Default Cycles: Self-Fulfilling Beliefs and Macroeconomic Dynamics

The paper begins by establishing a correlation between recessions, spikes in corporate default rates, and significant declines in business credit. It highlights that these events are not isolated incidents but rather cluster together, forming persistent credit cycles. Research by Giesecke et al. (2011) supports the existence of these prolonged episodes of clustered defaults. Furthermore, the paper notes that while some aspects of these cycles can be explained by observable firm-specific or macroeconomic factors, a considerable portion is driven by unobserved, correlated factors across firms and over time (Duffie et al., 2009). The observed credit spreads, moreover, often precede these cycles and cannot be fully explained by expected default losses, pointing to a more complex interplay of forces driving these macroeconomic phenomena. The paper argues that these credit and default cycles are not solely driven by fundamental economic factors but are significantly influenced by variations in self-fulfilling beliefs about credit market conditions. This sets the stage for the central argument: the crucial role of self-fulfilling beliefs in shaping credit market dynamics and their impact on broader macroeconomic activity.

A core thesis of the paper emphasizes the role of self-fulfilling beliefs in generating credit cycles. The authors posit that periods of low default and favorable credit conditions can transition into periods of high default and unfavorable conditions, and vice-versa. This transition isn't solely determined by fundamental economic shifts, but rather by changes in collective expectations. The paper argues that stochastic variation in these self-fulfilling beliefs is a significant factor in explaining the persistent nature of default rates and their interconnectedness with macroeconomic variables. This suggests that market sentiment and expectations play a non-trivial, even dominant role in shaping economic outcomes, beyond what is traditionally explained by standard economic models that emphasize fundamental shocks. The authors emphasize that these shifts in beliefs are not merely passive observations but actively shape the credit market and its subsequent impact on the real economy. The implications of this are profound, suggesting that market psychology can be a powerful force driving economic cycles.

The paper discusses the importance of modeling default cycles for understanding overall macroeconomic dynamics. It notes that when firms default, creditors recover only a fraction of their assets. The consequence extends beyond the immediate defaulting firm; it affects the net worth of firms with credit market access and impacts aggregate productivity and factor demand, creating a feedback loop. A high default rate can have a prolonged and significant negative effect on credit availability and overall output. The paper utilizes a vector autoregression (VAR) model to demonstrate that shocks to default rates, even when orthogonal to credit spreads and recovery rates, have a noticeable negative impact on output growth. This underscores the systemic risk associated with high default rates and highlights the need to understand the mechanisms driving these cycles. The analysis suggests that incorporating default risk and the resulting feedback loops is crucial for developing accurate macroeconomic models and for predicting economic downturns.

The paper positions its work within the existing literature on credit spreads, firm default, and macroeconomic implications. While citing works such as Bernanke et al. (1999), Christiano et al. (2014), Miao and Wang (2010), Gomes and Schmid (2012), and Gourio (2013), the authors highlight a key difference: their model uniquely incorporates the influence of self-fulfilling expectations on default incentives. Previous models, the paper argues, largely neglected this crucial aspect. The authors further distinguish their work by explicitly modeling the link between credit market conditions and aggregate factor productivity, a connection absent in prior research. The focus on self-fulfilling beliefs as the primary driver of default rate variation is presented as a novel contribution, offering a distinct perspective on the mechanisms behind credit cycles and their impact on macroeconomic outcomes. By emphasizing the self-fulfilling nature of credit market expectations, the paper sheds new light on the dynamics of financial crises and economic downturns.

This section introduces a simple partial equilibrium model to illustrate the impact of self-fulfilling expectations on credit market dynamics. The model features numerous firms operating over infinite discrete time periods. Firm owners are risk-averse, maximizing discounted expected utility. A key element is the introduction of limited commitment and equilibrium default. The model incorporates a linear technology for firms, allowing them to transform consumption goods into future output. Crucially, firms can obtain one-period credit from risk-neutral investors, creating a borrowing and lending environment. The interest rate spread and leverage are directly linked to the value that borrowing firms place on future credit market conditions. This value influences default decisions and is factored into optimal credit contracts, reflecting the forward-looking nature of the credit market. The model's design allows exploration of how variations in expectations about future credit conditions directly impact firms' current behavior, demonstrating the self-fulfilling nature of credit market dynamics.

A central concept explored is the 'credit market value,' a forward-looking variable reacting to self-fulfilling expectations. The model shows that a well-functioning credit market characterized by low interest rates and a low default rate holds significant value for firms. This high valuation makes credit contracts with few defaults self-enforcing, creating a positive feedback loop. In contrast, a weak credit market with high interest rates and high default rates is less valuable, making it challenging to sustain contracts that prevent defaults. This dichotomy illustrates how optimistic (or pessimistic) expectations can become self-fulfilling prophecies, dramatically influencing the equilibrium state of the credit market. This self-reinforcing mechanism is at the heart of the model's explanation of how credit market conditions can shift between periods of relative stability and periods of distress, demonstrating the crucial role of self-fulfilling prophecies in economic fluctuations.

The model demonstrates the existence of multiple equilibria, highlighting the impact of self-fulfilling expectations. While the equilibria are clearly ranked in terms of default rates, interest rates, and overall firm utility, the model reveals a nuanced relationship with leverage (debt-to-equity ratio). The lower interest rates and higher credit market valuations associated with the 'no-default' equilibrium allow for potentially higher leverage. However, preventing defaults across all firms might necessitate tighter borrowing constraints compared to situations where defaults are only partial. This complexity underscores the interaction between expectations, risk assessment, and financial leverage. The model demonstrates that the same underlying economic fundamentals can lead to distinct equilibrium outcomes depending on market participants' beliefs, thus underscoring the significance of expectations in shaping credit market dynamics and firm-level financial decisions.

The dynamic general equilibrium model incorporates heterogeneity among firms, differentiating them based on productivity and credit market access. High-productivity firms with good credit standing can borrow up to an endogenous credit limit at an interest rate that reflects expected default losses and includes an excess interest premium. This premium is introduced to account for the credit spread puzzle, where observed credit spreads exceed expected default losses (Elton et al., 2001; Huang and Huang, 2012). The model allows for fluctuations in the recovery rate, directly affecting expected default losses and influencing leverage and the credit spread. The introduction of firm heterogeneity is crucial because it allows the model to capture the differentiated response of firms to changes in credit market conditions, leading to aggregate effects on the macroeconomy. This nuanced approach to firm behavior is a key aspect of the model's ability to generate realistic credit cycles.

The model incorporates both fundamental and non-fundamental shocks to explore their influence on credit market dynamics. Fundamental shocks include those affecting the real or financial sector, such as shocks to the recovery rate, the excess premium, or aggregate productivity. Non-fundamental shocks, termed sunspot shocks, are unrelated to fundamentals but still impact credit market expectations. The model demonstrates that variations in self-fulfilling beliefs, whether induced by fundamental or sunspot shocks, are crucial for understanding the dynamics of default rates. An adverse sunspot shock, for instance, raises the default rate and depresses leverage. The inclusion of sunspot shocks is vital to capture the observed volatility in credit spreads and output growth that cannot be explained by fundamental shocks alone. This shows the non-trivial effect of market sentiment on real economic outcomes.

The model highlights the interaction between credit market conditions and aggregate factor productivity. Tightening credit or an increase in default rates reduces the capital operated by the most productive firms, leading to lower aggregate productivity and output. This feedback loop between financial markets and the real economy is a key feature of the model. The interplay between credit constraints, firm-level productivity, and aggregate output is explored in detail. When credit is restricted, productive firms reduce their borrowing and investments, leading to a decline in aggregate output and TFP. This underscores the systematic impact of credit market dynamics on the overall macroeconomic performance. This analysis demonstrates the crucial role of credit market conditions in determining the aggregate productivity and the overall health of the economy.

The model is calibrated using data to match observed values for key variables, including the recovery rate (42.15%), default rate (1.72%), and credit spread (2%). This provides a quantitative framework to test the model's ability to replicate real-world dynamics. The calibrated model effectively captures the characteristics of the Great Recession. Specifically, the model suggests that this period featured a combination of a decline in recovery ability, deteriorated credit market expectations (positive sunspot shocks), and a larger-than-usual intermediation cost shock. The model's ability to reproduce the characteristics of this significant economic downturn reinforces the importance of the modeled factors (recovery rate, market expectations, and intermediation costs) in driving actual macroeconomic outcomes. The case study of the Great Recession demonstrates the model's power to provide insights into the complex interplay of factors contributing to severe economic downturns.

The model is calibrated using data from 1982 to 2015, focusing on the US economy. Calibration targets include key macroeconomic variables such as the average default rate (1.72%), recovery rate (42.15%), and credit spread (2%). The model parameters (discount factor β, average default cost µ, variance of default costs σ, productivity ratio γ, recovery parameter λ, and intermediation cost Φ) are chosen to match these targets. The discount factor influences investment rates and capital-output ratios, while the average default cost shapes the default rate. The recovery parameter is directly linked to the observed recovery rate, and the intermediation cost is calibrated to reflect the excess bond premium (the part of the credit spread unexplained by expected default losses). The remaining parameters, variance of default costs and productivity ratio, are derived from average credit and the leverage ratio of constrained firms. This careful calibration ensures that the model is grounded in empirical data and can provide meaningful quantitative predictions.

The analysis presents smoothed shocks derived from maximum likelihood estimation. These shocks, normalized by their standard deviations, include those related to the recovery rate (λ), intermediation costs (Φ), aggregate productivity (A), and sunspot shocks (ε). The 2007-2009 Great Recession serves as a case study. The model suggests that this recession involved a combination of a decline in recovery ability (negative λ shocks), worsened credit market expectations (positive sunspot shocks), and a significant increase in intermediation cost shocks. The analysis of shocks to the recovery rate (λ) shows a correlation with the real estate boom and bust and subsequent government interventions. Similarly, shocks to intermediation costs (Φ) are linked to the “excess bond premium” during the financial crisis and subsequent government interventions that are meant to reduce risk aversion. This interpretation of the estimated shocks provides insights into the mechanisms driving the observed macroeconomic fluctuations.

Impulse response functions illustrate the transmission mechanisms of the various shocks. A one-standard-deviation shock to each variable is analyzed, starting from the steady state. The results demonstrate how the shocks impact variables such as leverage, default rates, credit spreads, output growth, and the real interest rate. Sunspot shocks cause persistent falls in leverage and output. Collateral shocks lead to short-lived leverage decreases but persistent impacts on default rates due to their effects on credit market expectations. Intermediation cost shocks cause significant credit spread increases, driving similar effects to collateral shocks due to effects on the recovery parameter and sunspot shocks. Negative productivity shocks generate persistent falls in output growth due to persistent productivity effects and their slight impact on sunspot shocks. A variance decomposition is used to assess the contribution of each shock to output and debt growth. Results indicate that roughly 21.1% of output growth variations are attributable to shocks affecting sunspots, primarily through their effect on firm factor demands.

The quantitative analysis reveals that shocks to the recovery rate, intermediation costs, and sunspot shocks significantly impact output growth and credit market conditions. The model successfully captures the dynamics of the 2007-2009 Great Recession, attributing it to a combination of negative collateral value shocks (reflecting reduced liquidity and pledgeability), deteriorated credit market expectations (positive sunspot shocks), and a substantial increase in intermediation costs. The analysis of impulse response functions shows how these shocks transmit through the economy, affecting variables like leverage, default rates, and output growth. Variance decomposition demonstrates that a substantial portion of output growth volatility (around 21.1%) is explained by shocks affecting credit market expectations (sunspots), primarily through their impact on firms’ factor demands. These results emphasize the importance of incorporating both fundamental and non-fundamental factors— particularly the role of self-fulfilling beliefs—in understanding macroeconomic fluctuations and credit cycles.

The paper suggests several avenues for future research. One promising direction is to examine the impact of long-term debt on the sensitivity of default rates to market expectations. It is hypothesized that long-term debt may reduce the responsiveness of strategic default to market sentiments. However, the authors also acknowledge that the ability to roll over long-term debt could be sensitive to investor sentiment. Another important area is investigating the link between market liquidity and self-fulfilling beliefs in the financial market. The model highlights the significant role of recovery shocks in influencing market expectations, suggesting a strong connection between asset liquidity and belief formation. Further research could explore how government policies aimed at stabilizing market liquidity can anchor these beliefs and reduce the vulnerability of the economy to self-fulfilling crises. These extensions would enhance our understanding of the complex interplay between financial markets, market sentiment, and macroeconomic outcomes.