New Keynesian Core Model

The New Keynesian model emerged from a two-decade effort to equip sticky-price intuitions with proper microfoundations. Calvo (1983) introduced the random-duration pricing friction. Taylor (1980) and Rotemberg (1982) proposed alternative nominal rigidity mechanisms. But it was the synthesis by Clarida, Gali, and Gertler (1999) and the treatise by Woodford (2003) that consolidated the canonical three-equation form: a forward-looking IS curve, a New Keynesian Phillips curve, and a Taylor-type interest rate rule. Gali's textbook (2008, revised 2015) made the derivation standard graduate curriculum.

The core mechanism works through three interlocking channels. First, Calvo pricing: each period, only a random fraction (1 - theta) of firms can reset their price, so the aggregate price level adjusts slowly. Firms that do reset set a forward-looking optimal price that accounts for the expected duration of their price being stuck. Second, the IS curve links the output gap to the expected real interest rate through the household Euler equation - when the central bank raises the nominal rate above expected inflation, real rates rise and households defer consumption. Third, the Taylor rule closes the system by specifying how the central bank reacts to inflation and output deviations, completing the feedback loop from policy to expectations to pricing to aggregate demand.

Central banks worldwide - the Federal Reserve, ECB, Bank of England, Riksbank, Bank of Canada, Reserve Bank of New Zealand - use medium-scale New Keynesian models as their primary forecasting and policy analysis tools. The Smets-Wouters (2007) model, which extends the basic NK core with capital, habit formation, wage rigidity, and several additional shocks, is the direct descendant of the three-equation structure defined here. The NK framework is the common language for discussions about optimal monetary policy, inflation targeting, and the output-inflation tradeoff.

Major extensions since the baseline include: Christiano, Eichenbaum, and Evans (2005) adding capital and investment adjustment costs; Erceg, Henderson, and Levin (2000) adding sticky wages; Gali and Monacelli (2005) opening the economy; Bilbiie (2008) and Debortoli and Gali (2018) introducing heterogeneous agents (TANK); and the large literature on the zero lower bound initiated by Eggertsson and Woodford (2003). Each extension grafts additional structure onto the three-equation core without replacing it.

The model has three equation blocks and three endogenous variables: the output gap ($x_t)$, inflation (pi_t), and the nominal interest rate ($i_t)$. The demand block is a dynamic IS curve derived from the household's consumption Euler equation - it links today's output gap to the expected future gap and the ex-ante real interest rate. The supply block is the New Keynesian Phillips curve (NKPC) derived from Calvo pricing - it links inflation to expected future inflation and the current output gap through the slope parameter kappa. The policy block is a Taylor rule that sets the nominal rate as a function of inflation and the output gap, plus an exogenous monetary policy shock.

The three equations form a system of linear expectational difference equations. The household side provides the IS curve through log-linearization of the Euler equation around the efficient steady state. The firm side provides the NKPC through the aggregation of optimal reset-price decisions under the Calvo lottery. The central bank provides the Taylor rule as a behavioral specification. Three structural disturbances drive the system: a demand shock (natural rate shift), a cost-push shock (markup disturbance to the NKPC), and a monetary policy shock (deviation from the Taylor rule).

Equilibrium determination requires the Taylor principle: the central bank must raise the nominal rate by more than one-for-one with inflation (phi_pi > 1). This ensures that the Blanchard-Kahn conditions are satisfied and that the rational expectations equilibrium is unique. When the Taylor principle is violated, sunspot equilibria arise and the model's predictions become indeterminate. The system is solved by standard rational expectations methods, yielding impulse response functions that trace how each shock propagates through the demand-supply-policy feedback loop.

The Federal Reserve Board's FRB/US model and the ECB's New Area-Wide Model (NAWM) are medium-scale descendants of the three-equation NK core. Policy staff at these institutions use NK-based models to evaluate interest rate paths, forecast inflation under alternative policy scenarios, and communicate policy trade-offs to decision makers. The three-equation structure is the skeleton that organizes every larger policy model in this family.

The NK model is the standard framework for analyzing optimal monetary policy design. Woodford (2003) showed that the welfare-relevant loss function for the representative household in the canonical NK model reduces to a quadratic penalty on output gap and inflation variance - providing the microfounded justification for flexible inflation targeting. Every discussion of the divine coincidence, the role of cost-push shocks, and the optimal response to supply versus demand disturbances is conducted within this framework.

The model fails at the zero lower bound, where the Taylor rule is constrained and conventional monetary policy cannot stimulate demand. It also fails when distributional effects matter (fiscal transfers, wealth effects from asset prices) because the representative agent cannot capture heterogeneous marginal propensities to consume. And it is silent on financial stability questions because there is no banking sector, no leverage, and no default risk. For these questions, TANK, HANK, or financial accelerator extensions are required.

The NK framework is also the workhorse for open-economy monetary policy analysis via Gali-Monacelli (2005), for the analysis of forward guidance effects (Del Negro, Giannoni, and Patterson 2015), and for the study of inflation persistence through indexation (Christiano, Eichenbaum, and Evans 2005). The three-equation core sits at the center of a vast applied literature.