The RBC model (Chapter 14) showed that technology shocks in a frictionless economy can generate realistic business cycle statistics. But it has a critical blind spot: monetary policy does nothing. In the RBC world, money is neutral — the Fed is irrelevant. This contradicts overwhelming evidence that monetary policy affects real output, at least in the short run.
New Keynesian (NK) economics solves this by adding nominal rigidities — sticky prices or wages — to the RBC chassis. The result is a model where monetary policy has real effects, the central bank faces meaningful tradeoffs, and the Taylor rule becomes the central equation of modern central banking.
This chapter's New Keynesian framework connects to three of the book's Big Questions. Each juncture appears after the section where the relevant model is developed.
In perfect competition, firms are price takers — there is no price to "stick." For price rigidity to matter, firms must have price-setting power. The standard NK setup uses Dixit-Stiglitz monopolistic competition:
Each firm faces a downward-sloping demand curve: $y_j = (p_j / P)^{-\varepsilon} Y$.
The optimal reset price is a weighted average of current and expected future marginal costs:
where $\pi_t$ is inflation, $x_t$ is the output gap, and $\kappa = \frac{(1-\theta)(1-\beta\theta)}{\theta} \cdot \frac{\sigma + \varphi}{1 + \varphi\varepsilon}$. Current inflation depends on expected future inflation (forward-looking!) and current marginal cost (proportional to output gap). With cost-push shocks:
Step 1: Under Calvo pricing with parameter $\theta$, fraction $(1-\theta)$ of firms reset prices each period. The aggregate price level evolves as: $P_t = [\theta P_{t-1}^{1-\varepsilon} + (1-\theta)(p_t^*)^{1-\varepsilon}]^{1/(1-\varepsilon)}$.
Step 2: Log-linearize: $\hat{p}_t = \theta\hat{p}_{t-1} + (1-\theta)\hat{p}_t^*$. Since $\pi_t = \hat{p}_t - \hat{p}_{t-1}$: $\pi_t = (1-\theta)(\hat{p}_t^* - \hat{p}_{t-1})$.
Step 3: The optimal reset price is a discounted sum of expected future marginal costs: $\hat{p}_t^* = (1-\beta\theta)\sum_{k=0}^\infty(\beta\theta)^k E_t[\widehat{mc}_{t+k} + \hat{p}_{t+k}]$.
Step 4: Recursive substitution yields: $\pi_t = \beta E_t\pi_{t+1} + \frac{(1-\theta)(1-\beta\theta)}{\theta}\widehat{mc}_t$.
Step 5: Real marginal cost is proportional to the output gap: $\widehat{mc}_t = \frac{\sigma+\varphi}{1+\varphi\varepsilon}x_t$. Defining $\kappa = \frac{(1-\theta)(1-\beta\theta)}{\theta}\cdot\frac{\sigma+\varphi}{1+\varphi\varepsilon}$ gives the NKPC: $\pi_t = \beta E_t\pi_{t+1} + \kappa x_t$.
Parameters: $\beta = 0.99$, $\kappa = 0.3$, $\sigma = 1$, $\phi_\pi = 1.5$, $\phi_x = 0.5$, $r^* = 2\%$, $r^n = 2\%$, $u = 0$.
Step 1: From NKPC (one-period shock, $E_t\pi_{t+1} = 0$): $\pi = \kappa x + u = 0.3x$.
Step 2: From IS (one-period, $E_tx_{t+1} = 0$): $x = -(1/\sigma)(i - r^n) = -(i - 2)$.
Step 3: Taylor rule: $i = 2 + 1.5\pi + 0.5x$.
Step 4: Substitute Taylor into IS: $x = -(2 + 1.5\pi + 0.5x - 2) = -1.5\pi - 0.5x$, so \$1.5x = -1.5\pi$, giving $x = -\pi$.
Step 5: Substitute into NKPC: $\pi = 0.3(-\pi) = -0.3\pi$, so \$1.3\pi = 0$ and $\pi = 0$, $x = 0$, $i = 2\%$.
Result: With no shocks, the equilibrium is $\pi = 0$, $x = 0$, $i = r^* = 2\%$. Divine coincidence holds.
The central bank minimizes $L = E_0\sum\beta^t[x_t^2 + \alpha_\pi\pi_t^2]$ with $\alpha_\pi = 0.5$, $\kappa = 0.3$.
Step 1: Under discretion, the central bank minimizes the one-period loss taking expectations as given: $\min_{x_t}\{x_t^2 + \alpha_\pi(\kappa x_t + u_t)^2\}$.
Step 2: FOC: \$1x_t + 2\alpha_\pi\kappa(\kappa x_t + u_t) = 0$. Solving: $x_t = -\frac{\alpha_\pi\kappa}{1 + \alpha_\pi\kappa^2}u_t = -\frac{0.5 \times 0.3}{1 + 0.5 \times 0.09}u_t = -\frac{0.15}{1.045}u_t = -0.144u_t$.
Step 3: Inflation: $\pi_t = \kappa x_t + u_t = -0.3(0.144)u_t + u_t = 0.957u_t$.
Step 4: The implied Taylor rule achieves this by responding aggressively to inflation. Higher $\alpha_\pi$ (inflation-averse) implies a larger $\phi_\pi$, reducing inflation at the cost of greater output gap volatility.
The output gap depends on the expected future gap minus the difference between the real interest rate and the natural rate. When the central bank sets the real rate below the natural rate, it stimulates demand.
Three equations, three unknowns ($\pi_t$, $x_t$, $i_t$):
| Equation | Name | Role |
|---|---|---|
| $\pi_t = \beta E_t\pi_{t+1} + \kappa x_t + u_t$ | NKPC | Inflation determination |
| $x_t = E_tx_{t+1} - \frac{1}{\sigma}(i_t - E_t\pi_{t+1} - r_t^n)$ | Dynamic IS | Demand |
| $i_t = r^* + \phi_\pi\pi_t + \phi_x x_t$ | Taylor rule | Monetary policy |
Adjust shocks and the Taylor rule aggressiveness to see how the NK equilibrium shifts. The left panel shows the NKPC and the monetary policy reaction (combining IS + Taylor rule) in $(\pi, x)$ space. The right panel shows the implied interest rate.
Figure 15.2. The 3-equation NK model. Left panel: NKPC (blue, upward slope) and monetary policy reaction function (red, downward slope) in ($x$, $\pi$) space. Right panel: Taylor rule interest rate. Adjust sliders to see how shocks and policy aggressiveness shift the equilibrium. Hover for values.
The Taylor principle is not an abstract theoretical curiosity — it is the single most important operational rule in modern central banking. The pre-Volcker Fed (1960s–70s) had $\phi_\pi \approx 0.83 < 1$, producing the Great Inflation. The post-Volcker Fed had $\phi_\pi \approx 2.15 > 1$, producing the Great Moderation.
Slide $\phi_\pi$ across the critical threshold of 1. Below 1, the economy is indeterminate: a rise in inflation lowers the real rate, fueling more inflation. Above 1, the real rate rises with inflation, stabilizing the economy.
Figure 15.3. Taylor principle visualization. The blue line is the Taylor rule ($i$ vs $\pi$). The gray dashed line is $i = \pi$ (constant real rate). When the Taylor rule is steeper than the 45-degree line ($\phi_\pi > 1$), real rates rise with inflation (stable). When flatter ($\phi_\pi < 1$), real rates fall with inflation (unstable).
You now have the 3-equation NK model with the Taylor rule. This is the modern framework that gives central banks a precise mandate, a precise tool, and a precise rule. Here's what it promises — and where it breaks.
The 3-equation NK model (NKPC + dynamic IS + Taylor rule) gives monetary policy real effects through sticky prices. The Taylor principle ($\phi_\pi > 1$) ensures determinacy — the central bank must raise interest rates more than one-for-one with inflation. When this holds, the system has a unique stable equilibrium: the Fed controls inflation by controlling the real interest rate, and divine coincidence means stabilizing inflation automatically stabilizes the output gap (absent cost-push shocks). The Taylor rule provides a systematic, transparent, and effective policy framework. The model's verdict: yes, central banks can control inflation and stabilize output, if they follow the right rule. The Great Moderation (1984–2007) — 23 years of low inflation and reduced output volatility under Greenspan and early Bernanke — is the strongest empirical support. Clarida, Gali, and Gertler (2000) showed that monetary policy satisfied the Taylor principle after Volcker but violated it before, explaining the shift from instability to stability.
The ZLB: When the natural rate $r^n$ goes negative, the Taylor rule prescribes a negative nominal rate — which is impossible. The central bank is stuck at $i = 0$ while the economy needs stimulus. This is not a theoretical curiosity: Japan since 1990, the US and Europe from 2009–2015, and potentially recurring. Unconventional policies (QE, forward guidance, negative real rates) are partial substitutes but weaker and more uncertain. The forward guidance puzzle: The NK model implies absurdly large effects from expected future rate cuts (Del Negro, Giannoni, Patterson 2015) — suggesting the model overstates central bank power even in its most optimistic framework. If the model overestimates the power of expectations-based policy, the Fed's ZLB toolkit may be weaker than the theory claims. Post-COVID inflation (2021–2023): The Fed kept rates at zero while inflation rose to 9%, calling it "transitory." When it finally raised rates aggressively, inflation fell — but whether the Fed caused the decline or supply normalization did the work is genuinely uncertain.
Post-2008, the profession developed frameworks for ZLB policy: forward guidance, quantitative easing, yield curve control, and average inflation targeting (the Fed's 2020 framework). But these tools are less precise and less well-understood than conventional rate policy. The mainstream now distinguishes between "normal times" (where the Taylor rule works well) and "crisis times" (where the central bank is significantly constrained). The honest assessment: the Fed overestimated its own power before 2008, and the profession has since recalibrated expectations downward.
Central banks are powerful but not omnipotent. In normal times, the Taylor rule framework works well — it explains the Great Moderation convincingly. At the ZLB, central banks are significantly constrained, and fiscal policy becomes the primary stabilization tool (connecting directly to BQ01 in the next section). The profession overestimated central bank power before 2008 and has since recalibrated. The NK model remains the best available framework, but its promise of central bank control comes with conditions that matter enormously in practice.
Does the central bank actually control inflation, or does fiscal policy? The Fiscal Theory of the Price Level (Chapter 16, §16.5) makes a radical case that fiscal policy determines the price level regardless of what the central bank does with interest rates. And the international dimension matters: for most countries, the impossible trinity constrains monetary policy further. Come back at Chapter 16 (§16.2, §16.5) for the time-inconsistency problem and the FTPL challenge, and Chapter 17 (§17.4) for the open-economy constraints.
Ron Paul and Peter Schiff built media empires on "End the Fed." The 2020–2023 inflation made their case go mainstream. The NK model says the Fed controls the economy through the Taylor rule. They say the Fed is the problem.
AdvancedThe nominal interest rate cannot go below zero: $i_t \geq 0$. When the natural rate $r_t^n$ falls below zero during a severe recession, the Taylor rule calls for a negative nominal rate — which is infeasible. Conventional monetary policy is powerless.
Slide the natural rate from positive to negative. When $r^n$ goes negative, the Taylor rule calls for a negative nominal rate, but the ZLB binds at zero. The gap between the required rate and zero represents monetary policy impotence.
Figure 15.4. ZLB trap. Left panel: Taylor rule prescribed rate (blue) vs actual rate (red, floored at 0). The shaded red region is the "monetary policy gap" — the amount of stimulus the central bank cannot deliver. Right panel: resulting output gap. Drag $r^n$ below zero to see the trap engage.
Ron Paul spent decades grilling Fed chairs on C-SPAN, and the clips became YouTube gold for the "End the Fed" movement. Peter Schiff turned "the Fed is debasing the currency" into a media empire. During 2020–2023, when the Fed's balance sheet ballooned from \$4 trillion to \$9 trillion and inflation hit 9%, "they're printing money" went from fringe libertarian talking point to dinner-table consensus. The New Keynesian model you just learned says the Fed controls the economy through interest rates, expectations, and the Taylor rule. The "End the Fed" crowd says the Fed is the problem. Who's right?
AdvancedYou've just seen the zero lower bound — where conventional monetary policy is powerless. This changes the entire fiscal policy debate. When the central bank is stuck at zero, fiscal policy becomes the only game in town.
In the NK model, when the natural rate of interest is negative and the nominal rate is stuck at zero, an increase in government spending $G$ raises output without crowding out. The mechanism is the reverse of normal times: with the interest rate pinned at zero, higher $G$ raises demand, which raises output, which raises inflation, which lowers the real interest rate (since the nominal rate can't adjust), which stimulates demand further. The multiplier at the ZLB can be 1.5–2.0+ in standard calibrations (Christiano, Eichenbaum & Rebelo 2011). Government spending is unambiguously expansionary — the crowding-out channel that weakens fiscal policy in normal times is completely shut off.
The ZLB multiplier is a model result that depends heavily on how expectations are modeled. The forward guidance puzzle literature shows NK models generate implausibly large effects from expected future policies — and if the model overstates the power of expectations-based channels, it may also overstate the fiscal multiplier at the ZLB. Additionally, the ZLB is a specific condition, not the normal state — basing fiscal doctrine on ZLB results is like designing a car for icy roads only. Empirically, estimating the fiscal multiplier during recessions faces severe identification problems: government spending rises because of recessions, making it difficult to isolate the causal effect. And even at the ZLB, Ricardian consumers may save rather than spend if they anticipate future tax increases to pay for the stimulus.
The post-2008 literature has been a back-and-forth. Empirical estimates of fiscal multipliers during recessions cluster around 1.5 (Ramey 2019 survey), higher than normal-times estimates of 0.6–1.0. The mainstream now distinguishes "state-dependent multipliers" — the answer genuinely changes depending on economic conditions. TANK and HANK models (two-agent and heterogeneous-agent NK) show that the fraction of liquidity-constrained households is the key parameter: more constrained households means a larger multiplier. The profession's view has converged on a nuanced position that would have seemed unusual in 2005: fiscal policy matters a lot sometimes and less at other times.
The ZLB matters enormously, and fiscal policy is genuinely more powerful there. This is not a theoretical curiosity — it describes the US from 2009 to 2015, the Eurozone for even longer, and Japan for decades. But the mainstream acknowledges that the ZLB is (usually) temporary and that fiscal policy outside the ZLB faces real crowding-out constraints. The correct answer to "does government spending help?" is genuinely "it depends on the state of the economy" — and this isn't a cop-out, it's the actual result of rigorous analysis across multiple model frameworks and empirical approaches.
We still haven't asked: how is the spending financed? If debt accumulates, what determines whether it's sustainable? The fiscal theory of the price level (Chapter 16, §16.5) challenges the entire monetary-fiscal separation. And the formal Ricardian equivalence result (Ch 16, §16.4) says that under specific conditions, government debt is not net wealth — so deficit-financed spending may have no effect at all. Come back at Chapter 16 (§16.3–16.8) for the full picture: the government budget constraint, Ricardian equivalence, FTPL, and the empirical evidence on multipliers.
The multiplier says a bigger stimulus would have kept unemployment below 8%. It hit 10%. Was the model wrong, or was the dose too small?
IntermediateA viral TikTok distilled MMT into one sentence: a sovereign currency issuer can never run out of money. The constraint is inflation, not solvency. The New Keynesian framework has a precise answer to why this is incomplete.
Advanced| Shock | RBC Response | NK Response |
|---|---|---|
| Technology + | Output up, hours ambiguous | Output up more slowly, hours may fall |
| Monetary expansion | No effect (neutral) | Output up, inflation up, rate down |
| Cost-push | Maps to tech shock | Inflation up, output down (stagflation) |
Compare impulse responses side by side. Toggle between a technology shock and a monetary policy shock to see what nominal rigidities add.
Figure 15.5. Side-by-side impulse responses. Left column: RBC (flexible prices). Right column: NK (sticky prices). Top row: output. Bottom row: inflation. Toggle between shock types. The monetary shock has no effect in RBC but real effects in NK — this is what price stickiness adds.
You've now seen the NK model alongside the RBC model. The NK framework nests RBC as a special case and adds demand shocks, sticky prices, and monetary non-neutrality. This is the synthesis — and the final stop for this Big Question.
The NK model nests RBC as a special case ($\theta \to 0$, all prices flexible). With sticky prices, three types of shocks cause recessions: (a) demand shocks — changes in $r^n$, confidence, or fiscal policy move output because firms can't immediately adjust prices; (b) monetary policy shocks — rate changes have real effects since prices are sticky; (c) cost-push shocks create stagflation (inflation up, output down). The model generates realistic impulse responses and matches key business cycle moments. Crucially, monetary policy matters — a rate cut stimulates demand when prices are sticky, unlike in RBC where money is neutral. The synthesis answers the central question: recessions are caused by a combination of demand and supply shocks interacting with nominal rigidities, and the economy can get stuck below potential when prices fail to adjust quickly enough.
Financial frictions are missing. The 2008 crisis was caused by financial leverage, panic, and credit contraction — none of which appear in the baseline NK model. Bernanke, Gertler, and Gilchrist (1999) added a financial accelerator, but the profession was slow to take it seriously pre-2008. The Great Recession was not a technology shock or a standard demand shock — it was a financial crisis that cascaded through credit markets. Heterogeneity is missing. Representative-agent models miss the distributional effects of recessions: unemployment falls on specific workers, not the "average" agent. HANK models (Kaplan, Molin, Violante 2018) address this but are frontier research. The Austrian persistence: Neither RBC nor NK explains why credit booms systematically precede busts. The Austrian theory of malinvestment — that artificially low interest rates cause unsustainable investment patterns — describes a recurring pattern that mainstream models don't capture.
Post-2008, the NK framework expanded substantially: financial frictions (Christiano, Motto & Rostagno 2014), heterogeneous agents (HANK), and occasionally binding constraints (ZLB). The frontier is "medium-scale DSGE" models with many shocks and frictions — Smets and Wouters (2007) use seven shocks and multiple frictions to match a broad set of macroeconomic moments. Central banks now run these models operationally. The profession also grew more honest about uncertainty: no single model explains all recessions, and the relative contribution of demand, supply, and financial shocks varies by episode.
The NK synthesis is the best available framework for understanding recessions: demand and supply shocks both matter, monetary policy has real effects, and the economy can get stuck below potential when prices are sticky. RBC's claim that recessions are efficient was rejected, but its methodological insistence on microfoundations was absorbed. The answer to "what causes recessions?" is genuinely plural — demand shocks (the Keynesian channel), supply shocks (the RBC channel), financial instability (the Minsky-Bernanke channel), and policy mistakes (the Friedman-Volcker channel) all contribute. The honest position is that no single theory explains all recessions, and the profession should be more forthright about this.
This is the final stop for BQ08, but the question isn't fully closed. Are we missing a fundamental mechanism? Financial crises, pandemics, and geopolitical shocks all cause recessions through channels that standard DSGE models struggle with. Agent-based models and network approaches that capture cascading failures are an active frontier. And the deepest question may be epistemological: can any single macro model capture the diversity of recession causes, or do we need a toolkit of models matched to circumstances? The profession's answer, increasingly, is the latter — and that humility may be the most important lesson of the last two decades of macroeconomics.
Yield curve inversions, consumer confidence drops, and leading indicators flash warnings. But predicting recessions is notoriously unreliable — the models that explain them after the fact can't reliably predict them in advance.
IntermediateThe multiplier says a bigger stimulus would have kept unemployment below 8%. It hit 10%. Was the model wrong, or was the dose too small?
IntermediateA grid of 100 firms. Each period, a random fraction $(1-\theta)$ gets to reset their price (green). The rest are stuck with their old price (red). Adjust $\theta$ and step through periods to see how price stickiness works.
Figure 15.1. Calvo pricing visualized. Green cells = firms that reset their price this period. Red cells = firms stuck with an old price. With $\theta = 0.75$, only 25% of firms adjust each quarter, so aggregate prices are sluggish. This is the micro-mechanism behind the NKPC. Click "Step Forward" or "Auto-Play" to advance.
Set $\phi_\pi = 0.8 < 1$. Show that sunspot equilibria are possible.
Step 1: Suppose agents suddenly believe inflation will be 2% next period (a sunspot). From the IS curve: $x = E_tx_{t+1} - (1/\sigma)(i - E_t\pi_{t+1} - r^n)$.
Step 2: Taylor rule: $i = r^* + 0.8\pi + 0.5x$. With $\phi_\pi = 0.8$, a 1% rise in inflation raises $i$ by only 0.8%. The real rate $r = i - E\pi$ falls by 0.2%.
Step 3: Lower real rate stimulates demand: $x$ rises. Higher output gap raises inflation via NKPC: $\pi = \kappa x > 0$. This validates the original belief.
Step 4: The sunspot is self-fulfilling: belief in higher inflation causes lower real rates, higher demand, and higher actual inflation. With $\phi_\pi > 1$, this loop is broken: the real rate rises with inflation, choking off demand.
A severe recession drives the natural rate to $r^n = -3\%$. Parameters: $\phi_\pi = 1.5$, $\phi_x = 0.5$, $\sigma = 1$, $\kappa = 0.3$.
Step 1: Without ZLB, Taylor rule: $i = 2 + 1.5(0) + 0.5(0) - 3 = -1\%$ (assuming $r^n$ enters). Negative rate is infeasible.
Step 2: ZLB binds: $i = 0$. Real rate: $r = 0 - E\pi \approx 0\%$ (if inflation near zero). But natural rate is $-3\%$. Monetary policy gap: $r - r^n = 0 - (-3) = 3\%$ too tight.
Step 3: From the IS curve: $x \approx -(1/\sigma)(r - r^n) = -3\%$. The output gap is severely negative.
Step 4: From NKPC: $\pi = \kappa x = 0.3(-3) = -0.9\%$. Deflation sets in, raising the real rate further and deepening the recession — the deflationary spiral.
Policy options: Forward guidance (promise low rates after recovery), fiscal stimulus (government spending has multiplier $> 1$ at ZLB), or unconventional monetary policy (QE).
Compare responses to a surprise 1% interest rate cut.
RBC model: Money is neutral. The nominal rate drop has no effect on any real variable. Output, consumption, investment, and hours are all unchanged. $\Delta y = \Delta c = \Delta i = \Delta h = 0$.
NK model: With $\theta = 0.75$ (prices reset once per year on average):
Step 1: The real rate falls by approximately 1% (prices are sticky, so lower $i$ passes through to lower $r$).
Step 2: From the IS curve, the output gap rises: $\Delta x \approx (1/\sigma)\Delta r = 1\%$.
Step 3: From the NKPC, inflation rises: $\Delta\pi = \kappa\Delta x = 0.3\%$.
Step 4: Over time, prices adjust. As more firms reset at higher prices, the price level catches up, the real rate returns to normal, and the output effect dissipates. Half-life: roughly \$1/(1-\theta) = 4$ quarters.
Key insight: Nominal rigidities convert a nominal shock into a real one. As $\theta \to 0$, the NK response converges to the RBC response (no real effects).
The Volcker disinflation (1979–82): Raising rates to 20% to break inflation.
When Paul Volcker became Fed Chair in August 1979, U.S. inflation was running at 13% and accelerating. Inflation expectations had become unanchored: workers demanded higher wages, firms raised prices, and the Phillips curve had shifted up repeatedly. The pre-Volcker Fed under Arthur Burns had responded to inflation with modest rate increases ($\phi_\pi \approx 0.83 < 1$), violating the Taylor principle and allowing inflation to become self-fulfilling.
Volcker's strategy was radical: he raised the federal funds rate to a peak of 20% in June 1981. The real interest rate exceeded 8% — the most restrictive monetary policy in modern U.S. history. The economy plunged into recession: unemployment peaked at 10.8% in November 1982, and GDP fell by 2.7%.
The result: Inflation fell from 13% to 3% by 1983. More importantly, inflation expectations were broken. The sacrifice ratio — the cumulative output loss per percentage point of disinflation — was approximately 2.3, within the range predicted by NK models with moderate price stickiness ($\theta \approx 0.75$).
NK interpretation: Volcker's policy implemented the Taylor principle with a vengeance ($\phi_\pi \gg 1$). By demonstrating that the Fed would tolerate severe recession to reduce inflation, he shifted from an indeterminate regime to a determinate one. Post-Volcker, the Fed maintained $\phi_\pi > 1$, producing the Great Moderation (1984–2007) — the longest period of macroeconomic stability in U.S. history.
Kaelani's central bank adopts an inflation-targeting regime with target $\pi^* = 3\%$ and Taylor rule: $i_t = 0.04 + 1.5(\pi_t - 0.03) + 0.5x_t$.
Scenario 1 (demand shock): Commodity price boom raises inflation to 5%. Taylor rule: $i = 0.04 + 1.5(0.02) + 0.5(0.02) = 8\%$. The real rate rises, cooling demand.
Scenario 2 (ZLB): Global recession drives $r^n = -2\%$. Taylor rule calls for $i = -1\%$, but the ZLB binds at 0%. The economy remains in recession. Options: fiscal stimulus, forward guidance, or unconventional monetary policy.
| Label | Equation | Description |
|---|---|---|
| Eq. 15.1–15.2 | Dixit-Stiglitz aggregation | Monopolistic competition |
| Eq. 15.4 | $\pi_t = \beta E_t\pi_{t+1} + \kappa x_t$ | New Keynesian Phillips Curve |
| Eq. 15.5 | $x_t = E_tx_{t+1} - \frac{1}{\sigma}(i_t - E_t\pi_{t+1} - r_t^n)$ | Dynamic IS curve |
| Eq. 15.6 | $i_t = r^* + \phi_\pi\pi_t + \phi_x x_t$ | Taylor rule |
| Eq. 15.7 | $\phi_\pi > 1$ | Taylor principle |
| Eq. 15.8 | NKPC with cost-push shock $u_t$ | Breaks divine coincidence |
| Eq. 15.10 | $i_t \geq 0$ | Zero lower bound |