Theories of banking and financial intermediation have come a long way, elaborating on the benefits and the inherent fragility of banking systems. In the meantime, macroeconomists have made a variety of attempts to incorporate realistic financial intermediaries l banks in particularl in dynamic general equilibrium models. A juxtaposition of the standard models of banking (Diamond and Dybvig 1983, Allen and Gale 1998, 2004) with a few dynamic macroeconomic models (Calstrom and Fuerst 1997, Gertler and Kiyotaki 2011) can clearly point to a yet to be filled gap between the micro theory of banking and macroeconomics.
The gap may be summarized as follows: Many macroeconomic models have successfully incorporated the complicated lender borrower relationship and analyzed its consequences and implications for the macroeconomy, while, conceivably, few macroeconomic models have crystallized the roles and perils of banking systems in the light of a number of real world experiences of a financial crisis (Caballero 2010).
This potential deficiency in macroeconomics manifests itself when the banks typically modeled in micro$theories of banking as well as in the real world are compared to the over simplified "banks" in macroeconomic models. Banks in the real world, as reasonably modeled by micro theories, provide unique services for their customers. Banks typically raise funds via short term liabilities (e.g., demand deposit, repos) and invest them, in part, in illiquid assets. This notable business line undertaken by banks is widely acknowledged as a maturity mismatch or maturity transformation. On top of this, as noted by Allen and Gale (2007), micro theories of banking have broadly emphasized other special elements in banking business, such as provision of liquidity insurance for depositors against liquidity (preference) shocks and inherent exposure to crisis risks. In contrast, however, these special elements in banks are given short shrift in macroeconomics.
This paper develops a dynamic general equilibrium model with a realistic banking sector to address basic yet unsolved questions: Does a banking sector with maturity mismatch affect macroeconomic fluctuations? If yes, how could it improve or undermine economic welfare? We lay out an overlapping generations (OLG) model where a liquidity shortage in banks with maturity mismatch precipitates in efficient financial crises that can result in a devastating decline in macroeconomic activity.
As opposed to many existing models with jbubbles,kfor example, where a bubble bursts at a given (exogenous) probability, our model shows that, while not including asset price bubbles, the probability of a crisis varies depending on the leverage that banks determine based on their rational decisions. More broadly, we argue that, regardless of bubbles taking place or not, the banking sector in a laissez faire economy generally cannot achieve the constrained optimum (a second best allocation) and tends to be overleveraged as a result of perfect competition.
