Kiyotaki–moore model

What Is the Kiyotaki–Moore Model?

The Kiyotaki–Moore model is a seminal macroeconomic model in financial economics that illustrates how small, temporary economic shocks can be amplified into large, persistent fluctuations in output and asset prices. It highlights the critical role of collateral constraints and imperfect credit markets in propagating business cycle fluctuations. The core mechanism of the Kiyotaki–Moore model revolves around the idea that borrowing is often secured by assets, and changes in the value of these assets can significantly impact the availability of credit, leading to a feedback loop that magnifies initial disturbances.

History and Origin

Developed by Nobuhiro Kiyotaki and John Moore, the Kiyotaki–Moore model was first formally introduced in their influential 1997 paper, "Credit Cycles," published in the Journal of Political Economy. An earlier version of their work, titled "Credit Chains," was circulated as a working paper in 1995 and revised in 1997. The model emerged as a significant contribution to the understanding of financial frictions within dynamic economic frameworks. Prior to their work, many real business cycle theories relied on substantial exogenous shocks to explain fluctuations in aggregate output. Kiyotaki and Moore demonstrated how relatively minor shocks could suffice to explain such fluctuations when credit markets exhibit imperfections. This framework provided a new lens through which economists could analyze the interplay between financial markets and real economic activity, particularly the role of collateral in amplifying economic downturns and upturns.

Key Takeaways

• The Kiyotaki–Moore model demonstrates how collateral constraints can amplify minor economic shocks into significant, persistent fluctuations.
• It posits that assets serve a dual role: as factors of production and as collateral for debt.
• A fall in asset values reduces borrowing capacity, leading to decreased investment and further asset price declines, creating a vicious cycle.
• The model helps explain credit cycles and the "financial accelerator" effect.
• It emphasizes that imperfections in credit markets are crucial for understanding the propagation of economic disturbances.

Formula and Calculation

The Kiyotaki–Moore model is a theoretical framework and does not present a single, universally applied formula like those for financial ratios. Instead, its "formula" lies in the dynamic equations that describe the behavior of agents (patient "gatherers" and impatient "farmers" or entrepreneurs) and the evolution of asset prices and borrowing constraints. The core mechanism can be understood through the relationship between the value of collateralizable assets and the amount of debt that can be sustained.

A simplified representation of the collateral constraint in the model can be expressed as:

Where:

• ( b_{t+1} ) represents the amount of new borrowing by firms at time ( t ) for period ( t+1 ).
• ( q_t ) is the market price of the collateralizable capital (e.g., land or durable assets) at time ( t ).
• ( k_{t+1} ) is the quantity of capital held by firms in period ( t+1 ) that can serve as collateral.

This inequality implies that the amount a firm can borrow for the next period is constrained by the market value of the assets it holds in the current period that can be used as collateral. This relationship is central to the model's amplification mechanism, as a change in ( q_t ) directly impacts ( b_{t+1} ).

Interpreting the Kiyotaki–Moore Model

The Kiyotaki–Moore model offers a crucial interpretation of how financial market imperfections can drive real economic fluctuations. It suggests that the value of collateralizable assets plays a pivotal role in the economy's ability to finance investment. When asset values decline, perhaps due to a minor negative economic shock, the amount of collateral available to borrowers diminishes. This tightening of credit constraints forces indebted agents to reduce their spending and investment, which in turn reduces demand for assets, driving their prices down further. This creates a self-reinforcing cycle—a "financial accelerator" effect—that amplifies the initial shock into a more severe and prolonged downturn, characteristic of a recession. The model helps explain why downturns can be deeper and more persistent than implied by the initial shock alone.

Hypothetical E¹¹xample

Consider an economy where a significant portion of firms relies on commercial real estate as collateral for their operational loans and expansion investment.

1. Initial Shock: A minor, temporary slowdown in the global economy slightly reduces demand for goods, leading to a small drop in corporate profits.
2. Asset Price Decline: This reduction in profits makes future income from commercial real estate look less attractive to investors, causing a marginal decrease in commercial property prices.
3. Collateral Constraint Tightens: As property prices fall, the value of the collateral held by firms decreases. Lenders, adhering to their loan-to-value ratios, reduce the amount of credit they are willing to extend, or demand more collateral for existing loans.
4. Reduced Investment and Spending: Faced with tighter credit and less access to financing, firms cut back on new projects, postpone expansion plans, and may even reduce current operations to conserve cash. This dampens overall investment and economic activity.
5. Amplification: The reduction in firm activity further weakens economic prospects and demand for commercial real estate, causing property prices to fall even more. This creates a feedback loop, continuously tightening credit conditions and exacerbating the economic slowdown. What began as a minor profit dip becomes a more significant recession due to the amplified effects through the collateral channel.

Practical Applications

The Kiyotaki–Moore model has significant practical applications in several areas of financial economics and policymaking:

• Monetary Policy and Financial Stability: Central banks consider the insights of the Kiyotaki–Moore model when formulating monetary policy. Understanding how credit cycles can amplify shocks influences decisions regarding interest rates and unconventional measures like quantitative easing. For example, during financial crises, central banks might intervene to stabilize asset prices and ease liquidity constraints, aiming to mitigate the financial accelerator effect.
• Macroprudential ¹⁰Regulation: Regulators use the model's insights to design policies aimed at preventing excessive leverage and fostering financial resilience. This includes setting capital requirements for banks and loan-to-value limits for certain types of lending to curb the build-up of systemic risk that can arise from collateral feedback loops.
• Understanding Business Cycles: The model provides a theoretical foundation for understanding why economic downturns can be so severe and prolonged, even in response to relatively small initial economic shocks. It shifts focus from solely productivity shocks to the crucial role of financial market imperfections as propagation mechanisms.
• Real Estate Mark⁹et Analysis: Given that the original model often uses land or real estate as the collateralizable asset, it offers a framework for analyzing the interaction between real estate valuations, credit availability, and broader economic activity. Fluctuations in property values can have widespread effects through this mechanism.

Limitations and Criticisms

While highly influential, the Kiyotaki–Moore model has several limitations and has faced various criticisms:

• Quantitative Significance: Some studies have questioned the quantitative importance of the credit constraint mechanism described in the original Kiyotaki–Moore model. Research has suggested that in an otherwise standard dynamic general equilibrium model, the propagation and magnification effects of typical total factor productivity (TFP) shocks through the Kiyotaki–Moore mechanism might be small. The perceived quantitative i⁸nsignificance could be attributed to asset market dynamics and the relatively low participation of loans in economic activity in some economies.
• Simplifying Assumptions: The model, in its basic form, employs simplifying assumptions regarding agent heterogeneity (e.g., patient "gatherers" and impatient "farmers") and the nature of assets. While these assumptions aid tractability, they may not fully capture the complexity of real-world financial markets and the diverse behaviors of economic agents.
• Absence of Default/Bankruptcy: A key characteristic of the "costly enforcement" approach, which the Kiyotaki–Moore model falls under, is that in equilibrium, there is typically no actual default or bankruptcy. This contrasts with other models that explicitly incorporate such events and their implications for the financial system.
• Exogenous Shocks: Alth⁷ough the model shows how small shocks can be amplified, it still relies on an initial exogenous shock to trigger the mechanism. It does not fully explain the source of these initial disturbances, or how the economy might move between constrained and unconstrained regions.
• Limited Policy Implicati⁶ons in Early Versions: Early versions of the model primarily focused on the amplification mechanism, with less direct emphasis on specific monetary policy interventions, beyond the general understanding that policies affecting liquidity or asset values could have real effects. Subsequent extensions have explored these policy implications in more detail.

Kiyotaki–Moore Model vs. F⁵inancial Accelerator

The Kiyotaki–Moore model is fundamentally a specific framework that generates and explains the financial accelerator effect. The financial accelerator is a broader concept in macroeconomics, referring to the mechanism by which small changes in fundamental economic conditions (like productivity or demand) are amplified into larger fluctuations through financial market imperfections. This amplification often occurs because a borrower's financial health, particularly their net worth or the value of their collateral, affects their access to external finance and the cost of borrowing.

The Kiyotaki–Moore model provides a rigorous, micro-founded explanation for how this accelerator works by focusing on limited enforceability in debt contracts, necessitating collateral. When an initial shock reduces asset values, it directly reduces the available collateral, tightening borrowing constraints and forcing cuts in investment. This reduced investment further depresses asset prices, creating the positive feedback loop characteristic of the financial accelerator. Other models, such as those by Bernanke and Gertler, also explain the financial accelerator but might use different financial friction mechanisms, such as information asymmetry that leads to an external finance premium.

FAQs

What problem does the ⁴Kiyotaki–Moore model address?

The Kiyotaki–Moore model addresses how relatively small economic shocks can lead to large and persistent business cycle fluctuations, particularly through the amplification role of financial markets and collateral constraints.

What is the role of collateral in t³he Kiyotaki–Moore model?

In the Kiyotaki–Moore model, collateral plays a dual role: it is both a productive input in the economy and a necessary security for loans. The amount of credit available to borrowers is directly tied to the market value of their collateralizable assets. Fluctuations in these asset prices directly affect borrowing capacity.

How does the Kiyotaki–Moore model relat²e to credit cycles?

The Kiyotaki–Moore model explicitly demonstrates how financial imperfections, particularly collateral requirements, can generate credit cycles. A downturn in asset values triggers a contraction in credit, which further depresses asset values, leading to a self-reinforcing downward spiral. Conversely, rising asset values can lead to a credit expansion and an upward spiral, thus creating cyclical behavior.

Is the Kiyotaki–Moore model still relevant ¹today?

Yes, the Kiyotaki–Moore model remains highly relevant. Its core mechanism—the financial accelerator—is a foundational concept in understanding the dynamics of financial crises and how financial frictions amplify real economic fluctuations. Its insights inform modern macroeconomic policy, particularly in areas of financial stability and macroprudential regulation.