A condensed summary of the core results of the course.
Money and prices
- Quantity equation: \(\pi\approx\Delta m+\Delta v-\Delta y\); money and inflation move together across long horizons and across countries, but velocity shocks dominate at low inflation.
- Welfare cost of inflation: the area under the inverse money-demand curve; small for moderate inflation. The Friedman rule \(i=0\) is optimal in flexible-price money models.
- Classical model: money is neutral; an interest-rate peg leaves the price level indeterminate; \(\phi_\pi>1\) restores a unique equilibrium.
The New Keynesian core
- Phillips curve: \(\pi_t=\beta E_t\pi_{t+1}+\kappa\tilde y_t\), with \(\kappa\) falling steeply in the Calvo parameter \(\theta\).
- Dynamic IS: \(\tilde y_t=E_t\tilde y_{t+1}-\sigma^{-1}(i_t-E_t\pi_{t+1}-r^n_t)\).
- Determinacy under a Taylor rule: \(\kappa(\phi_\pi-1)+(1-\beta)\phi_y>0\).
- Welfare loss: \(\tfrac12E_0\sum\beta^t(\pi_t^2+\vartheta\tilde y_t^2)\) with \(\vartheta=\kappa/\epsilon\).
- Discretion: \(\kappa\pi_t=-\vartheta\tilde y_t\). Commitment: \(\kappa\pi_t=-\vartheta(\tilde y_t-\tilde y_{t-1})\), which makes the price level stationary; price-level targeting mimics this history dependence.
Extensions
- Small open economy: the model keeps its closed-economy form in domestic inflation; strict domestic-inflation targeting is optimal in the baseline, and pegs raise output volatility.
- Financial accelerator: net worth falls after a tightening, the external finance premium rises, and the output loss is larger and more persistent.
- Zero lower bound: falling inflation raises the real rate in a trap; forward guidance works through expected inflation and output, but the standard model exaggerates distant promises (forward-guidance puzzle).
- Monetary–fiscal interactions: a unique equilibrium needs one active and one passive authority; with passive money and active fiscal policy, the price level adjusts to make debt sustainable (fiscal theory).
- Heterogeneity: in TANK the IS slope is scaled by \(\delta=\frac{1-\lambda}{1-\lambda\chi}\); high MPCs make indirect income effects dominate transmission.
Evidence
- Bayesian estimation: state-space likelihood from the Kalman filter, priors, posterior mode and Metropolis–Hastings; the inflation response in the policy rule is often weakly identified.
- Identification: recursive VARs show a price puzzle; narrative and high-frequency shocks with local projections give larger output effects and a smaller price puzzle.
- Central banking: inflation targeting is associated with lower inflation risk, but much of the measured effect reflects global disinflation and reforms that came before adoption.