Individual Versus Aggregate Collateral Constraints and the - - PDF document

Individual Versus Aggregate Collateral Constraints and the Overborrowing Syndrome

by Mart ´ ın Uribe

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“The history of investment in South America throughout the last century has been one

• f confidence followed by disillusionment,
• f borrowing cycles followed by widespread
• default. ”

Royal Institute of International Affairs, 1937, cited in Dornbusch 1983 and McKinnon and Pill, 1993.

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A Central Question in Emerging- Market Macroeconomics: What factors

lead countries to accumulate excessive levels of external debt? Relevance of the Question: Overborrowing countries may be prone to balance-of-payments crises and sudden stops.

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Overborrowing: Theories

• Deposit Guarantees (McKinnon, 1973; McKinnon

and Pill, 1993)

• Temporariness Hypothesis (Calvo, 1986, 1987;

Mussa, 1986; Daveri, 1991)

• Aggregate Credit Constraints:

Emerging markets tend to overborrow when the lending decisions of foreign investors are guided by macroeconomic indicators and not by careful assessment of individual borrowers’ abilities to repay.

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Focus of this Paper:

Investigate whether lending practices based on aggregate indicators of solvency can lead emerging countries to overborrow.

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• An Aggregate Borrowing Constraint

At+1 ≤ κ – Households do not internalize the constraint. – Credit rationing (i.e., clearing of the domestic financial market) is brought about by adjustments in the interest rate.

• An Individual Borrowing Constraint

at+1 ≤ κ – Households internalize the constraint. – The interest rate equals the world interest rate at all times. – In equilibrium, At = at.

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Main Finding: No Overborrowing

The economy with the aggregate borrowing limit does not generate higher levels of debt than the economy with the individual borrowing limit.

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An Economy with an Aggregate Debt Limit

Households max E0

∞

• t=0

θtU(ct, ht), subject to at+1 Rt = at + ct − eztF(ht) and a no-Ponzi-game constraint. Optimality Conditions Uc(ct, ht) = RtβtEtUc(ct+1, ht+1) −Uh(ct, ht) Uc(ct, ht) = eztF ′(ht)

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Clearing of the Domestic Financial Market Rt ≥ R∗ At+1 ≤ κ (Rt − R∗)(At+1 − κ) = 0

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Rents from Financial Rationing and the Aggregate Resource Constraint

• Rents Accrue Domestically

At+1 R∗ = At + Ct − eztF(Ht)

• Rents Accrue to Foreign Lenders

At+1 Rt = At + Ct − eztF(Ht)

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Individual Debt Limit

max E0

∞

• t=0

θtU(ct, ht) subject to at+1 R∗ = at + ct − eztF(ht) at+1 ≤ κ Optimality Conditions Uc(ct, ht) = R∗ 1 − R∗ξt βtEtUc(ct+1, ht+1) −Uh(ct, ht) Uc(ct, ht) = eztF ′(ht), ξt ≥ 0 (at+1 − κ)ξt = 0 Define Rt = R∗ 1 − R∗ξt

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No Overborrowing: The equilibrium dynamics

• f ct, ht, yt, and at are identical in the economy

with an individual debt limit and in the economy with an aggregate debt limit with rents from financial rationing accruing to domestic households.

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Robustness: The no-overborrowing result

contines to hold when the model is modified to allow for:

• Capital accumulation
• A larger battery of shocks, such as random

disturbances to preferences, endowments,

• r the world interest rate.
• Alternative specifications of the discount

factor (e.g., β(ct, ht) instead of β(Ct, Ht)).

• Rents from financial rationing accruing to

foreign lenders.

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Debt Distribution When Financial Rents Accrue Abroad

−10 −5 5 10 15 20 0.01 0.02 0.03 0.04 0.05 0.06 0.07 external debt Probability No Resource Costs Resource Costs No Debt Limit

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The Role of Stock Prices

Technology: yt = eztF(kt, ht) kt = = stock of land, in fixed aggregate supply k∗ Aggregate Debt Limit: At+1 ≤ κqtk∗ Individual Debt Limit: at+1 ≤ κqtkt+1 qt ≡ price of land

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Price of Land with an Aggregate Debt Limit qt = Et

∞

• j=1

Λt,t+jezt+jFk(k∗, ht+j) Price of Land with an Individual Debt Limit qt = Et

∞

• j=1

Λt,t+j ezt+jFk(k∗, ht+j)

j−1

s=0[1 − κ(1/R∗ − 1/Rt+s)]

Interest Rate Under Individual and Aggregate Debt Limits 1 = RtEtΛt,t+1

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Equilibrium Dynamics with a Time-Varying Debt Limit

−10 −5 5 10 0.01 0.02 0.03 0.04 0.05 Unconditional Distribution of Debt External Debt probability Indiv CC Agg CC −5 5 10 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 Average Stock Prices External Debt Eqt Indiv CC Agg CC −5 5 10 9.2 9.4 9.6 9.8 10 10.2 Average Consumption External Debt Ect Indiv CC Agg CC −5 5 10 1.03 1.035 1.04 1.045 1.05 1.055 Average Interest Rate External Debt ERt Indiv CC Agg CC

Conclusion: The price of land should be expected to be higher under an individual debt limit than under an aggregate debt limit.

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Homogeneous Agents

Result: The economy borrows κ regardless

• f whether the debt limit is imposed at the

individual or aggregate level.

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Heterogeneous Agents

Result: The economy borrows more when the debt limit is imposed at the aggregate level.

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Debt-Elastic Interest Rate

• Aggregate Debt Limit

Rt = R(At+1); R′ > 0 Steady state 1 = R(A∗)β Individual Debt Limit Rt = R(at+1); R′ > 0 Steady State 1 − A∗∗R′(A∗∗) R(A∗∗) = R(A∗∗)β Implication A∗∗ < A∗ ⇒ Overborrowing

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Conclusion

• Lending practices based on aggregate indicators
• f solvency per se do not lead emerging

countries to overborrow.

• Additional theoretical elements must be added

capable of generating a market price of foreign funds lower than the social price.

• Two avenues for generating this price discrepancy

are suggested: – Debt-elastic country premiums (possibly due to default risk). – Heterogeneous agents.

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