Capital Requirements, Risk Choice, and Liquidity Provision in a Business Cycle Model

Summary by N. Aaron Pancost
Begenau embeds a banking sector into a dynamic stochastic general equilibrium model to determine the optimal capital requirement for banks. In the model, banks take on excessive risks because they enjoy a government-guaranteed bailout in bad times. Higher capital requirements lower bank risk-taking and economic volatility, but also reduce the total supply of debt, which households value. Optimal capital requirements balance this trade-off; after calibrating the model to data from the National Income and Product Accounts and the Federal Deposit Insurance Corporation, Begenau finds that the optimal capital requirement is 14% of risk-weighted assets, significantly higher than the 10% share of risky assets that banks hold as Tier 1 capital on average.

The model features two productive sectors: a standard constant returns to scale Cobb-Douglas production function using labor and capital, and a banking sector that uses capital with decreasing returns to scale. Both production functions have an autocorrelated total-factor productivity term, but the banking sector also chooses the volatility of its own productivity. This volatility affects their average productivity in such a way that there is a trade-off between the mean and variance of banker productivity.

The central friction in the model arises because the government subsidizes the banking sector in accordance with their volatility and leverage. In particular, the subsidy induces a complementarity between leverage and risk-taking that causes banks to choose more than the socially-optimal leverage. The first-best government action in this model would be to remove the subsidy; however, because Begenau does not explicitly model the social benefits from the subsidy, she instead analyzes how the government can achieve a second-best outcome by varying banks’ capital requirements.

Previous studies of the effect of capital requirements on macroeconomic variables have found that higher required capital ratios typically reduce volatility but also reduce output. In this model, the effect on output is reversed because of the liquidity demand of households. When the government raises the capital requirement, banks decrease the amount of bank debt outstanding, which hurts households that value such debt for the transactions services it generates—specifically, bank debt enters directly into their utility function. However, because the marginal utility of bank debt to households is decreasing, households value debt even more when it is scarce, and to to clear the market for bank debt the interest rate decreases. If interest rates fall enough, it can offset the increased share of equity in banks’ capital structure and actually lower their total cost of capital, increasing investment, output, and consumption. The optimal capital requirement balances the lower utility from fewer transactions services against increased consumption and lower volatility that results.

Many macro-financial models stop as soon as they illustrate an interesting tradeoff on which they can make qualitative policy recommendations. Begenau goes one step further by showing that her model can match observable macroeconomic and banking dynamics. She calibrates the model by matching each parameter to a specific data moment, taking care to understand the link between data and model counterparts. For example, she sets the proportionality constant ?3 of the government subsidy to banks to match the tax benefit of debt as estimated by Graham (2000, Journal of Finance). She sets the elasticity of the households’ bank holdings to consumption ratio ? to match the volatility of this ratio in the data to the volatility of output. Every parameter in the model is assigned a target data moment, clarifying the calibration exercise.

By matching each parameter to a particular data moment, Begenau can examine how well the model fits other data moments not included in the calibration and argue that the model delivers a reasonable fit to the data. The model is able to match the volatility of GDP (ascribing most of it to the volatility of the banking sector), as well as the volatility of bank balance-sheet variables. The model also matches many business-cycle correlations, including the procyclicality of bank output, balance-sheet variables, and bank interest rates. The model is not a perfect success everywhere: it understates the volatility of consumption (a common problem in business cycle models with production) and predicts an incorrect sign for correlations between book equity, dividend payouts, and the return on capital to balance sheet variables. Some of these correlations in the data are highly dependent on the time-horizon of measurement, something the model is not rich enough to address.

The calibrated model allows Begenau to make plausible welfare calculations. To do so, she solves the model under a variety of different capital requirements, then simulates the model under the benchmark 10.75% requirement many times, switching randomly to the new capital requirement at different points in time. This procedure takes into account not only the welfare from being in a different capital requirement regime but also the welfare effects of the average transition between regimes. She finds that the optimal capital level is 14%, or 17% ignoring the transition. She also computes the dynamics of various bank variables in response to the regulatory change, finding that banks respond to the increased capital requirement by raising equity and reducing debt simultaneously. This is because in the new regime the interest rate falls enough to lower their total cost of capital inclusive of the higher equity requirement, inducing them to grow even as they take on less risk.