Kiyotaki–Moore Credit Cycle Model

Kiyotaki–Moore Credit Cycle Model is a foundational dynamic general-equilibrium framework in macroeconomics, macro-finance, and business and economics theory, formulated by Japanese economist Nobuhiro Kiyotaki and British economist John H. Moore in their landmark 1997 Journal of Political Economy article "Credit Cycles." Designed to explain how small, temporary shocks to productivity or interest rates can generate large, persistent fluctuations in aggregate output and asset prices, the model embeds the Hart–Moore incomplete-contracts theory of inalienable human capital (1994) into a dynamic economy with two classes of agents—productive, impatient credit-constrained "farmers" (entrepreneurs with discount factor β) and less productive, patient unconstrained "gatherers" (lenders with discount factor β′ > β)—who compete for a fixed durable asset ("land" K). Because farmers cannot pre-commit their human capital and can threaten to withdraw their specialized labor after borrowing, lenders limit any loan b_t so that gross debt repayment R b_t never exceeds the future liquidation value of the farmer's tangible collateral q_t+1 k_t. Consequently, durable land k_t plays a dual role as both a factor of production and loan collateral. When a temporary adverse productivity shock hits at date t, farmers suffer a drop in net worth that forces them to cut land purchases k_t; as land is reallocated to less productive gatherers, the marginal product of land for gatherers falls, depressing future and current land prices q_t (which equal the present discounted value of future user costs u_t+s). The drop in q_t further erodes farmer net worth q_tk_t−1 − R b_t−1 at date t itself, creating a mutually reinforcing static and intertemporal collateral multiplier that propagates the downturn across subsequent periods.

From Modigliani–Miller to Hart–Moore (1994) Inalienability of Human Capital

In a frictionless neoclassical real business cycle (RBC) model where the Modigliani–Miller theorem holds, corporate balance sheets, leverage ratios, and asset-price fluctuations have zero causal feedback on physical resource allocation: durable assets are allocated so as to equate marginal products across all users at every date, and temporary productivity shocks produce only temporary, proportional changes in output.

Following the collapse of the late-1980s commercial real estate and equity bubbles in Japan, Scandinavia, and the United Kingdom, macroeconomists sought a microfounded explanation for why sharp declines in land and real estate prices coincided with prolonged contractions in corporate investment and credit. While Ben Bernanke and Mark Gertler (1989) modeled credit frictions using Townsend's costly state verification, Kiyotaki and Moore (1997) built their credit friction on Oliver Hart and John H. Moore's (1994) Quarterly Journal of Economics paper "A Theory of Debt Based on the Inalienability of Human Capital":

1. Specificity of Entrepreneurial Human Capital: When a borrower (a "farmer") invests in a productive project on land k_t, the project's full output consists of a tradable component (a k_t) and a non-tradable / entrepreneur-specific component (c k_t) that vanishes if the entrepreneur walks away and withdraws their specialized human capital before harvest at t + 1.
2. Inalienability and Renegotiation: Because courts cannot enforce involuntary servitude, an entrepreneur who has promised a debt repayment R b_t > q_t+1k_t can threaten right after investment at date t to abandon the project unless the lender renegotiates the debt down to the liquidation value of the physical asset q_t+1 k_t (the market resale price of the land at date t + 1, which is all the lender can recover without the farmer's human capital).
3. The Endogenous Borrowing (Collateral) Constraint: Anticipating this ex-post hold-up renegotiation, rational lenders at date t refuse to advance any loan whose gross repayment R b_t exceeds the next-period market value of the tangible land collateral q_t+1k_t:

where R = 1 + r is the gross risk-free interest rate, b_t is the amount borrowed by the farmer at date t, k_t is the quantity of durable land held by the farmer at date t, and q_t+1 is the market price of a unit of land at date t + 1.

Preferences, Technologies, and Factor Supply

Consider a discrete-time economy (t = 0, 1, 2, …) with a nondurable consumption numeraire ("fruit") and a durable productive asset ("land") in fixed aggregate supply K̄ = K_t + K_t′:

1. Farmers (Credit-Constrained Productive Sector, Measure 1):
   • Preferences: Farmers maximize expected discounted fruit consumption E_t[∑_s=0^∞ β^s x_t+s] with discount factor β ∈ (0, 1).
   • Linear Constant-Returns Production Technology: Holding k_t units of land at date t yields y_t+1 = (a + c) k_t units of fruit at date t + 1. Because c k_t requires the farmer's inalienable human capital, only a k_t is tradable to pay consumption, buy new land, or service debt; the remaining c k_t is consumed directly by the farmer (x_t+1 ≥ c k_t).
2. Gatherers (Unconstrained Patient Lenders, Measure m):
   • Preferences: Gatherers maximize E_t[∑_s=0^∞ (β′)^s x_t+s′] with discount factor β′ > β (gatherers are more patient than farmers).
   • Concave Diminishing-Returns Production Technology: Holding k_t′ units of land at date t produces G(k_t′) units of tradable fruit at date t + 1, with G′ > 0, G″ < 0, and G′(0) > a R > G′(K̄). Gatherers' output is fully tradable and they face no borrowing constraints.

Equilibrium Interest Rate, Binding Collateral Constraint, and the User Cost of Land (u_t)

Unconstrained gatherers' Euler equation pins down the gross real interest rate R = 1 / β′ < 1 / β. Because farmers are less patient than the market interest rate (βR < 1) and earn a high return on land, Proposition 1 of Kiyotaki and Moore (1997) establishes that near the steady state, farmers consume only their non-tradable output (x_t = c k_t−1), reinvest 100% of their tradable net worth into land, and borrow up to the maximum collateral limit b_t = (q_t+1 / R)k_t.

Substituting b_t = (q_t+1/R)k_t into the farmer's flow-of-funds constraint q_tk_t = a k_t−1 + q_tk_t−1 − R b_t−1 + b_t yields the fundamental farmer land-demand equation:

Define u_t ≡ q_t − q_t+1 / R as the user cost of land (which also equals the required down payment per unit of land, since buying one unit of land at q_t allows borrowing q_t+1/R), and define N_t ≡ (a + q_t)K_t−1 − R B_t−1 as aggregate farmer net worth. Then aggregate farmer land demand is:

Meanwhile, unconstrained gatherers hold the residual land K_t′ = K̄ − K_t and equate their discounted marginal product of land to the user cost u_t:

Because G″ < 0, u(K_t) is an increasing function of farmer land holdings K_t (u′(K_t) > 0). Iterating q_t = u_t + q_t+1/R forward under the no-bubble condition expresses the current land price q_t as the present discounted value of future user costs:

The Inefficient Steady-State Allocation (K^*, q^*)

In the deterministic steady state (K_t = K^*, q_t = q^*, R B^* = q^*K^*), farmer net worth is N^* = a K^* and steady-state user cost is u^* = [(R − 1)/R]q^* = (r/R)q^*. Equating N^* = u^*K^* pins down:

In steady state, gatherers' marginal product of land is G′((K̄ − K^*)/m) = R a, which is lower than farmers' total marginal product a + c (since a + c > R a). Because of the collateral constraint, too little land K^* is allocated to productive farmers, and any positive shift ΔK_t > 0 raises aggregate output Y_t+1 by (a + c − R a)ΔK_t > 0.

Log-Linearized Dynamics: Static vs. Intertemporal Multipliers

Suppose the economy is in steady state at t − 1 and an unanticipated one-period productivity shock changes tradable productivity from a to a(1 + Δ) at date t only (returning to a for t + 1, t + 2, …). Because inherited debt R B_t−1 = q^*K^* is unindexed, date-t farmer net worth is N_t = [a + aΔ + (q_t − q^*)]K^*, while for all subsequent periods s ≥ 1 with perfect foresight:

Let k̂_t = (K_t − K^*)/K^* and q̂_t = (q_t − q^*)/q^* denote percentage deviations from steady state, and let 1/η ≡ d ln u / d ln K |_K^* > 0 (where η > 0 is gatherers' land-supply elasticity). Log-linearizing the post-shock transition equation for s ≥ 1 and the date-t land-demand and asset-pricing equations gives:

Because farmers are leveraged up to the full value of their land (q^*/u^* = R/(R − 1) = 1/r ≈ 25 at r = 4%), a 1% increase in the current land price q̂_t raises farmer net worth by 1/r ≈ 25%! Solving the simultaneous system compares the static multiplier (q_t+1 fixed at q^*) against the full dynamic intertemporal multiplier (q_t+1 endogenous):

In the full dynamic equilibrium, because farmer land holdings remain elevated in future periods (k̂_t+s > 0), the next-period land price q_t+1 also rises, which relaxes the date-t collateral constraint b_t ≤ (q_t+1/R)k_t (shrinking the required down payment u_t = q_t − q_t+1/R) while simultaneously boosting q_t and net worth N_t. Because (R + 1)/(R − 1) ≈ 2/r is around 50 for r = 4%, the intertemporal multiplier amplifies a 1% temporary shock by several hundred percent.

In Section III of their 1997 paper, Kiyotaki and Moore extended the baseline model so that only a fraction π ∈ (0, 1) of farmers receive an opportunity to invest in depreciating capital in any period t. This staggered investment structure transforms the law of motion for K_t into a second-order autoregressive process AR(2) that generates hump-shaped impulse responses and endogenous damped oscillations ("credit cycles"), while unindexed nominal debt reproduces Irving Fisher's (1933) debt-deflation spiral. Subsequent macro-finance work embedded Kiyotaki–Moore collateral constraints into New Keynesian housing-cycle models (Iacoviello, 2005) and emerging-market Sudden Stop models (Mendoza, 2010).

Why must land play a dual role as both a productive input and collateral for the Kiyotaki–Moore multiplier to operate?

When a negative shock forces collateral-constrained farmers to sell land ΔK_t < 0 to unconstrained gatherers, the gatherers experience diminishing marginal returns (G″ < 0) on the extra land they absorb. This drop in gatherers' marginal product lowers the market user cost u(K_t) and depresses the equilibrium price of land q_t, which feeds back into the collateral constraint by wiping out farmer net worth (q_t − q^*)K^* and forcing deeper land fire sales.

What is the difference between the static multiplier and the intertemporal dynamic multiplier in Kiyotaki and Moore (1997)?

The static multiplier holds next period's land price q_t+1 fixed at q^*: a rise in q_t increases farmer net worth by [R/(R − 1)]*q̂*_t, but raises the required down payment u_t = q_t − q^*/R by the same amount, yielding k̂_t = Δ. The intertemporal dynamic multiplier accounts for the persistence of k̂_t+s > 0 into future periods, which raises future land prices q_t+1, relaxing today's borrowing limit b_t ≤ (q_t+1/R)k_t and multiplying the initial shock by a factor proportional to (R + 1)/((R − 1)η) ≈ 2/(rη).

How does the Kiyotaki–Moore (1997) credit cycle model differ from the Bernanke–Gertler–Gilchrist (1999) financial accelerator?

The Bernanke–Gertler–Gilchrist financial accelerator (1999) is built on ex-post asymmetric information (costly state verification), where higher leverage increases expected deadweight bankruptcy auditing costs and raises the external finance interest premium. Kiyotaki–Moore (1997) is built on incomplete contracts (Hart–Moore 1994 inalienability of human capital), where borrowers borrow at the risk-free rate R with zero equilibrium default but face a hard quantity rationing limit R b_t ≤ q_t+1k_t tied to the resale price of tangible collateral.

Why don't farmers insure themselves against aggregate land-price shocks using state-contingent contracts?

In Kiyotaki and Moore (1997), debt contracts R b_t−1 are unindexed non-contingent bonds. As Arvind Krishnamurthy (2003) showed, if farmers could write state-contingent insurance contracts indexed to aggregate productivity shocks Δ or land prices q_t, they would hedge against downturns so that their net worth would not collapse when q_t falls, dampening the collateral amplification mechanism.

1. Kiyotaki, N., & Moore, J. (1997). "Credit Cycles." Journal of Political Economy, 105(2), 211–248. https://doi.org/10.1086/262072
2. Hart, O., & Moore, J. (1994). "A Theory of Debt Based on the Inalienability of Human Capital." Quarterly Journal of Economics, 109(4), 841–879. https://doi.org/10.2307/2118350
3. Krishnamurthy, A. (2003). "Collateral Constraints and the Amplification Mechanism." Journal of Economic Theory, 111(2), 277–292. https://doi.org/10.1016/S0022-0531(03)00098-X00098-X)
4. Iacoviello, M. (2005). "House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle." American Economic Review, 95(3), 739–764. https://doi.org/10.1257/0002828054201477
5. Mendoza, E. G. (2010). "Sudden Stops, Financial Crises, and Leverage." American Economic Review, 100(5), 1941–1966. https://doi.org/10.1257/aer.100.5.1941