Booms, Busts, and the IS Curve

Introduction to Short Run Macroeconomics

• Focus Area: The second half of the course focuses on short-run macroeconomics, specifically centering on the following topics:     * Economic Booms and Recessions.     * Inflation dynamics and expectations.     * Monetary and fiscal policy interventions.     * Financial crises.     * Exchange rates and international finance.     * The interaction of COVID-19 with macroeconomics.

• Class Outline:     * Distinguishing between the Short-Run and the Long-Run.     * Defining Short-Run Output.     * Understanding Okun’s Law and the costs associated with recessions.     * Deriving the IS curve, which serves as the first building block of the Short-Run (SR) Model.     * Practical applications of the IS curve through various examples.     * Evaluating the effectiveness of fiscal stimulus measures.

The Long Run vs. The Short Run

• Long-Run Model: Primarily concerned with Potential Output and long-run trends in inflation.

• Short-Run Model: Focuses on deviations from the trend, specifically Current Output and current inflation.

• Defining the Short-Run: The specific length of time over which economic deviations from the long-run trend occur, typically estimated as being between two to four years.

• Trends and Fluctuations:     * Actual Output ($Y_t$) is the sum of Potential Output ($\bar{Y}_t$) and the deviation through short-run fluctuations.     * The mathematical representation of total output is: $Y_t = \bar{Y}_t + (Y_t - \bar{Y}_t) = \bar{Y}_t + \bar{Y}_t imes ilde{Y}_t$.     * Interpretation of $\tilde{Y}_t$: This variable represents the percentage deviation of actual output from the long-run trend.

Economic Fluctuations and Short-Run Output

• Recession Definition: A period where short-run output ($\tilde{Y}$) is less than zero (\tilde{Y} < 0).

• Potential vs. Actual Output:     * Potential Output ($\bar{Y}$): Refers to the level of production the economy would achieve if all resources were used at their normal rates.     * Actual Output ($Y$): The observed production level, which can fluctuate above or below potential.     * Above Potential: Output can be above potential (e.g., $+2\%$, where \tilde{Y} > 0) during economic booms when resources are over-utilized.

Historical Data and US Economic Fluctuations

• Potential Real GDP Construction: In the United States, potential output is constructed by the Congressional Budget Office (CBO) for years following 1949. This is based on the Solow growth model where $\bar{Y}$ is influenced by factors such as investment and Total Factor Productivity (TFP).

• US Trends:     * Growth average since 2009Q2: $+2.0\%$.     * The CBO identifies low investment and a TFP slowdown as contributors to changes in potential output trends.

• Specific Short-Run Output Data Points ($\tilde{Y}$):     * 2009Q2: $-5.3\%$     * 2020Q2: $-10.8\%$     * 2022Q1: $-1.3\%$

• US Unemployment Fluctuations: Statistics show significant spikes in unemployment during recessionary periods, notably peaking around 2010 and 2020.

Okun’s Law

• Concept: Okun’s Law is an empirical relationship used to translate between measures of short-run output and unemployment.     * Recession Characteristics: Characterized by low short-run output and high unemployment.     * Boom Characteristics: Characterized by high short-run output and low unemployment.

• Mathematical Formula: $u - \bar{u} = - rac{1}{2} imes ilde{Y}$.

• Conversion Rule: Every percentage point of cyclical unemployment ($u - \bar{u}$) corresponds to approximately two percentage points of lower short-run output ($\tilde{Y}$).

• US Economy Evidence: Historical data from 1960 to 2022 supports this slope, showing data points like 1982, 1983, 2009, and 2020 as periods of high cyclical unemployment and negative short-run output.

Comparing Recessions (Table 10.1)

Overview of the Short-Run Model

• Key Questions Addressed:     * Why does actual GDP differ from potential GDP?     * Why do recessions often follow peaks in the inflation rate?     * What is the specific role of monetary and fiscal policy in smoothing fluctuations?     * How do national economic fluctuations spill over to other countries?

• Three Premises of the Model:     1. The economy is constantly subjected to various shocks.     2. Monetary policy affects the real economy in the short run (indicating the failure of the Classical Dichotomy).     3. A dynamic tradeoff exists between output and inflation. Governments cannot simply keep output as high as possible indefinitely because of this tradeoff.

• Two-Sentence Summary:     * A booming economy increases inflation, while a slumping economy causes inflation to decline.     * The government, through the central bank and fiscal authority, can influence short-run output.

• Three Building Blocks:     1. The IS Curve: Shows that short-run output depends on the real interest rate.     2. The MP Curve: Shows how the central bank sets the real interest rate.     3. The Phillips Curve: Links inflation to the state of the economy (booming vs. slumping).

The IS Curve

• The Component Equation: Total short-run output is derived from the national income accounting identity: $Y_t = C_t + I_t + G_t + NX_t$.

• Investment Function: Investment is proportional to potential GDP but is a decreasing function of the real interest rate ($R_t$):     * $I_t / \bar{Y}_t = \bar{a}_I - \bar{b}(R_t - \bar{r})$.     * Rationale: Firms have a "menu" of investment projects with varying returns; as $R_t$ rises, fewer projects remain profitable.

• Other Components: Consumption ($C_t$), government spending ($G_t$), and net exports ($NX_t$) are treated as proportional to potential GDP:     * $C_t / \bar{Y}<em>t = \bar{a}_C$     * $G_t / \bar{Y}_t = \bar{a}_G$     * $NX_t / \bar{Y}_t = \bar{a}</em>{NX}$

• Equation Form: $\tilde{Y}<em>t = \bar{a} - \bar{b}(R_t - \bar{r})$.     * $\tilde{Y}_t$: Short-run output.     * $\bar{a}$: Aggregate demand shock (usually zero). Calculated as $\bar{a} = \bar{a}_C + \bar{a}_I + \bar{a}_G + \bar{a}</em>{NX} - 1$.     * $R_t$: Real interest rate determined in financial markets.     * $\bar{r}$: The marginal product of capital.     * $\bar{b}$: The sensitivity of investment to changes in the interest rate.

• Deriving the Name: "IS" stands for "Investment equals Savings." Rearranging the national income identity ($Y_t - C_t - G_t - NX_t = I_t$) and accounting for taxes ($T$) demonstrates: $(Y_t - T_t - C_t) + (T_t - G_t) + (IM_t - EX_t) = I_t$.     * Private Savings + Public Savings + Foreign Savings = Investment.

Using and Shifting the IS Curve

• Movement Along the Curve: Occurs when the Fed changes the interest rate. If the Fed raises the real interest rate ($R \uparrow$), the economy moves from point A to point B, resulting in lower short-run output ($\tilde{Y} \downarrow$).

• Shift - Increase in Demand (e.g., IT Boom): An increase in the aggregate demand shock ($\bar{a} \uparrow$) shifts the IS curve to the right ($IS o IS'$), increasing output ($\tilde{Y}$) for any given interest rate.

• Shift - Decrease in Demand (e.g., COVID-19): A decline in demand ($\bar{a} \downarrow$) shifts the IS curve to the left ($IS o IS'$), reducing output for a given interest rate.

Microfoundations of Consumption

• Permanent Income Hypothesis: Proposed by Milton Friedman and Franco Modigliani. Consumption depends on expected average future income ("permanent income") rather than just current income.     * Rationale: Consumers prefer to smooth consumption due to diminishing marginal utility.     * Example: Winning $10 million in a lottery payable in 5 years would increase consumption today even before the cash is received.

• Life-Cycle Model: Illustrates that individuals borrow while young, save during peak-income working years, and dissave during retirement.

• Borrowing Constraints and Multipliers:     * Empirically, current income matters more than the Permanent Income Hypothesis suggests because some fraction ($\bar{x}$) of people are borrowing-constrained.     * Including this fraction creates a multiplier effect: $\tilde{Y}_t = rac{1}{1 - \bar{x}} imes [\bar{a} - \bar{b}(R_t - \bar{r})]$.     * This magnifies the effects of shocks but the IS curve operates with the same fundamental downward slope.

Fiscal Stimulus and Austerity

• Effect of Government Spending ($G$): Increases in government spending generally stimulate the economy, though several factors limit the impact:     * No Free Lunch: Spending must eventually be paid for by taxes (today or in the future).     * Ricardian Equivalence: The theory that the timing of tax financing does not matter; consumers anticipate future taxes and save accordingly, offsetting the stimulus.     * Monetary Offset: The Federal Reserve may react to high output by raising interest rates ($R_t$), effectively neutralizing the fiscal expansion.

• Empirical Evidence:     * Normally, $1 of government spending increases GDP by 70-80 cents in the short run.     * If monetary policy does not provide an offset, the impact of $1 of spending can rise to $1.50.