INTRODUCTION

The conventional framework of risk-taking channel of monetary policy (RTCMP) addresses the transmission mechanisms by which monetary policy may act on increasing the risk levels of financial institutions. To address risk-taking behavior, the empirical literature uses variables that represent the evolution of the risks of financial firms, and from this, it relates to the monetary policy variable. Through the relationship found, if the downward variations of the second “cause” statistically the first to vary upward, it is that the existence of a causality called “risk-taking” is established.

Nonetheless, as pointed out by the fallacy of composition, the evolution of risks of financial institutions is not enough to address financial stability (^{Baker, 2014}; ^{Kabundi & De Simone, 2020}; ^{Kemp, 2017}; ^{Osiński et al., 2013}). The fallacy of composition arises because systemic risk has many characteristics that cause it to behave differently to the individual financial risks, the relation between two phenomena is non-linear, self-reinforcing and adaptative to the environment. These characteristics, in turn, indicate that systemic risk is a complex system.

Does this complexity, especially nonlinearity, condition how monetary policy affects systemic risk- taking? My hypothesis is that it does, the sign of impact of monetary on systemic risk can change through the time. The leverage mechanism developed by ^{Adrian and Shin (2010)} suggests that positive asset price shocks induce an increase in financial sector leverage, which in turn, generates market-wide risk pressures. Notwithstanding, what happens with negative shocks? This mechanism indicates that in this situation there is a decrease in the leverage of the system through a systematic sale of assets, which, as ^{Danielsson et al. (2014)} indicate, in times of crisis, increases systemic risk. The important thing to recognize in the mechanics of financial sector leverage is that shocks can come from changes in the stance of monetary policy.

Although more recently much empirical research has addressed the systemic risk-taking channel of monetary policy (S-RTCMP), this approach does not have considered the complexity of systemic risk. In this paper, my objective is to provide evidence about the S-RTCMP following this consideration. For this purpose, I use the TVP-VAR model with structural factor augmented (SFA-TVP-VAR), which allows me to capture the complex relationship between monetary policy and systemic risk-taking. Additionally, this model has the advantages of addressing many problems in the estimation of this monetary channel: 1) the endogeneity presented between monetary policy and systemic risk, 2) the complex behavior of systemic risk when a shock has impacted it; 3) the difficulty of measuring systemic risk.

The SFA-TVP-VAR model considers the system variables as latent and maintains monetary policy as an observable variable. For this reason, in this paper I do not try to consider one specific pressure of systemic risk and its relation with monetary policy, instead I employ financial stress and conditions indexes and I assume a latent variable called “systemic risk” drives the behavior of these metrics. Through the impulse response functions of this latent variable to shocks in monetary policy stance, I infer the systemic risk-taking channel of monetary policy.

In order to give robust evidence, I estimate the model with two different variables of monetary policy stance, the Taylor rule residual and the Wu-Xia Shadow Federal Funds Rate, changing in both cases the parameters and the priors of the model.

Considering the state of the art discussed in Section I and II of this paper, the novel contribution of this paper is to provide evidence of the existence of complexity, specifically, nonlinearity in the S-TRCMP. The posterior estimation of the model gives evidence that in longer periods the S-RTCMP behaves as usually is postulated by the current literature: in longer periods, expansive monetary policy increases systemic risk- taking. Nevertheless, in short term, before and during a financial crisis, the relationship is complex: a restrictive shock of one standard deviation in the monetary policy stance, instead of decreasing the systemic-risk taking, increases it. This evidence is consistent with what I have termed the leverage mechanism.

The outline of this paper is the following. In the first section, I lay out the micro risk-taking channel of monetary policy (M-RTCMP) framework, where I answer the question about how monetary policy shapes the risks of financial institutions from an individual perspective. Then, in section II, I explain the nature of systemic risk, and from this, why the M-RTCMP and the conventional framework of S-RTCMP are limited for addressing the impact of monetary policy on systemic risk-taking. The conclusion of this section is that it is necessary to evaluate the S-RTCMP from a perspective of complex system. In section III, I present the econometric methodology for evaluating this channel from this sight, furthermore, I show the variables of the model, the case study, and the data. In section IV, I present and explain the empirical results. Finally, the conclusions are presented.

I. THE MICRO RISK-TAKING CHANNEL OF MONETARY POLICY

Monetary policy has the capacity to change asset prices, such as the present values of loans and the prices of securities. In the first case, the rationale for this impact derives from the basic present value formula: monetary policy through the different channels established by macroeconomic theory, can influence the interest rate on loans of different maturities, therefore when a loose monetary policy condition prevails, the interest rate falls, moving up the price of loans. The prevalence of this condition for longer periods, as some economists point out (see for example ^{Taylor (2011)}), could promote the growth of bubbles in credit markets, such as real estate. Although the full responsibility of monetary policy of promoting the overall increase in housing and other loan prices is controversial in academic and political circles, we cannot ignore the impact that low rates have on loan prices. In the second case, as established by overreaction framework, Tobin’s q theory, as well as the wealth effect, downward movements in policy rates lead to increases in stock prices (^{Alves & Carvalho, 2020}; ^{Bernanke & Kuttner, 2005}; ^{Mishkin, 2014}).

Based on this rationale, the RTCMP framework has exposes many mechanisms by which monetary policy manages to affect the risk-taking behavior of financial institutions. One of the reasons why there is more than one mechanism is that each of them assesses the reaction of different types of financial risks.

A first mechanism has to do with the paper of ^{Borio and Zhu (2012)}. The idea is clear: a fall in interest rates triggers a process that increases asset prices, collateral values and profits, which in turn creates a condition in which financial intermediaries reduce their risk perception due to lower risk levels of risk metrics and increased wealth. As these authors point out, the change in risk perception then is manifested in a strategy of increased risk-taking.

A second mechanism has to do with the one postulated by ^{Rajan (2005)}, he emphasizes several ways in which monetary policy could affect risk-taking, nevertheless, the general idea is the same: because of rigidity of rate of returns of asset managers, the low interest rates promoted by the central bank provoke a “search- for-yields” strategy to compensate for the situation. This behavior would then cause these agents to begin to have a greater risk appetite and, therefore, begin to grant riskier loans or invest in more volatile assets with the expectation of obtaining precisely the rates of return commensurate with the target. Although there is no explicit profitability target of banks, this asset substitution mechanism establishes that lower interest rates conditions promote a search-for-yield behavior when risk-neutral and generally risk-averse banks reduce the weight of safe assets in the portfolio composition and increase the weight of riskier assets (^{De Nicolò et al., 2010}).

These mechanisms account for how monetary policy affects the individual or micro risks-taking. Following to ^{Kabundi & De Simone (2020)}, I denominate this as the micro risk-taking channel of monetary policy (M-RTCMP). Based on these mechanisms, many researchers have produced empirical studies focusing on specific cases of national economies or covering regions as in the cases of European studies. A list of notable empirical studies, but incomplete, is presented in Table 1.

These studies, albeit with some nuances, provide empirical evidence of the negative relationship between monetary policy and the micro risk-taking.

This theoretical body and its empirical support claim a clear impact of monetary policy on risk-taking, nonetheless, other economists have argued that this relation is in fact convoluted in some cases.

^{Dell’Ariccia et al. (2014)} in their model of financial intermediation, in which main risk-taking mechanism of banks is the reduction in their efforts to monitor lenders, argue that the impact could in fact be ambiguous. When interest rate fall, there are three effects that condition the banks’ balance sheet behavior. The first has to do with the “interest pass-through effect”, which refers to the weak incentives to monitor lenders after a fall in gross returns caused by the lowering of the reference rate. The second has to do with the tendency of banks with higher levels of leverage to make less risky investments as the value of their liabilities falls, and to maximize their profits they will tend to spend more on monitoring their lenders, an effect the authors call “risk shifting”. Both effects occur in cases where there is a fixed capital structure, and it is worth noting the sign of the impact of monetary policy on risk-taking is ambiguous. However, in the case of an adjustable capital structure the sign of impact is already clear, since, in addition to the two previous effects, we must add the “leverage effect”, which refers to the tendency of banks to be leveraged without needing to hold capital when interest rates fall.

Source: own elaboration.

At the empirical level, many studies have found that, in fact, the sign of impact of monetary policy on risk-taking is positive. For example, ^{Ngambou Djatche (2019)} finds that large deviations of monetary policy from the Taylor rule can trigger an increase in the risks of banks; nonetheless, when the deviation is sufficiently low, the effect is the opposite. Similarly, ^{Dang and Dang (2020)} conclude that decreases in interest rates promote bank stability. In addition, ^{Sarkar and Sensarma (2019)} provide evidence that expansionary monetary policy decreases liquidity and market risks. This risk-taking behavior in the face of lower interest rates is in fact consistent with the effect of monetary policy on bubbles, as I explain in the following section.

Another mechanism that has indirectly pointed out the ambiguity of the relationship between monetary policy and risk-taking has to do with the leverage effect in the spirit of ^{Adrian and Shin (2010)}. Unlike the previous mechanisms, this effect can account for the direct relationship between systemic risk and monetary policy. Also, I will elaborate this one in the next section.

II. SYSTEMIC RISK-TAKING AND MONETARY POLICY

Systemic and individual risks: some principles

There is no consensus about what systemic risk is, indeed, its identification and measurement subsequently face several challenges (^{Lars Peter, 2015}). One definition that could compressively capture systemic risk is that of the ^{European Parliament and of the Council of European Union (2010)}, as the risk of disruption of the financial system, with potential consequences for financial markets and the real economy (see ^{Kemp, 2017} for discussion on the definition of systemic risk, and in particular of this one).

The individual risks differ from systemic risk in different ways. The former refers to the risks faced by individual entities in isolation, while the latter refers to the risk borne by the financial system.¹ Nonetheless, this distinction does not tell us much; rather, the dynamics of both types of risk over time may account for why the two are not the same.

Increasing the risks of an institution, some of them or an entire sector can translate into an increase in systemic risk due to the interrelationships among all market participants, the failure of one firm can quickly spread to several institutions, and the larger the relative size of the distressed entity, the greater the repercussion may be at the systemic level (X. ^{Huang et al., 2012}; ^{Kemp, 2017}; ^{Omarova, 2019}). The channels of contagion, that is, the paths by which individual risks can spread through the financial system are contractual, informational, and psychological networks (^{Borio, 2003}).

However, the same cannot be said when the risk of some institutions or of an entire industry decrease. For example, an investment bank may find that its market risk exposure is considerably high, so it may decide to sell its risky securities to meet the target of economic capital. When this occurs, this bank is effectively managing its market risk, nevertheless, systemic risk is increasing because by selling its assets, it is bidding down prices, which causes other institutions (which, may be healthy or not) to start with liquidations, this deleveraging process induces an increase in systemic risk (^{Mishkin, 2014}).² To what extent this process triggers a systemic event depends, firstly, on whether systemically important banks enter a distressed phase; and secondly, on whether the different systemic “pressures” are in an incubation or burst period, while in the first scenario market participants can absorb it quickly and the effect can evaporate quickly as well, in times of crisis market participants amplify the effects (^{Adrian & Shin, 2010}; ^{Danielsson et al., 2014}), and will stop until the confidence is restored, this process is illustrated in Figure 1.

Source: own elaboration.

Figure 1 Leverage and systemic risk 

Additionally, from a cross-sectional point of view, the two types of risks differ from each other. As ^{Beale et al. (2011)} point out, following the principle of investment diversification, the individual risks faced by financial firms may decrease, however, if many institutions follow the same diversification pattern, systemic risk increases.

This shows that systemic risk and individual risks do not necessarily share the same dynamics in time and space, the former is not the simple sum of the latter.³ The relation between the two evolves over time and is nonlinear (^{Renn et al., 2020}). This feature will be important for explaining the empirical results of this paper.

A second characteristic of the relation between individual risks and systemic risk has to do with the direction of the causal relationship. As I indicated above, a singular event can trigger a systemic event depending on the state of systemic pressures, but this does not happen overnight, but occurs through a feedback process that amplifies the singular event (^{Danielsson et al., 2014}). This shows that the causal line not only runs from individual risk to systemic risk, but also in the opposite direction. For this reason, it is not surprising that a differentiator among all systemic risk metrics is the casual line.⁴

All these properties derive from the network structure of the subunits, i.e., from the individual risks that make up the system. These characteristics explain the domino effect that leads to increases in systemic risk. Nonetheless, the accumulation of systemic risk is not only endogenous in nature, but is also caused by exogenous factors. The financial system faces common risks that have the capacity to damage all financial institutions at the same time, or at least a large part of them, and these exposures can be external pressures, changes in interest rate, economic activity, and so on. The shocks from these macroeconomic risks factors to systemic risk have been referred in the literature as the “tsunami effect” leading to systemic financial distress (^{Borio, 2003}; ^{Kemp, 2017}).

Roughly speaking, systemic risk as the system with the risks of financial institutions as fundamental subunits, is characterized as an emergent phenomenon since the interaction of the different subunits results in a system that goes beyond the sum of each component. Moreover, the relation between the system and the subunits is characterized by being nonlinear and self-reinforcing, where the subunits are interdependent and, as I will elaborate later, the system is able to respond (although not in the most rational way) to the environment. All these qualities allow us to see that systemic risk is a complex system.

III. THE ASSESSMENT

Based on the literature review and the elements that characterize systemic risk, I identify at least three challenges for assessing the S-RTCMP: 1) the endogeneity between systemic risk and monetary policy;

2) the self-reinforcing and nonlinearity of systemic risk once a shock has occurred, and their possible implications for the S-RTCMP; 3) the complexity in measuring systemic risk.

For this reason, a model that attempts to capture the S-RTCMP should consider these points. In this section, first, I show the model that have the ability to address these issues; second, I present the variables in the system of equations that I use to infer the S-RTCMP; finally, I present the data and their transformations prior to estimation.

Variables, ordering, prior and data

Monetary policy

I take the U.S. case to study the S-RTCMP, and the reference period I use as sample runs from January 1994 to February 2023. During this period, the main instrument for conducting monetary policy has been the federal funds rate. Nonetheless, this variable may be endogenous to macroeconomic variables, which biases the empirical results in approximating the impact of monetary policy on risk-taking behavior (^{Delis et al., 2017}; ^{Segev, 2020}). Although in the VAR model endogeneity can be easily addressed, for more robust results I will use, as in other empirical research, many indicators that can reflect the “monetary stance”.

In order to find robust results, I estimate the SFA-TVP-VAR model with two different metrics of monetary policy stance. The first variable I use is the Taylor rule residual. Assuming the identification of ^{Taylor (1993)}, the Taylor rule is defined as

itTaylor=rt+πt+aπt-πtO+bYt-Ytp (12)

where the itTayloris the interest rate of the Taylor rule, rtis the natural real interest rate, πtis the inflation, πtOis the target inflation rate, Yt-Ytpis the output gap. Then, the monetary policy stance is defined as the residual of the effective federal funds rate and the Taylor rule rate, where positive differences indicate a restrictive monetary stance and negative differences indicate the opposite. As in ^{Segev (2020)}, I assume that rt=2%, πtO=2%, a=0.5and b=0.5.

Finally, as monetary stance variable I employ the Shadow Rate of ^{Wu and Xia (2016)}, which has the advantage of measuring the central bank rate beyond the lower bound and considering the other tools used by the Fed to affect the economy. One way to interpret this indicator is that when it is negative it indicates a loose monetary policy, and when it is positive and high, indicates a restrictive stance.

In the remainder of this paper, when I mention the variable "monetary policy stance", I am referring to both variables, the Taylor Rule Residual and Wu-Xia Shadow Federal Funds Rate. In Figure 2, I show the variables of monetary stance and the effective federal funds rate.

Sources: FRED, Federal Reserve Bank of Atlanta, author’s calculations.

Figure 2 Effective Federal Funds Rate and Monetary Policy Stance Metrics 

Systemic risk

Systemic risk is a “latent” variable; however, it can be inferred by monitoring the different systemic pressures that reflect the condition of the agents, markets, or functions that comprise the financial system. In this paper I will infer the state of systemic risk based on the financial market conditions. As I discussed earlier, one of main measures used today by central banks to monitor financial stability are the financial market conditions and stress indexes, which are calculated from publicly available data.

As discussed in the previous section, systemic risk is measured by pressures in the system. In financial markets, these pressures manifest in the form of a generalized widening of the gap between returns on risky assets and risk-free assets in the credit, funding and real estate markets; deviations of financial sector equity returns from the equity market; equity market crashes; divergence of covered interest rate parity in the foreign exchange market, indicating disruptions in international funding markets; reduced liquidity in the interbank funding market; changes in the yield curve spread; and the coordinated movement of all these indicators.

The idea behind the stress indexes is that systemic risk materializes in a change of state or equilibrium, from a positive to a crisis state (^{Hendricks et al., 2007}; ^{Kliesen & Smith, 2010}; ^{Oet et al., 2015}), which is reflected in specific levels of the key variables mentioned previously (^{Hakkio & Keeton, 2009}).

Furthermore, related to the stress indexes, there is the approach that seeks to assess the state of the financial system by monitoring the evolution and interconnectedness of financial variables regarding their long-term trend or how they evolve with respect to crisis conditions, this is the approach of financial conditions indexes.

Both types of indexes differ in their objectives, the financial stress indexes seek to assess the state of risk of the financial system, while the financial condition indexes seek to report on whether the state of financial markets is in a crisis or normalcy episode.

In this paper, I assume that financial conditions and financial markets stress are driven by an underlying variable called “systemic risk”. For this purpose, I use the Kansas City Financial Stress Index, St. Louis Fed Financial Stress Index, and Chicago Fed Adjusted National Financial Conditions Index. I show these indexes in Figure 3.

Source: FRED.

Figure 3 Systemic Risk Metrics 

Other Variables

As I discussed in Section II, systemic risk can be generated internally through existing networks between subunits (^{Borio, 2003}; ^{Danielsson et al., 2014}; ^{Kemp, 2017}). Empirically, this source has been approached from the network science, with methods such as cascades, graph and percolation models, which requires explicit consideration of the microstructure of the financial system (^{Abergel et al., 2013}; ^{Baruník & Křehlík, 2018}; ^{Hurd, 2016}). Integrating these models with the macroeconometric model used in this paper involves studying how a shock propagates through time and among the elements that compose the financial system. Such an amalgamation is beyond the scope of this paper. Nevertheless, this disadvantage can be remedied since the SFA-TVP-VAR model considers lags of the systemic risk variable, this feature may be trivial in normal times, however in crisis episodes, the feedback loop between systemic risk is a manifestation of the interconnectedness factor.

Additionally, it is important to consider that systemic risk has causes from outside the financial system. The impact of these sources has been referred to in the literature as the “tsunami effect” (^{Kemp, 2017}), and the empirical evidence of the M-RTCMP (see Table 1) has pointed out that these factors should be considered in the estimation process. To consider the “tsunami effect” in the estimation of the S-RTCMP, I add to the system of equations the factors of real economy, inflation, external pressures and government debt, which in turn, are estimated through an extensive list of series.

Ordering, parameters and priors

In the empirical analysis with Structural VAR models, it is usual to assume an ordering of the system of variables. For the model with monetary policy stance as Taylor rule residual, I assume the following ordering of the factors: 1) labor market factor; 2) real economy factor; 3) inflation factor; 4) external pressures factor;

5) monetary policy stance; 6) government debt factor; 7) systemic risk factor. Additionally, I assume the following parameters: rα=3, rlog⁡σ=3, p=6, c1=1, c0=0.003.

For the prior, in this first model I use the SSVS specification as in ^{Chan et al. (2020)}, but without the Minnesota prior,

θ0|δ~N(0,cδθV_θ) (13)

δ~0.5δ1-0.51-δ (14)

fα,0~N0,Irα (15)

fσ,0~N0,Irlog⁡σ (16)

vecAα~N0,1103IB+k+1rα (17)

vecAσ~N0,1103IB+k+1rlog⁡σ (18)

where θ0=α0',log⁡σ0'', k=B+1p+1+B2

In the second model, where the monetary policy stance is the Wu-Xia Shadow Rate, I use a more limited system of equations. I employ the following system in this order: 1) real economy factor; 2) inflation factor; 3) monetary policy stance; 4) systemic risk factor. And I set the following parameters: rα=2, rlog⁡σ=1, p=1.

In this second model, I employ the Minnesota prior with the following parameters:

θ0~N(0,VMIN)V_MIN=1, forlog⁡σ0, μ0 and b0152n, for π014nl3 , for γl,0 for l=1,…,p (19)

For the estimation of both models, I follow the two-step process in the spirit of ^{Korobilis (2013)}, I first approximate the factors through the PC method, then, I estimate the parameters of the VAR equation through the methodology of ^{Chan et al. (2020)}, changing the VAR to a VEC form and restructuring it. Since the parameters λt=λand Qϵ,t=Qϵ, the MCMC algorithm is the same specified in ^{Chan et al. (2020)} when log⁡σtand αtare independent of each other. Finally, I estimate both models with 30,000 MCMC simulations, and I discard the 10,000 initial draws.⁵

Data

The series that I use to model the factors and monetary policy are listed in Appendix A. All the data I employ are from FRED, except for the Wu-Xia Rate, which is from the webpage of Federal Reserve Bank of Atlanta. All labor market, real economy, inflation, external pressures and public debt series are on a monthly basis. Regarding the Taylor rule series, the only variable that does not have a monthly basis is the output gap, and in order to estimate the missing values, I employ the cubic spline method. The St. Louis Fed Financial Stress Index and the Chicago Fed Adjusted National Financial Conditions Index series are in a weekly frequency, to transform them to a monthly basis I take the simple monthly average. The Kansas City Financial Stress index is monthly.

I transform some of these series to induce stationarity. The details of the transformation of each series can be seen in the index of the last column of the table in Appendix A.

IV. RESULTS

The systemic risk factor and the different metrics described in Section 4 are presented in Figure 4. To identify the S-RTCMP, I rely on the dynamic impulse-response functions obtained from the SFA-TVP-VAR model. Since all system variables were standardized prior to estimation, the results of these functions indicate a one positive standard deviation shock and a response in standard deviation points.⁶ The impulse-response functions of monetary policy stance variables to systemic risk for 25 horizons are presented in Figure 5; in more detail, I present these functions at different horizons, in Figure 6 I show the response at t=0, and in Figure 7 the response at t=6,12,24. According to NBER’s Business Cycle Dating, three crisis episodes occurred during analysis period, and I refer to these events in Figures 6 and 7 as shadow areas: 1) from March to November 2001, preceded by a financial bubble and exacerbated by the 9/11 events; 2) from December 2007 to June 2009, due to the GR; 3) from February 2020 to April 2020, triggered by the COVID-19 pandemic. This privileged sample can shed light on how systemic risk-taking of monetary policy behaves in a scenario of a bubble created by irrational exuberance, a bubble created by credit growth and a crisis with an origin external to the financial system.

Sources: author’s calculation based on FRED and Federal Reserve Ban of Atlanta data.

Figure 4 Factors 

Source: author’s calculation based on FRED and Federal Reserve Bank of Atlanta data.

Figure 5 Impulse response functions of systemic risk factor to monetary policy shocks 

Source: author’s calculation based on FRED and Federal Reserve Bank of Atlanta data.

Figure 6 Immediate response of systemic risk factor to monetary policy shock 

The results of the two models presented in Figure 7 show that in longer periods the impact of monetary policy is negative, which is in line with the current S-RTCMP framework (^{Bubeck et al., 2020}; ^{Colletaz et al., 2018}; ^{Faia & Karau, 2021}; ^{Jin & Nadal De Simone, 2020}; ^{Kabundi & De Simone, 2020}; ^{Kapinos, 2021}), i.e., low interest rates promote risk-taking behavior of an entire system. Nonetheless, in short-term periods we see that the impact is different, in fact, it is positive in some periods.

Source: author’s calculation based on FRED and Federal Reserve Bank of Atlanta data.

Figure 7 Response of systemic risk to monetary policy shock at different horizons 

First, in the period preceding the 2001 crisis, characterized by the development of the dot-com bubble, the Figure 6, mainly in the graph with the monetary policy stance as Wu-Xia rate, shows peaks indicating that a positive standard deviation of the monetary policy stance from the its mean, i.e., a tightening of interest rates, has a positive impact on the systemic-risk taking.

Something similar happens with the period prior to the 2008 financial crisis, in the two graphs in Figure 6, prior to the recession we see how the sign of the impact of one standard deviation of the monetary policy stance from its average, i.e., a restrictive stance on interest rates, to the systemic risk-taking changes from negative to positive, with peaks even before the crisis begins.

However, the systemic risk-taking channel of monetary policy does not behave in the same way in a crisis whose origins are outside the financial system as in a crisis whose factors are inside the system. In the period before the COVID-19 pandemic, the two pictures in Figure 6 do not indicate any peak; simply, when the recession begins, the positive impact of a tight monetary policy on systemic risk-taking starts to be very pronounced, and then drops abruptly.

The positive relationship between a restrictive monetary policy and systemic risk-taking in periods before and during a crisis whose origin is inside the financial system is consistent with the leverage mechanism summarized in Equation 1. This evidence has important implications for monetary policy, assuming that a central bank could identify an increase in systemic risk, how should respond to these episodes? The evidence presented previously indicates that if the central bank tightens interest rate levels to decrease the identified systemic risk, the result may be counter-prudent, since instead of decreasing this risk, it would be causing it to increase further.

Indeed, this relationship in periods of crises adds an additional cost to the lean position in the “lean versus clean” debate. Although the cost of cleaning up a financial crisis after it has occurred could be high in terms of damage to the real economy (^{Mishkin, 2011}, ²⁰¹⁴), especially if this crisis has its origin in credit bubbles, adopting a “lean against the wind” policy could also be detrimental, because it further amplifies systemic risk that ultimately harms the real economy.

Finally, it is worth noting that although the TVP-SFA-VAR model used in this paper cannot directly elucidate the feedback process between systemic risk and its subunits, we can indirectly infer this complex relationship through the impulse-response functions of systemic risk to self-induced shocks.

V. CONCLUSION

The nature of systemic risk is characterized by several elements, such as the interdependence of the subunits that comprise it, the non-linearity between the latter with the behavior of the whole, the self-reinforcement between the whole and the subunits and the response to the environment in which the system operates. The M-RTCMP framework analyzes the behavior of the subunits in a monetary policy environment with a loose stance and although it is very important to analyze this relationship, this view is limited when studying the risk behavior of the financial system as a whole, since it does not consider the features that characterize the latter.

Considering systemic risk as a complex system has important implications for the way we think about the relationship between monetary policy and financial instability, from this angle we can observe the impact of interest rates on systemic risk-taking.

My objective in this paper has been to provide evidence of a systemic risk-taking channel of monetary policy considering the complex nature of systemic risk with the hypothesis that this relationship is complex, specifically, nonlinear. Using the SFA-TVP-VAR model, which helps us to infer the relationship between latent variables, the results provide evidence in favor of the hypothesis: it exists a complexity in the way that S-RTCMP operates, the relationship between systemic risk-taking and monetary policy is nonlinear over time and adapts to the economic environment, while in normal times we can observe that restrictive shocks in the monetary policy stance led to a decrease in the systemic risk-taking, in uncertain periods, they imply greater risk-taking by the financial system.

This evidence is consistent with the mechanism of leverage: a positive shock, which may have its origin in an expansionary monetary policy, decreases the level of risk measured by the risk metrics of financial institutions. Specifically, if we consider the overall VaR of financial firms, we see that it decreases, which in turn reduces the economic capital held by institutions. Through the inverse relationship between capital and leverage, a decrease on the capital side implies an increase on the leverage side. This leverage cycle has the potential to create a bubble if the lower interest rate stance is maintained for extended periods, which in turn, can create further systemic risk pressures. In this environment or in a crisis period, however, a sharp increase in interest rates does not necessarily means a reduction in systemic risk levels, as a deleveraging cycle promotes greater instability in financial markets, which tends to increase the risk of a disruption of the financial system.

Derived from these results, we can see that the policy of “lean against the wind” has an additional cost: an increase in systemic risk. Additionally, it is important to highlight that there are still more questions to be addressed from these results, such as their implications for the relationship between macroprudential policy and monetary policy, the design of better instruments for the prevention of systemic crises, and even the way of doing macroeconomics, since the financial system has proven to be one of the triggers of economic fluctuations.