Individual Versus Aggregate Collateral Constraints and the - PDF document

Individual Versus Aggregate Collateral Constraints and the Overborrowing Syndrome by Mart ´ ın Uribe 1

“The history of investment in South America throughout the last century has been one of confidence followed by disillusionment, of borrowing cycles followed by widespread default. ” Royal Institute of International Affairs, 1937, cited in Dornbusch 1983 and McKinnon and Pill, 1993. 2

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. 3

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. 4

Focus of this Paper: Investigate whether lending practices based on aggregate indicators of solvency can lead emerging countries to overborrow. 5

• An Aggregate Borrowing Constraint A t +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 a t +1 ≤ κ – Households internalize the constraint. – The interest rate equals the world interest rate at all times. – In equilibrium, A t = a t . 6

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. 7

An Economy with an Aggregate Debt Limit Households ∞ � max E 0 θ t U ( c t , h t ) , t =0 subject to a t +1 = a t + c t − e z t F ( h t ) R t and a no-Ponzi-game constraint. Optimality Conditions U c ( c t , h t ) = R t β t E t U c ( c t +1 , h t +1 ) − U h ( c t , h t ) U c ( c t , h t ) = e z t F ′ ( h t ) 8

Clearing of the Domestic Financial Market R t ≥ R ∗ A t +1 ≤ κ ( R t − R ∗ )( A t +1 − κ ) = 0 9

Rents from Financial Rationing and the Aggregate Resource Constraint • Rents Accrue Domestically A t +1 = A t + C t − e z t F ( H t ) R ∗ • Rents Accrue to Foreign Lenders A t +1 = A t + C t − e z t F ( H t ) R t 10

Individual Debt Limit ∞ � max E 0 θ t U ( c t , h t ) t =0 subject to a t +1 = a t + c t − e z t F ( h t ) R ∗ a t +1 ≤ κ Optimality Conditions R ∗ U c ( c t , h t ) = β t E t U c ( c t +1 , h t +1 ) 1 − R ∗ ξ t − U h ( c t , h t ) U c ( c t , h t ) = e z t F ′ ( h t ) , ξ t ≥ 0 ( a t +1 − κ ) ξ t = 0 Define R ∗ R t = 1 − R ∗ ξ t 11

No Overborrowing: The equilibrium dynamics of c t , h t , y t , and a t 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. 12

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, or the world interest rate. • Alternative specifications of the discount factor (e.g., β ( c t , h t ) instead of β ( C t , H t )). • Rents from financial rationing accruing to foreign lenders. 13

Debt Distribution When Financial Rents Accrue Abroad 0.07 No Resource Costs Resource Costs No Debt Limit 0.06 0.05 0.04 Probability 0.03 0.02 0.01 0 −10 −5 0 5 10 15 20 external debt 14

The Role of Stock Prices Technology: y t = e z t F ( k t , h t ) k t = = stock of land, in fixed aggregate supply k ∗ Aggregate Debt Limit: A t +1 ≤ κq t k ∗ Individual Debt Limit: a t +1 ≤ κq t k t +1 q t ≡ price of land 15

Price of Land with an Aggregate Debt Limit ∞ Λ t,t + j e z t + j F k ( k ∗ , h t + j ) � q t = E t j =1 Price of Land with an Individual Debt Limit e z t + j F k ( k ∗ , h t + j ) ∞ � q t = E t Λ t,t + j � j − 1 s =0 [1 − κ (1 /R ∗ − 1 /R t + s )] j =1 Interest Rate Under Individual and Aggregate Debt Limits 1 = R t E t Λ t,t +1 16

Equilibrium Dynamics with a Time-Varying Debt Limit Unconditional Distribution of Debt Average Stock Prices 0.05 1.01 Indiv CC 1 Agg CC 0.04 0.99 probability 0.03 0.98 Eq t 0.97 0.02 0.96 0.01 Indiv CC 0.95 Agg CC 0 0.94 −10 −5 0 5 10 −5 0 5 10 External Debt External Debt Average Consumption Average Interest Rate 10.2 1.055 10 1.05 9.8 1.045 ER t Ec t 9.6 1.04 9.4 1.035 Indiv CC Indiv CC Agg CC Agg CC 9.2 1.03 −5 0 5 10 −5 0 5 10 External Debt External Debt Conclusion: The price of land should be expected to be higher under an individual debt limit than under an aggregate debt limit. 17

Homogeneous Agents The economy borrows κ regardless Result: of whether the debt limit is imposed at the individual or aggregate level. 18

Heterogeneous Agents Result: The economy borrows more when the debt limit is imposed at the aggregate level. 19

Debt-Elastic Interest Rate • Aggregate Debt Limit R ′ > 0 R t = R ( A t +1 ); Steady state 1 = R ( A ∗ ) β Individual Debt Limit R ′ > 0 R t = R ( a t +1 ); Steady State 1 − A ∗∗ R ′ ( A ∗∗ ) = R ( A ∗∗ ) β R ( A ∗∗ ) Implication A ∗∗ < A ∗ ⇒ Overborrowing 20

Conclusion • Lending practices based on aggregate indicators of 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. 21