Optimal long-run inflation with occasionally binding financial constraints

•I study optimal long-run inflation with occasionally binding financial constraints.•The optimal long-run inflation rate is positive (1-3% annually).•Positive inflation is a result of an endogenous asymmetric cost-push shock.•The positive mean of the cost-push shock makes the mean of inflation positive.•Positive inflation smoothes the financial constraint-induced “labor wedge”.

This paper studies the optimal long-run inflation rate in a simple New Keynesian model with occasionally binding collateral constraints that intermediate-good firms face on hiring labor. The paper finds that the optimal long-run annual inflation rate is around 1.5% if the economy is hit by a total factor productivity (TFP) shock and nearly 2.5% if the economy is subject to a markup shock. The shadow value of the collateral constraint is akin to an endogenous cost-push shock. Differently from usual cost-push shocks, however, this shock is asymmetric as it takes non-negative values only. Since the mean of this asymmetric endogenous cost-push shock is positive, inflation is also positive on average. In addition, a binding collateral constraint resembles a time-varying tax on labor, which the monetary authority can smooth by setting a positive inflation rate. More generally, the basic result is related to standard Ramsey theory in that optimal policy smoothes distortions over time.