Monday, March 12, 2012

Capital Regulation, Liquidity Requirements and Taxation in a Dynamic Model of Banking

Capital Regulation, Liquidity Requirements and Taxation in a Dynamic Model of Banking. By Gianni De Nicolo, Andrea Gamba and Marcella Lucchetta
IMF Working Paper No. 12/72
March 01, 2012

This paper studies the impact of bank regulation and taxation in a dynamic model with banks exposed to credit and liquidity risk. We find an inverted U-shaped relationship between capital requirements and bank lending, efficiency, and welfare, with their benefits turning into costs beyond a certain requirement threshold. By contrast, liquidity requirements reduce lending, efficiency and welfare significantly. The costs of high capital and liquidity requirements represent a lower bound on the benefits of these regulations in abating systemic risks. On taxation, corporate income taxes generate higher government revenues and entail lower efficiency and welfare costs than taxes on non-deposit liabilities.


The 2007-2008 financial crisis has been a catalyst for significant bank regulation reforms, as the pre-crisis regulatory framework has been judged inadequate to cope with large financial shocks. The new Basel III framework envisions a raise in bank capital requirements and the introduction of new liquidity requirements, while several proposals have been recently advanced to use forms of taxation with the twin objectives of raising funding to pay for resolution costs in stressed times, as well as a way to control bank risk-taking behavior.1 To date, however, the relatively large literature on bank regulation o ers no formal analysis where a joint assessment of these policies can be made in a dynamic model of banking where banks play a role and are exposed to multiple sources of risk. The formulation of such a dynamic banking model is the main contribution of this paper.

Our model is novel in three important dimensions. First, we analyze a bank that dynamically transforms short term liabilities into longer-term partially illiquid assets whose returns are uncertain. This feature is consistent with banks' special role in liquidity transformation emphasized in the literature (see e.g. Diamond and Dybvig (1983) and Allen and Gale (2007)).

Second, we model bank's financial distress explicitly. This allows us to examine optimal banks' choices on whether, when, and how to continue operations in the face of financial distress. The bank in our model invests in risky loans and risk-less bonds financed by (random) government-insured deposits and short-term debt. Financial distress occurs when the bank is unable to honor part or all of its debt and tax obligations for given realizations of credit and liquidity shocks. The bank has the option to resolve distress in three costly forms: by liquidating assets at a cost, by issuing fully collateralized bonds, or by issuing equity. The liquidation costs of assets are interpreted as fire sale costs, and modeled introducing asymmetric costs of adjustment of the bank's risky asset portfolio. The importance of fire sale costs in amplifying banks financial distress has been brought to the fore in the recent crisis (see e.g.  Acharya, Shin, and Yorulmazer (2010) and Hanson, Kashyap, and Stein (2011)).

Third, we evaluate the impact of bank regulations and taxation not only on bank optimal policies, but also in terms of metrics of bank efficiency and welfare. The first metric is the enterprise value of the bank, which can be interpreted as the efficiency with which the bank carries out its maturity transformation function. The second one, called \social value", proxies welfare in our risk-neutral world, as it summarizes the total expected value of bank activities to all bank stakeholders and the government. To our knowledge, this is the first study that evaluates the joint welfare implications of bank regulation and taxation.

Our benchmark bank is unregulated, but its deposits are fully insured. We consider this bank as the appropriate benchmark, since one of the asserted roles of bank regulation is the abatement of the excessive bank risk-taking arising from moral hazard under partial or total insurance of its liabilities. We use a standard calibration of the parameters of the model |with regulatory and tax parameters mimicking current capital regulation, liquidity requirement and tax proposals| to solve for the optimal policies and the metrics of efficiency and welfare. 

We obtain three sets of results. First, if capital requirements are mild, a bank subject only to capital regulation invests more in lending and its probability of default is lower than its unregulated counterpart. This additional lending is financed by higher levels of retained earnings or equity issuance. Importantly, under mild capital regulation bank efficiency and social values are higher than under no regulation, and their benefits are larger the higher are fire sale costs. However, if capital requirements become too stringent, then the efficiency and welfare benefits of capital regulation disappear and turn into costs, even though default risk remains subdued: lending declines, and the metrics of bank efficiency and social value drop below those of the unregulated bank. Thus, there exists an inverted-U-shaped relationship between bank lending, efficiency, welfare and the stringency of capital requirements. These novel findings suggest the existence of an optimal level of bank-specific regulatory capital under deposit insurance.

Second, the introduction of liquidity requirements reduces bank lending, efficiency and social value significantly, since these requirements hamper bank maturity transformation. In addition, the reduction in lending, efficiency, and social values increases monotonically with their stringency. When liquidity requirements are added to capital requirements, they also eliminate the benefits of mild capital requirements, since bank lending, efficiency and social values are reduced relative to the bank subject to capital regulation only. We should stress that these results do not have to be necessarily interpreted as an indictment of liquidity requirements. 

If liquidity requirements were found to be optimal regulations to correct some negative externalities arising from excessive bank's reliance on short term debt -which we do not model- then our results indicate how large the costs associated with these negative externalities should be to rationalize the need of liquidity requirements.

On taxation, an increase in corporate income taxes reduces lending, bank efficiency and social values due to standard negative income e ects. However, tax receipts increase, generating higher government revenues. With the introduction of a tax on non-deposit liabilities, which in our model is short-term debt, the decline in bank lending, efficiency and social values is larger than that under an increase in corporate taxation, while the increase in government tax receipts is lower. Therefore, in our model corporate taxation is preferable to a tax on non-deposit liabilities, although both forms of taxation reduce lending, efficiency and social value.


This paper has formulated a dynamic model of a bank exposed to credit and liquidity risk that can face financial distress by reducing loans, issuing secured debt, or issuing equity at a cost. We evaluated the joint impact of capital regulation, liquidity requirements and taxation on banks' optimal policies and metrics of bank efficiency of and welfare.

We have uncovered an important inverted U-shaped relationship between bank lending, bank effi ciency, social value and regulatory capital ratios. This result suggests the existence of optimal levels of regulatory capital, which are likely to be highly bank-specific, depending crucially on the configuration of risks a bank is exposed to as a function of the chosen business strategies. Similarly, our results on the high costs of liquidity requirements point out the adverse consequences of the repression of the key maturity transformation role of bank intermediation.  Given our finding of the adverse e ffects of liquidity requirements, the argument by Admati, DeMarzo, Hellwig, and Peiderer (2011) that capital requirements can be designed to substitute for liquidity requirements is reinforced. Finally, for the purpose of rising tax revenues, corporate income taxation seems preferable to taxation of non-deposit liabilities, since the former generates higher revenues and lower efficiency and welfare costs.

Overall, our results suggest that implementing non-trivial increases in capital requirements, liquidity requirements and taxation may be associated with costs significantly larger than what proponents of these policies may have thought. This implies that the benefits of these requirements in terms of their ability to abate systemic risk should at least o set the costs we have identified.