Interest Rate Policies in Consumption - Savings Dynamic Models

We examine the effect of interest rate policies on an agent’s consumption and savings when her income is fluctuating. In each period a long-lived agent decides how much to save (i.e., invest in a risk-free bond) and how much to consume while her income is uncertain and depends on the state of the economy. The central bank, on the other hand, fixes a policy, called an interest rate policy, which determines the state-dependent interest rate. This interest rate is the rate of return on the risk-free bond which the agent takes into consideration when deciding on her savings. We compare interest rate policies and show that under concavity of the consumption function, a condition that ensures that the substitution effect dominate the income effect, lower interest rates encourage the agent’s consumption across all states.