# 1 Introduction

The active use of prudential instruments to control credit volumes and allocations fell into disgrace in the 1990s, when the regulatory pendulum swung toward financial liberalization.<sup>1</sup> Then, in 2008, the global financial crisis hit financially developed economies hard and exposed the limits of the existing prudential framework in dealing with systemic risk. This swung the pendulum back, and the active use of prudential instruments such as reserve requirements, loan-to-value ratios, taxes on credit, and capital requirements to smooth the credit cycle and avert major crises (macroprudential policies, according to the current jargon) gained momentum. The global financial crisis also uncovered the dangerous liaisons between micro and macro stability and forced macroeconomists to give a serious look at the interaction between business cycles and financial frictions.<sup>2</sup> The latter started being incorporated in standard DSGE models and with them the rationale for macroprudential policies became evident.<sup>3</sup> However, in (necessarily) stylized DSGE models, taxes on debt, capital, and liquidity requirements end up being equivalent forms of Pigouvian taxation that can effectively deal with the negative overborrowing externalities.<sup>4</sup> This raises the question of how robust such results are—that is whether in a more micro-founded model such equivalence results still hold.

This is the question we address in this paper. Using a very stylized model where a bank maximizes profits choosing lending rates and the riskiness of its portfolio, we show that, from a microprudential perspective, the choice of macroprudential instruments does indeed matter. It is true that capital requirements, liquidity requirements and taxes on debt all have an adverse effect on banks’ incentives to lend, which means that all these instruments successfully address overborrowing externalities. However, while capital requirements, by increasing the banks’skin in the game, make banks more prudent, liquidity requirements and taxes on debt make banks engage in riskier behavior.

There are a number of studies discussing the purposes of macroprudential regulation in dealing with different kind of externalities, and a growing one looking at the effectiveness of macroprudential measures in smoothing the business cycle; Galati and Moessner (2011) and Hanson et. al. (2011) are excellent surveys. However, little is still known about how the choice of different prudential instruments affects the incentives of the single institutions to take on risk. This paper is an attempt to fill such a gap.

The model we present is similar to Dell’Ariccia et al. (forthcoming) who study the interaction between monetary policy and the capital structure of the bank. The questions we raise in this paper are similar to those in De Nicolò et al. (2012) who study how, in the presence of credit and liquidity risk, capital and liquidity requirements affect a bank’s risk-taking incentives in a calibrated dynamic

> 1 This regulatory view was supported by macroeconomic models built in a Modigliani-Miller world where the absence of financial frictions made regulation and supervision unnecessary. Even when macro models such as Bernanke and Gertler (1996) and Kiyotaki and Moore (1997) highlighted the possibility that simple agency problems could lead to potentially dangerous credit cycles, the idea of using prudential instruments to smooth business cycle fluctuations was considered as passé. Given such a background, it is not surprising that prudential regulation was generally analyzed in micro-models (as the one surveyed in Freixas and Rochet, 2008) and its macro impact generally overseen.

> 2 Usually in the form of collateral contraints that create externality problems that lead to episodes of overborrowing and subsequent Fisherian deflation.

> 3 Macroprudential policies force agents to internalize the external cost of borrowing making the economy less vulnerable to financial crises. This is the argument for Pigouvian taxes in Jeanne and Korinek (2010), and Bianchi (2011).

> 4 Bianchi (2011) formally proves the equivalence between these different instruments.

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