBS 19.618*** cannot reject at *** 5.091(***-2) cannot reject at *** 6.155 (ns-3) cannot reject at *** FD_ICOB 0.000(ns) cannot reject at *** 10.147(*-1) rejected 1.602 (ns-1) cannot reject at *** FD_ILIQS 23.065*** rejected 4.663(*-2) cannot reject at *** 5.483 (ns-3) cannot reject at *** FX_AUD_CIS 35.682*** rejected 14.301(***-1) rejected 11.286 (***-1) rejected FX_AUD_CRSH 0.000(ns) cannot reject at *** 1.469(ns-2) cannot reject at *** 8.035 (**-1) cannot reject at * FX_CAD_CIS 33.218**** rejected 12.070(***-1) rejected 11.794 (***-1) rejected FX_CAD_CRSH 0.000(ns) cannot reject at *** 1.683(ns-4) cannot reject at *** 14.372 (ns-12) cannot reject at *** FX_EUR_CIS 50.294*** rejected 3.947(ns-4) cannot reject at *** 12.333 (***-1) rejected FX_EUR_CRSH 0.000(ns) cannot reject at *** 4.434(ns-3) cannot reject at *** 12.048 (ns-12) cannot reject at *** FX_JPN_CIS 30.677*** rejected 36.657(***-1) rejected 34.646 (***-1) rejected FX_JPN_CRSH 0.000(ns) cannot reject at *** 0.513(ns-4) cannot reject at *** 3.674 (ns-4) cannot reject at *** FX_MEX_CIS 2.759 * cannot reject at *** 4.945(*-2) cannot reject at *** 0.347 (ns-3) cannot reject at *** FX_MEX_CRSH 0.400(ns) cannot reject at *** 5.387(ns-3) cannot reject at *** 16.029 (ns-12) cannot reject at *** FX_UK_CIS 46.469*** rejected 13.583(***-1) rejected 5.559 (ns-12) cannot reject at *** FX_UK_CRSH 0.000(ns) cannot reject at *** 4.076(ns-6) cannot reject at *** 7.712 (ns-6) cannot reject at *** FX_ZAR_CIS 14.235*** rejected 11.213(***-1) rejected 9.514 (ns-7) cannot reject at *** FX_ZAR_CRSH 10.623** rejected 7.139(ns-8) cannot reject at *** 10.461 (ns-11) cannot reject at *** RE_CRE 0.000(ns) cannot reject at *** 7.930(***-1) rejected 9.146 (**-1) cannot reject at * RE_RRE 0.000(ns) cannot reject at *** 6.527(**-2) cannot reject at *** 6.176 (**-1) cannot reject at * Note: * estimated coefficients significant at 10%; **estimated coefficients significant at 5%; ***estimated coefficients significant at 1%

39

Normality: Table A2 provides skewness and kurtosis statistics for the 23 continuously

scaled variables in the dataset, as well as the results of the normality tests: Kolmogorov-Smirnov,

Lilliefors, Cramer-von Mises, Watson, Anderson-Darling, and Jarque-Bera. Common to these

normality tests is the null hypothesis that the sample population is normally distributed. The

significance of 0.000 in all the test statistic results support the alternative hypothesis of non-

normality. The lack of normality does not invalidate the use of factor analysis, however, it

suggests that during factor extraction, maximum likelihood extraction may not be the optimal

choice (Fabrigar et al., 1999).

Table A2—Normality testing Variable Skewness Kurtosis

Kolmogorov-Smirnov

(Sig.)

Lilliefors (Sig.)

Cramer-von Mises (Sig.)

Watson (Sig.)

Anderson-Darling (Sig.)

Jarque-Bera (Sig.)

CFSI 0.537 2.523 .093 (.000)

0.093 (.000)

11.561 (.000)

9.853 (.000)

66.526 (.000)

312.938 (.000)

ABSS 0.771 2.573 .117 (.000)

0.117 (.000)

22.906 (.000)

19.308 (.000)

152.923 (.000)

580.379 (.000)

BBS 0.106 2.102 .073 (.000)

0.073 (.000)

9.245 (.000)

9.235 (.000)

55.398 (.000)

192.868 (.000)

CMBSS 0.933 2.377 .247 (.000)

0.247 (.000)

81.111 (.000)

74.039 (.000)

435.847 (.000)

876.416 (.000)

CPTBS -0.012 1.727 .091 (.000)

0.091 (.000)

14.720 (.000)

14.708 (.000)

95.483 (.000)

367.140 (.000)

CRES 0.235 2.555 .043 (.000)

0.043 (.000)

2.848 (.000)

2.747 (.000)

24.160 (.000)

94.805 (.000)

CBS -0.046 1.970 .056 (.000)

0.056 (.000)

5.210 (.000)

5.179 (.000)

38.096 (.000)

242.025 (.000)

CIS 0.469 2.777 .072 (.000)

0.072 (.000)

6.139 (.000)

5.537 (.000)

53.078 (.000)

210.770 (.000)

CM 0.645 3.081 .062 (.000)

0.062 (.000)

7.107 (.000)

5.311 (.000)

43.948 (.000)

378.506 (.000)

EM 0.242 2.268 .067 (.000)

0.067 (.000)

6.400 (.000)

6.251 (.000)

44.786 (.000)

174.144 (.000)

FB 0.211 2.165 .098 (.000)

0.098 (.000)

12.850 (.000)

12.746 (.000)

74.354 (.000)

198.233 (.000)

FXM 0.333 2.061 .062 (.000)

0.062 (.000)

7.553 (.000)

6.818 (.000)

57.691 (.000)

300.352 (.000)

ICB 0.279 2.158 .076 (.000)

0.076 (.000)

6.322 (.000)

5.984 (.000)

46.925 (.000)

230.843 (.000)

ILS 0.016 1.788 .077 (.000)

0.077 (.000)

11.764 (.000)

11.763 (.000)

76.701 (.000)

333.044 (.000)

IM 0.923 4.006 .056 (.000)

0.056 (.000)

6.731 (.000)

4.363 (.000)

56.002 (.000)

1001.455 (.000)

LS -0.040 1.946 .069 (.000)

0.069 (.000)

5.627 (.000)

5.614 (.000)

46.870 (.000)

253.083 (.000)

REM 0.163 2.610 .045 (.000)

0.045 (.000)

1.029 (.000)

0.979 (.000)

14.370 (.000)

58.726 (.000)

RMBSS 0.786 2.333 .189 (.000)

0.189 (.000)

49.202 (.000)

44.870 (.000)

313.262 (.000) 660.4900

RRES 0.002 1.843 .077 (.000)

0.077 (.000)

11.037 (.000)

11.035 (.000)

68.825 (.000)

303.1411 (.000)

SM 0.695 2.351 .153 (.000)

0.153 (.000)

28.217 (.000)

25.164 (.000)

191.904 (.000)

532.585 (.000)

SMC 0.242 2.268 .067 (.000)

0.067 (.000)

6.400 (.000)

6.251 (.000)

44.786 (.000)

174.144 (.000)

TYCS -0.105 1.804 .071 (.000)

0.071 (.000)

9.165 (.000)

9.086 (.000)

68.522 (.000)

333.943 (.000)

WDC 0.333 2.061 .062 (.000)

0.062 (.000)

7.553 (.000)

6.818 (.000)

57.691 (.000)

300.352 (.000)

40

Linearity: Figure A1, Panel A provides scatterplot results comparing the CFSI dependent

variable (DV) and the market stress independent variables (IVs): CM (credit market stress), EM

(equity market stress), IM (funding market stress), FXM (foreign exchange market stress), REM

(real estate market stress), and SM (securitization market stress). The figure suggests that the

relationship of several IVs (particularly CM, EM, FXM, IM and REM) with DV may be non-

linear. Figure 1, Panels B through E show the relationship of DV with the components of market

stress in credit market (panel B), interbank market (panel C), securitization market (panel D),

and real estate market (panel E). Several of these relationships appear to be possibly non-linear:

particularly the relationships with CIS, CPTBS, and TYCS components in the credit market; ILS

components in the interbank market; and CRES and RRES in the real estate market. Many of

these scatterplots are characterized by concentrated clusters of data within a wide dispersion of

DV data, a pattern that may be indicative of moderating variables influencing the IV-DV

relationship.

Figure A1—Scatterplot matrix of CFSI and market stress variables

PANEL A: CFSI vs. market stress variables

CFS

I

CM EM FXM IM REM SM PANEL B: CFSI vs. credit market stress variables

CFS

I

LS CIS CPTBS TYCS CBS PANEL C: CFSI vs. interbank market stress variables

41

Given these results, it is useful to test linearity among the DV and IV variables and their

components more rigorously. Table A3 provides results of ANOVA deviation from linearity F-

test.

Table A3—ANOVA deviation from linearity F-test Variable F p Linear PANEL A: CFSI vs. market stress variables

CM 1705.136 .019 non-linear EM 53.561 .000 non-linear FXM 39.178 .000 non-linear IM 211.968* .000* linear* REM 7.569* .006* linear* SM 3966.186* .000* linear*

PANEL B: CFSI vs. credit market stress variables LS 16.113 .000 non-linear CIS 5.664 .000 non-linear CPTBS 417.028 .000 non-linear TYCS 65.493 .000 non-linear CBS 128.195 .000 non-linear

PANEL C: CFSI vs. interbank market stress variables FB 10.952 .000 non-linear ICB 22.804 .000 non-linear BBS 40.296 .000 non-linear ILS 61.905 .000 non-linear

PANEL D: CFSI vs. securitization market stress variables RMBSS 1.596 .000 non-linear CMBSS 6.434 .000 non-linear ABSS 11.473 .000 non-linear

PANEL E: CFSI vs. real estate market stress variables CRES 144.562 .000 non-linear RRES 11.986 .000 non-linear

Note: * indicates results of pairwise ANOVA linearity F-test

CFS

I

FB ICB BBS ILS

PANEL D: CFSI vs. securitization market stress variables

CFS

I

RMBSS CMBSS ABSS PANEL E: CFSI vs. real estate market stress variables

CFS

I

CRES RRES

42

Outliers: Outliers in the IVs are considered in Figure A2, panels A through E. Two

market stress variables, CM and IM, in panel A show several outliers.15 However, no outliers are

present in the various market stress components shown in panels B-E. Thus, no data exclusion is

performed.

Figure A2—Outlier boxplots of market stress variables PANEL A: Market stress variables

PANEL B: Credit market stress variables

PANEL C: CFSI vs. interbank market stress variables

PANEL D: CFSI vs. securitization market stress variables

PANEL E: CFSI vs. real estate market stress variables

15 Review of this data reveals the outliers mainly include the data from the financial crisis of 2008-2009 and also include odd starting values.

43

Factorability: Seventeen of the original twenty-three variables are retained for further

analysis to avoid matrix analysis problems.16 Visual inspection of the correlation matrix (Table

A4) reveals that roughly half of the correlations are larger than 0.3, suggesting that the dataset

may be factorable. All communalities (Table A5) are above 0.2—a welcome result for

factorability, however the communality for CFSI (the dependent variable) is greater than 1--an

ultra-Heywood case. This result suggests that there is something wrong with the dataset.17

Table A4—Correlation matrix

CFSI ABSS CMBSS RMBSS CRES RRES BBS FB ILS ICB CIS LS CPTBS TYCS CBS SMC WDC

CFSI 1.000 .630 .618 .573 .130 -.066 .663 -.121 -.002 -.039 -.044 .496 -.110 -.147 .640 .737 .393

ABSS .630 1.000 .771 .438 -.312 -.311 .619 -.072 .111 -.086 -.400 .428 .016 .087 .296 .364 .342

CMBSS .618 .771 1.000 .496 -.078 -.099 .754 -.180 -.232 -.258 -.372 .786 -.337 -.359 .607 .273 .409

RMBSS .573 .438 .496 1.000 .070 -.207 .376 -.171 -.307 -.252 -.304 .597 -.456 -.040 .429 .090 .078

CRES .130 -.312 -.078 .070 1.000 .694 -.117 .184 -.270 -.114 .222 .178 -.260 -.203 .441 -.086 -.112

RRES -.066 -.311 -.099 -.207 .694 1.000 -.119 .151 .175 .152 .195 -.120 .154 -.017 .267 -.134 -.391

BBS .663 .619 .754 .376 -.117 -.119 1.000 -.252 -.084 -.202 -.172 .578 -.185 -.330 .713 .464 .318

FB -.121 -.072 -.180 -.171 .184 .151 -.252 1.000 .200 .318 .459 -.109 .218 -.050 -.134 -.278 -.084

ILS -.002 .111 -.232 -.307 -.270 .175 -.084 .200 1.000 .627 .154 -.636 .937 .516 -.298 .150 -.345

ICB -.039 -.086 -.258 -.252 -.114 .152 -.202 .318 .627 1.000 .319 -.375 .618 -.009 -.327 .075 -.280

CIS -.044 -.400 -.372 -.304 .222 .195 -.172 .459 .154 .319 1.000 -.172 .288 -.330 -.014 -.071 .032

LS .496 .428 .786 .597 .178 -.120 .578 -.109 -.636 -.375 -.172 1.000 -.682 -.644 .651 .068 .441

CPTBS -.110 .016 -.337 -.456 -.260 .154 -.185 .218 .937 .618 .288 -.682 1.000 .452 -.404 .067 -.251

TYCS -.147 .087 -.359 -.040 -.203 -.017 -.330 -.050 .516 -.009 -.330 -.644 .452 1.000 -.419 -.007 -.359

CBS .640 .296 .607 .429 .441 .267 .713 -.134 -.298 -.327 -.014 .651 -.404 -.419 1.000 .341 .182

SMC .737 .364 .273 .090 -.086 -.134 .464 -.278 .150 .075 -.071 .068 .067 -.007 .341 1.000 .139

WDC .393 .342 .409 .078 -.112 -.391 .318 -.084 -.345 -.280 .032 .441 -.251 -.359 .182 .139 1.000

Although significance for the Bartlett’s Test (Table A6) supports the sampling adequacy

of the dataset for the Exploratory Factor Analysis (EFA), the Kaiser-Meyer-Olkin (KMO)

Measure of Sampling Adequacy (MSA) is below 0.5 indicating that the dataset is not suitable.

Essentially, the conflicting evidence suggests that although the data is factorable, it is not very

useful. Consideration of the MSAs from the diagonals of the anti-image correlation matrix

16 By original dataset construction, six of the twenty-three variables were linear combinations of the remaining seventeen variables causing the resulting matrix to lose positive and definite properties.

17 The reasons may include too few common factors or lack of factorability for the dataset (see https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_factor_sect022.htm)

44

provides further insight into suitability of individual variables (Table A7). As shown, all

variables except for two have unacceptably low MSA (below 0.5). Thus, the factorability

problems posed by this dataset are pervasive and factor analysis should not be used in this case.18

Table A5—Communality CFSI 1.05 ABSS 0.86 BBS 0.77 CMBSS 0.96 CPTBS 0.92 CRES 0.81 CBS 0.82 CIS 0.69 FB 0.49 ICB 0.49 ILS 0.99 LS 0.95 RMBSS 0.54 RRES 0.91 SMC 0.73 TYCS 0.93 WDC 0.38

Table A6—KMO and Bartlett’s Test Kaiser-Meyer-Olkin Measure of Sampling Adequacy. .233

Bartlett's Test of Sphericity Approx. Chi-Square 126262.359 df 136 Sig. .000

Table BA7—Anti-image correlation matrix CFSI ABSS CMBSS RMBSS CRES RRES BBS FB ILS ICB CIS LS CPTBS TYCS CBS SMC WDC MSA

CFSI 0.225 (0.842) (0.238) (0.995) (0.908) (0.903) (0.652) (0.853) (0.478) (0.778) (0.913) (0.661) (0.654) (0.759) (0.791) (0.998) (0.993) 0.225

ABSS (0.842) 0.259 (0.124) 0.835 0.742 0.825 0.453 0.641 0.480 0.591 0.775 0.533 0.457 0.480 0.708 0.835 0.831 0.259 CMBSS (0.238) (0.124) 0.800 0.237 0.341 0.031 0.131 0.216 (0.092) 0.324 0.345 (0.165) 0.241 0.377 0.139 0.235 0.215 0.800

RMBSS (0.995) 0.835 0.237 0.166 0.896 0.912 0.647 0.863 0.458 0.757 0.898 0.624 0.675 0.725 0.782 0.994 0.991 0.166

CRES (0.908) 0.742 0.341 0.896 0.121 0.695 0.688 0.725 0.506 0.702 0.844 0.563 0.566 0.688 0.612 0.902 0.891 0.121 RRES (0.903) 0.825 0.031 0.912 0.695 0.111 0.587 0.805 0.402 0.665 0.805 0.633 0.585 0.645 0.691 0.908 0.915 0.111

BBS (0.652) 0.453 0.131 0.647 0.688 0.587 0.392 0.606 0.257 0.568 0.608 0.461 0.415 0.611 0.248 0.646 0.647 0.392

FB (0.853) 0.641 0.216 0.863 0.725 0.805 0.606 0.088 0.293 0.617 0.684 0.527 0.669 0.625 0.681 0.863 0.854 0.088 ILS (0.478) 0.480 (0.092) 0.458 0.506 0.402 0.257 0.293 0.517 0.171 0.471 0.465 (0.224) 0.219 0.260 0.471 0.492 0.517

ICB (0.778) 0.591 0.324 0.757 0.702 0.665 0.568 0.617 0.171 0.183 0.761 0.522 0.504 0.842 0.715 0.768 0.780 0.183

CIS (0.913) 0.775 0.345 0.898 0.844 0.805 0.608 0.684 0.471 0.761 0.110 0.614 0.485 0.814 0.680 0.908 0.898 0.110 LS (0.661) 0.533 (0.165) 0.624 0.563 0.633 0.461 0.527 0.465 0.522 0.614 0.439 0.411 0.697 0.454 0.669 0.653 0.439

CPTBS (0.654) 0.457 0.241 0.675 0.566 0.585 0.415 0.669 (0.224) 0.504 0.485 0.411 0.375 0.493 0.601 0.662 0.635 0.375

TYCS (0.759) 0.480 0.377 0.725 0.688 0.645 0.611 0.625 0.219 0.842 0.814 0.697 0.493 0.192 0.609 0.756 0.755 0.192 CBS (0.791) 0.708 0.139 0.782 0.612 0.691 0.248 0.681 0.260 0.715 0.680 0.454 0.601 0.609 0.317 0.781 0.791 0.317

SMC (0.998) 0.835 0.235 0.994 0.902 0.908 0.646 0.863 0.471 0.768 0.908 0.669 0.662 0.756 0.781 0.109 0.991 0.109

WDC (0.993) 0.831 0.215 0.991 0.891 0.915 0.647 0.854 0.492 0.780 0.898 0.653 0.635 0.755 0.791 0.991 0.118 0.118

18 Note: The factorability limitation is ignored in sections 2, 3 and 4 and remedied in section 5.

Financial system stress: From empirical validity to ... · Financial system stress: From empirical validity to theoretical foundations [Authors Removed] * June 2014 . A review of

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