Giosuè Cavagna

Medium-scale DSGE models with occasionally binding constraints (OBC) became the theoretical benchmark for the study of the interaction between the financial sector and the real economy. While these models are often praised for their ability to capture qualitative aspects of financial amplification, we demonstrate that they do not feature substantial non-linearities beyond the occasionally binding leverage constraint and hence are insufficient to match banks' risk-taking behaviour adequately. This lack of substantial non-linearities leads to a poor match with key empirical moments, particularly regarding the volatility of financial sector leverage and the strength of financial amplification. Using proprietary granular bank balance sheet data, we provide empirical underpinning for risk-taking behaviour of financial intermediaries that is unmatched by standard setups of models with financial frictions. In particular, we show that the extent of risk-shifting of banks' portfolios in response to changes in the economic and financial environment crucially depends on the initial riskiness of their portfolios. In other words, riskier banks are faster to adjust their portfolios in response to shocks compared to less risky financial intermediaries. Specifically, this mechanism is absent in benchmark models, where the response to shocks does not depend on banks' initial risk exposure. To overcome these shortcomings of benchmark models with financial frictions, we examine the impact of an alternative, non-linear formulation of the OBC in an otherwise standard model similar to Gertler and Karadi (2011). Instead of the standard assumption that banks can divert a constant fraction of their asset holdings, the modification introduces risk-dependency to the leverage constraint. The higher the share of risky assets in banks' portfolios, the higher the fraction of assets that can be diverted. The risk-dependent diversion rate also accounts for the asymmetric information between banks and their depositors. We demonstrate that the parsimonious modification to the formulation of the occasionally binding leverage constraint significantly improves the model's performance in replicating qualitative properties of banks' risk-taking behaviour and in matching empirical moments in comparison to a standard model. This results from the model being able to generate a stronger pass-through from the financial sector to the real economy, thereby improving the transmission mechanism of financial shocks. Moreover, it introduces non-linearities beyond the standard OBC, allowing for richer dynamics. Finally, the model offers precise control over the degree of non-linearity, making it adaptable to various calibration needs.