Primitive elements of field extension ()/() are counted using (1) principle of inclusion-exclusion, (2) Möbius inversion, and (3) Euler function. Then, an identityis obtained, where > 1, a prime, (·) Euler function, and , …, the all distinct prime divisors of

We examine the implications of less powerful forward guidance for optimal policy using a sticky-price model with an effective lower bound (ELB) on nominal interest rates as well as a discounted Euler equation and Phillips curve. When the private-sector agents discount future economic conditions...

The authors solve the IS puzzle for the G7 countries. They find that five of the G7 countries have the expected significant negative relationship between the output gap and the real-rate gap; the time series of the remaining two show material deviation from expected IS-curve behavior. The...

The rational addiction model is usually tested by estimating a linear second-order difference Euler equation, which may produce unreliable estimates. We show that a linear first-order difference equation is a better alternative. This empirical specification is appropriate under the reasonable...

At the zero lower bound, the New Keynesian model predicts that output and inflation collapse to implausibly low levels, and that government spending and forward guidance have implausibly large effects. To resolve these anomalies, we introduce wealth into the utility function; the justification...

The paper presents the welfare cost of inflation in a banking time economy that models exchange credit through a bank production approach. The estimate of welfare cost uses fundamental parameters of utility and production technologies. It is compared to a cash-only economy, and a Lucas (2000)...