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The Limits to Credit Growth: Mitigation Policies and Macroprudential Regulations to Foster Macrofinancial Stability and Sustainable Debt


In this paper we study an economy with a high degree of financialization in which (non-financial) firms need loans from commercial banks to finance production, service debt, and make long-term investments. Along the business cycle, the economy follows a Minsky base cycle with firms traversing through the various stages of financial fragility, i.e. hedge, speculative and Ponzi finance (cf., Minsky in The financial instability hypothesis: a restatement. Hyman P Minsky archive paper, vol 180, pp 541–552, 1978; Stabilizing an unstable economy. Yale University Press, 2nd edn 2008, McGraw-Hill, New York, 1986; The financial instability hypothesis. Economics working paper archive wp74. The Jerome Levy Economics Institute of Bard College, 1992). In the speculative financial stage cash flows are insufficient to finance the repayment of principle but sufficient for paying interest, so banks are willing to roll-over credits in order to prevent loan defaults. In the Ponzi financial position even interest payments cannot be served, but banks my still be willing to keep firms alive through “extend and pretend” loans, also known as zombie-lending (Caballero et al. in Am Econ Rev 98(5):1943–1977, 2008). This lending behavior may cause credit bubbles with increasing leverage ratios. Empirical evidence suggests that recessions following such leveraging booms are more severe and can be associated to higher economic costs (Jordà et al. in J Money Credit Bank 45(s2):3–28, 2013; Schularick and Taylor in Am Econ Rev 102(2):1029–1061, 2012). We study macroprudential regulations aimed at: (i) the prevention and mitigation of credit bubbles, (ii) ensuring macro-financial stability, and (iii) limiting the ability of banks to create unsustainable debt bubbles. Our results show that limiting the credit growth by using a non-risk-weighted capital ratio has slightly positive effects, while using loan eligibility criteria such as cutting off funding to all financially unsound firms (speculative and Ponzi) has strong positive effects.

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  1. According to data from the World Bank Enterprise Surveys reported in Demirguc-Kunt et al. (2015), the median contribution of SMEs to total employment amounts to 66% in EU countries, 55% in the UK, and 50% in the US.

  2. In addition to the base cycle, Minsky also defined a financial super-cycle, in which the stabilizing institutions of the economy are slowly eroding, including the regulations. Minsky called these the “thwarting institutions”, since they prevent the financial sector from destabilizing the macroeconomy. Here we only consider the base cycle, keeping the institutions constant over time, but we make comparisons across different institutions by varying the scenarios in the policy analysis.

  3. The literature features models linking financial intermediaries and growth in endogenous growth models (Greenwood and Jovanovic 1990; Bencivenga and Smith 1991, 1993; Boyd and Smith 1998) and models of financial fragility and contagion through interbank markets (Bernanke and Gertler 1989; Goodhart et al. 2005).

  4. We use some abbreviations in the overview: JST stands for Jordà et al. (2013), DILT stands for Dell’Ariccia et al. (2014), CKT stands for Claessens et al. (2012), RR stands for Reinhart and Rogoff (2009), CS stands for Cerra and Saxena (2008).

  5. This could be a sign that finance is being used for more non-productive investment, which is defined roughly as expenditures that do not contribute to a potential expansion of the production capacity of the economy. But no empirical data exists to measure how much of total finance is used for non-productive investment, cf. Bank of England (2016).

  6. This could be a sign of debt-led growth.

  7. A possible explanation for the observation that highly leveraged expansions are typically followed by a credit crunch is that banks have to rebuild their balance sheets, so they even restrict credit supply to businesses that have real investment opportunities. Such recoveries with weak credit supply are also known as “creditless recoveries” (Abiad et al. 2011). This credit supply-oriented explanation should be complemented by a credit demand-focussed explanation that households and businesses are also rebuilding their balance sheets and are deleveraging. In this explanation it is weak credit demand, rather than weak credit supply, that explains the slowdown in credit growth after a financial crisis.

  8. These results imply that the impact of the credit-intensity during the boom phase works through the amplitude rather than through the duration of the recession. The average duration of recessions is insensitive to the leverage, while the amplitude is affected by the credit-intensity of the prior boom.

  9. This result indicates that there should be no reason to fear any inflationary pressures from an expansionary monetary policy after a financial crisis episode.

  10. See the FLAME website for downloads.

  11. The classic reference to business cycle dating algorithms is the original Bry-Boschan (BB) algorithm developed by Bry and Boschan (1971), and the quarterly Bry-Boschan (BBQ) algorithm proposed by Harding and Pagan (2002). For this paper, we have implemented our own version of the BBQ algorithm in the software package R. More details can be found in “Appendix A”. The code is included in the source code that is available from our website.

  12. The typical number of replications is 100 runs per parameter setting. The random number seeds are themselves randomly drawn from a uniform distribution, and then stored.

  13. Below we re-use some material that was previously developed in van der Hoog and Dawid (2017).

  14. In other words, the investments in previous periods are spread out across multiple periods as calculatory costs, in order to prevent the expenditures for investments to have a large impact on profits in those months. For convenience, the time over which the calculatory costs are written off is equal to the time over which the loan is paid off.

  15. If there is credit rationing firms do not care about the volume of credit obtained, so the choice of bank is a purely price-driven decision. An alternative modelling choice would be to consider a volume-based decision by the firm. I thank one of the referees for this remark.

  16. Note however that we do not yet have a clear separation between the regulatory capital (equity) and a loan loss reserve on the balance sheet of the bank. Normally, whenever a loan is issued, the bank makes a loan loss provision (a flow) by transferring equity to the loan loss reserve (a stock). This is a liability transformation. Any bad debt is written off from the loan loss reserve and does not affect the equity directly. However, if the write-off is substantial and exceeds the loan loss reserve, then this starts to eat into the bank’s equity nonetheless.

  17. The new term Risk Exposure Amount (REA) is replacing the Risk-Weighted Assets (RWA) as the new terminology in use by the regulatory authorities.

  18. A similar specification for the interest rate rule can be found in Delli Gatti et al. (2011, p. 67). The difference with our specification is that we use the probability of default, while they use the leverage ratio.

  19. An alternative behavioural rule for the bank that we have tested is “partial rationing”: when the credit risk exceeds the risk exposure budget \(V^{b}\), then firm i only receives a proportion of its request, up to the constraint. This rule implies that banks always exhaust their available risk budget and does not result in a viable economy. It leads to more credit rationing rather than less, since firms coming to the bank after a very risky firm has already secured a loan will not be able to receive any loans, because the bank has already exhausted its risk budget.

  20. Note that for the liquidity requirement we use “partial rationing”, while for the capital requirement we used “full rationing” for credit requests that would exceed the binding constraint. This implies the equity constraint always has some slackness, while the liquidity constraint can be strictly binding. The reason is that we assume the Central Bank has a fully accommodating monetary policy such that if the bank has a binding liquidity constraint, the Central Bank will always provide it with new reserves. However, the Central Bank will not provide new equity if the bank would have a strictly binding equity constraint, since we do not assume there is an automatic bail-out or other recapitalization mechanism in place.

  21. In the ex post credit market states the first index \(x=2,3,4\) refers to the Minsky states defined above. There are thus \(12+1\) states in total, including the firms in Minsky state \(M_{1}\) that only use internal funds to finance production. Note that we do not track whether the firm was credit rationed as a result of the bank’s liquidity constraint or the equity constraint.

  22. Appendix B reports on an extensive robustness analysis, confirming the result that scenario D is the most successful policy even when varying the parameter settings.

  23. These losses can be measured in various ways, from output not produced during the downturn, to the additional number of unemployed, or the total sales foregone.

  24. The code for the recession analysis is included in the source code that is available from our website.

  25. The results are robust against using output levels or actual sales.


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This paper has benefited from discussions at the annual meetings of the Society for Computational Economics, CEF 2013 in Vancouver and CEF 2014 in Oslo; the CeNDEF@15 Symposium in Amsterdam, October 2013; the 1st Workshop on Agent-based Macroeconomics in Bordeaux, November 2013; the 1st Joined Bordeaux-Milano Workshop on Agent-based Macroeconomics in Bordeaux, June 2015; the Post-Keynesian Economics Conference in Kansas City, September 2014; the Conference of the Eastern Economics Association in New York City, February 2015; and the participants at a seminar held at the Financial Stability Department of Bank of Canada. I am grateful for helpful suggestions by Herbert Dawid, Domenico Delli Gatti, Sebastian Krug, Andrea Roventini, Frank Riedel, and Tania Treibich, and I am indebted to two anonymous referees for very useful criticisms and suggestions that helped improve this paper substantially. Furthermore, I acknowledge my colleagues Philipp Harting and Simon Gemkow for their substantial contributions to the development and implementation of the Eurace@Unibi model (Gemkow et al. 2014), and for the associated R scripts for data analysis (Gemkow and van der Hoog 2012). We made extensive use of software provided by the R Project (R Development Core Team 2008). The simulations for this paper were performed using the Flexible Large-scale Agent Modelling Environment (FLAME website:, software available from: http://www.github/FLAME-HPC). The FLAME Xparser and Libmboard library are made available under the LGPL v3 (Coakley et al. 2012a). Finally, I thank the Regional Computing Center of the University of Cologne (RRZK) for providing computing time on the DFG-funded High Performance Computing (HPC) system CHEOPS as well as for their user support.

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Correspondence to Sander van der Hoog.

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This research has received funding under Horizon 2020 Grant Agreement No. 649186 - Project ISIGrowth (“Innovation-fuelled, Sustainable, Inclusive Growth”).


Appendix A: Business Cycle Dating Algorithm and Recession Analysis

The algorithm that was used to obtain the results for this paper is based on well-established methods from the empirical literature to study macroeconomic time series data. A classic reference to business cycle dating algorithms is the original BB algorithm developed by Bry and Boschan (1971). A quarterly Bry-Boschan algorithm, known as the BBQ-algorithm, was proposed by Harding and Pagan (2002). We adopt a similar methodology to time series data analysis as in Claessens et al. (2012). The only difference is that we use the synthetic data being generated by our simulation model, while normally such algorithms are used on empirical data.Footnote 24

1.1 Terminology and Definitions

The following definitions are taken from Claessens et al. (2012, pp. 10–12). The definitions can either be based on the time series of the units of output produced, or on actual sales levels. In our time series analysis, we have used the output-based definitions.Footnote 25

Peaks and troughs A peak in a timeseries \(y_t\) occurs at time t if there are 2 periods of increase before, and 2 periods of decrease after t:

$$\begin{aligned} (y_t - y_{t-2}>0 , y_t - y_{t-1}>0) \text { and } (y_{t+2} - y_t<0 , y_{t+1}-y_t<0) \end{aligned}$$

A trough in a timeseries \(y_t\) occurs at time t if there are 2 periods of decrease before, and 2 periods of increase after t:

$$\begin{aligned} (y_t-y_{t-2}<0 , y_t-y_{t-1}<0) \text { and } (y_{t+2}-y_t>0 , y_{t+1}-y_t>0)) \end{aligned}$$

Recession A recession/downturn is the period between a peak a trough.

Expansion An expansion/upturn is the period between a trough and a peak.

Recovery A recovery is the early part of the expansion phase, defined as the time it takes for output to rebound from the trough to the peak level before the recession.

Duration of recessions The duration of a recession/downturn is the number of quarters, k, between a peak (\(y_0\)) and the next trough (\(y_k\)) of a variable.

Duration of recoveries The duration of a recovery/upturn is the number of quarters (r) it takes for a variable to reach its previous peak level after the trough: \(\{r>k: y_r \ge y_0\}\).

Amplitude for recessions The amplitude of a recession/downturn \(A_c\), measures the change in \(y_t\) from a peak (\(y_0\)) to the next trough (\(y_k\)): \(A_c = y_k - y_0\)

Amplitude for recoveries The amplitude of a recovery/upturn, \(A_u\), measures the change in \(y_t\) from a trough to the level reached in the first four quarters of an expansion (\(y_{k+4}\)): \(A_u = y_{k+4} - y_k\).

Slope for recessions The slope of a recession/downturn is the ratio of the amplitude to the duration of the recession/downturn: \(S_c = A_c/D_c\).

Slope for recoveries The slope of a recovery/upturn is the ratio of the change of a variable from the trough to the quarter at which it attains its last peak divided by the duration: \(S_r = (y_r - y_0)/D_u\). The slope is an approximation of the average economic growth rate over the duration of the recovery.

Cumulative loss for recessions The cumulative loss for a recession with duration k combines the duration and amplitude as a measure for the overall costs of recession: \(F^c = \sum _{j=1}^k (y_j - y_0) - A^c/2\), where \(y_0\) is the level of output at the start of the recession, and \(y_j\) are the successive terms during the recession.

1.2 Detecting Peaks and Troughs

Figure 7 shows the detection of peaks and troughs in the time series of output for the business cycle (panel a) and for the time series of total debt for the financial cycle (panel c). Figure 7b shows expansions and recessions from peak to trough for the business cycle. This plot does not coincide exactly with the peaks and troughs detected in Fig. 7a due to the fact that sometimes two peaks can follow each other without having a trough in the middle. This is because the trough does not necessarily signal a recession, since it might be too short. In such cases the event is censored, i.e. removed from the plot. Figure 7c, d provides the same type of analysis for the credit cycle. Here the solid lines coincide with peaks in the credit cycle, i.e. with the start of a downturn. Dotted lines indicate troughs in the credit cycle, i.e. the start of an upturn or recovery.

Fig. 7
figure 7

Peaks and troughs for the business cycle and the financial cycle, for 500 months (167 quarters). Solid lines peaks, or start of a recession; dotted lines: troughs, or start of an expansion. a, c Detection of peaks and troughs. b, d Recessions and expansions (for the business cycle), and upturns and downturns (for the financial cycle)

Fig. 8
figure 8

Boxplots of a recession amplitudes and b cumulative economic losses. Parameter settings: \((\alpha ,\beta )=\{1,8\}\times \{0,0.1,1\}\). The scenarios A till G for the default setting \((\alpha =8\), \(\beta =0.1)\) correspond to sets 29–35. Scenario I for \((\alpha =1\), \(\beta =0)\) corresponds to set 1 and scenario H for \((\alpha =1\), \(\beta =1)\) corresponds to set 15. Downturns less than 500 units are censored

Appendix B: Robustness Analysis

In this section we provide a robustness analysis of the results presented in the main text. As parameter settings we consider all combinations for \(\alpha =(0,8.0)\) and \(\beta =(0,0.1,1)\), yielding 6 cases. Combining this with the scenarios A through G (7 scenarios), this yields 42 scenarios in total.

Table 3 Summary statistics for recession data across 100 simulation runs
Table 4 Summary statistics for recession amplitudes in 42 scenarios
Table 5 Summary statistics for recession cumulative losses in 42 scenarios

As statistics for the analysis we consider the amplitude and cumulative loss as metrics for recession severity. Figure 8 shows boxplots for the recession amplitudes and cumulative losses for each of the 42 scenarios. In Table 3 we report the extreme value of the lower whisker of the distribution of each metric. For the recession duration we report the median values. All distributions are based on 100 simulation runs and the full ensemble of recessions observed during the runs is considered. The minimal required recession duration is set to two quarters, and the minimal required amplitude is set to 500 units. Recessions with downturns smaller than 500 units are censored from the distribution.

The scenarios A to G from the main text correspond to group 5 (rows \(29-35\)). Scenario I \((\alpha =1\), \(\beta =0)\) corresponds to row 1 in group 1, and scenario H \((\alpha =1\), \(\beta =1)\) corresponds to row 1 in group 3. Table 4 shows descriptive statistics for the recession amplitudes, while Table 5 shows the descriptive statistics for cumulative losses. In each table the overall best policy within each group is indicated with a star (\(\star \)), while a dagger (\(\dagger \)) indicates the best single policy (from A, B, C, D, E). The ranking criterion for Table 3 is the smallest absolute value of the lower whisker, for Table 4 it is the smallest absolute value of the minimum amplitude, and for Table 5 it is the smallest absolute value of the cumulative loss.

Three main conclusions can be drawn from this robustness analysis. First, Table 3 shows that the ranking is rather robust between groups. The ranking we obtain for the default parameter setting (group 5) is maintained for three other parameter settings, including scenario I (groups 1, 2 and 4). For these cases, the overall best scenario is F (a mixed scenario), followed by the best single policy D (cutting off funding to all financially unhealthy firms). Second, for the remaining two parameter settings (group 3 and 6) the overall best scenario is the single policy C (using non-risk weighted capital ratios). The latter two groups have in common that they feature the full reserve requirement (\(\beta =1\)). Third, if we consider the cumulative loss as the ranking criterion, the overall best scenario for most parameter settings is again policy D (cutting off funding to all financially unhealthy firms). The only groups for which this is not the case are groups 3 and 6, for which A is the overall best policy (no intervention).

Therefore, the main conclusion to draw from this extensive robustness analysis is that cutting off the funding to financially unhealthy firms and using a non-risk-weighted capital ratio are the two most promising candidates for reducing the amplitude and cumulative losses due to recessions.

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van der Hoog, S. The Limits to Credit Growth: Mitigation Policies and Macroprudential Regulations to Foster Macrofinancial Stability and Sustainable Debt. Comput Econ 52, 873–920 (2018).

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  • Macroprudential regulation
  • Full reserve banking
  • Full equity finance
  • Agent-based macroeconomics

JEL Classification

  • C63
  • E03
  • G01
  • G28