A basic macroeconomic agent-based model for analyzing monetary regime shifts

Florian Peters1*, Doris Neuberger1, Oliver Reinhardt2, Adelinde Uhrmacher2,

1 Deparment of Economics, Faculty of Economic and Social Sciences, University
of Rostock, Rostock, Germany

2 Visual and Analytic Computing, Faculty of Computer Science and Electrical
Engineering, University of Rostock, Rostock, Germany

*<EMAIL_ADDRESS>
## Abstract

In macroeconomics, an emerging discussion of alternative monetary systems
addresses the dimensions of systemic risk in advanced financial systems.
Monetary regime changes with the aim of achieving a more sustainable financial
system have already been discussed in several European parliaments and were
the subject of a referendum in Switzerland. However, their effectiveness and
efficacy concerning macro-financial stability are not well-known. This paper
introduces a macroeconomic agent-based model (MABM) in a novel simulation
environment to simulate the current monetary system, which may serve as a
basis to implement and analyze monetary regime shifts. In this context, the
monetary system affects the lending potential of banks and might impact the
dynamics of financial crises. MABMs are predestined to replicate emergent
financial crisis dynamics, analyze institutional changes within a financial
system, and thus measure macro-financial stability. The used simulation
environment makes the model more accessible and facilitates exploring the
impact of different hypotheses and mechanisms in a less complex way. The model
replicates a wide range of stylized economic facts, including simplifying
assumptions to reduce model complexity.

##  1 Introduction

The financial system is a complex system [1] that is inherently prone to
fragility. During the last decades it has been subject to various crises [2].
Notably, the crisis of 2007/2008 triggered a debate about possible alternative
monetary system approaches and how to improve the stability of the financial
system towards endogenous and exogenous shocks.

The monetary system is a central constituent of the financial system, and
embraces accounting measures concerning banks’ credit creation potential and
the institutional organization of financing economic activity. The main system
ingredient relates to the fractional reserve system which defines the
interplay of the Central Bank, banks, and the real economy to ensure the
financial scheme or credit creation structures. A more detailed description is
provided in Section 3.1.

There are two contrary reorganization approaches to the current monetary
system that both claim to lead to a less fragile financial system: First, the
sovereign money system that centralizes money creation towards sovereign
control via a strict separation of money and credit (full reserve system) [3].
A more detailed overview and recent political developments are summarized by
KPMG [4]. And second the free banking system that decentralizes money creation
with little or no sovereign interference [5].

To explore such what-if scenarios, we aim to provide a baseline simulation
model that will support studies to compare different monetary systems
concerning macro-financial stability features. Here, the current system serves
as a baseline since the simulation output can be calibrated and validated
according to empirical evidence.

To measure (in)stability conditions, the corresponding analysis has to
incorporate the emergence of systemic risk. According to Borio [6], Bank of
England [7], and Galati and Moessner [8], systemic risk is classified as time-
varying and cross-sectional risk. Time-varying risk belongs to the pro-
cyclical behavior of the financial sector, caused by solvency, liquidity, and
contagion risk [9], which drives the financial cycle [10]. Cross-sectional
risk is related to the structural composition of the financial sector, such as
the distribution of risk within the financial network, co-varying risks across
balance sheets, systemically important financial institutions and opacity of
complex network interdependencies [9].

Two simulation approaches appear to be eligible for such a macroeconomic
analysis: Dynamic Stochastic General Equilibrium (DSGE) models and
Macroeconomic Agent-Based Models (MABM). Since we are interested in examining
feedback effects between economic sectors arising from financial instability
dynamics, DSGE models appear to be more limited than MABM. According to
Alexandre and Lima [11], a key element to grasp the occurrence of financial
crashes is an understanding of nonlinear feedbacks among financial and real
variables. Incorporating nonlinearities is limited within DSGE models [11] but
a fundamental feature of agent-based models [12]. Furthermore, Bookstaber [13]
argues that the representative agent used in DSGE models, which involves
optimizing behavior and full rationality assumptions, is not appropriate for
analyzing crisis dynamics, such as excessive leverage, funding fragility,
liquidity limits, coordination failures, market freezes, and bankruptcies
cascades. This is because such assumptions are based on historical
relationships, which are not valid during instability phases [11]. In
contrast, the aggregate dynamic of MABMs is based on the emergent property via
the interaction among adaptive heterogeneous agents [14, 15, 16]. Further
building blocks of agent-based models, and a detailed comparison between DSGE
and MABM can be seen in [12, 17, 18, 19, 20]. Lastly, socio-economic systems
are inherently non-stationary [12], stochastic, non-ergodic, and structurally
evolve over time [21], making MABMs a natural fit.

Consequently, we find a few agent-based models that analyze, if not regime
shifts, but the impact of policy variations, which partially incorporate
specifications of the current monetary system [22, 23, 24, 25]. Here, we
contribute with a basic model that captures the main systemic risk features of
the current monetary system. Further details and related literature are
discussed in Section 6. Moreover, for exploring the mentioned what-if
scenarios, the MABM must be implemented in a way to allow for successive
extensions and easy exchange of central model components. Despite the inherent
complexity of the financial system, it is expedient to easily access and to
discuss the model, not only to work with it, but also to assess its quality.
Therefore, we use a compact and expressive domain-specific language that
facilitates more succinct and accessible model specifications than
realizations in a general-purpose language [26].

The paper is structured as follows. In the following Section materials &
methods are described. The requirements for the model and corresponding model
specifications are presented in Section 3. Afterward, the calibration process
is described in Section 4 and simulation validation results are shown in
Section 5. Finally, Section 6 compares the contribution of the presented model
to related literature.

##  2 Materials and methods

###  2.1 The Modeling Language for Linked Lives

To realize the model, we make use of the Modeling Language for Linked Lives
(ML3) [27]. ML3 has been originally designed for agent-based demographic
models, in which live-courses of interacting individuals are simulated.
However, its application is not limited to demography, and the economic
processes could be easily mapped to its modeling concepts.

At the core of ML3 is the concept of stochastic rules, which are used to model
the behavior of agents. Each rule is associated with one type of agents (e.g.,
households, firms, banks, …) and consists of the following three parts:

First, the guard is a condition that allows to specify to which agents of that
type the rule applies.

Second, the rate determines when the rule is executed. It defines the
parameter of an exponential distribution from which the waiting time is drawn.
In some rules this may be replaced by a fixed waiting time, resulting in
periodic events, or no waiting time at all, in which case the rule is applied
instantly.

Third, the effect determines what happens when the rule is executed. As an
example, we may want to model that firms produce some goods at a certain rate.
For simplicity’s sake, we assume that every agent of type firm produces goods,
hence the guard condition should always be fulfilled, i.e., true (see Figure
1, line 2). The production rate may vary between the different agents of type
firm. It is saved as an attribute production_rate of the firm-agent. The
keyword ego gives access to the specific agent a rule is applied to, and the
production rate for this agent is then ego.production_rate (see line 3). The
effect of this rule should be that the stock of inventories increases by 1
(see line 4).

⬇

1Firm

2| true

3@ ego.production_rate

4-> ego.inventory := ego.inventory + 1

Fig 1: An example of a rule, modelling the production of a good at a certain
rate.

During the simulation, a waiting time is drawn for each rule of every agent.
The rule and agent with the lowest waiting time are selected and the rule is
executed for that agent. The simulation time is then advanced by that waiting
time. The resulting underlying mathematical processes, i.e., the semantics of
ML3, are formally defined as Generalized Semi-Markov Processes in [27]. The
model description in Section 3.3.1 and 3.3.3 provides further exemplary
applications of the rule concept.

ML3’s rule-based modeling approach completely separates model logic (i.e., the
behavior of agents) and simulation logic (i.e., the execution of that
behavior). The former is implemented by the modeler using the modeling
language of ML3. And the latter has been implemented independently of a
specific model by the developers of the modeling language. This separation of
model and simulator improves accessibility both for the modeler and a later
reader of the model. They do not need to be concerned with implementation
details of the simulator, but only with specifying the model within the
modeling language.

The stochastic rules allow for viewing the different kinds of behavior an
agent can exhibit (e.g., for a firm: production, hiring, investment, and
others) independently of each other. As the simulation does not advance in
time steps, no priority among or ordering the various behaviors of different
agents needs to be specified. Each rule fires with its own rate sampled from
an exponential distribution. This allows us to separate the model into
different components, each consisting of only a few rules, describing a part
of the model, and to combine components step by step to yield the complete
model.

###  2.2 Provenance

For documenting the simulation model and its foundation in economic theory we
complement a textual description of the model with a provenance model [28,
29]. While the former focuses on the mechanics of the model, the latter
captures information about the context of the model, and the process of its
creation. It relates the components of the model to economic theories they are
based upon, and shows the central steps in the model’s creation. This adds
crucial information for assessing the simulation model itself, as well as the
results it generates, by making its foundation, and therefore its qualities
and limitations, more transparent.

The provenance model is based on the PROV standard [30]. Thereby, the
provenance is modelled as a directed acyclic graph, containing two types of
nodes (see Figure 3). Entities (shown as circles) represent the different
artifacts involved in the modeling process, both as inputs (e.g., data,
earlier models, economic theory), and as products (e.g., model components, the
complete model). Activities (shown as squares) represent the processes that
link them (e.g., modelling, composing components, performing simulation
experiments). The edges of the graph relate the entities and activities
explicitly and visually, showing which entities were _used by_ a given
activity, or which entities were _generated by_ it.

##  3 Model outline

As described in the introduction, this paper serves as a methodological
amendment to macroeconomic agent-based models (MABMs) to analyze alternative
monetary system regimes concerning macro-financial stability. The requirements
for such a (baseline) model are specified in the following paragraphs.

###  3.1 Model requirements

To measure and compare financial and macroeconomic stability features on an
aggregate level of an economy (macro-financial stability) the interrelation
between the financial and real sectors is crucial to consider to capture
credit demand and supply and related feedback effects.

Hence, a business cycle (requirement 1) is needed which defines the real
sector and comprises the interaction of households (consumption behavior) and
firms (investment behavior) to take credit demand into account. Furthermore,
the business cycle allows to grasp the economy’s performance (e.g., GDP -
Gross Domestic Product, employment, inflation, firm bankruptcies) and serves
as a foundation to measure the impact of a reorganized credit supply.

The financial cycle (requirement 2) defines the credit cycle [31, 32, 33, 34],
specifically banks’ credit supply in interaction with the real sector. As
suggested by Borio [10], the financial cycle needs to be modeled in the way
that […] the financial system does not just allocate, but also generates,
purchasing power, and has very much a life of its own […], which is in line
with the non-neutrality of money assumption [35] and congruent to the
methodological approach of MABMs as described in the introduction. To analyze
systemic risk that might arise from overshooting credit cycles, as claimed by
proponents of sovereign money [3], the overinvestment hypothesis needs to be
considered. The investment behavior of firms can be characterized as a state
of under- or overinvestment due to asymmetric information and the circumstance
that firm managers tend to maximize their utility rather than the firm value.

In addition to firms’ behavior, banks contribute to overshooting credit
behavior by profiting from supplying more money than absorbed by the
production capacity and causing unsustainable credit growth [10]. Here, a
clear indication of credit creation potential is needed which banks strive to
exploit and expand. Furthermore, the distinction between productive and
unproductive credits is expedient to identify macro-financial stability
effects of different monetary regimes. Unproductive credits might be induced
by rolling over of existing debt, leading to unnecessary prolongation of firm
existence with high default risk [36, 23].

Next to systemic risk sources described in requirements 1 and 2, the main
focus is steered to the organization of money creation, which is covered by
the following requirements.

The fractional reserve system (requirement 3) defines the structure of the
current monetary system which is a two-tier split-circuit system in accordance
with the circuit theory [3]. A two-tier structure consists of a Central Bank
and a private banking sector. Split-circuit describes the dichotomy of banking
money (public circuit) and central bank money (interbank circuit) [3]. Banks
need only a fractional amount of reserves (central bank money) to refinance
credit receivables and process payments that bear liquidity risks (see
requirement 4). This distinction between money and credit is essential to
compare alternative systems. A sovereign monetary system can be defined as a
two-tier single-circuit money system (central bank money as the only legal
tender) and free banking as a one-tier single-circuit money system (only
private bank money circulation without Central Bank intervention). Hence, the
implementation requires an endogenous payment scheme and credit network.

Endogenous money creation (requirement 4) describes the money issuance process
between Central Bank, banks, and the real sector according to the prevailing
opinion [37, 38]. Within the current system, banks’ credit supply to firms
plays a key role, which involves creation of deposits (maturity
transformation). Banks are exposed to credit default risks, interest-change
risks (arbitrage between long-term credit and short-term deposit interests)
and liquidity risks. Proponents of alternative monetary systems claim that
liquidity risk might be mitigated [3] because the co-evolution of the re-
organized credit and interbank market is more stable than the current system.
This would prevent liquidity freezes and related knock-on or spillover effects
to the real sector.

Macroprudential regulation (requirement 5), according to the Basel III
framework [39], is a mechanism to mitigate systemic risks originated by banks
described in the previous model requirements. The regulation framework
includes banks’ capital and liquidity requirements, which might reduce
unproductive credit creation (less overshooting credit cycle) and dampen
crisis dynamics (less severe downturns and bank bailouts). Since alternative
monetary regimes address the same systemic risk, this mechanism is crucial to
compare the de-risk effectiveness.

The basic monetary transmission mechanism(requirement 6) indicates the impact
of monetary policy by the Central Bank on general economic conditions and, in
particular, the price level. This transmission is influenced by the monetary
system via transmission channels and identifies feedback effects between the
real and financial sectors. According to the single monetary policy in the
Euro area [40], interest rate changes by the Central Bank affect firms’
investment decisions via funding costs (capital cost and income effect) and
correspondingly credit demand (interest rate channel). Interest rate changes
also affect credit supply (credit channel). For example, an increase in
interest rates negatively affects the financing conditions of firms and banks
charge a risk premium which might lead to credit selection and rationing (bank
lending channel of the credit channel). Furthermore, interest rate changes
affect the net worth of firms and their expected cash flow, which in turn
affects firms’ collateral and the ability to borrow (balance sheet channel of
the credit channel). Such fluctuations in the creditworthiness of borrowers
might lead to an acceleration of credit demand, known as financial accelerator
[41]. This pro-cyclical behavior also affects the risk-taking behavior of
banks and borrowers. The expectation of a sustained increase in collateral
values in boom phases combined with low-interest rates leads to higher risk-
taking. Banks might soften credit standards, which can boost excessive lending
(risk-taking channel). All channels are interdependent and lead to aggregate
demand and price changes, thereby affecting the business cycle (requirement 1)
and credit cycle (requirement 2). For simplicity, the expectation channel and
indirect effects via financial portfolio decisions, and exchange rate changes
are excluded in the basic model.

###  3.2 Model overview

The implementation of the desired model requirements in ML3, described in the
previous Section, is gradually composed of sub-models, as shown in Figure 3
and described in the following Sections.

The agent-based model structure is based on five different agents types
(households, firms, banks, Central Bank, and government) which interact within
and between the real and financial sector, as shown in Figure 2.

The real sector is composed of the following market segments:

  * •

A labor and goods supply market where households selling their labor
(employees) to firms to produce homogeneous goods in exchange for wages to
consume (labor and goods supply specification in Figure 3). Wages are
households’ financial wealth used for payments (deposits) and are entirely
consumed.

  * •

A consumption market where households interact with firms to generate
consumption demand (goods demand specification in Figure 3).

  * •

An investment market where firms interact with each other to generate
investment demand (investment market sub-model in Figure 3).

Whereas the financial sector is composed of the following market segments:

  * •

A credit market where firms interact with banks to finance investments,
production/supply, and outstanding debt (credit market sub-model in Figure 3).
According to the endogenous monetary theory [37, 38], banks create loans and
deposits for firms and indirect deposits for households via wages.

  * •

An interbank market where banks interact with each other and the Central Bank
to guarantee financial transactions and monetary policy transmission
(interbank and monetary policy specification in Figure 3). All transactions
are account-based and flow between balance sheets of all agents, and are
settled by banks in combination with the interbank market. A more detailed
balance sheet overview of all agent types can be found in Table 7 in Appendix
A.

  * •

A deposit market where firms and households hold deposits at bank accounts,
which is included within the interbank market.

The public sector is set by the Central Bank and government. The Central Bank
controls the flow of reserves via open market operations and influences the
interest rate level for bank loans. The government collects taxes and
redistributes them to households and banks via unemployment benefits and bank
bailouts.

Fig 2: Stylized stock-flow structure following Caiani et al. [42]. Arrows
point from paying to receiving agent.

####  3.2.1 Design concept and limitations

The model represents economic activities between heterogeneous agents based on
heuristic behavior rules to emphasize the complexity of the allocation process
in the real world and to simulate emergent financial crisis dynamics. An
agent’s behavior rules do not change over time and have no learning
capabilities. Time is measured in periods, thus a transition rate of 0.5 would
represent two waiting periods on average. Besides accounting measures (e.g.,
wages, profits, loan repayments, etc.), agent behavior rules are not bound to
sequence or discrete events but rather occur concurrently in continuous time,
as described in Section 2.1. Agent expectations are based on simple averages
of past events (i.e., cash flow expectation in Section 3.5.2), and the
matching process between agents within implemented market structures follows a
weighted random selection (see lines 11 and 12 in Figure 5).

Concerning limitations on the modeled economic structure, the following
simplifying assumptions are made: The agent population, labor productivity,
and wages are fixed over the entire simulation run. Thus, the model cannot
capture long-term growth. Firm investments function as demand drivers but are
not implemented in firms’ production processes. The model does not incorporate
a capital or bond market, and households do not own firms to keep the
necessary structures simple. Hence, it is assumed that government expenditures
are not restricted (e.g., for bank bailouts). This circumstance makes the
model not stock-flow consistent, according to Godley and Lavoie [43]. Other
financial sources considered are bank loans and deposits. Cash money/banknote
holding is not assumed. Finally, the model does not incorporate shadow
banking.

Fig 3: Provenance model

Note: The figure shows the provenance of the composed macroeconomic agent-
based model Mak(h)ro_0 including entities from theory, empirics and simulation
models from literature. Section references are labeled in parentheses and
citations in brackets. For a short description of the entities and activities
in this figure, see Table LABEL:tab:provenance in Appendix A.

In the following sections, we will describe and discuss the different sub-
models, the entities, and activities that contributed to their development
following the provenance model as depicted in Figure 3.

###  3.3 Goods market

The real economy consists of two sub-models (goods and investment market)
which simulate the business cycle (requirement 1 in Section 3.1). The goods
market builds on four central mechanisms for which separate model
specifications have been developed, as shown in Figure 3.

####  3.3.1 Supply mechanism of firms

A fundamental component in the real sector is the behavior of firms and their
adaptation to demand impulses. As apparent in Figure 2, demand is based on
consumption by households (Section 3.3.3) and investments by other firms
(Section 3.4). The supply mechanism models the update rule for pricing and
production based on a heuristic behavioral rule, according to Gualdi et al.
[44]. Its implementation in ML3 is shown in Figure 4. The production is based
on a homogeneous good used for consumption and investment, which is common in
macroeconomic agent-based simulation (see an overview by Dawid and Delli Gatti
[45]).

⬇

1Firm

2| true

3@ ego.strategy_change_rate()

4-> ego.set_strategy()

Fig 4: Update rule of firms for prices and production quantity in ML3

Note: The figure shows the supply mechanism rule, modelling firm production
behavior as shown in Equation 1 at the transition rate defined in Equation 2.

To make it simple, it is assumed that labor productivity $\alpha$ is fixed
over time and capital is not a production input. The production capacity
$Y_{i}$ of firm $i=1...N_{F}$ is a product of the hired amount of labor
$\Lambda_{i}$ and labor productivity.

To adapt to demand impulses, firms determine their labor demand
$\Lambda_{i}^{T}$ via setting a production target $Y_{i}^{T}$. At the same
time, the firm needs to find a sensible price $p_{i}$ for their good. Both
together form the firm’s strategy (ego.set_strategy()), which is updated as
follows:

$\displaystyle\begin{split}Y_{i}\leq D_{i}\ \text{and}\ p_{i}\geq\overline{p}\
\text{and}\ u>u_{nat}&\Rightarrow\ Y_{i}^{T\prime}=\
Y_{i}\cdot[1+\gamma_{y}\cdot\xi]\\\ Y_{i}\leq D_{i}\ \text{and}\
p_{i}<\overline{p}\ \text{and}\ u>u_{nat}&\Rightarrow\
p^{\prime}_{i}=p_{i}\cdot[1+\gamma_{p}\cdot\xi]\\\ Y_{i}\leq D_{i}\
\text{and}\ u<u_{nat}&\Rightarrow\
p^{\prime}_{i}=p_{i}\cdot[1+\gamma_{p}\cdot\xi]\\\ Y_{i}>D_{i}\ \text{and}\
p_{i}\leq\ \overline{p}\ &\Rightarrow\ Y_{i}^{T\prime}=\
Y_{i}\cdot[1-\gamma_{y}\cdot\xi]\\\ Y_{i}>D_{i}\ \text{and}\
p_{i}>\overline{p}\ &\Rightarrow\
p^{\prime}_{i}=p_{i}\cdot[1-\gamma_{p}\cdot\xi]\\\ \end{split}$ (1)

where $D_{i}$ represents the demand for the firm’s goods since the last
strategy change and $\overline{p}$ the current average price of all firms. To
control the price path, the average price is calibrated at a fixed value of
1.5.

The parameters $\gamma_{y}$ and $\gamma_{p}$ define the sensitivity to
production and price adaptions, respectively. $\xi\ $ is a random variable
$U[0,1]$ to implement uncertainty. An extension to Gualdi et al. [44] is the
full employment state where firms only increase their price. This state is
reached when the aggregated unemployment rate $u$ is lower than the Non-
Accelerating Inflation Rate of Unemployment (NAIRU), which is assumed to be 5%
and in line with the average Euro area statistics before the financial crisis
2007/2008. The behavior described in Equation 1 is subject to the profit
orientation of firms. Firms tend to get more market share or exploit arbitrage
opportunities in a monopolistic price setting. The cost-covering price for
each firm is based on wage and borrowing cost per unit and defines the minimum
price.

The transition rate $rate_{i}^{prod}$ (ego.strategy_change_rate()) is
dependent on the firm’s stock of inventories variable $N_{i}$ concerning their
stock target of inventories $N_{i}^{T}$, which is a parameter and assumed to
be twice as high as the production capacity:

$rate_{i}^{prod}=\frac{N_{i}}{N_{i}^{T}}\ or\
1+\left(1-\frac{N_{i}}{N_{i}^{T}}\right)\ \text{if}\ rate_{prod}<1$ (2)

The higher the delta between current inventories and inventory target, the
higher the strategy transition rate and vice versa. This has the effect that
firms hold a buffer of real inventories against unexpected demand swings [46]
and avoid supply constraints [42]. In combination with Equation 1, the effect
is that prices and production capacity constantly increase in boom phases and
the other way around in recessions. Combined with the following model
specifications, this effect leads to a typical business cycle behavior
(requirement 1).

####  3.3.2 Labor market

To reach the firms’ targeted production capacity (Equation 1), each firm needs
to hire or fire labor. The labor market operates on a simple hire-fire
principle following Gualdi et al.[44], as shown in Figure 3. The rates for
hiring and firing are dependent on the mismatch of labor demand
$\Lambda_{i}^{T}$ to current labor $\Lambda_{i}$. The greater this mismatch,
the higher the rate for hiring (or firing) employees:

$\displaystyle\begin{split}\text{hire
rate:}\left(\frac{\Lambda_{i}^{T}}{\Lambda_{i}}\right)^{\zeta_{h}}\text{if}\
\Lambda_{i}^{T}>\Lambda_{i}\\\ \text{fire
rate:}\left(\frac{\Lambda_{i}}{\Lambda_{i}^{T}}\right)^{\zeta_{f}}\text{if}\
\Lambda_{i}^{T}<\Lambda_{i}\end{split}$ (3)

Thereby, $\zeta_{h}$ and $\zeta_{f}$ are sensitivity parameters defined for
the hire and fire process respectively, and set via calibration. The effect of
the rules is hiring or firing one unit of labor.

####  3.3.3 Demand mechanism of households

The nexus between supply and demand is coordinated by the price for a
homogeneous good. The consumption rate (line 3 of Figure 5) is dependent on a
household’s financial wealth, which consists of wages or unemployment benefits
as shown in Figure 2.

⬇

1Household

2| true

3@ ego.wealth

4-> if (firm.size() > 0 & ego.wealth > firm.price) then

5 ego.wealth -= ?firm.price

6 firm.liquidity += ?firm.price

7 firm.inventory -= 1

8 firm.demand += 1

9 end

10where firms := Firm.all.filter(alter.inventory > 0)

11 firm := firms.weightedRandom(

12 Mercury.average_Price() / alter.price)

Fig 5: Household consumption rule in ML3

Note: The figure shows the demand rule, modelling household consumption or
expenditure of financial wealth in exchange for homogeneous goods from firms.
Mercury is an auxiliary agent, which otherwise has no interactions with other
agents.

The rate indicates that households aim to fully consume their income during
each period unless constrained by supply (firm.size() >0) or prices
(ego.wealth > firm.price), shown in line 4 of Figure 5. The selection process
is modeled as a weighted random selection (lines 11, 12). The function
weightedRandom returns a random element of the set whereby the probability of
selecting a particular firm $i$ with price $p_{i}$ is proportional to its
weight. Only firms are considered (filter()) within the entire agent
population of firms (Firm.all) with a good left in their stock of inventories
(alter.inventory > 0) (line 10). After a successful match, the transaction is
completed in lines 5 to 8. The demand variable of a firm is reset after each
strategy update, described in Section 3.3.1.

The stochastic nature of the matching protocol serves to model incomplete
price information of the households according to bounded rationality [47].
Households prefer to select a supplier with a price below average but will
usually not be able to find the one with the lowest price.

The share of consumption to nominal GDP is calibrated to culminate at around
50% according to the Euro area in recent years [48] (see Figure 3). This also
includes government expenditures (Section 3.7). The remaining 50% is related
to demand generated by firm investments (Section 3.4).

####  3.3.4 Bankruptcy of firms

The bankruptcy mechanism belongs to an accounting process and defines when and
how a firm goes bankrupt. The rule is not dynamic and is only activated once a
period when the debt ratio (Equation 10) exceeds the insolvency hurdle. The
insolvency hurdle is assumed at a debt ratio of 200%, which is calibrated in
combination with the Minsky base cycle described in Section 3.5.1.

The rule’s effect is that all credit lines are terminated, thereby burdening
banks’ equity (see Section 3.5.3). Employees are fired up to a calibrated
minimum size of five employees. Hence, firms are assumed not to be reborn and
are, on average smaller than their non-bankrupt counterparts, which is in line
with Caves [49] and Bartelsman et al. [50], found in Dosi et al. [51] (see
Figure 3).

###  3.4 Investment market

Next to household consumption (Section 3.3.3), the second demand pillar is the
investment demand and the corresponding market implementation. The investment
market is modeled endogenously in a non-growth environment, according to
Lengnick [52] and Popoyan [25], to keep the model structure as simple as
possible. There are no capital firms, no technological changes, and
investments are not accumulated on the balance sheet.

####  3.4.1 Investment cycle

To incorporate over- and underinvestment and to set the basis for an
overshooting credit cycle (requirement 2 in Section 3.1), the investment
process is based on the stylized theoretical approach by Keynes [53] (see
Figure 3), where firms indirectly generate their future profits with current
investments in a macroeconomic perspective. The higher the aggregate
investments of firms, the higher the average demand of all (other) firms in
upcoming periods. From a microeconomic perspective, the demand generated by a
single firm triggers other firms to increase investments, which induces demand
for the firm that initially set investment impulses.

The update rule of firms in ML3 to set their targeted investment amount
$inv_{i}^{T}$ follows the same structure as Figure 4 with the following
strategy:

$\displaystyle\begin{split}ret_{i}>0\ \text{and}\ inv_{i}\leq\
lim_{i}&\Rightarrow\ inv_{i}^{T}=\ inv_{i}\ \cdot\ [1+\gamma_{inv}\ \cdot\
\xi]\\\ ret_{i}>0\ \text{and}\ inv_{i}>\ lim_{i}&\Rightarrow\ inv_{i}^{T}=\
lim_{i}\\\ ret_{i}<0\ &\Rightarrow\ inv_{i}^{T}=\ lim_{i}\\\ \end{split}$ (4)

where $ret_{i}$ represents the investment return of previous investment cycles
($t\rightarrow n$). The calibration parameter $\gamma_{inv}$ regulates the
sensitivity of investment amount changes, and $\xi$ is a random variable
$U[0,1]$. The liquidity limit $lim_{i}$ models the firm’s creditworthiness on
the average credit market interest rate and expected profit or, in other
words, the assumption of the maximum available loan redemption rate that the
firm can afford. A more detailed description of the creditworthiness mechanism
is presented below in Section 3.5.1 (Equation 7). Hence, the investment amount
depends on investment return.

The investment return is the difference between investment turnover and
investment costs from a micro perspective. Investment turnover includes sales
from firm $i$ to all other firms $n$, and costs are investment purchases by
firm $i$ from all other firms $n$. A positive investment return leads to
higher liquidity limit/targeted investment amount due to higher expected
profit and the other way around.

As noted in Equation 4, firms can set the investment amount above the limit.
This mechanism meets the need to exploit profits in boom phases, ignoring the
internal creditworthiness indicator. In this case, firms can only obtain a
loan from banks at an interest rate below the average interest rate on the
credit market. Otherwise, the credit demand is rationed (see below in Section
3.5).

The pro-cyclicality of firm investment behavior is generated with the
transition rate $rate_{i}^{inv}$:

$rate_{i}^{inv}=\text{if}\ \frac{S_{i}}{S_{i}^{T}-int_{i}}\ \leq\ 1\
\text{then}\ \frac{1}{cap_{i}}\ \text{else}\ \frac{1}{cap_{i}+S_{i}}\ $ (5)

where $cap_{i}$ is the distance between the average production capacity of all
firms (average production capacity with full employment across all firms) and
the current production of a firm. The solvency rate $S_{i}$ is defined as the
debt ratio (Equation 10), and $S_{i}^{T}$ is the insolvency hurdle described
above in Section 3.3.4. The variable $int_{i}$ symbolizes interest pressure,
calculated as the relation between the latest loan interest and principal
payments.

The lower the distance to the average production capacity, the higher the
incidence of investment activities. The highest incidence is assumed to reach
a three-period cycle on average. From a macroeconomic perspective, a low
distance to the average production capacity across all firms tends to close
the output gap (reaching full employment), which comes along with inflationary
pressure. Higher prices lead to higher investment returns and again stimulate
new investments. This cascade is slightly relaxed by interest pressure
$int_{i}$. Since this pro-cyclical rally towards full employment becomes more
severe over time when more and more firms get involved, the overall interest
rate level is increased by the Central Bank (see Section 3.6.2), which
decreases the expected profit and investment demand (interest rate channel -
requirement 6).

On the other hand, a high distance to the average production capacity has a
contrary effect with a low investment incidence. The lowest incidence is
dependent on the average production capacity and the minimum number of firms’
employees (Section 3.3.4). This aligns with the Minsky cycle [54, 55], where
firms behave risk-averse in bust phases and risk-seeking in boom phases.

####  3.4.2 Investment demand

The market implementation of firm investments occurs when firms purchase
homogeneous goods from other firms. For simplicity, no differentiation between
household consumption and investment goods is made. Investment demand
impulses, or the matching of investing firms to suppliers, work in the same
way as the demand mechanism of households (lines 11 and 12 in Figure 5). The
purchase incidence rate depends on the investment amount described in the
previous Subsection (like line 3 in Figure 5).

##### Funding condition

In line with Dosi et al. [51], it is assumed that capital markets are
imperfect, and the financial structure of firms matters (e.g., [56, 57, 58]).
According to Myers [59], internal or external borrowing priority follows the
pecking order theory. Internal resources, like liquidity and equity, are used
for investments as long as enough surplus is detected. The surplus of internal
resources is the difference between existing internal resources and the
expected need for external borrowing on the credit market (see next Section).

###  3.5 Credit market

The credit process embraces the circulation of banking money within the
monetary system or the interaction of firms and banks to meet the demand for
financing generated by the real economy. As shown in Figure 2.2, the credit
market has a similar demand and supply structure as the goods market, assuming
that banks do not require labor.

####  3.5.1 Credit demand

The investment cycle in Section 3.4 and the credit creation process determine
the credit request incidence. Hence, no particular incidence rate is needed.
Banks are chosen according to weighted random selection (Figure 5, lines
11,12) when a firm decides to request a loan, based on the interest rate
offered (Equation 11). The preconditions (Figure 5, line 4) are based on
creditworthiness and regulatory requirement due to Basel III, as described in
the next Section.

####  3.5.2 Credit supply

Banks’ credit supply is structured into the credit creation process and the
corresponding bank strategy to update equity, interest, and risk variables.

##### Credit creation

The credit creation process is based on credit demand generated by firms’
investment behavior (see previous Section) and liquidity shortages. Liquidity
shortages are characterized by the scenario that firm $i$ cannot hold
sufficient liquidity $Liq_{i}$ for the targeted production. In this case, the
firm instantly requests a credit corresponding to its financial need or target
liquidity $Liq_{i}^{T}$:

$Liq_{i}^{T}=max\Big{(}W_{i}^{T}\ -\ Liq_{i},0\Big{)}$ (6)

where $W_{i}^{T}$ illustrates expected wage costs, dependent on target
production (Equation 1) and corresponding labor demand (Equation 3). The
credit approval process by banks is subject to two restrictions: credit
assessment restriction of firms and regulatory restrictions according to Basel
III [39].

Banks’ credit assessment of firm credit requests evaluates whether the credit
demanding firm can fund the loan redemption rate and have sufficient
collateral composed of liquid assets (firm liquidity and equity). Following
Schasfoort et al. [22], the bank grants a loan if the expected return
$r_{b}^{e}$ $\geq$ 0:

$r_{b}^{e}\ =\
\underbrace{\sum\limits_{n=1}^{dur}\frac{\Pi_{i}^{e}}{(1+i^{L})^{n}}-L_{ib}^{\prime}}_{\text{NPV}}\
-\ \underbrace{lgd_{ib}\ \cdot\ pd_{ib}\ \cdot\ L_{ib}^{\prime}}_{\text{EL}}$
(7)

The expected return consists of net present value (NPV) and expected loss
(EL). The net present value discounts the expected profits $\Pi_{i}^{e}$ with
the borrowing interest rate $i^{L}$ over loan duration $dur$ minus the
potential loan $L_{ib}^{\prime}$. The offered interest rate is composed of the
key rate (Section 3.6.2) + the fixed standing facility spread of 1% (Section
3.6.1) + margin/mark-up 11. In line with van der Hoog [23], the loan duration
is assumed to be 18 periods. The expected profit is the linear extrapolation
of firm turnover over the last three periods plus nominal variation of
inventories, deposit interest earnings minus wages, and interest costs [42].
Hence, the NPV reveals the maximum financial absorption capacity for
investments (Section 3.4), generating credit purchasing power [10].

The expected loss consists of the loss given default $lgd_{ib}$ and
probability of default $pd_{ib}$ concerning risk exposure $L_{ib}^{\prime}$.
The loss given default is the relation between collateral $C$ and risk
exposure $L_{ib}^{\prime}$ and indicates the unsecured credit amount:
$\frac{L_{ib}^{\prime}-C}{L_{ib}^{\prime}}$. The definition of a bank’s
expected probability of default $pd_{ib}$ is implemented via a logistic
function in line with Caiani et al. [42]:

$pd_{ib}=\frac{1}{1+e^{\left(\frac{OCF_{i}^{e}\ -\
\upsilon_{b}LR_{i}^{\prime}}{LR_{i}^{\prime}}\right)}}$ (8)

where $\upsilon_{b}$ indicates the bank’s risk attitude and $LR_{i}^{\prime}$
depicts the loan redemption rate of the hypothetical loan:
$(i_{b}^{\prime}+\frac{1}{dur})L^{\prime}$. For simplicity, the interest
expenses are distributed equally over the loan period $dur$, which leads to
equal loan redemption rates per period. The expected operating cash flow
$OCF_{i}^{e}$ is the linear turnover extrapolation of the last three periods
minus production (wages) and borrowing costs (coupon and interest payments)
per period [42].

Here, we follow the interpretation of Caiani et al. [42], that the expected
operating cash flow (OCF) indicates a firms’ borrowing absorption capacity or
Minskian litmus paper: a positive OCF indicates excess cash flow to absorb
current and upcoming $LR_{i}^{\prime}$ (hedge position). A negative
$OCF_{i}^{e}$ with an absolute value less or equal to the principal repayment
still can cover interest costs due and can be classified as a speculative
position. Whereby a negative OCF with an absolute value greater than principal
payments signals a Ponzi position. The speculative and Ponzi position might
lead to credit booms (unproductive credits - requirement 2) and severe
recessions [33].

The implementation of the expected return has a pro-cyclical effect because
expected profits and collateral increase/decrease until borrowing costs and
production capacity reach the tipping point.

If the credit assessment is positive, the bank either grants the full loan or
only the maximum possible loan amount corresponding to the firm´s
creditworthiness, thus conducting credit rationing [56]. Firms can utilize
several parallel credit lines. If a requested loan is not fully granted by a
bank, firms switch their (partial) credit request to another bank. If no bank
grants the requested (partial) loan, an overdraft facility can be used which
is restricted via debt ratio (Equation 10) and insolvency hurdle (Section
3.3.4). The overdraft facility is only related to loan requests due to
liquidity shortages (Equation 6) and functions as a liquidity buffer.

The second credit restriction is related to the regulatory framework
(requirement 5) which determines the regulatory credit creation potential
$\tilde{C}_{b}$:

$\tilde{C}_{b}=\frac{E_{b}}{\overline{\sigma}_{b}\cdot CAR}$ (9)

where $E_{b}$ is the equity capital, and $CAR$ represents the capital adequacy
requirement of 7% according to Basel III [39] (core capital of 4.5% and
capital conservation buffer of 2.5%). The parameter $\overline{\sigma}_{b}$
depicts the risk weighting of all loans for a bank, including the new
potential loan $L_{ib}^{\prime}$. Whereas a solvency rating, according to
Basel III regulation [39], defines the weight inbetween 0.2 (high solvency)
and 1.5 (low solvency) [24]. The solvency rate $S_{i}$ (see also Equation 5)
is defined as the debt ratio which is derived from the relation between a
firm’s liabilities (total loans $L$ and overdraft facility $O_{i}$) and total
assets (liquidity $Liq_{i}$, equity $E_{i}$ and expected operating cash flow
$OCF_{i}^{e}$):

$DR_{i}=\frac{\sum\limits_{k=1}^{n}L_{k}+O_{i}}{Liq_{i}+E_{i}+OCF_{i}^{e}}$
(10)

According to Basel III [39], the capital requirement is extended by a counter-
cyclical buffer $CCycB_{b}$ and in line with Krug [24]:
$CCycB_{b}=[(G-G^{T})-J]\cdot\frac{2.5}{H-J}$. $G$ stands for the current
aggregate credit-to-GDP gap and $G^{T}$ for its long-term trend, which is
updated every 12 periods and calculated as the simple moving average over the
last 60 periods [25].

A further regulatory requirement is the leverage requirement, calculated as
the ratio between equity and total assets and required to be above 3%. If a
bank does not meet the capital or leverage requirements, credit creation is
discontinued until enough equity is gathered or less risky credit receivables
are balanced.

Liquidity constraints according to Basel III (Liquidity Coverage Ratio and Net
Stable Funding Ratio) [39] are not implemented as, for simplicity, no active
bank liquidity management is assumed.

Banks’ credit potential can be increased by accepting low-risk loans or
expanding equity, whereas risk weighting is adjusted every period. Combined
with firms’ pro-cyclical creditworthiness, this mechanism captures the
financial accelerator (balance sheet channel - requirement 6) because the
relative risk weight is evaluated at a lower level in boom phases than in bust
phases. Hence, the described price-return cascade of investments (Section 3.4)
is fueled by credit supply (purchasing power of credits and potential
unsustainable credits - requirement 2). Credit potential is expanded pro-
cyclically, and regulatory restrictions are circumvented over time due to
higher bank profits and corresponding equity (Equation 9). Via this mechanism
unproductive credits are produced (requirement 2). High expected profits and
high collateral disguise the high default risk of firms.

##### Bank strategy

The update rule of banks to adapt to credit demand $CD_{b}$ and increase the
capacity to grant loans and related profits is similar to Figure 4 and
Equation 1:

$\displaystyle\begin{split}\tilde{C}_{b}<CD_{b}\ \text{and}\ m_{b}\leq\
\overline{m}_{b}\Rightarrow\ E_{b}^{\prime}\ &=\
E_{b}+min(Liq_{b}^{A},E_{b}^{N});\\\ m_{b}^{\prime}\ &=\
m_{b}+\gamma_{m}\cdot\xi\\\ \tilde{C}_{b}<CD_{b}\ \text{and}\
m_{b}>\overline{m}_{b}\Rightarrow\ E_{b}^{\prime}\ &=\
E_{b}+min(Liq_{b}^{A},E_{b}^{N});\\\ \upsilon_{b}^{\prime}\ &=\
\upsilon_{b}\cdot[1-\gamma_{r}\cdot\xi]\\\ \tilde{C}_{b}>CD_{b}\ \text{and}\
m_{b}>\overline{m}_{b}\Rightarrow\ m_{b}^{\prime}\ &=\
m_{b}-\gamma_{m}\cdot\xi\\\ \tilde{C}_{b}>CD_{b}\ \text{and}\ m_{b}\leq\
\overline{m}_{b}\Rightarrow\ \upsilon_{b}^{\prime}\ &=\
\upsilon_{b}\cdot[1+\gamma_{r}\ \cdot\xi]\\\ \end{split}$ (11)

The parameter $\tilde{C}_{b}$ represents the banks’ credit creation potential
(Equation 9) and $E_{b}$ equity capital. The variable $m_{b}$ depicts the
interest margin and $\overline{m}_{b}$ the average margin of banks at time
$t$. The margin is changed stepwise using a calibration parameter $\gamma_{m}$
and a random variable $\xi$ ($U[0,1]$).

Due to regulatory restrictions, banks can only expand credit supply via a
higher equity level, which is mainly increased by the retention of profits:
$min(Liq_{b}^{A},E_{b}^{N})$. Whereby the variable $Liq_{b}^{A}$ defines
available liquidity after anticipating liquidity outflow of interbank and
Central Bank credit interest charges (Section 3.6.1). $E_{b}^{N}$ is the
equity need to meet credit demand and credit creation potential in Equation 9.
The variable $\upsilon_{b}$ represents the risk attitude of the bank and
influences the credit assessment (see Equation 8) and collateral valuation
(risk channel - requirement 6). A low-risk level equals risk aversion, which
devalues firms’ collateral and fuels overshooting credit supply in boom phases
and vice versa.

The underlying structure of the incidence rate is comparable to line 3 in
Figure 4 or the corresponding Equation 2. The banks’ production variable is
the credit creation potential in Equation 9. The credit creation target is
determined by the maximum risk exposure allowed by the regulatory framework
[39] with a calibrated buffer parameter. The lower the buffer to the maximum
risk exposure, the higher the incidence rate, and vice versa.

####  3.5.3 Bank bailout mechanism

The bailout mechanism defines how the government recapitalizes insolvent
banks. Insolvent banks exhibit negative equity, caused by non-performing loans
from bankrupt firms, as described in Section 3.3.4. The government has no debt
restrictions in the model and can intervene anytime and with any amount. The
bailout mechanism is related to Popoyan [25] and Krug [24] (see Figure 3): It
is assumed to keep the number of banks constant. The bailout sum depends on
losses from non-performing loans and minimum capital requirements due to Basel
III regulation (Section 3.5.2). Banks get at least the minimum amount of
equity to fulfill capital requirements.

###  3.6 Monetary system

While the banking money circuit is similar within alternative monetary
regimes, the institutional framework of the interbank circuit is different.
Mak(h)ro_0 incorporates the current monetary system, also known as the
fractional reserve system.

####  3.6.1 Interbank market

The interbank market defines the interaction between banks and the Central
Bank to guarantee payment settlements of economic transactions. In co-
evolution with the credit market the interbank market distinguishes between
banking and Central Bank money. Banking money circulates when endogenously
issued by credit supply to firms (Section 3.5 and requirement 4). Hence,
deposits are created when banking money is issued directly to firms (when
borrowing) and indirectly to households (via wages, when employed with
external financed investments).

All economic transactions (e.g., household consumption, wage payments,
investment purchases, etc.) are settled via deposit accounts of the respective
bank (see also Table 7 in Appendix A). According to the monetary policy
operation framework [40, 60, 61], transactions across banks require Central
Bank money (reserves). The settlement of all transactions across all banks is
assumed to be twenty times within a period and is instantly balanced with
reserves. However, reserves are constantly unevenly distributed due to
heterogeneous agent behavior (more/less transaction volume for a specific
bank). Therefore, banks with a shortage of reserves can borrow from banks with
excess reserves on the interbank market at the end of each settlement period.
This system is also called a fractional reserve system because only a fraction
of reserves are required to let money circulate (requirement 3). The
oversupply (excess reserves $R_{b}^{E}$) or undersupply (reserves demand
$RD_{b}$) of reserves is indicated by the interest rate for interbank loans
$im_{b}$:

$\displaystyle\begin{split}R_{b}^{E}=RD_{b}\ \text{and}\ im_{b}>\
\overline{im}_{b}&\Rightarrow\ im_{b}^{\prime}\ =\
im_{b}-\gamma_{i}\cdot\xi\\\ R_{b}^{E}=RD_{b}\ \text{and}\ im_{b}<\
\overline{im}_{b}&\Rightarrow\ im_{b}^{\prime}\ =\
im_{b}+\gamma_{i}\cdot\xi\\\ R_{b}^{E}<RD_{b}\ &\Rightarrow\ im_{b}^{\prime}\
=\ im_{b}+\gamma_{i}\cdot\xi\\\ R_{b}^{E}>RD_{b}\ &\Rightarrow\
im_{b}^{\prime}\ =\ im_{b}-\gamma_{i}\cdot\xi\\\ \end{split}$ (12)

The market mechanism is similar to the update rule of Equations 1 and 11,
where $\gamma_{i}$ is a calibration parameter, and $\xi$ a random variable
($U[0,1]$). The incidence rate is assumed to be 20, which means that the
strategy is conducted twenty times on average within a period. The match
between excess and deficit reserve banks is implemented based on the matching
protocol in lines 11 and 12 in Figure 5. The interbank loan request is similar
to the firm credit market in Section 3.5, whereas the creditworthiness of
other banks is evaluated based on their solvency. If the bank that requests an
interbank loan does not have sufficient equity to fulfill the Basel III
requirements, no interbank loan will be granted, and the Central Bank has to
intervene as Lender of Last Resort.

##### Open market operations

Further unbalancing effects of payment transactions and the corresponding need
for reserves are caused by the credit creation process from banks to firms
(Section 3.5). Higher credit amount/deposits in the economy lead to new/more
transactions and vice versa. However, when banks cannot gather enough reserves
from other banks, the Central Bank provides a marginal lending facility
(short-term credit line). Short-term is defined with an incidence rate of 20,
as described above. On the other hand, when too many reserves are circulating,
they are posted to the deposit facility by the Central Bank, which is an
interest-bearing account. The marginal lending and deposit facility (standing
facilities) are set at 100 basis points above/below the key rate (main
refinancing operations rate) as it reflects the European Central Bank strategy
prior to the financial crisis of 2007/2008. Hence, the interbank rate will
always be kept between the standing facilities.

To keep the interbank rate close to the key interest rate and the
corresponding volatility low, the Central Bank intervenes via open market
operations. It is assumed that the Central Bank provides/withdraws reserves
when the average interbank rate diverges from the key rate. The higher the
deviation from the key rate, the more frequent the intervention.

##### Maintenance period and reserve target

Banks have to hold a minimum reserve requirement to stabilize the interbank
rate, which means they need a fraction of reserves in relation to their
deposits. The fraction is set at 1% [61] and needs to be held on average over
the reserve maintenance period of every two periods. Banks can also use those
fixed reserves, during that time, which dampens ad hoc reserve demand within
the interbank market and stabilizes the interbank rate. It is assumed that
banks are willing to close the minimum reserve shortage gap as soon as
possible, reflecting the fact that banks face uncertainty regarding interest
changes and the ability to gather enough reserves to fulfill the reserve
requirement. The model does not include autonomous factors that influence
banks’ liquidity like cash requirements and government deposits.

The reserve target follows the maintenance period and an expected reserves
outflow based on the latest average firm investments, household consumption,
and firm wage transactions.

Open market operations or Central Bank credits are empirically based on banks’
securities/collateral, such as covered bonds, asset-backed securities, etc.
Here we assume an unsecured interbank market. Banks have no lending
restrictions concerning reserves [37], because the Central Bank will keep the
interbank rate close to the key rate and always provides sufficient liquidity
(see fine tuning operations[40]). It is assumed that endogenous interbank
crashes are very scarce since the Central Bank always acts as a Lender of Last
Resort and keeps enough required liquidity to dampen interbank rate
fluctuations. Hence, an interbank shutdown can only be triggered by an
exogenous shock which generates high interbank market imbalances and leads to
credit supply stops and a disruption in the payment mechanism. When conducting
experiments, an interbank specification can be activated in the model to
measure liquidity risk via interbank risk premia and exploitation of Central
Bank standing facilities, which can impede credit supply costs. Bank runs are
not assumed.

##### Bank deposit strategy

To implement changing bank relationships and the desire to attract reserves,
households change their bank account on average every 12 periods and firms
every 100 periods. The deposit interest rate determines the incentive for
households and firms to invest their deposits at a particular bank. The
deposit margin/mark-up is adapted according to demand via an equivalent
mechanism in Equation 12. The selection process for depositors is based on the
known matching protocol (lines 11, 12 in Figure 5).

##### Interest spreads

The spread of the interest corridor of the standing facilities is assumed not
to change with interest level changes. The assumption holds true for the
interest spreads between several interest types. The offered loan interest
rate to firms by banks is composed of the key rate plus the fixed standing
facility spread of 1% and the individual bank loan mark-up (Equation 11).
Banks’ deposit rate offered to depositors comprises the key rate minus the
fixed standing facility spread of 1% and a calibration parameter of 3% plus
the individual bank deposit mark-up.

####  3.6.2 Monetary policy mechanism

As already described in the previous Section, monetary policy is based on
inflation targeting, according to Bindseil [61]. The central bank measures the
average inflation over 12 periods and compares the value with the inflation
target of 2%. The inflation target influences the general interest level
within the model and is set based on a corresponding calibration process
concerning stylized facts (see next Section and 5). Furthermore, monetary
policy considers the output gap, implemented via the original Taylor rule
[62]:

$i_{c}=i^{*}\ +\ a_{\pi}(\pi-\pi^{*})\ +\ a_{\pi}(y-y^{*})$ (13)

where $i_{c}$ is the key rate, $\pi$ the inflation rate measured over the last
12 periods, $\pi^{*}$ the inflation target and $y-y^{*}$ the real output gap
in relative terms. The potential real output $y^{*}$ is assumed to be 95% of
full production (i.e., all households are employed) which is in line with the
Non-Accelerating Inflation Rate of Unemployment (NAIRU) in advanced economies
(see Section 3.3.1). Within the model, 5% serves as a buffer for inflationary
pressure which means that the output gap can become temporarily positive. One
of the main components in the model is the natural interest parameter $i^{*}$
in Equation 13, which is calibrated at 10%.

###  3.7 Fiscal mechanism

The government raises taxes to finance unemployment benefits and bank bailout
measures. The tax is applied to wages and firm/bank profits. Since firm
profits are part of the creditworthiness, taxes impact the model behavior.
They are calibrated in combination with the Taylor rule in the previous
Section that defines the general interest level. If households become
unemployed, the government provides a tax-exempt unemployment benefit
calibrated at half of the fixed wage. Bank bailouts are described in Section
3.5.3. All bankruptcy costs are covered by the government, which has no
liquidity limit.

##  4 Calibration

The model input refers to parameter values as well as the initial values of
variables, for a complete list see the supplement [63]. One possibility to
determine suitable values is their calibration [12].

##### Parameter calibration

As shown in Figure 3, the model is composed of various sub-models. Each sub-
model has undergone a sensitivity analysis based on theoretical and empirical
plausibility with a one-factor-at-a-time (OFAT) approach [64]. Furthermore, a
Plackett-Burman experimental design has been applied to the sub-models goods
market and investment cycle to identify parameter limits in line with desired
stylized behavior. An OFAT-analysis supported this process for each sub-model,
sub-models compositions (real sector), and the final composite model. The
monetary policy specification is only calibrated with the final composite
model. Since no productivity growth is assumed, the calibration of the final
model is based on an aggregate credit amount that is allowed to fluctuate but
should not show a growing trend.

##### Initialization

As stated in Fagiolo and Roventini [12], complex stochastic models are
characterized by high levels of dimensionality, leading to the circumstance
that the statistical equilibria are unknown to the modeler. To keep that
problem under control, we adopt the approach of Dosi et al. [51] to choose
economically meaningful variables. Initial values are anticipated from the
average production capacity for each firm. The average production capacity per
firm is the total number of households divided by the total number of firms.
The initial demand sources, households (wages), and firms (investment amount),
in combination with bank credit creation potential (bank equity), are
initialized with adequate values to let firms emerge to their full production
capacity in an aggregate perspective. All other related values (inventories,
liquidity, equity of firms) are calibrated/iterated according to their
respective average values in the model output. Initial economic values affect
the length of the warm-up but not the model behavior. Hence, adequate values
refer to a set of values that minimize the impact of the warm-up phase, which
can be appraised between 100 and 200 periods. Furthermore, all agents are
initialized homogeneously. The heterogeneous agent structure emerges during
the simulation via the stochastic feature of ML3.

The size of each agent (sub-)population is selected in a manner that its scale
to other sub-populations appears plausible following model assumptions
(Section 3.2.1) and other MABM [24, 23, 25, 42]. For each bank, we assume four
times as many firms [65] and 40 times as many households (e.g., with 50 banks,
200 firms, and 2000 households).

A change of agent size relations comes with an adaption of the calibration to
replicate stylized facts (see next Section) but does not change the
fundamental model behavior. However, a constant relation between agent sizes
does not affect the model behavior between population size variations of 10 to
200 firms. Too small population sizes might affect simulation results due to
stochasticity. With the current simulator, more than 200 firms cannot be
tested due to technical restrictions. The validation is conducted with a
population size of 12 banks, 48 firms and 480 households, and one Central Bank
and government. The simulation is run for 600 periods of simulated time.

##  5 Validation

The purpose of the model is to analyze the effects of institutional system
changes or policy experiments in terms of macro-financial stability. A common
method to test whether the model output can be used to identify policy
experiment effects is to reproduce jointly a wide range of macroeconomic and
microeconomic stylized facts [66]. A history-friendly approach [21] that
describes a strict adaptation to historical data would not be recommendable
for the purpose of the present model due to the methodological pitfall of
counter-factual histories.

Our validation is based on the set of macro, and microeconomic stylized facts
(SF) suggested by Dosi et al. [66], which is considered the most comprehensive
set of stylized facts in the macro-finance realm [24]. Long-term growth-
related stylized facts are not under examination (see the discussion of model
assumptions and limitations in Section 3.2.1). The validation is based on 20
replications, which can be interpreted as representative since the average
real GDP standard deviation across all 20 replications is very small ($\rho$ =
3.471e-04).

To validate the model output following stylized facts, the micro-founded model
outcome has to be aggregated. An important economic output indicator is the
Gross Domestic Product (GDP) which measures the aggregate value of all
finished goods and services in a certain period of time within an economy.
Here, (real) GDP is defined as the aggregated quantity of final goods produced
by firms for household consumption $C$ and firm investment $I$ plus change in
inventories $\Delta N_{i}$ in production units $q$ (homogeneous good) within a
period [66]:

$GDP^{real}=\sum\limits_{i=1}^{n}q_{i}^{C}+\sum\limits_{i=1}^{n}q_{i}^{I}\equiv
C+I+\Delta N_{i}$ (14)

Nominal GDP is measured similarly to Equation 14 with firm prices. To extract
the “business cycle component” of a given time series variable within a
particular band of frequencies, we use the Baxter-King filter with standard
configurations for economic time series. Stock and Watson [67] state that
business cycles last from 6 to 32 quarters which specifies the lower and upper
bound of the cycle periodicity. The filter’s fixed lead/lag length or order is
set at 12. These configurations are used for quarterly data in reality and are
indicated with the following notation: bpf(6,32,12). Our model is calibrated
such that one period corresponds to a quarter in reality, thus, 400 periods
correspond to 100 years. All validation outputs are based on the same
parameter and variable setting. The analysis is conducted in R, and can be
found in the supplement [63].

Table 1: Stylized facts replicated by the model

Code |  Stylized fact |  Empirical studies (examples)
---|---|---
SF1 |  Relative volatility of GDP/invest./consum. |  Stock and Watson [67]; Napoletano et al.[68]
SF2 |  Recession duration exponentially distributed |  Ausloos et al. [69]; Wright [70]
SF3 |  Cross-correlations of macro variables |  Stock and Watson [67]; Napoletano et al. [68]
SF4 |  Pro-cyclical aggregate R&D investment |  Wälde and Woitek [71]
SF5 |  Cross-correlations of credit-related variables |  Lown and Morgan [72]
SF6 |  Lagged correlation between firm indebtedness & credit defaults |  Foos et al.[73]; Mendoza and Terrones [74]
SF7 |  Banking crises duration is right skewed |  Reinhart and Rogoff [75]
SF8 |  Fat-tailed distribution of fiscal costs of banking crises-to-GDP ratio |  Laeven and Valencia [76, 2]
SF9 |  Lumpy investment rates at firm-level |  Doms and Dunne [77]
SF10 |  Firm bankruptcies are counter-cyclical |  Jaimovich and Floetotto [78]
SF11a |  Philipps curve |  Phillips [79]
SF12 |  Okun’s law |  Okun [80]
SF13 |  Interbank market |  BIS [81]

  * a

Described as a general characteristic of an economy, i.e., without an explicit
notion of empirical studies, and found in Riccetti et al. [82], Krug[24] and
Delli Gatti et al. [17].

###  5.1 Relative volatility of GDP, investment and consumption - SF1

The first stylized fact depicts the behavior at business cycle frequencies
related to GDP and firm investment time series. Figure 5.1 shows that the
model output can replicate empirical findings in the sense that investment
fluctuations are more volatile than GDP time series [67, 68]. To keep the
graph uncluttered, consumption is not included and can be found in the
Appendix A (Figure 15). Consumption shows a less volatile behavior with a
standard deviation. Using 20 simulation replications, the relative standard
deviation compared to real GDP of real consumption is 0.44, 4.58 for real
investment and 13.51 for unemployment. Empirical observations [83] show a
relative standard deviation compared to real GDP of 0.80, 4.61 for investment,
and 8.22 for unemployment. As described in Section 3.4 consumption is crowded
out by investment activities which leads to a lower consumption volatility. A
calibration with a higher government tax rate (e.g., tax = 0.13) lowers the
relative unemployment standard deviation and consumption, but keeps investment
at around 4.60. In addition, the model output can replicate persistent
fluctuations [84, 85, 67] but no long-term growth due to model assumptions
(see Section 3.2.1).

Fig 6: SF1: Deviations of real GDP and real investment time series from trend:
bandpass-filtered (6,32,12)

Note: The figure depicts deviations of average real GDP (solid line) and
average real firm investment (dashed line) from trend in %. The simulation
output is a representative run and shows an extract to keep the line profile
more identifiable without the warm-up phase of 200 simulation periods. The
grey shaded area represents the 90% confidence interval.

###  5.2 Recession duration exponentially distributed - SF2

The recession duration is defined as the length of periods in which real GDP
growth percentage change is less than zero [70]. The model output is presented
in figure 7 and shows a clear exponential distribution, which is in line with
empirical data [70, 69].

Fig 7: SF2: Exponential fit of recession durations

Note: Graphical analysis of the frequency of recession duration plotted as a
cumulative probability distribution in log-log scale according to Wright [70]
and Dosi et al. [66]. The points present the simulated outcome and the solid
line depicts the exponential fit to the data. The recession duration is
defined as the length of periods in which real GDP growth percentage change is
less than zero. The simulation output is a representative run without the
warm-up phase of 200 simulation periods.

###  5.3 Cross-correlations of macro variables - SF3

The third stylized fact that can be replicated by the model is related to
several macro variables which are presented in Table 2. Investment, change in
inventories and inflation are pro-cyclical and unemployment counter-cyclical
which is in line with Wälde and Woitek [71]. Investment is leading real GDP,
because investment demand is satisfied by firms’ inventory capacities and not
by current production capacity, as demonstrated with an alternative GDP
measure in Table 2 (GDP $-\Delta$ inventories). This circumstance can be
adapted by introducing a separate agent type for investments, but this in turn
makes the model more complex.

Changes in inventories lag real GDP because of the gradual build-up of
production capacity (Section 3.3.1). Demand impulses cause an adaption of the
production target which in turn activates the hire/fire mechanism (Section
3.3.2) and finally the production capacity. Inflation is lagging GDP by up to
three lags, because inflation is measured over three periods. In contrast to
Wälde and Woitek [71] prices are pro-cyclical. However, this is in line with a
monetary or demand-driven economy [86] and thus with the purpose of the model
to compare monetary systems. Counter-cyclical prices are caused by supply
shocks. Due to fixed wages and productivity, a supply shock is not
incorporated, but can be implemented via external shocks.

Table 2: Cross-correlation of macro variables - SF3

  * •

Correlation structure of simulated macro variables to real GDP.

  * •

The correlation coefficients are related to the dependent variable GDP. The
simulation output comprises 20 representative runs to increase the sample with
a total number of 12,000 period observations without the warm-up phase of 200
simulation periods.

  * •

Bpf: bandpass filtered (6,32,12) series.

Series (Bpf) |  Output (Bpf)
---|---
| t$-$4 | t$-$3 | t$-$2 | t$-$1 |  $-\\!$t | t$+$1 | t$+$2 | t$+$3 | t$+$4
GDP | $0.189$ | $0.465$ | $0.731$ | $0.927$ | $1$ | $0.927$ | $0.731$ | $0.465$ | $0.189$
Investment | $0.516$ | $0.318$ | $0.073$ | $-0.191$ | $-0.438$ | $-0.635$ | $-0.755$ | $-0.788$ | $-0.738$
Change in inventories | $0.271$ | $0.002$ | $0.302$ | $0.578$ | $0.779$ | $0.872$ | $0.854$ | $0.746$ | $0.579$
Inflation | $0.004$ | $0.19$ | $0.365$ | $0.515$ | $0.626$ | $0.687$ | $0.689$ | $0.626$ | $0.502$
Prices | $0.418$ | $0.561$ | $0.663$ | $0.707$ | $0.679$ | $0.575$ | $0.402$ | $0.183$ | $-0.052$
Unemployment | $-0.353$ | $-0.555$ | $-0.724$ | $-0.822$ | $-0.819$ | $-0.706$ | $-0.5$ | $-0.242$ | $0.023$
GDP $-\Delta$ inventoriesa | $0.06$ | $0.349$ | $0.66$ | $0.906$ | $1$ | $0.906$ | $0.66$ | $0.349$ | $0.06$
Investment | $0.084$ | $0.364$ | $0.659$ | $0.892$ | $0.985$ | $0.903$ | $0.673$ | $0.37$ | $0.077$

  * a

Cross-correlation between investment and GDP measurement without change of
inventories.

###  5.4 Pro-cyclical aggregate R&D investment - SF4

Aggregate investments of firms per period are pro-cyclical which can be shown
graphically in figure 8. As described in the previous Subsection, investment
is characterized by a leading feature relative to real GDP.

Fig 8: SF4: Pro-cyclical aggregate firm investment

Note: The figure depicts average real GDP as a dashed line and aggregated
total investment as a solid line. The simulation output is a representative
run and shows an extract to keep the line profile more identifiable without
the warm-up phase of 200 simulation periods. The grey shaded area represents
the 90% confidence interval.

###  5.5 Cross-correlation of credit variables - SF5

Lown and Morgan [72] indicate that bank profits and total debt outstanding in
the firm sector are pro-cyclical. The related model output presented in Table
3 can confirm these empirical findings. Bank profits are lagging real GDP by
one lag, because the loan redemption starts one period after the loan was
granted.

Firm debt includes bank credits for investments and liquidity injections as
described in Section 3.5.1. The concurrent behavior to real GDP shows that
demand and supply in the goods market is dependent on the financial absorption
capacity.

Credit defaults of firms occur in concurrence with investment activities
(Table 2) which define the business and credit cycle (Section 3.4). An
investment demand decrease causes lower (expected) profits (Equation 7) and
cash flow, which in turn leads to a lower debt-bearing capacity and credit
defaults. This effect becomes more severe with increasing indebtedness (see
Minskian litmus paper in Section 3.5.2).

Table 3: Cross-correlation of credit variables - SF5

  * •

Correlation structure of simulated credit variables to real GDP.

  * •

The correlation coefficients are related to the dependent variable GDP. The
simulation output comprises 20 representative runs to increase the sample with
a total number of 12,000 period observations without the warm-up phase of 200
simulation periods.

  * •

Bpf: bandpass filtered (6,32,12) series.

Series (Bpf) |  Output (Bpf)
---|---
| t$-$4 | t$-$3 | t$-$2 | t$-$1 |  $-\\!$t | t$+$1 | t$+$2 | t$+$3 | t$+$4
GDP real | $0.189$ | $0.465$ | $0.731$ | $0.927$ | $1$ | $0.927$ | $0.731$ | $0.465$ | $0.189$
Bank prof. | $-0.04$ | $0.229$ | $0.493$ | $0.716$ | $0.864$ | $0.915$ | $0.865$ | $0.731$ | $0.539$
Firm debt | $0.085$ | $0.225$ | $0.347$ | $0.435$ | $0.473$ | $0.46$ | $0.402$ | $0.315$ | $0.213$
Credit def. | $-0.002$ | $-0.012$ | $-0.024$ | $-0.023$ | $0.001$ | $0.039$ | $0.073$ | $0.084$ | $0.064$

###  5.6 Cross-correlation between firm debt and loan losses - SF6

The time-series correlation of aggregated loan losses in relation to
aggregated firm debt is positive and lagged, which is demonstrated in figure 9
and in line with Mendoza and Terrones [74]. Firm debt is mainly driven by bank
credit borrowing. As described in the previous Section, high firm debt
accumulation of firms turns into a leverage cycle and will further burden
banks’ equity [73].

Fig 9: SF6: Firm debt and loan losses time series

Note: The figure depicts average firm debt as a dashed line and average loan
losses as a solid line. The simulation output is a representative run and
shows an extract to keep the line profile more identifiable without the warm-
up phase of 200 simulation periods. The grey shaded area represents the 90%
confidence interval.

###  5.7 Banking crisis duration is right-skewed - SF7

Banking crisis duration is defined as the length of periods with bank failures
in a row. According to Reinhart and Rogoff [75] the distribution of bank
failures duration is right skewed. The model can replicate empirical
observations, shown in the second column of Table 4.

Table 4: Distribution related stylized facts

  * •

The simulation output comprises 20 representative runs to increase the sample
with a total number of 12,000 period observations without the warm-up phase
of 200 simulation periods.

| SF7: Banking crisis duration | SF8: Fiscal costs/GDP ratio
---|---|---
Skewness | 1.227 | 1.345
Kurtosis | 4.888 | 3.676
Mean | 7.032 | 0.146
Standard dev. | 6.813 | 0.082
Min | 1 | 6.124e-04
Max | 49 | 0.680
Median | 4 | 0.135
Mode | 1 | 0.017

###  5.8 Fiscal cost of banking crisis to GDP distribution is fat-tailed - SF8

In relation to the previous Subsection, banks are bailed out by the
government. The corresponding ratio of fiscal costs-to-GDP of banking crises
duration has a distribution with the feature of excess kurtosis and heavy
tails as presented in the third column of Table 4. This observation is in line
with empirical finding with regard to Laeven and Valencia[76, 2]. A Jarque-
Bera test for normality yield a p-value of 0.00 and a test statistic of
1922.3, indicating that a normal distribution has to be rejected. The same
holds true with a Shapiro-Wilk test.

###  5.9 Lumpy investment rates at firm-level - SF9

Lumpy investments are infrequent and large (lumpy) establishment-level capital
adjustments [87]. Figure 11 depicts the investment behavior per period of
three randomly chosen firms. It can be observed that investments do not follow
a smooth behavior, but rather indicate periods with successive spikes and low
or even no investment activity (Section 3.4.1).

Fig 10: SF9: Individual firm investment time series

Note: The figure depicts investment frequencies for three randomly chosen
firms. The dashed line shows the firm with identification number (id) 10, the
solid line the firm with id 19 and the dotted line the firm with id 27. The
simulation output is a representative run and shows an extract to keep the
line profile more identifiable without the warm-up phase of 200 simulation
periods.

###  5.10 Firm bankruptcies are counter-cyclical - SF10

Empirical findings according to Jaimovich and Floetotto [78] state that firm
bankruptcies are counter-cyclical. As shown in figure 11 the model is able to
replicate the counter-cyclical behavior. Firm bankruptcies are leading by two
lags in relation to real GDP (with $\rho=-0.230$; bandpass filtered
(6,32,12)). The leading feature indicates the beginning of the tipping point
between boom and bust states. Firm bankruptcies are dependent on solvency or
leverage (Equation 10). In boom phases investments and thus prices increase
until the maximum financial absorption capacity. This process is influenced by
higher interest rates level (monetary policy - Section 3.6.2), full production
capacity and credit rationing (Section 3.5.2).

Fig 11: SF10: Real GDP and firm bankruptcies time series

Note: The figure depicts average real GDP as a dashed line and firm
bankruptcies as a solid line in bars. The simulation output is a
representative run and shows an extract to keep the line profile more
identifiable without the warm-up phase of 200 simulation periods. The grey
shaded area represents the 90% confidence interval.

###  5.11 Philipps curve - SF11

The model is able to replicate a standard Philipps curve which is shown in
figure 11. The time measurement is based on inflation, which is measured every
three periods in the model.

Fig 12: SF11: Inflation in relation to unemployment

Note: The figure shows a scatter plot of average inflation percentage change
and unemployment rate (minus natural unemployment rate) with following
regression feature: $Natural\ unemployment\ rate\
(0.012-0.154x+\epsilon);R^{2}=0.369$. The natural unemployment rate is assumed
to be 0.05. The simulation output comprises 20 representative runs to increase
the sample with a total number of 12,000 period observations without the warm-
up phase of 200 simulation periods. The grey shaded area represents the 90%
confidence interval.

###  5.12 Okun’s law - SF12

Okun [80] finds a negative statistical relationship between real GDP growth
and unemployment rate which can be replicated by Mak(h)ro_0 ABM as shown in
Figure 13. Okun’s law has been empirically re-investigated several times
afterwards and can be derived in various ways (e.g., Rahman and Mustafa [88]
and Obst [89]). For simplicity we show the difference version which relates to
changes in the unemployment rate to changes in real GDP per period. The gap
version is tested as well and unveils very similar results.

Fig 13: SF12: GDP growth in relation to unemployment growth

Note: The figure shows a scatter plot of aggregated real GDP and unemployment
percentage change with following regression features: $Unemployment\ rate\
(0.007-0.913x+\epsilon);\ R^{2}=0.295$. The natural unemployment rate is
assumed to be 0.05%. The simulation output comprises 20 representative runs to
increase the sample with a total number of 12,000 period observations without
the warm-up phase of 200 simulation periods. The grey shaded area represents
the 90% confidence interval.

###  5.13 Interbank market - SF12

Concerning the interbank market behavior, Mak(h)ro_0 can replicate three
stylized facts according to Bech and Monnet [81]. Here, we conducted an
experiment and let the Central Bank inject 10 nominal units per period for
every bank between period 50 and 100. The periods before and after the
experiment phase depict normal open market operations by the Central Bank
(Section 3.6.1). The key rate is assumed to be at 1% with an interest corridor
of $\pm$1%.

Figure 14 shows, that increasing the amount of excess reserves drives the
overnight interbank rate towards the floor of an interest rate corridor [81]
between period 50 and 100. Second, increasing the amount of excess reserves
reduces overnight interbank volume [81]: average interbank volume between
period 50 and 100 (29.299 nominal units) are significantly lower (p-value:
0.003) than the periods before (53.805 nominal units). Third, increasing the
amount of excess reserves lowers overnight rate volatility [81]: average
standard deviation between period 50 and 100 (8.374e-04) is significantly
lower (p-value: 0.000) than the periods before (2.038e-03). Here, we do not
include the impact of excess reserves on the recourse to the Central Bank
lending facility, since we assume that banks with excess reserves are always
willing to lend.

Fig 14: SF13: Interbank market

Note: The figure depicts average interbank rate as a dashed line and excess
reserves as a solid line. The simulation output is a representative run with
an interbank experiment between period 50 and 100. The grey shaded area
represents the 90% confidence interval.

##  6 Discussion and literature review

To show the additional benefit of this model in comparison to other related
MABMs, Table 5 gives a concise overview according to the model requirements.
It should be noted that the purpose of the related MABMs is analyzing various
economic policy experiments rather than (alternative) options of monetary
regime shifts, whereby the current monetary system is modeled as a source for
bank liquidity constraints [25] and monetary policy transmission [22, 24],
e.g., to grasp macroprudential policy changes in interdependence with price
stability [24, 25] or the influence of monetary policy transmission on price
stability [22]. A first modification of the monetary system has been examined
by van der Hoog [23] (more details below). For a more general and
comprehensive overview about MABMs the reader is referred to Dawid and Delli
Gatti [45] who provide an extensive comparison.

Table 5: Related literature and model requirements

  * •

The Table shows a comparison of related macroeconomic agent-based models
(MABM) in accordance with requirements to model the current monetary system
(as stated in Section 3.1).

  * •

Model requirement definition:

  * •

1\. Business cycle; 2. Financial cycle; 3. Fractional reserve system;

  * •

4\. Endogenous money creation; 5. Regulatory framework; 6. Monetary
transmission

| Model requirement
---|---
MABM | 1 | 2 | 3 | 4 | 5 | 6
1\. Caiani/Schasfoort [42, 22] | $++$ | $++$ | $+$ | $++$ | $+$ | $++$
2\. Van der Hoog [23] | $++$ | $++$ | $-$ | $+$ | $+$ | $++$
3\. Krug [24] | $++$ | $+$ | $++$ | $++$ | $++$ | $+$
4\. Popoyan [25] | $++$ | $+$ | $+$ | $-$ | $+$ | $++$

  * •

Note: applicable ($++$); partly applicable ($+$); not applicable or
identifiable ($-$)

The business cycle (requirement 1) described in Section 3.3 and its behavior
shown in Section 5.1 to 5.4 and 5.10 to 5.12 is not particular different to
related MABMs in Table 5. However, the source of credit demand is modeled
differently which has an influence on the credit cycle as required and
described in the next paragraph.

The credit cycle (requirement 2) described in Section 3.5 is highly
intertwined with the business cycle. Krug [24] investigates the interrelation
between monetary and macroprudential policy, which requires a model with a
focus on the cost-induced inflation theorem and omits a separate investment
cycle. However, this approach does not capture credit overshooting behavior by
banks as required. Excess demand by the purchasing power of credit supply is
not incorporated since credit demand is restricted via the price-wage relation
by firms and households. Mak(h)ro_0 simulates asset-price-related demand-
induced inflation that omits a price-wage spiral. The corresponding rally of
firms to reach the production potential makes the influence of credit supply
on the business cycle more transparent, which is or can be covered by Caiani
et al./Schasfoort et al. [42, 22] and van der Hoog [23]. Furthermore, Caiani
et al./Schasfoort et al. [42, 22], van der Hoog [23], and Krug [24] do not
clarify how banks exploit and expand credit creation potential with quasi-
automated fractional refinancing and circumvent capital adequacy and liquidity
requirements. Concerning Popoyan et al. [25], the dynamic of the credit cycle
is not transparent and accessible but seems to follow similar behavior as Krug
[24].

The fractional reserve system (requirement 3) is highly interrelated with
requirement 2 and defines the institutional framework of the monetary system
or how money creation is organized. Krug [24] exhibits a clear distinction
between Central Bank money creation (reserves) and its relation to commercial
bank money creation (two-split circuit system). This is in line with the
theory of endogenous money creation (requirement 4) to identify liquidity
risks of banks. Popoyan et al. [25] show an alternative way to implement the
interbank market and to model the liquidity risk of banks while modeling bank
liquidity management. However, a flow of reserves to fulfill the payment
scheme, which is crucial for capturing the fractional reserve system, is not
implemented. In comparison, even though Schasfoort et al. [22] included an
interbank market, it is not clear how reserves are used for the payment scheme
or how open market transactions are used to stabilize the interbank rate.
Finally, van der Hoog [23] does not incorporate an interbank market and thus
no adequate fractional reserve refinancing scheme to compare evolving
liquidity risk across monetary regimes.

Endogenous money creation (requirement 4) defines the money issuance process
of reserves and credit money (Section 3.6.1). Whereas Caiani et al. [42] and
Krug [24] strictly follow the endogenous money theory, van der Hoog [23]
partly implements the requirement 4 by setting bank credit creation dependent
on reserve requirements. However, reserve requirements play a minor role when
it comes to credit restrictions within the current fractional reserve system
[37, 38]. By assuming this restriction (as van der Hoog [23] does), the
current monetary system might appear inherently more stable, which could bias
the comparison with alternative monetary systems. Reserves, especially the
minimum reserve, assumes the function of a liquidity buffer and are steered in
the fractional reserve system via open market operations by the Central Bank
(requirement 3). Finally, the requirement 4 could not be identified within the
model description of Popoyan et al. [25].

The regulatory framework (requirement 5) defines the macroprudential policy,
which restricts the credit creation process of banks. Caiani et al./Schasfoort
et al. [42, 22] and van der Hoog [23] do not implement the leverage ratio
restriction for banks, which dampens banks’ credit creation when leverage is
high. In addition, Caiani et al./Schasfoort et al. [42, 22] and Popoyan et al.
[25] do not specify an adaptation of risk-weighted assets according to the
solvency state of firms through the financial cycle. This aspect could lead to
banks overestimating their credit creation potential (see Equation 9), which
impacts firms’ demand via the purchasing power of credits [90].

Here we challenge the conclusion of van der Hoog [23] that only the quality of
credit matters. In general, debtors and borrowers are confronted with
asymmetric information which means that the quality of borrowers is not fully
accessible. Therefore, the macroprudential policy according to Basel III
(indirectly) addresses credit quantity to dampen excessive leverage. However,
direct restrictions of banks’ investment portfolios are more effective than
indirect restrictions through capital, leverage, and liquidity regulations
[91]. Furthermore, unproductive credits might also be caused by macroeconomic
conditions and shocks. Credit rationing could worsen the financial situation
for otherwise sound firms and might lead to contagion risks. Even when banks
can choose unexceptionally productive credits or financially sound firms,
systemic risk is still present. Beyond this statement, shadow banking and the
corresponding influence on money creation need to be considered.

The monetary transmission mechanism (requirement 6) defines a basic monetary
transmission mechanism that is necessary to analyze how monetary policy can
control/influence the aggregate money supply in an economy. With respect to
the model mechanism of Caiani et al./Schasfoort et al. [42, 22], van der Hoog
[23] and Popoyan et al. [25] no significant differences can be detected.
However, the model description of Krug [24] does not provide a financial
accelerator mechanism which extends the credit creation potential of banks and
thus increases the vulnerability of the economy.

Concerning the implementation of alternative monetary regimes, van der Hoog
[23] evaluated an equity based approach of a full reserve system where banks
act as equity fund managers without risk transformation and refinancing risks.
However, the current discussion of a sovereign monetary system is related to a
debt financed approach [92, 3] where banks act as pure financial
intermediaries, which includes maturity transformation and corresponding
liquidity risks.

Beyond the agent-based methodology, models that incorporate a full reserve
system are a Stock-Flow Consistent model [93], a sustainable-finance model
based on differential equations [94], an accounting system dynamics model
[95], and a DSGE model [96].

To our knowledge, there is no MABM that considers a free banking system. Here,
Mak(h)ro_0 might serve as a baseline model to implement and analyze such a
monetary regime shift with regard to macro-financial stability.

##  7 Conclusion

As stated in the introduction the aim of this model is to support studies for
comparing alternative monetary regimes with a simple model of the current
monetary system as a baseline. The model structure is built based on pre-
defined requirements (Section 3.1) and fully implemented within the continuous
time agent-based modeling language ML3 (Section 2.1). ML3 allows to easily
access, improve, expand, and discuss the model, not only to work with it but
also to assess its quality. To analyze economic implications of monetary
regime changes it is necessary that the model follows at least basic
theoretical and/or empiric-economic interdependencies which have been made
explicit within a provenance graph. It allows to easily identify and relate
the various sources (such as theories or earlier simulation studies), separate
mechanisms, submodels, and activities that contributed to generating
Mak(h)ro_0, and it facilitates reuse and (together with the composite model
design supported in ML3) future refinements and extensions. It can be shown
that the model can replicate a wide range of stylized economic facts (Section
5) even with incisive limitations to reduce model complexity (Section 3.2.1).
The replication of stylized facts is necessary to show that the simulated
model macro-/microeconomic dynamics are plausible and capture characteristic
patterns and distributions of empirical data. Hence, in the context of the
defined model requirements, it can be concluded that the ABM Mak(h)ro_0
presents a possible starting point for exploring and analyzing alternative
monetary regimes in comparison with the current monetary system.

##  8 Acknowledgments

We are grateful for helpful suggestions by all colleagues from the Department
of Economics at the University of Rostock and the savings bank of Rostock for
valuable practical insights. Furthermore, we acknowledge the Modeling and
Simulation Group of the Institute of Visual and Analytic Computing at the
University of Rostock for very useful criticisms and suggestions that helped
improve this paper substantially. The contributions by Oliver Reinhardt and
Adelinde Uhrmacher were supported by the German Research Foundation (DFG) via
the research grant Modeling and Simulation of Linked Lives in Demography
(UH–66/15).

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##  Appendix A Appendix

Table 6: Entities and processes shown in Figure 3 Id. |  Description |  Reference
---|---|---
Basel III |  Basel III regulation |  BCBS[39]
Bank bailout |  Model specification of bailout of insolvent banks |  Section 3.5.3
Bankruptcy |  Firm bankruptcy model specification |  Section 3.3.4
Caiani/ Schasfoort |  Credit market components related to Caiani et al. and Schasfoort et al. |  Caiani et al.[42] and Schasfoort et al. [22]
Credit demand |  Model specification of matching protocol between credit demand and supply |  Section 3.5.1
Credit market |  Submodel of credit market |  Section 3.5
Credit supply |  Model specification of credit creation potential |  Section 3.5.2
Delli Gatti |  Theory based on Delli Gatti and co-authors |  Delli Gatti [17]
Dichotomy |  Theory of classical dichotomy |
Dosi |  Bankruptcy model specification in accordance with Dosi et al. |  Dosi et al. [51]
ECB |  Monetary Policy Operation Framework according to the European Central Bank |  ECB [40, 60] and Bindseil [61]
Financial sector |  Submodel of credit cycle and fractional reserve system |  Section 3.5 and 3.6
Fiscal |  Fiscal policy |  Section 3.7
GDP EU |  Relation of investment and consumption in relation to Gross Domestic Product (GDP) |  [48]
Goods demand |  Model specification of demand of homogeneous goods |  Section 3.3.3
Goods market |  Submodel of goods market |  3.3
Goods supply |  Model specification of supply of homogeneous goods |  Section 3.3.1
Gualdi |  Goods market components related to Gualdi et al. |  Gualdi et al.[44]
Interbank |  Model specification of interbank and deposit market |  Section 3.6.1
Investment market |  Submodel of investment market |  Section 3.4
Invest. cycle |  Model specification of investment cycle |  Section 3.4.1
Invest. demand |  Model specification of investment demand |  Section 3.4.2
Krug |  Interbank components related to Krug |  Krug [24]
Labor |  Model specification of hire and fire of labor |  Section 3.3.2
Mak(h)ro ABM |  Final macroeconomic agent-based model. First version: Mak(h)ro_0 |
Minsky/ Keynes |  Investment theory to Keynes |  Minsky [53]
Monetary policy |  Model specification of monetary policy |  Section 3.6.2
Monetary system |  Submodel of fractional reserve system |  Section 3.6
Popoyan |  Bailout model specification in accordance with Popoyan et al. |  Popoyan [25]
Real economy |  Submodel of credit cycle and fractional reserve system |  Section 3.3 and 3.4
Stock-Flow |  Stock Flow Consistency theory |  Lavoie and Zezza [97]
Simon |  Model specification of price setting in line with bounded rationality |  Simon [47]
Taylor |  Theory based on Taylor rule |  Taylor [62]
Table 7: Balance sheet structure of all agent types

  * •

The corresponding agent type subscripts are indicated in parentheses in the
first column.

  * •

Balance sheet items have to be interpreted in aggregated form.

Agent | Assets | Liabilities
---|---|---
Households (h) | Bank depositsa ($Liq_{h}$) | Equity ($E_{h}$)
Firms (i) | Bank deposits ($Liq_{i}$ \+ $Inv_{i}$) | Loan liabilities ($L_{ib}$)
| Inventory ($N_{i}$) | Interest obligations ($I_{ib}^{L}$)
|  | Equity ($E_{i}$)
Banks (b) | Reserves ($R_{bc}$) | Deposits
|  | ($Liq_{h}$; $Liq_{i}$ \+ $E_{i}$ \+ $Inv_{i}$)b
| Interest receivables ($I_{bi}^{L}$) | Wholesale liabilities ($L_{bb}^{l}$)c
| Business loans ($L_{bi}$) | CB liabilities ($L_{bc}$)
| Wholesale loans ($L_{bb}^{r}$)d | Equity ($E_{b}$)
Central Bank (c) | Loan receivables ($L_{cb}$) | Reserves ($R_{cb}$)
|  | Equity ($E_{cb}$)
Government (g) | Liquidity ($Liq_{g}$) | Public debt ($D_{g}$)
|  | Equity ($E_{g}$)

a Bank deposits of households consists of financial wealth originated from
wages or unemployment benefits.
b Retail deposits consists of household liquidity; firm liquidity, equity and
investment amount.
c Interbank loan liabilities ($l$).
d Interbank loan receivables ($r$).

Fig 15: SF1: Deviations of real GDP and real consumption time series from
trend: bandpass-filtered (6,32,12)

Note: The figure depicts deviations of average real GDP (dashed line) and
average real household consumption (solid line) from trend in %. The
simulation output is a representative run and shows an extract to keep the
line profile more identifiable without the warm-up phase of 200 simulation
periods. The grey shaded area represents the 90% confidence interval.