The AD-AS Model, the Phillips Curve, and the Lucas Critique

Overview of the AD-AS Model

• The Aggregate Demand and Aggregate Supply (AD-AS) model serves as a fundamental link between short-run neoclassical business cycle theory and long-run classical theory.
• It combines an Aggregate Demand (AD) curve with a Short-Run Aggregate Supply (SRAS) curve to determine the aggregate price level ($P_t$) and the level of output ($Y_t$) in the short run.
• The model illustrates the temporal evolution of $P_t$ and $Y_t$, showing how an economy eventually converges to its long-run equilibrium.
• A central feature of the model is the crucial role of price expectations:
  • Firms frequently set prices for their products based on expectations regarding the aggregate price level ($P^e_t$).
  • The position of the SRAS-curve in any period $t$ is dependent on the expected aggregate price level for that same period ($P^e_t$).
  • Consequently, the position of the SRAS-curve shifts over time as expectations about the aggregate price level are adjusted.

The Link Between Short-Run and Long-Run Dynamics

• In the Long Run:
  • The level of output ($Y$) is equal to the natural level of output ($Y_n$).
  • In this context, $Y_n$ is exogenous; for simplification, it is assumed to remain constant over time.
  • The Long Run Aggregate Supply curve (LRAS-curve) is defined by the vertical line: $Y = Y_n$.
• In the Short Run:
  • To simplify the analysis, the model assumes a closed economy.
  • Short-run business cycle fluctuations, given a specific price level ($P$), are described by the IS-LM model.
  • The Aggregate Demand curve (AD-curve) represents the relationship between the aggregate price level ($P$) and the level of output ($Y$) for which both goods and money markets are in equilibrium.
  • This relationship is inverse: an increase in the aggregate price level leads to a decrease in output ($P \uparrow \Rightarrow Y \downarrow$).

The Short-Run Aggregate Supply (SRAS) Curve

• The SRAS-curve establishes that in the short run, the price level ($P_t$) depends on the expected price level ($P^e_t$).
• Mechanism for Price Rigidity:
  • Some firms maintain fixed output prices for specified periods, setting these prices based on their expectations of input costs and competitor pricing.
  • Nominal wages are often fixed for certain periods based on price expectations, which directly impacts the output prices set by firms.
• Relation to the Business Cycle:
  • There is a direct relationship between the stage of the business cycle (measured as the deviation of output from its natural level, $Y_t - Y_n$) and the price level ($P_t$).
  • Higher aggregate demand leads firms to charge higher prices for their products.
  • If nominal wages are fixed, a higher aggregate price level reduces the real wage, incentivizing firms to hire more labor and increase production.
• Key SRAS Characteristics:
  • Output is at the natural level if and only if the price level equals the expected price level: $Y_t = Y_n \iff P_t = P^e_t$.
  • Output exceeds the natural level if and only if the price level is higher than expected: $Y_t > Y_n \iff P_t > P^e_t$.
  • Output is below the natural level if and only if the price level is lower than expected: $Y_t < Y_n \iff P_t < P^e_t$.

Economic Equilibrium and Long-Run Convergence

• Short-Run Equilibrium Adjustments:
  • Excess demand in the goods market (Aggregate demand > Aggregate production): Leads to an increase in $P$ and $Y$ until equilibrium is reached, represented by a shift to the right along the SRAS-curve.
  • Excess supply in the goods market (Aggregate demand < Aggregate production): Leads to a decrease in $P$ and $Y$ until equilibrium is reached, represented by a shift to the left along the SRAS-curve.
• Long-Run Convergence Mechanisms:
  • If production is above the natural level ($Y_t > Y_n$), then the actual price level is higher than expected ($P_t > P^e_t$). This causes expectations to rise ($P^e \uparrow$), shifting the SRAS-curve to the left. A new short-run equilibrium is formed, and the process repeats until $Y = Y_n$ and $P = P^e$.
  • If production is below the natural level ($Y_t < Y_n$), then the actual price level is lower than expected ($P_t < P^e_t$). This causes expectations to fall ($P^e \downarrow$), shifting the SRAS-curve to the right until the economy reaches long-run equilibrium where $Y = Y_n$ and $P = P^e$.
• Application to Demand Expansion:
  • Initially, the economy is in long-run equilibrium: $Y_1 = Y_n$ and $P_1 = P^e_1 = P^e_2$.
  • Period 2: A demand expansion shifts the AD-curve to the right, creating excess demand. The economy moves to point $E_2$ along the initial SRAS ($SRAS_1$), where $Y_2 > Y_n$ and $P_2 > P^e_2$.
  • Eventually: As expectations adjust upwards ($P^e \uparrow$), the SRAS-curve shifts left until the economy settles at a new long-run equilibrium ($E_\infty$) where $Y = Y_n$ and $P = P^e > P_1$.
• Monetary Neutrality:
  • If a demand expansion is driven by monetary expansion, the classical dichotomy does not hold in the short run (output increases) but does hold in the long run (only prices increase).

The Phillips Curve

• The Phillips curve represents the relationship between the unemployment rate ($u$) and the inflation rate ($\pi$), derived directly from the relationship between output and price levels in the SRAS-curve.
• Correlation Table:
  • Natural levels: $Y_t = Y_n \iff u_t = u_n$ and $P_t = P^e_t \iff \pi_t = \pi^e_t$.
  • Overheating: $Y_t > Y_n \iff u_t < u_n$ and $P_t > P^e_t \iff \pi_t > \pi^e_t$.
  • Recession: $Y_t < Y_n \iff u_t > u_n$ and $P_t < P^e_t \iff \pi_t < \pi^e_t$.
• The Phillips Curve Equation:
  • $\pi_t = \pi^e_t - \beta \cdot (u_t - u_n) + \nu_t$, where $\beta > 0$.
• Components of the Equation:
  • First term ($\pi^e_t$): Inflation expectations feed into actual inflation, making inflation persistent.
  • Second term ($-\beta \cdot (u_t - u_n)$): Demand-pull inflation. A lower cyclical unemployment rate leads to higher inflation.
  • Third term ($\nu_t$): Supply shocks. Unfavorable shocks ($\nu > 0$, e.g., unexpected oil price increase) cause higher inflation and potentially stagflation (high inflation and low growth). Favorable shocks ($\nu < 0$, e.g., unexpected oil price decrease) lower inflation.

Case Study: Inflation and Unemployment in the U.S. (1960–2021)

• 1960s: Demand expansion due to tax cuts ($T \downarrow$) and increased government spending ($G \uparrow$) for the Vietnam War. Result: Demand-pull inflation ($\pi \uparrow, u \downarrow$).
• 1973–1975 and 1979–1981: Unfavorable supply shocks due to rising oil prices. Result: Cost-push inflation ($\pi \uparrow, u \uparrow$).
• 1981–1982: Demand contraction caused by monetary tightening. Result: Reversed demand-pull inflation ($\pi \downarrow, u \uparrow$).
• 1984–1986: Favorable supply shocks due to falling oil prices. Result: Reversed cost-push inflation ($\pi \downarrow, u \downarrow$).
• 1990–1991: Demand contraction during the First Gulf War. Result: Reversed demand-pull inflation ($\pi \downarrow, u \uparrow$).
• 1998–2000: Demand expansion during the IT-bubble. Result: Demand-pull inflation ($\pi \uparrow, u \downarrow$).
• 2007–2009: Demand contraction due to the Financial crisis. Result: Reversed demand-pull inflation ($\pi \downarrow, u \uparrow$).
• Included Data Years for U.S. Inflation/Unemployment: 1963, 1969, 1973, 1974, 1975, 1979, 1980, 1981, 1982, 1983, 1984, 1985, 1986, 1990, 1991, 1992, 1998, 1999, 2000, 2007, 2008, 2009, 2019, 2020, 2021.

Expectations and Policy Implications

• Adaptive Expectations:
  • Assumptions: Expectations extrapolate from past observations (e.g., $P^e_t = P_{t-1}$ or $\pi^e_t = \pi_{t-1}$).
  • Outcome: A short-run trade-off exists between $\pi_t$ and $u_t$. Fiscal and monetary authorities can systematically influence $u$ and $Y$. However, disinflation (reducing inflation) is costly as it increases unemployment.
• Rational Expectations and the Lucas Critique:
  • Definition of Rational Expectations: People are forward-looking and use all available information, including anticipated policy changes, to forecast the future.
  • Anticipated Shocks: If shocks are anticipated and expectations are rational, the expected price level ($P^e_t$) will account for the policy change such that the actual price level ($P_t$) equals the expected level ($P_t = P^e_t$). If they were unequal, the expectation would not be rational.
  • Resulting Relationship: Since $P_t = P^e_t$, output remains at the natural level ($Y_t = Y_n$) and unemployment remains at the natural rate ($u_t = u_n$).
• Policy Implications of the Lucas Critique:
  • No short-run trade-off between $\pi_t$ and $u_t$ exists for anticipated policies.
  • Anticipated expansion results in higher inflation ($\pi \uparrow$) but no change in unemployment ($u \leftrightarrow$). Authorities cannot systematically influence output through anticipated policy.
  • Disinflation can be painless if the contractionary policy is anticipated, as $\pi^e_t$ will drop immediately.
  • Only unanticipated shocks affect unemployment and output.
• Conclusion of the Lucas Critique:
  • To predict the effect of economic policy, one must account for how policy affects the expectations of economic agents.
  • Traditional models like IS-LM and AD-AS are criticized as inappropriate frameworks for evaluating policy if they ignore these feedback effects on expectations.
  • Modern macroeconomics addresses this by utilizing micro-foundations, specifically micro-foundations for expectations.