Appendix 1: Proof of Proposition 2
PROOF: Rewrite the FOC (3) as
It follows that22
Then by implicit function theorem, we have:
Since pB > pG, we have
Appendix 2: Proof of Proposition 3
PROOF: Rewrite the planner’s FOC (6) as
It follows that
By implicit function theorem, we have
for the constrained planner’s equilibrium.
The proof of Proposition 2 indicates that θπ(πt, αt) < 0 and θα(πt, αt) > 0, provided
Appendix 3: Proof of Lemma 1
PROOF: Take the total derivative of the IV equation with respect to π:
So the slope of IV equals
Notice that —θπ = pB(α) – pG(α) > 0 and
Similarly, the slope of IE equals
Then we have
if and only if
which is the SCC. Q.E.D.
Appendix 4: Proof of Proposition 6
PROOF: Since 0 < (1 – τS)θP < 1, 0 < (1 – τR)θP < 1, μS > 0, and μR > 0, we have D* < 1.
Now suppose D* ≤ 0, that is, μS[1 – (1 – τS)θP] ≥ μR[1 – (1 – τR)θP]. Using μR – μS = Δ0 and τRμR – τSμS = Δ1, this implies:
However, the planner’s FOC (5) implies that
where the last inequality used
inequality (16). Therefore, we have D* > 0 for any πt. Q.E.D.
Appendix 5: Proof of Proposition 7
PROOF: The analytical solution of D*, equation (11), implies that
Since μSμR > 0, we have
Assumption Δ1 < 0 implies that
Recall that θt ≡ πtpG(αt) + (1 – πt)pB(αt), we have
The first term of equation (17), θπ(αt, πt) = pG(αP) – pB(αP), is negative and captures the direct effect of π on θP: as investors and the constrained planner become more optimistic that the financial industry is strong (in which case the crisis would be less likely to occur), the unconditional crisis probability θP perceived by them tends to be lower. The second term
Rearrange equation (17) and we get:
Since θα(αt, πt) > 0, we have
Acemoglu, D., Ozdaglar, A., Tahbaz-Salehi, A., 2013. Systemic Risk and Stability in Financial Networks. Technical report, National Bureau of Economic Research.
Acharya, V. V., 2009. A Theory of Systemic Risk and Design of Prudential Bank Regulation. Journal of Financial Stability, 5, 224–255.
Acharya, V., Pedersen, L., Philippon, T., Richardson, M. P., 2009. Regulating Systemic Risk. In Restoring Financial Stability: How to Repair a Failed System, edited by Acharya, V. V., Richardson, M.P.. John Wiley & Sons: Hoboken, NJ.
Acharya, V., Pedersen, L., Philippon, T., Richardson, M. P., 2010. Taxing Systemic Risk. In Regulating Wall Street: The Dodd-Frank Act and the New Architecture of Global Finance, edited by Acharya, V. V., Cooley, T., Richardson, M. P., Walter, I.. John Wiley & Sons: Hoboken, NJ.
- Search Google Scholar
- Export Citation
)| false Acharya, V., Pedersen, L., Philippon, T., Richardson, M. P., 2010. Taxing Systemic Risk. In Regulating Wall Street: The Dodd-Frank Act and the New Architecture of Global Finance, edited by . Acharya, V. V., Cooley, T., Richardson, M. P., Walter, I. John Wiley & Sons: Hoboken, NJ.
Adam, K., Beutel, J., Marcet, A., Merkel, S., 2015. Can A Financial Transaction Tax Prevent Stock Price Booms? Journal of Monetary Economics, 76, S90–S109.
Barberis, N., Greenwood, R., Jin, L., Shleifer, A., 2015. X-CAPM: An Extrapolative Capital Asset Pricing Model. Journal of Financial Economics, 115 (1), 1–24.
Bhattacharya, S., Goodhart, C.A.E., Tsomocos, D., Vardoulakis, A., 2015. A Reconsideration of Minsky’s Financial Instability Hypothesis. Journal of Money, Credit and Banking, 47 (5), August, 931–973.
Bianchi, J., 2011. Overborrowing and Systemic Externalities in the Business Cycle. American Economic Review, 101 (7), 3400–3426.
Bianchi, J., Boz, E., Mendoza E., 2012. Macro-prudential Policy in a Fisherian Model of Financial Innovation. IMF Economic Review, 60 (2), 223–269.
Borio, C., 2012. The Financial Cycle and Macroeconomics: What Have We Learnt? BIS Working Paper No. 395. http://www.bis.org/publ/work395.pdf.
Boz, E., Mendoza, E. G., 2014. Financial Innovation, the Discovery of Risk, and the U.S. Credit Crisis. Journal of Monetary Economics, 62, 1–22.
Brownlees, C. T., Engle, R. F., 2012. Volatility, Correlation and Tails for Systemic Risk Measurement. SSRN Working Paper 1611229.
Brunnermeier, M., Sannikov, Y., 2014. A Macroeconomic Model with a Financial Sector. American Economic Review, 104 (2), 379–421.
Danielsson, J., Valenzuela, M., Zer, I., 2016. Learning from History: Volatility and Financial Crises. Federal Reserve Board Finance and Economics Discussion Series.
Dell’Ariccia, G., Igan, D., Laeven, L., Tong, H., Bakker, B., Vandenbussche, J., 2012. Policies for Macrofinancial Stability: How to Deal with Credit Booms. IMF Staff Discussion Note.
Drehmann, M., Borio, C., Gambacorta, L., Jiménez, G., Trucharte, C., 2010. Countercyclical Capital Buffers: Exploring Options. BIS Working Paper No. 137.
Drehmann, M., Borio, C., Tsatsaronis, K., 2012. Characterising the Financial Cycle: Don’t Lose Sight of the Medium Term! BIS Working Paper No. 380. http://www.bis.org/publ/work380.pdf.
Farhi, E., Werning, I., 2016. A Theory of Macroprudential Policies in the Presence of Nominal Rigidities. Econometrica, 84 (5), 1645–1704.
Fernandez de Lis, S., Garcia-Herrero, A., 2012. Dynamic Provisioning: A Buffer Rather Than A Countercyclical Tool? Working Paper. BBVA Bank, Economic Research Department.
Gertler, M., Kiyotaki, N., 2015. Banking, Liquidity, and Bank Runs in An Infinite Horizon Economy. American Economic Review, 105 (7), 2011–2043.
Gordon, R., Kalambokidis, L., Slemrod, J., 2004. Do We Now Collect Any Revenue from Taxing Capital Income? Journal of Public Economics, 88, 981–1009.
Gordy, M. B., 2009. First, Do No Harm: A Hippocratic Approach to Procyclicality in Basel II. In: Paper presented at the Conference Procyclicality in the Financial System, jointly organised by the Netherlands Bank and the Bretton Woods Committee, 9–10 February.
- Search Google Scholar
- Export Citation
)| false Gordy, M. B., 2009. First, Do No Harm: A Hippocratic Approach to Procyclicality in Basel II. In: Paper presented at the Conference Procyclicality in the Financial System, jointly organised by the Netherlands Bank and the Bretton Woods Committee, 9–10 February.
Gordy, M. B., Howells, B., 2006. Procyclicality in Basel II: Can We Treat the Disease without Killing the Patient? Journal of Financial Intermediation, 15, 395–417.
International Monetary Fund Staff Discussion Note (prepared by E. W. Nier, J. Osinski, L. I. Jacome, and P. Madrid), 2011. Institutional Models for Macroprudential Policy.
Jeanne, O., Korinek, A., 2010. Excessive Volatility in Capital Flows: A Pigouvian Taxation Approach. American Economic Review: Papers & Proceedings, 100 (2), 403–407.
Jiménez, G., Ongena, S., Peydró, J.-L., Saurina, J., 2017. Macroprudential Policy, Countercyclical Bank Capital Buffers and Credit Supply: Evidence from the Spanish Dynamic Provisioning Experiments. Journal of Political Economy (forthcoming).
Jimenez, G., Saurina, J., 2006. Credit Cycles, Credit Risk, and Prudential Regulation. International Journal of Central Banking, 2, 65–98.
Kowalik, M., 2011. Countercyclical Capital Regulation: Should Bank Regulators Use Rules or Discretion? Federal Reserve Bank of Kansas City Economic Review.
Krznar, I., Morsink, J., 2014. With Great Power Comes Great Responsibility: Macroprudential Tools at Work in Canada. IMF Working Paper No. 14/83.
Masciandaro, D., Passarelli, F., 2013. Financial Systemic Risk: Taxation or Regulation? Journal of Banking and Finance, 37 (2), 587–596.
Poledna, S., Thurner, S., 2016. Elimination of Systemic Risk in Financial Networks by Means of A Systemic Risk Transaction Tax. Quantitative Finance, 16 (10), 1599–1613.
Reinhart, C. M., Rogoff, K., 2009. This Time Is Different: Eight Centuries of Financial Folly. Princeton University Press, Princeton, NJ.
Schüler, Y. S., Hiebert, P. P., Peltonen, T. A., 2017. Coherent Financial Cycles for G-7 Countries: Why Extending Credit Can Be An Asset. European Systemic Risk Board Working Paper Series No. 43.
Segoviano, M. A., 2006. Consistent Information Multivariate Density Optimizing Methodology. Financial Markets Group, London School of Economics and Political Science.
Strohsal, T., Proano, C. R., Wolters, J., 2015. Characterizing the Financial Cycle: Evidence from A Frequency Domain Analysis. Discussion Papers 22/2015, Deutsche Bundesbank.
Zlatic, V., Gabbi, G., Abraham, H., 2015. Reduction of Systemic Risk by Means of Pigouvian Taxation. PLoS ONE 10(7): e0114928. https://doi.org/10.1371/journal.pone.0114928
Basak and Zhao are affiliated with the Indian School of Business and the IMF, respectively. We are extremely grateful for the helpful discussions with Viral Acharya, Tobias Adrian, Jorge Alvarez, Anil Ari, Woon Gyu Choi, Martin Cihak, Luis Cortavarria-Checkley, Udaibir Das, Alan Xiaochen Feng, Daniel Garcia-Macia, Gaston Gelos, Dan Greenwald, Javier Hamann, Xing Hong, Aaditya Iyer, James Morsink, Saptarshi Mukherjee, Maurice Obstfeld, Miguel Segoviano, Bowen Shi, Ennio Stacchetti, Di Wu, participants at NYU Stern Finance Student Seminar in Spring 2016, participants at the IMF MCM Policy Forum in July 2017, numerous internal reviewers at the IMF, and especially Alexander Murray, Tao Zha, and Divya Kirti. Mayur Choudhary has provided excellent research assistance. All remaining errors are our own.
One difference between our model and Brunnermeier and Sannikov (2014)’s is that the former focuses on the role of learning in a simple portfolio model, whereas the latter highlights the role of liquidity in a full macroeconomic model.
Recessions associated with systemic financial crises tend to be particularly deep and long-lasting. Laeven and Valencia (2010) document that the median output loss of the recent financial crisis is 25 percent. Reinhart and Rogoff (2009) observe that in financial crises the unemployment rate increases by 7 percentage points and remains high for over four years on average.
IMF (2017a) also warns that the longer booms last and the larger credit grows, the more dangerous they become.
“More stringent” is meant as a statement about change over time, not about comparisons with other models or with real-world policy; that is, “more stringent” than when the market had not been tranquil for that long (the market confident was not so high).
For example, Financial Times reported on August 23, 2017, that: “Hedge funds are embracing an esoteric credit product widely blamed for exacerbating the financial crisis a decade ago, as low volatility and near record prices for corporate debt tempt them into riskier areas to seek higher returns. The market for ‘bespoke tranches’ — bundles of credit default swaps that are tied to the risk of corporate defaults — has more than doubled in the first seven months of 2017.” IMF (2017b) also warned that “Risk appetite has grown markedly as near-term stability risks have declined.” In a speech at Jackson Hole in late August 2017, the Federal Reserve chair Janet Yellen also warned that memories of the last crisis “may be fading.” (Financial Times, August 25, 2017).
This is a form of Pigouvian taxation, and is similar to the systemic risk taxation proposed by Acharya and others (2010). For convenience, the capital income tax in our paper is levied based on the gross investment income rather than net investment income (that is, investment return), as in the standard capital income tax. Our derivations show that our results apply if we switch to the standard definition instead. For discussions of the benefits and costs associated with the capital income tax (under the standard definition), see Gordon and others (2004) and the references therein. Our results also apply if we use financial transaction tax instead. For discussions of the financial transaction tax, see Adam and others (2015).
In particular, we do not model the mechanism by which investment in the risky asset may lead to a systemic crisis. Our focus is on the interaction between investors’ learning process and the degree of excessive risk buildup, not on the underlying reasons for the crisis. Thus, rather than focus on a particular model of financial crises, we exogenously specify the crisis probability as a function of the aggregate risky asset position and ask how the dynamics of financial market efficiency (or inefficiency) depends upon the properties of this function (together with investors’ learning process). Our framework may be regarded as a reduced-form version of some more fully developed models of financial crisis (for example, Biais and others, 2015; Gertler and Kiyotaki, 2015).
All our results also hold if the underlying state is not fixed and follows a Markov process instead, that is, a good state may become bad or a bad state may become good. The main difference from the fixed-state case is that now agents may never learn the true state. See Section V for more details.
Using cross-country data from primary debt capital markets, Kirti (2018) shows that lending standards help separate good credit booms from bad credit booms contemporaneously.
For example, in 2013 Robert Samuelson argued that “many of the institutions that came to grief — banks, investment banks — were regulated. But regulators shared the optimistic consensus concerning the economy’s transformation. Complacency made regulation permissive. It was the Great Moderation that gave us the financial crisis and Great Recession.” The famous admission of Alan Greenspan in 2008 that s/he had “made a mistake in presuming that the self-interest of organizations, specifically banks, is such that they were best capable of protecting shareholders and equity in the firms” was an ex post acknowledgement that regulators had overestimated the resilence of the financial system in the runup to the crisis.
A related literature discusses some practical issues while implementing countercyclical regulations. For example, in the context of countercyclical capital requirements, Kowalik (2011) points out that the effectiveness of countercyclical regulations depends on how they are implemented, and finds that the rule-based approach has more advantages than the discretion-based approach. In addition, McCoy (2016) points out five challenges to the successful execution of countercyclical regulation: the federal government’s data collection initiatives; how to track threats from new financial products and respond to them; how to justify intervention through rules when risks are small; regulatory capture and inertia; and the likelihood of regulatory arbitrage.
Farhi and Werning (2016) also propose an extended framework to incorporate both pecuniary externality and aggregate demand externality, and characterize the optimal macroprudential policy that can correct for these externalities.
We follow this literature in viewing excessive risk-taking as the result of a financial market externality. Other mechanisms that can generate excessive risk-taking include neglected disaster risk (Gennaioli and others, 2012, 2013; Baron and Xiong, 2016), extrapolative expectations (Greenwood and Shleifer, 2014; Barberis and others, 2015; Barberis and others, Forthcoming), diagnostic expectations (Bordalo and others, 2016), and “this-time-is-different” thinking (Reinhart and Rogoff, 2009). The key difference is that our mechanism does not rely on the behavioral assumptions.
Our paper falls into the macroprudential literature also in the sense that the macroprudential orientation treats the aggregate risk as an endogenous variable that depends on the collective behavior of all financial institutions rather than being exogenously given by the market (Kahou and Lehar, 2017).
Note that the parameter |ξπ| (that is,
The assumption that
Since the aggregate risky investment in the unconstrained planner’s equilibrium
Following the standard notations in calculas, Fx(x, y) denotes the partial derivative of F(x, y) with respect to x, treating y constant. Similar comments apply to Fy(x, y), Fxy(x, y), Fxx(x, y), etc.
To ensure there is no trivial welfare implication, it is assumed that tax revenues are rebated lump-sum to investors. Since this does not affect the optimization problem, we abstract it from the objective function.
”Mechanically” means that the regulator does not learn about |ξπ|, but instead makes a mechanical and persistent judgment about it.