Does the Fed Care About the Joneses? Optimal Interest-Rate Smoothing with Consumption Externalities

Changes in monetary policy are typically implemented gradually, an empirical observation known as interest-rate smoothing. This finding is a puzzle for most monetary models because they predict an immediate response of monetary policy to macroeconomic developments. We propose an explanation of optimal interest-rate smoothing by applying the recent lesson from the related literature on the monetary transmission mechanism that time-non-separable preferences may be key to understanding dynamics in a monetary economy. Because empirical evidence supports consumption externalities, we introduce this feature, in a time-non-separable way, into the preferences of a representative agent in a cash-in-advance economy and find that optimal monetary policy does react gradually to exogenous shocks. In addition, the Friedman Rule, the optimal policy in many monetary models, fails to be optimal because the inflation tax reduces the distortion caused by the externality. In the interest of building a model that can explain both optimal policy and key business cycle facts, we also extend our basic model to investigate the effects of capital formation and staggered price-setting on the dynamics of optimal monetary policy. Optimal policy is largely unchanged in the presence of staggered price-setting, but becomes counterfactually gradual in the presence of capital formation. ∗E-mail address: [email protected]. I thank Bill Dupor, Jesús Fernández-Villaverde, and Dirk Krueger for their guidance, and S. Borağan Aruoba for many helpful discussions.