30" International Conference of the System Dynamics Society
St. Gallen, Switzerland
July 22-26, 2012
Systemic Financial Feedbacks - C onceptual Framework and
Modeling Implications
Dieter Gramlich' and Mikhail V. Oet”
1 Baden-Wuerttemberg Cooperative State University,
Marienstr. 20, 89518 Heidenheim, Germany, gramlich@ dhbw-heidenheim.de
? Federal Reserve Bank of Cleveland,
1455 East 6th Street, Cleveland, OH 44114, USA, mikhail.v.oet@clev.frb.org
Abstract
Different approaches to model feedbacks in financial systems are assessed based on require-
ments for the conceptualization of the feedback dynamics. Given the non-linear, behavior
driven, and interconnected characteristics of systemic financial feedbacks (SFFs), modeling
concepts from System Dynamics (SD) theory provide appropriate and attractive features.
Surprisingly, few SD models exist to explain systemic financial feedbacks. The scarcity of
SD modeling for SFFs may be attributed to the lack of required economically-sound founda-
tions for theoretical modeling. This paper considers a conceptual framework for SFFs that
emerges from the synthesis of formal principles of economics and SD. In doing so, this study
links existing SFF models to concepts of SD and provides suggestions for further modeling.
Keywords: Feedbacks, Modeling, System Dynamics, Simulation
JEL: B40, C15, C63, E47, G01, G17
This study 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.
1. Introduction
Analyses of the recent turmoil in global financial systems yield a major finding of the
highly dynamic, interdependent, and non-linear character of crisis mechanisms (Allen and
Carletti 2010, Brunnermeier 2009, FSA 2009). In the center of the crisis, the behavior of
market players was determined from exaggerations, incomplete information, herding, and
flight to quality, thereby incentivizing further rounds of contagion. In turn, financial systems’
characteristics, such as credit spreads, stock prices, and foreign exchange (FX) rates (Adrian
et al. 2010), experienced extreme acceleration effects to levels far-distanced from the histori-
cal norms, fed back on themselves and generated a series of critical tail events. During these
phases, the central assumptions of efficient markets such as complete information and ra-
tional behavior appeared to fail. This particular type of dynamic spillovers on financial mar-
kets, further referred to as systemic financial feedbacks (SFFs), provided in-situ evidence of a
structural breakdown in interactions between financial system agents. As a consequence, the
agents’ dependence on the macro-financial crisis factors (systemic risk) as a source of indi-
vidual risk (micro-financial risk) has received a higher importance.
As it is mostly stated, models for systemic financial risk before the crisis have not been
able to explain this behavioral pattern sufficiently (ECB 2010, p. 138). Particularly, the ac-
celerating and self-feeding propagation mechanisms within the system have not been as-
sessed adequately. A new class of models for systemic financial risk is therefore reclaimed,
emphasizing particularly the SFFs. The necessity for improved understanding of SFFs is both
recent and urgent. As recently as 2010, the European Central Bank (ECB 2010, p. 138) urged
that “very significant further research efforts” in this area are needed. May and Arinaminpa-
thy (2010, p. 823) state that attention towards financial dynamics has been focused only rela-
tively recently and that “a super-exponential expansion of work” has occurred as a conse-
quence of the financial crisis. As will be shown, most of these models approach the new dy-
namic non-linearities in an improved way, but still have insufficiencies. Increasingly, new
models address the SFF dynamics through the techniques of discrete dynamic programming
and iterative simulations. These approaches, however, still prove to be too functional and
quasi-deterministic. They are missing the specific, stochastic, and highly interdependent
characteristic of spillover effects.
By comparison, System Dynamics (SD) modeling approaches should be particularly well
suited for the study of financial system non-linearities (An et al. 2009, Morecroft 2008,
Radzicki 2011). The SD models offer explanatory power for self-feeding, exponential and
interdependent processes and have a rich history in social science problems. Surprisingly,
there are few SD models for SFFs. This scarcity may be attributed to the lack of required
economically-sound foundations for theoretical modeling (Qudrat- Ullah 2011, p. 1). At first
glance, simulation and feedback models based on experimental design do not provide full
transparency about the effect causes and therefore are questioned by the researchers and pub-
lic alike. On the other hand, the failure of mainstream economic models to address SFFs,
leaves a functional void. Thus, SD models become attractive by virtue of their facility to test
theories of SFFs and their dynamics. In summary, the conceptualization and probably integra-
tion of SD approaches with economically-sound theories seems to be highly beneficial. In the
light of these considerations, the objectives of this study are:
the assessment of concepts for the modeling of financial feedback and amplification ef-
fects and their discussion in the light of conceptual requirements for modeling financial
system’s dynamics,
the analysis of specific conditions of appropriateness of SD modeling for the represen-
tation of financial feedbacks.
2. Concepts of Financial Feedbacks
2.1, Characteristics and Typology
The basic concept of feedbacks has mainly been developed within cybernetic theory as an
approach to the dynamic behavior of complex systems (Wiener 1948). As a core element
within cybernetics, the feedback concept has been applied to very different types of dynamic
environments such as physical, social, biological and economic systems (Morecroft 2008, pp.
7-57). While definitions of feedbacks undergo some historical and interdisciplinary altera-
tions, there are common characteristics. First, feedbacks reference to an underlying system!
as the specific environment determining their origin, propagation and intensity. While cyber-
netics has been applied to almost all forms of dynamic systems, the relevant environment for
' Generally, a system is defined as a set of related elements, where the scope of the system, selected
elements, and levels of connectivity can be applied flexibly.
this study is the financial system composed from the macrofinancial environment on the one
hand (financial and real markets) and the microfinancial environment (financial institutions)
on the other. A major challenge for this system is representational: that is the inclusion of
appropriate system elements and their connectivity. For example, an economic system could
be represented as comprising only firms and banks or be designed with a richer array of eco-
nomic agents: firms, government, households, banks, and other financial intermediaries. Ac-
cordingly, connectivity among these agents could be considered via a number of channels
where agent interactions arise from productivity, solvency, liquidity channels, etc. (spillover
effects).
Irving Fisher (1932) provides an early example of feedbacks in the productive system of
an economy describing the concept of debt deflation: When firms are highly leveraged, a
small shock affecting their productivity can trigger a series of bankruptcies. This, in tum,
generates a decline in investment, and thus in demand for intermediate goods, as a conse-
quence in prices. Resulting decrease in asset value further aggravates the indebtedness of
firms. In the next round, new failures may occur with cumulative effects on asset prices and
the net value of firms. More recently, the emergence of bubbles (Dehnad 2010) and spillover
effects on interbank funding markets may be considered as further examples for financial
feedbacks.
Second, feedbacks are conceived as a response to some excitation of the system affecting
the system's level of activity. More specifically, the response may go back to the excitation
itself (a procyclical or boomerang effect; “self-feeding” process, Korinek 2009, p. 3) thereby
altering the level of excitation with further effects for the system. Third, and more generally,
feedbacks are a driver of the system’s dynamic behavior. This includes impacts on the sys-
tem’s activity or equilibrium level where the variation may have a positive (amplifying) or
negative (attenuating) consequence or may have a complex mixed dynamic from alternating
accelerating and dampening effects. Similarly, feedbacks are conceived as multi-round ef-
fects, that is a series of incentives and responses over time. In literature this is described as
further-round, contagion, cascade or snowballing effect (Kapadia et al. 2012, p. 3)?
° The pattem aspect of dynamic response can be the source of qualitative assessment of systemic
feedback models. See Barlas and Kanar (2000).
Bemanke, Gertler and Gilchrist (1996) show that adverse shocks can propagate through
economic systems with an amplifying effect, introducing the concepts of “financial accelera-
tor” and “financial propagation mechanism.” In a study of agent behavior, Bikhchandani and
Sharma (2001, p. 288) point out that propagation of effects through economic systems fre-
quently follows “cascades” and is characterized by “positive feedback”, stating that “behavior
in cascades is fragile with respect to small shocks.” Borio, Furfine and Lowe (2001) empha-
size that a financial system’s amplification mechanisms result in “adverse feedback effects”
and are prone to “contagion” and “procyclicality.” De Bandt and Hartmann (2000, p. 43)
generalize various “propagation mechanisms”, “propagation chains”, and “contagion” as
manifestations of feedback effects. The authors make a key connection of this concept to sys-
temic risk: “At the heart of systemic risk are contagion effects, various forms of external ef-
fects. The concept also includes financial instabilities in response to aggregate shocks.” The
authors distinguish that the systemic feedback effects may emerge either through narrow or
wide shocks: “The second key element in systemic events in the narrow sense is the mecha-
nism through which shocks propagate from one financial institution or market to the other. In
our view, this is the very core of the systemic risk concept.”
Often the concepts of feedback, contagion, amplification and procyclicality are applied in
parallel (Gai and Kapadia 2010, Korinek 2009, Tirole 2009). Mostly, feedbacks are referred
to as processes leading subsequently from one state of systemic activity to another thereby
spreading out from one element of the system to another (contagion). Accordingly, amplifica-
tion gives some sense of the magnitude and speed of these dynamic processes - mostly in the
sense of acceleration and magnification of already existing developments (procyclicality,
Bijlsma et al. 2010, p. 39). Hence, whereas feedbacks can be related to the direction of dy-
namic effects and contagion to the series of elements involved, amplification and procyclical-
ity reflect the intensity of these processes. While feedback, contagion, amplification, and pro-
cyclicality, therefore, may point to different dimensions of a system’s dynamics, they are
often used in a similar way with amplification and procyclicality caused by feedbacks and
contagion or feedbacks assumed to produce some variable (increasing or decreasing) effects
via transmission across different elements.*
3 Eg. Gersl and Jakubik (2010, p. 2) refer to multi-round feedbacks as a “magnification of swings”
and as a major driver for procyclicality. See as well Gai and Kapadia (2010), p. 3.
It is useful to integrate the above aspects into a succinct statement: financial feedbacks are
dynamic, ensuing responses to excitations of a financial system. They are time-dependent,
generally non-linear and multi-step processes defining the relative stability of the system.
Financial feedbacks may originate from endogenous or exogenous incentives to monetary
markets and institutions, and are propagated via interactions within the system. The cumula-
tive causal outcomes of feedback effects may range from amplification and procyclicality in
positive-simple loop feedbacks, to dampening and countercyclicality in negative-simple loop
feedbacks, to generally complex, asymmetric, time-dependent patterns in complex multi-loop
feedback mechanisms. These outcomes are thus mainly determined by the structure and the
behavior (May and Arinaminpathy 2010) of the system which in turn depends on the number
of elements, their connectivity and sensitivity to excitations (see Fig. 1). This dependency on
organizational and dynamic aspects of systems can be summarized by referring to financial
feedbacks as “systemic financial feedbacks” (Korinek 2009, Brunnermeier et al. 2010).
System structure
-elements
-connectivity
(vertical)
System behavior (process)
-amplification/ attenuation
-one-step/ multi-step
(horizontal)
Fig. 1: Systemic feedbacks as multi-round, non-linear response processes - system
structure and system behavior as drivers
Given the diversity of systemic structures and processes as drivers of feedbacks, a number
of different types of feedbacks have to be considered and can be combined in multiple ways
(Aikman et al. 2009; Gramlich and Oet 2011, pp. 280-282). In the context of economic-
financial systems, Aikman et al. (2009, pp. 7, 9, 24) distinguish six aspects of financial feed-
backs. These refer to:
- Intensity: constant, increasing, decreasing,
1)
2) linear, non-linear,
3) one-step, multiple (cumulative) steps,
- Direction: 4) direct, indirect (with at least one element between departing and ending
point of the process),
- Origin: 5) starting from the macro-economy or the financial system with an emphasis
on the asset-side (banks’ lending behavior) or the liability-side (banks’ fund-
ing behavior),
- Sensitivity: 6) active, latent (depending on attainment or lack of a critical threshold).
These aspects are particularly interesting from the perspective of financial system agents.
Private agents may use this information to estimate the feedback effects for risk management.
Supervisors are particularly interested in the feedbacks’ sensitivity to change - a question that
is particularly relevant as supervisors seek to maintain or to reestablish financial stability and
to dampen undesirable feedback effects. The concept of “threshold breakpoints” (May and
Arinaminpathy 2010, p. 823) becomes crucial for feedbacks, where a “seemingly minor hap-
penstance” may initiate catastrophic changes. Consequently, May et al. (2008, p. 893) point
out the specific need for ex ante policy. Kiyotaki and Moore (1997, pp. 213-214) emphasize
the aspect of duration of feedbacks with timely limited or extended impact. Therefore, further
aspects of feedbacks can be added that are more related to the effects from feedbacks:
- Duration 7) static (within 1 period), dynamic (intertemporal)
- Diffusion: 8) uni-directional, multi-directional (bifurcation)
- Impact: 9) positive (trend is increased), negative (trend is decreased).
2.2. Basic Modeling Requirements
Given the multiple patterns of systemic financial feedbacks, these processes have to be
conceived as ambivalent dynamic phenomena. This dynamic ambivalence challenges the
modeling of feedbacks based on past outcomes and makes forecasts of SFF’s behavior very
problematical. Propagation mechanisms from feedbacks and modeling approaches for feed-
backs have to be judged in this context.
Feedbacks are not only important to explain the development of crises but may be consid-
ered for the treatment of crises as well. Their high impact on the financial system's dynamic
condition requires careful modeling. Experience suggests that once processes of amplification
and spillover have started, it becomes very difficult to control these mechanisms. A basic
requirement, conventional for all modeling, is that financial feedback models have to be con-
structed in a way where the model architecture reflects both the characteristics of the model-
ing object and the objectives of the model user. As has been analyzed before, SFFs are
mainly characterized by:
- distinct self-feeding mechanisms, where a particular feedback’ s effects influence the inputs
and incentivize second round effects, creating a causal loop;
- inter-connectedness, where several feedbacks create spillover effects to system areas differ-
ent from the feedbacks’ origins;
- dynamic non-linearities, where the amplifying or dampening behavior of several feedbacks
may largely be explained by the presence of thresholds, exceedance of which changes
speed and direction of feedbacks.
A number of authors study interactions and construct combinations of individual feed-
backs. FSA (2009, p. 6) suggested that a complex set of six interrelated feedbacks (see Fig. 2)
has been responsible for the transatlantic financial crisis: “Very low yields, both real and
nominal, on risk-free government securities created the macro-economic background which,
combined with financial innovation, produced six interrelated effects that ultimately proved
unsustainable.”
Leverage in Extension of,
Banking
System
(a) Ans) Credit
Standards
Leverage in
Shadow Banking
System: -
—_ Return Se
Other Asset Volume of
Price I~ Gof (es Securitizations
Error in
Estimate of R10
Liquidity Risk
Liquidity
Risk
Fig. 2: Combined effects from feedbacks as causes of the financial crisis
Ref: FSA - Financial Services Authority (2009, p. 6) (own representation)
With respect to their cross-sectional behavior, a main question is how the feedback rele-
vant system is defined. Basically, there are multiple links between an economy’s financial
and real markets. Financial feedbacks and their effects are motivated from incentives within
these two types of markets. As the ECB (2010, pp. 138-139) states, the financial system is
already highly complex and displays a high degree of inter-connectivity between banks and
other financial institutions. Feedback models have to capture both structural connectivity,
reflecting the compositional complexity of the components or areas of the relevant system,
and behavioral connectivity, reflecting effects coming from the interactions of the systems
elements.
Modeling structural connectivity is mostly straightforward, since it refers to the interac-
tion of observable and known components. For example, in a fair value based accounting
system, losses of a financial institution from declining asset prices will result in write-downs
in a first step (feedbacks from fair value accounting on systemic risk are assessed from ECB
2004 and IMF 2008). Consequently, these losses will reduce the institution’s equity and
therefore trigger regulatory constraints with further consequences for the volume and value of
assets held. Ensuing downgrades from the rating agencies following the resultant balance
sheet and equity ratios may cause the institution further rounds of deteriorating asset valua-
tions and may extend its increasing troubles. In addition, asset losses together with problems
in responding to regulatory requirements and signals from rating agencies may raise concem
from the institution’s shareholders and from its market counterparties. Depending on the in-
tensity of problems and the overall state of the market, these concems may exceed a critical
level (threshold) and then get out of control often implying a herd behavior from other market
participants as well. This example shows that non-linear dynamics can arise both from struc-
tural connectivity that accounts for the technical connections of the financial system agents
and from behavioral connectivity arising from agent behaviors like irrational decision-making
and herding.
10
1. Conceptual Aspects
- definition of intended purpose
- suitability of model philosophy
-- adjustable to a dynamic and changing environment
-- capturing non-linear effects and flexible dynamics
-- adjustable to multiple time horizons
2. Model Architecture
- adjustment to the modeling objectives
- representation of structural and behavioral connectivity
- modular design of systemic environment
3. Model Structure and Elements
- consideration of the financial system and the real economy
- integration of structural, behavioral and interconnective elements
- optimization of the degree of heterogeneity (of abstractness)
4. Model Dynamics
- positive and negative causal loops (self correcting mechanisms)
- consideration of thresholds
- integration of behavioral feedbacks, parallelism of actions
Table 1: Modeling requirements for systemic financial feedbacks
Modeling requirements for SFFs (see Table 1) comprise principles for the conceptual de-
sign of the model as well as for single components. Modeling objectives are initially aimed as
simple analysis of SFF effects. Once the nature of feedbacks is sufficiently explained through
simple models, this knowledge may be used for further purposes. Private institutions may use
feedback models to estimate the patterns of feedbacks’ dynamic outcomes and apply these
estimates for risk/ retum management.’ Forecasting and prevention of crises associated with
adverse systemic feedbacks is a central task for supervisors.’ Subsequent to incorporation of
SFF models into an early warning modeling framework, supervisors may seek to intelligently
apply and/or modify specific feedbacks to achieve stabilizing counter-mechanisms within a
4 E,g., Bijlsma et al. (2010, p. 9) suggest that in the context of systemic feedbacks individual insti-
tutions must extend their consideration of “the external effects of their own risk taking on other
banks.”
E.g., the Banque de France (2001, p. 3) demands that prudential supervision target prevention of
stress amplification beyond the normal degree. Haldane and May (2011, p. 354) suggest limiting
the potential for risk spillovers to high capital standards for systemic banks. Allen and Carletti
(2008, p. 11) refer to deposit assurance to prevent the possibility of panics.
11
crisis. In this, the mechanism features may contribute to balancing the situation in financial
markets in a quasi-automatic way.
3. Feedback Modeling Approaches
3.1. Typology of Models
Modeling concepts for financial feedbacks first require causal foundations that are able to
explain financial system’s dynamics and second an algorithm to functionalize these dynamic
mechanisms. Given the complex character of feedbacks, a variety of models exists. Over-
views of modeling approaches for financial system’s dynamic problems are given in Gertler
(1988), Bernanke, Gertler and Gilchrist (1996), De Bandt and Hartmann (2000), Borio,
Furfine and Lowe (2001), and Freixas and Rochet (2008, pp. 195-196). Feedbacks in the first
generation of models are mainly related to macroeconomic dynamics that subsequently im-
pact financial markets. Dynamic processes originate in the real economy, while the structure
of the financial system mainly has been considered under the “working hypothesis” to be
irrelevant (Gertler 1988, p. 559).
Among the first to analyze the macro-financial dynamics, Bernanke and Gertler (1989)
develop an analytical framework to explain the effect of companies’ net value on business
fluctuations. A relation is set up between the soundness of entrepreneurs’ balance sheets, the
cost of monitoring from external lenders and the provision of outside funds. A main assump-
tion is that the healthier an entrepreneur is and the higher his net value, the lesser are the costs
of state verification (agency costs). Cyclical dynamics from a positive shock (e.g. higher pro-
ductivity) are based on higher net worth of borrowers, subsequent reduced agency costs and,
therefore, increased lending and higher investment. This applies vice versa for economic
downturns. An asymmetric effect may occur, since in good times there is a high net value and
some kind of over-collateralization while investing capacities cannot be further extended. In
contrast, during economic downturns the above interactions may lead to a continuous reduc-
tion in investments.
Authors further address feedbacks from liquidity and interbank effects. Esser and Monch
(2003) develop an amplifying feedback mechanism driven by formal elements and narrowing
its economic application on the topic of stochastic liquidity feedbacks. Aikman et al. (2009,
p. 7) study interbank feedback in times of crisis, arguing that reducing credit lines and rising
12
interest rates in times of crisis decrease the growth potential of the real economy, leading to
adverse second round effects, such as higher default rates. This, in tum, may result in down-
grades of financial intermediaries and reducing credit and liquidity extensions to the financial
intermediaries in the interbank markets in further rounds. Amplification mechanisms during
liquidity crises are further modeled in Krishnamurthy (2010). Two amplification channels are
looked at, the first one generated by some market shock and the subsequent need for liquid-
ity. Since the sale of assets leads to declining prices and less cash flow from sales, further
disinvestment is needed and a balance sheet amplification mechanism is generated. The sec-
ond mechanism is induced by the dynamic effects of rising market opacity and demand for
liquidity.
More recent models are discussed by Allen and Carletti (2008), Freixas and Rochet
(2008, pp. 195-203), Kida (2008),° Tirole (2009), Bijlsma et al. (2010), ECB (2010, Analyti-
cal), Sarkar and Shrader (2010), Gai et al. (2011), and the ECB (2011). The ECB (2010, Ana-
lytical) and Blake and Gondat-Larralde (2010) point out the results of workshops on macro-
economic modeling held at the European Central Bank and the Bank of England respectively,
including also suggestions for further modeling of financial dynamics. Newer feedback mod-
els center more on the dynamics originating in the financial markets themselves.
Sarkar and Shrader (2010, pp. 2-4) see the decreasing net worth of institutions and collat-
erizable value for secured funding (balance sheet mechanism) as explanatory for first round
of crisis. Further rounds are then triggered by asymmetric information and concems about
default risk of banks (adverse selection mechanism).’ While this may imply assistance from
monetary authorities, Meh and Moran (2010) argue differently in their study on interactions
for banking feedbacks with monetary policy: They find that “moderate downturns associated
with well-capitalized banks require less aggressive actions from monetary authorities.”
Krishnamurthy (2010, p. 1) distinguishes two broad classes of feedback mechanisms: “bal-
ance sheet amplifiers (e.g., leverage, tight credit conditions, limited capital) and information
5 Kida (2008, pp. 24-31) gives a concise summary of three different types of macro feedback mo-
dels.
7 While this may imply assistance from monetary authorities, Meh and Moran (2010) argue that
downturns associated with well-capitalized banks may imply less aggressive actions of central
banks.
13
amplifiers (e.g., opacity, complexity, and uncertainty).” Gersl and Jakubik (2010, pp. 2-3)
consider a wide range of interconnected factors such as “natural” factors (information asym-
metry, over-optimism, herd behavior, fluctuations in balance-sheet quality, financial innova-
tion) and “other” factors (regulation, accounting). Using this complex aggregation of feed-
backs, they simulate effects for the Czech economy during the transatlantic financial crisis of
2007-2009. In their model declining asset values lead to decreases in bank equity. As credit
standards rise due to bank defensive actions, credit extension decreases, resulting in a 1-2%
reduction in the Czech GDP.
Gai and Kapadia (2010) model complex networks of direct loss and indirect write downs
showing bank contagion and amplification effects. Their study applies evidence from central
network theory to model dynamic contagion effects inside banking systems. In a balance
sheet approach, banks hold illiquid external assets and interbank assets as well as liabilities
from other banks. This makes the banks vulnerable to shocks from the default of other banks
and from writing down the value of assets. Within this system, the intensity of shock propa-
gation is particularly based on the degree of incoming and outgoing links between banks, the
extent of the shock, and bank capital. For example, the default of a bank is modeled as a
function of the loss from interbank claims, loss from assets, and the bank’s capital buffer.
Based on a network with 1,000 banks and assumptions about banks balance sheet and capital
buffer, numerical simulations are run. Main result of modifying the degree of interbank links
is that as the connectivity within the system goes up the frequency of contagion is reduced
while the extent of contagion losses is increased (“robust-yet-fragile”). In a similar approach,
Kapadia et al. (2012) model feedback effects for the funding of banks arising from failures of
other banks and liquidity hoarding and integrate this into a more comprehensive model for
systemic financial risk (see Fig. 3).
Confidence’
effects
1 1
4 4 5 Counterparty
credit risk
1 Fail if
Funding problems —_ bankA.
at bank A
Liquidity Hoarding
Asset sales
Fig. 3: Funding feedback model from Kapadia et al. (2012)
Ref.: Kapadia, Drehmann, Elliott and Steme (2012), p. 4
Funding problem:
at other banks
0
An extended overview of models discussed in literature is presented in Table 2. The matrix
groups the models according to their assumptions about sources of feedbacks originate (rows)
and the chosen methodological framework for quantifying the effects (columns). As can be
seen, existing models tend to focus on the transmissions between the real economy and finan-
cial markets. Models of the dynamics within financial markets are less frequent and tend to
focus on the relationships between banks. There are only a few models considering the inter-
actions between banking supervision and the financial system or between monetary policy
and the financial markets.
15
Network theory Econometric ap- General Equilib- Further concepts
proaches rium Models
-regression based _-formal equation
Macro-financial = Nier et al. 2007 = Bemanke and = Aguiar and Dru- = Shimizu 1997
feedbacks/ am- Gertler 1989 mond 2006 (neural network)
plifications (shocks on bor- = Kiyotaki and
rowers net worth, * Liu etal. 2010 Moore 1997
effects on agency (am of macroecon- (am from changing
costs and outside omy through credit collateral value)
funding) constraints) = Krishnamurthy
= Chen 2001 2003
(production (collateral am ef-
shock with fb on fects from incom-
collateral and plete hedging)
capital) = Gallegati et al.
= Kroszner et al. 2003
2007 (simulation of in-
(crises, firm teracting bank and
value, and finan- agent)
cial market = Ozdenoren and
depth) Yuan 2008 (am via
= Aikman etal. information effects
2009 and endogenously
(fb from funding determined cash
tisk) flows)
= Gersl and Ja- = Anderson et al.
kubik 2010 2011 (SD model for
(several rounds testing financial
effects of credit and macro-financial
crunch on GDP) stress factors)
= White et al. 2011
(fb via quantile
regressions)
Financial feed- == Gai and Kapadia = Esser and Monch = Kerry 2008
backs/ amplifi- 2010 2002 (liquidity indicator)
cations, (vulnerability from = Sarrand Lybek = May and Ari-
Financial mar- interlinkages and 2002 naminpathy 2010
kets, neighbours) = Bliss and Kauf- (banking ecosys-
Banking super- _* Gai, Haldane and man 2003 tems, successive
vision/ Mone- Kapadia 2011 (integrated capi- failures)
tary policy (interbank lending, tal and reserve = Vayanos and Wool-
am from complex- constraints) ley 2010 (momen-
ity) = Gertler and Kiyo- tum, reversal via
taki 2010 (credit/ rational agents)
equity injections) = Haldane and May
= Sarkar and 2011 (econophys-
Shrader 2010 ics, instability from
complexity)
= Neugebauer 2011
(SD model Taylor)
Combined =Bernanke et al. = Meh and Moran = Anetal. 2009 (SD
macro-financial 1999 2010 model of interac-
and financial =Kida 2008 (simulations in a tions among bank-
feedbacks/ am- (credit-interest quantitative equi- ing, housing and
plifications rate risk, fb banks- librium model) economic markets)
real economy)
Table 2: Conceptual approaches of feedbacks and amplifications in macro-financial systems
(am = amplification, fb = feedback)
16
3.2. Discussion of models
Financial feedbacks in a systemic context are complex phenomena that are difficult to as-
sess and may probably not be captured with a singular approach. The validation of SFF mod-
els mainly is based on how appropriately the non-linear dynamics and the complexity of in-
teractions are modeled. As has been shown, these primary characteristics may further be de-
composed into behavior-related, partially irrational and stochastic components, and structure-
related elements that reflect the multiplicity, complexity, and interaction of the financial sys-
tem’s components.
Existing models of SFF take account of these aspects. In most cases they are well-
considered, sophisticated approaches emphasizing multiple perspectives of market dynamics.
The degree up to which this dynamics is reflected is different, ranging from single basic func-
tions to interacting loop structures. However, there are two prevalent modeling deficits that
require recognition and that are crucial in the context of SFFs. First, modeling equations are
mostly predefined, suggesting that SFF develop along determined processes and making
SFFs calculable.® In the light of the recent financial turmoil this feature has to be considered
too mechanical and limiting the model’s degrees of freedom. Second, most authors center on
specific aspects of financial markets dynamics in a rather isolated way, modeling the feed-
backs in a manner too restricted to sufficiently account for interactions from connectivity (see
Table 3). These restrictions in modeling seem comprehensible in the context of highly com-
plex markets and the already achieved degree of model complexity. Further, an open model
architecture would not be in line with formal clarity required for academic research. How-
ever, even if these limitations seem understandable from the model builder's point of view,
current approaches do not yet satisfactorily represent the relevant characteristics of SFFs.
Given the design principles, feedback and simulation models on the basis of SD would
suit the modeling requirements for SFFs particularly well. This review and discussion of cur-
rent models reveals that there are surprisingly few existing approaches utilizing SD for mod-
E.g., Gai et al (2011) as a very recent and advanced modeling approach for feedbacks run simula-
tions of systemic liquidity, whereby simulation is conceived as changing the parameters of the
function but not the function itself. Similarly, Gai and Kapadia (2010, p. 10) model contagion in a
“relatively mechanical fashion.”
17
eling financial feedbacks (e.g. An et al. 2009, Anderson et al. 2011, Neugebauer 2011). One
possible explanation for this is that SD approaches may be considered by economists to lack
the formal clarity and replicability demanded for scientific research.° Particularly, simulation
technique is considered to be critical, since it does not provide sufficient explanation “why
the model does what it does” (Mojtahedzadeh 2011, p. 358). Further, while many SD models
are set up and communicated via causal loop diagrams, these diagrams may be considered
lacking in theoretical transparency, and precision in the description of variables, their links
and behavior. Therefore, SD models may be considered lacking a sufficient basis for the rig-
orous deduction of behavior (Lane 2008, pp. 12-14).
Hence, a basic conflict has to be stated: where traditional models are limited by their
principles of modeling to explain modem financial markets behavior, SD models would be
able to capture non-linear dynamics and connectivity, but are criticized for their lacking for-
mal exactness. This conflict appears similarly for all models and theories trying to integrate
non-formal behavioral aspects into modern financial theory. Olsen (2008, p. 1), states that
behavioral finance is a “thorn in the side of many finance traditionalists.” Y alamova and
McKelvey (2011, p. 169) refer to the efficient market hypotheses as the basic paradigm and
to fractal finance as some “competing schools of thought.” Smith (2008, p. 51) demands to
move from an “Efficient to a Behavioral Market Hypothesis.” Szyszka (2011, p. 216) con-
cludes that neoclassical theory lost its strength and “should be modified in line with dynami-
cally changing financial environment.” The question is therefore, how these contradictory
positions - formal clarity but modeling deficits on one hand versus modeling appropriateness
yet formal deficits on the other - can be matched.
A further step is to develop basic principles guiding the integration of these two classes of
models to achieve a new, combined, class of formal simulation models.
a Gallegati and Richiardi (2011, p. 42) discuss a “common misunderstanding” between (agent
based) simulations and mathematical models - different degree of abstractness, superiority in so-
lution finding - and conclude that, in principle, simulation is mathematics.
Effects
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Propagation factors
Behavior
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(1) ooys 18410}
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Bemanke and Gertler 1989
Kiyotaki and Moore 1997
Banque de France 2001
Borio et al. 2001
Gallegati et al. 2003
Borio 2007
Allen and Carletti 2008.
Persaud 2008
Aikman et al. 2009
Hirano 2009
Bijlsma et al. 2010
Gai and Kapadia 2010
Ger’ and Jakubik 2010
Krishnamurthy 2010
May and Atinaminpathy 2010
Sarkar and Shrader 2010
Gai, Haldane and Kapadia 2011
Haldane and May 2011
Kapadia et al. 2012
(3) Market (in)completeness, financial development
(2) From innovation, technology
(1) Political, environmental shocks
‘Table 3: Causes, propagation and effects of feedbacks
19
4. Implications for Further Feedback Modeling
The operational deficits from SFF treatment by the traditional models of quantitative fi-
nance and the problem of lacking formal evidence by the SD models are discussed in critical
literature. This literature also provides suggestions for handling the SFF modeling challenges.
Radzicki (2011, p. 730) suggests three basic strategies for combining economic models and
SD approaches. Klejnen (1995) refers to the integration of statistical methods, such as regres-
sion analysis and design of experiments, to optimize simulation-based models. Lane (2008, p.
21) requires that causal loop modeling should only be applied by those who are aware of and
trained in simulation modeling. The different suggestions refer to (see Fig. 4)
- conceptual aspects for the modeling approach,
- model architecture,
- model implementation,
- model validation.
1. Model Concept 2. Model Architecture 3. Model Implemen- 4. Model Validation
tation
- philosophy - overall design - application - testing
- integration - components - interpretation - improving
Fig. 4: Relevant model dimensions for the integration of formal and simulation modeling
While looking for possibilities how to model increasing dynamics and complexity, tradi-
tional formal modeling and more recent simulation-based approaches should not be conceived
as competing or opposite. They have a “separate-but-equal status” (Y alamova and McKelvey
2011, p. 169), and the question is not which one to replace by the other, but to what extent
these concepts may be integrated thus accommodating situations with higher complexity and
feedback dynamics. The strengths of both concepts are to be combined, making the resultant
integrated approach both formally clear and sufficiently flexible. Different suggestions are
provided to achieve this synthesis. While these suggestions mostly refer to operational aspects
applied to different steps of the modeling process, a general condition for the estimation of
these models is the acceptance of simulation techniques for modeling. This is a matter of con-
sciousness, and there is an “impressive need for more Systems’ Thinking at universities”
(Weber 2005, p. 3).
20
The combination of traditional and SD modeling should allow for a higher degree of het-
erogeneity and should be conceived as a two step process (Radzicki 2011, p. 730 suggests
three principal ways). As a first step and in order to provide a sound theoretical foundation for
the model and model outcome, modeling should be based on formal equations as far as possi-
ble (Y alamova and McKelvey 2011, p. 170), and the results from these equations should be
made transparent. As a second step, iterative simulations should be viewed in aggregate, and
the simulation effects should be compared to prior results.'° The direct consequence of this
approach is the avoidance of premature amalgamation of the formal modeling and partially
random simulation results. The two-stage process also allows a more sound problem-specific
approach, thus avoiding “canned” outcomes of application of pre-defined software tools to the
modeling problem.'' Although a dual step modeling is suggested, this does not mean that
both modeling steps are independent. Rather, the modeling process takes into account the
strengths and weaknesses of the two modeling approaches in every phase. The process is thus
synthetic, rather than merely additive. This is conceptually similar to the Radzicki (2011, p.
730) proposed third or “hybrid” approach, where the advantages of economic and SD model-
ing are blended.
Higher heterogeneity of combined models can be achieved by a more detailed representa-
tion of structural components and from considering explicitly structural and behavioral con-
nectivity. As the overall model thereby gets increasingly difficult to solve analytically, SD
simulation and optimization approaches support the model solution. As problem scope ex-
tends, at some point of the relevant feedback system, the researcher has to confront and con-
sider additional modeling choices. This would include choices for the heterogeneous agents
from real and financial markets, and detailed factors or markets’ infrastructure and agent be-
havior such as liquidity, solvency, risk aversion, agent linkages, and the regulatory constraints
of these factors. While running the model in SD environment, the algorithms used and the
results obtained have to be kept as clear as possible. For example, Mojtahedzadeh (2011, p.
363) suggests using a metric of pathway participation to show the consistency of model com-
10 A good example for the integration of formal basic equations, simulation and validation is the SD
model from Neugebauer (2011) investigating the Taylor rule for Brazil.
Vice versa, in the context of “simplifications” for setting up formal equations, Moss (2011, p. 24)
states that assumptions for simplifying the nature of an empirical problem makes the problem con-
form to the requirements of the mathematical technique.
21
ponents: Comparison of the effects from different loops in the model allows detection of
feedbacks that remain dominant throughout the simulation. This helps to prevent phantom
loops from engaging in the dominant structure of the model and helps to maintain mathemati-
cal consistency while allowing essential feedback complexity. To improve the modeling of
connectivity of different variables, Klejnen (1995) suggests regression analysis to predefine
the most efficient combinations and make the selection of combinations more objective. Criti-
cally, the research design and central results must be transparently stated —a principle em-
phasized in Lane’s discussion (2008, pp. 17-20) of clear communication of links, equations
and diagrams.
Finally, the validation (Barlas 1996, Coyle and Exelby 2000, Qudrat-Ullah 2011) of the
hybrid models has to be adjusted to accommodate the more heterogeneous and opaque model-
ing approach. Where traditional models are primarily validated on the consistency between
model assumptions and model equations (from “the left to the right” in Fig. 4), the adequacy
of the dual models may be more difficult to assess in this way. Given the different approach
of dual models to provide a more realistic framework for the complexity and dynamics of
financial markets, validation may focus more on the model output, on its consistency with
objectives, and on the empirical context to be explained (from “the right to the le),” Refer-
ring to the mentioned two step process for the combination of traditional and SD modeling,
model validation integrates both validation of the model itself and the model building process
(Qudrat-Ullah 2011, p. 2).
Overall, the dual approach to modeling based on formal equations and SD simulations
seems appropriate to assess the effects from SFFs. Among its principal merits is a more realis-
tic representation of the inherent heterogeneity and non-linearity of financial feedbacks. Criti-
cally, however, the higher complexity and opacity of this approach necessitates particular
conceptual strength and technical quality. To advance the quality of SFF models, research
may follow a rigorous dual process that starts with sound theoretical foundations. Methodol-
ogically, this process should incorporate explicit recognition of the strengths and weaknesses
of the constituent modeling techniques, the analysis of stable and reliable components, clear
communication of simulation results, and an empirical validation of the model quality.
2 In this context, Moss (2011, p. 23) states that neoclassical economy has no empirically based mi-
cro foundation and its assumptions are not justified empirically.
22
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