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This paper models the impact of interest rates in an economy with limited commitment. A firm's temptation to default endogenously induces credit constraints in their optimal long-term relationship with banks. The history of the relationship determines the credit limits generating a non-trivial life-cycle for firms. Collateral takes time to accumulate and raises the scale of operations and firm's survival probabilities.

Firms in many different stages of their life-cycle will coexist in the economy. In this environment, a positive interest rate shock decreases the survival probability of constrained firms while unconstrained firms respond primarily by adjusting their scale of operations. Increases in the interest rate affect the mass and cross-section of active firms, partly through a reduction of the number of new ones. Higher interest rates also tighten constraints of newly created firms, raising the number of periods needed to achieve maturity.