Comprehensive Macroeconomic Principles: Business Cycles, Indicators, Tax Incidence, and the Quantity Theory of Money

Price Elasticity and Tax Incidence

Determinants of Tax Burden Distribution:
- The relative price elasticities of supply and demand determine the division of the economic burden (tax incidence) between buyers and sellers in a market.
- When demand is relatively more inelastic than supply, buyers have fewer viable substitutes or alternatives and bear the larger share of the tax burden.
- When supply is relatively more inelastic than demand, sellers find it more difficult to adjust output or reallocate capital/resources and bear the larger share of the tax burden.

Tax incidence and relative elasticity of supply and demand

Graphical Analysis of Elasticity and Incidence:
- Inelastic Demand Relative to Supply:
- Initial market equilibrium price is established at $\$1.10$ .
- A per-unit tax of $\$0.30$ is introduced, shifting the supply curve upward vertically by the amount of the tax to form the new supply curve.
- Due to relatively steep (inelastic) demand and flatter (elastic) supply, the price paid by buyers increases to $\$1.35$ .
- The net price received by sellers falls to $\$1.05$ .
- Tax incidence on buyers is calculated as: $\$1.35 - \$1.10 = \$0.25$ .
- Tax incidence on sellers is calculated as: $\$1.10 - \$1.05 = \$0.05$ .
- Buyers absorb $\frac{5}{6}$ ( $\approx 83.33\%$ ) of the tax burden, while sellers absorb only $\frac{1}{6}$ ( $\approx 16.67\%$ ).
- Inelastic Supply Relative to Demand:
- Initial market equilibrium price is established at $\$1.10$ .
- A per-unit tax of $\$0.30$ is imposed, shifting the supply curve upward vertically by $\$0.30$ .
- Because supply is steep (inelastic) and demand is flat (elastic), the price paid by buyers rises modestly to $\$1.15$ .
- The net price received by sellers decreases significantly to $\$0.85$ .
- Tax incidence on buyers is calculated as: $\$1.15 - \$1.10 = \$0.05$ .
- Tax incidence on sellers is calculated as: $\$1.10 - \$0.85 = \$0.25$ .
- Sellers absorb $\frac{5}{6}$ ( $\approx 83.33\%$ ) of the tax burden, while buyers absorb $\frac{1}{6}$ ( $\approx 16.67\%$ ).
Deadweight Loss (DWL) Principles:
- Deadweight loss is greater when the sides of the market (both demand and supply) are more elastic, as higher price sensitivity causes a larger reduction in equilibrium transaction volume away from the socially optimal quantity.
- Deadweight loss increases disproportionately when taxes are higher; deadweight loss grows as a quadratic function of the tax rate.

Business Cycle Concepts and Stages

Definition and Nature of Business Cycles:
- Business cycles represent short-term fluctuations in aggregate economic activity around the long-term trend.
- No two business cycles are identical in duration, amplitude, or underlying catalyst.
- Fluctuations in the aggregate economy are highly irregular and unpredictable rather than mechanical or periodic.
Stages and Technical Thresholds of the Business Cycle:
- Peak: The highest point of economic activity reached before a downturn begins.
- Downturn: A phase of declining economic activity characterized by $1$ or more quarters of negative percentage change in real Gross Domestic Product (Real GDP).
- Trough: The lowest turning point in economic activity where contraction ends and recovery commences.
- Recession: A sustained period of declining economic activity officially marked by $2$ or more consecutive quarters of negative percentage change in Real GDP.
- Depression: An severe, protracted contraction defined by $12$ or more consecutive months of negative percentage change in Real GDP.
- Expansion: A period of increasing economic activity identified by $1$ or more quarters of positive percentage change in Real GDP.

Real GDP fluctuations showing peak, recession, trough, and expansion

Empirical Path of Real GDP ( $2004 - 2018$ ):
- Real GDP expanded steadily from approximately $\$14\text{ trillion}$ in $2004$ toward $\$16\text{ trillion}$ by late $2007$ .
- The economic peak occurred in $2008$ , preceding the Great Recession.
- A sharp contraction occurred during $2008 - 2009$ , reaching a trough below the pre-recession peak.
- A sustained, long-term expansion followed from the $2009$ trough through $2018$ , surpassing $\$18\text{ trillion}$ .

Characteristics and Empirical Dynamics of Business Cycles

Core Asymmetric Characteristics:
- Recessions are typically short and sharp: economic contractions unfold rapidly with steep drops in output and employment over short spans of time.
- Expansions are long and gradual: economic recoveries and booms build slowly, adding jobs and productive capacity over extended horizons.

Output gap behavior demonstrating short, sharp recessions and slow, gradual expansions

Output Gap Trajectory ( $1990 - 2020$ ):
- The output gap measures the percentage deviation of actual Real GDP from potential output ( $Y - Y^*$ ).
- During the $1990 - 1991$ recession, the output gap dropped sharply toward $-4\%$ , followed by an extended, gradual expansion that peaked near $+3\%$ to $+4\%$ in the late $1990\text{s}$ .
- The $2001$ contraction caused a rapid decline back toward $-2\%$ , which was succeeded by an expansion peaking slightly above $0\%$ around $2006 - 2007$ .
- The $2007 - 2009$ recession saw the output gap plunge sharply below $-6\%$ (approaching $-7\%$ ), followed by a slow, decade-long expansion that steadily climbed back above $0\%$ by $2018 - 2019$ .

Sectoral, Geographic, and Indicator Synchronization

Systemic Co-Movement in the Macroeconomy:
- Economic fluctuations affect virtually every sector of the aggregate economy simultaneously.
- A positive impulse or distress in one sector rapidly spills over into related markets, generating synchronized aggregate movements.

State-by-state unemployment rates across the United States from 1998 to 2018

Geographic Distribution and Regional Variation:
- State unemployment rates across all $50$ U.S. states and the District of Columbia largely rise and fall together across national cycles ( $1998 - 2018$ ).
- Despite nationwide synchronization, distinct economic "pockets" emerge where specific states diverge based on local industrial compositions:
- States heavily reliant on manufacturing, automotive, or housing (e.g., Nevada, Michigan, Florida, California, Rhode Island) experienced unemployment surges well above $10\%$ (peaking near $13\% - 15\%$ ) during the $2008$ crisis.
- Resource- and agriculture-heavy states (e.g., North Dakota, South Dakota, Nebraska, Iowa) maintained far lower and more stable unemployment trajectories throughout the same period.

Annual growth rates of real GDP, employment, real retail sales, and industrial production

Synchronization Across Major Aggregates ( $1998 - 2018$ ):
- Real GDP, Employment, Real Retail Sales, and Industrial Production consistently move in tandem.
- Output and retail indicators exhibit greater volatility than overall employment:
- Industrial production experienced the deepest decline during the $2008 - 2009$ recession, falling to approximately $-17\%$ to $-20\%$ annual growth.
- Real retail sales fell sharply below $-10\%$ during the same window.
- Employment exhibited smoother, less volatile movements, dipping to roughly $-5\%$ annual growth.

Employment growth over the past year across various industries

Industry Cyclicality and Divergence:
- Most major industries move synchronously across the business cycle, including Business Services, Construction, Finance, Information, Leisure, Manufacturing, Other Services, and Trade.
- Cyclical sensitivity varies drastically by sector:
- Highly cyclical industries: Construction and Manufacturing experienced severe contractions in $2008 - 2009$ , with employment growth collapsing toward $-15\%$ and nearly $-20\%$ .
- Less cyclical / defensive industries: Services, Trade, and Finance experienced more moderate declines, retaining higher relative stability.

Macroeconomic Measurement: Levels, Changes, and Indicator Timing

Levels versus Changes:
- Levels describe where the economy currently stands:
- Evaluated by comparing the current level of Real GDP to potential output to gauge absolute economic utilization and resource slack.
- Changes describe where the economy is heading:
- Evaluated by analyzing Real GDP growth rates, revealing the direction and momentum of the economy (accelerating, decelerating, expanding, or contracting).
Temporal Classification of Indicators:
- Leading Indicators: Variables that shift before aggregate economic activity changes, serving as predictive signals for future economic turning points.
- Lagging Indicators: Variables that shift only after aggregate economic activity has already changed, confirming long-term trends and structural adjustments with a delay.

The Ten Core Economic Indicators and Tracking Dashboard

Exhaustive Breakdown of the Top Ten Indicators:
- 1. Real GDP (Gross Domestic Product):
- The broadest comprehensive measure of aggregate economic activity.
- Quantifies total production, total spending, and total income generated across the economy.
- Formulated via the national expenditure identity: $Y = C + I + G + NX$ , where $C$ is consumption, $I$ is investment, $G$ is government purchases, and $NX$ is net exports.
- 2. Real GDI (Gross Domestic Income):
- Measures economic performance by aggregating all forms of income earned across the economy (wages, profits, rents, taxes on production).
- Conceptually identical to GDP in theoretical equilibrium, but calculated from separate source data.
- Frequently signals turning points and flashing warnings sooner than GDP due to earlier statistical availability.
- 3. Nonfarm Payrolls:
- Measures the net number of paid jobs created or lost each month by commercial, industrial, and government entities (excluding agricultural employment).
- Offers a high-frequency, reliable, and early assessment of the pace of employment growth.
- 4. Unemployment Rate:
- Quantifies the proportion of the civilian labor force actively seeking employment but unable to find work.
- Serves as an essential snapshot of labor market slack and productive excess capacity.
- 5. Initial Unemployment Claims:
- Weekly count of individuals filing first-time applications for state unemployment insurance benefits.
- Serves as a timely, high-frequency indicator of layoffs and real-time labor market deterioration.
- 6. Business Confidence:
- Measured through metrics such as the ISM Purchasing Managers' Index (PMI).
- Tracks expectations, forward orders, and operational plans of procurement and corporate managers.
- Downward trends in manager sentiment frequently signal impending macroeconomic slowdowns or recessions.
- 7. Consumer Confidence:
- Tracked via survey instruments such as the University of Michigan Index of Consumer Sentiment.
- Gauges consumer attitudes regarding personal finances, job security, and general business conditions.
- Expands during economic booms when consumer optimism spurs household consumption.
- 8. Inflation Rate:
- Measured by the annual percentage change in price indices, such as the Consumer Price Index (CPI).
- Tracks changes in the aggregate cost of living and purchasing power of currency over time.
- 9. Employment Cost Index (ECI):
- Quantifies changes in total labor costs incurred by employers, covering wages, salaries, and non-wage employee benefits.
- Sustained growth in labor compensation signals strong labor demand and overall economic health.
- 1. Stock Market (S&P 500 Index):
- Reflects equity valuations and the capitalized present value of expected future corporate profitability.
- Incorporates forward-looking market expectations regarding macroeconomic growth and business conditions.

Economic indicator dashboard with corresponding FRED time-series series

Economic Indicator Dashboard Benchmarks and Data Codes:
- Federal Reserve Economic Data (FRED) Dashboard Link: https://fredaccount.stlouisfed.org/public/dashboard/1151
- Detailed Statistical Distribution of Core Dashboard Metrics:
- Real GDP Growth (annualized quarterly rate):
  - Metric: Quarterly growth at an annualized rate
  - FRED Code: GDPC1
  - Historical Median: $2.6\%$
  - Interquartile Range (IQR): $1.2\% - 3.8\%$
- Real GDI Growth (annualized quarterly rate):
  - Metric: Quarterly growth at an annualized rate
  - FRED Code: A261RX1Q020SBEA
  - Historical Median: $2.5\%$
  - Interquartile Range (IQR): $0.6\% - 4.5\%$
- Change in Nonfarm Payrolls:
  - Metric: Monthly change in thousands of jobs
  - FRED Code: PAYEMS
  - Historical Median: $157{,}000$
  - Interquartile Range (IQR): $12{,}500 - 248{,}000$
- Unemployment Rate:
  - Metric: Percent share of the civilian labor force
  - FRED Code: UNRATE
  - Historical Median: $5.4\%$
  - Interquartile Range (IQR): $4.7\% - 6.7\%$
- Initial Unemployment Claims:
  - Metric: Weekly initial claims in thousands
  - FRED Code: ICSA
  - Historical Median: $339$
  - Interquartile Range (IQR): $312 - 396$
- Business Confidence:
  - Metric: ISM Purchasing Managers' Index (PMI)
  - FRED Code: Not available
  - Historical Median: $52.5$
  - Interquartile Range (IQR): $49.9 - 55.3$
- Consumer Confidence:
  - Metric: University of Michigan Index of Consumer Sentiment
  - FRED Code: UMSCENT
  - Historical Median: $89.2$
  - Interquartile Range (IQR): $77.5 - 95.8$
- Inflation Rate:
  - Metric: Annual percent change in the Consumer Price Index (CPI)
  - FRED Code: CPIAUCSCL
  - Historical Median: $2.4\%$
  - Interquartile Range (IQR): $1.7\% - 3.0\%$
- Employment Cost Index (ECI):
  - Metric: Annual percent change in total compensation
  - FRED Code: ECIALLCIV
  - Historical Median: $2.6\%$
  - Interquartile Range (IQR): $2.0\% - 3.5\%$
- Stock Market Growth:
  - Metric: S&P 500 percent change over the past year
  - FRED Code: SP500
  - Historical Median: $11.7\%$
  - Interquartile Range (IQR): $0.0\% - 21\%$

The Quantity Theory of Money and the Equation of Exchange

Theoretical Framework:
- The Quantity Theory of Money models the relationship between money supply, the speed of monetary circulation, the aggregate price level, and physical output.
- Governed by the fundamental Equation of Exchange:
- $P \times Q = M \times V$
- National Income Accounting Identity:
- $\text{Nominal GDP} = \text{Money Supply} \times \text{Velocity}$
- Definitional Components:
- $M$ : Nominal money stock (e.g., M2 monetary aggregate).
- $V$ : Velocity of money, defined as the average number of times a single unit of currency exchanges hands in purchasing final goods and services over a specified time period.
- $P$ : Aggregate price level of final output (measured by the GDP Deflator).
- $Q$ : Real output / Real GDP.
- $P \times Q$ : Nominal Gross Domestic Product.
Long-Run Neutrality and Inflation Dynamics:
- Classical monetary theory holds that in the long run, Real GDP ( $Q$ ) is determined exclusively by real structural factors of production: the aggregate capital stock, labor force size and quality, and technological progress.
- Because real productive capacity is independent of the nominal money stock in the long run, variations in the money supply ( $M$ ) transmit directly into proportional changes in the aggregate price level ( $P$ ).
- A sustained increase in the money supply in excess of real productive capacity leads directly to higher prices and persistent inflation.

Quantity theory of money parameters for the United States in 2017 Q1

Empirical Application to the U.S. Economy ( $2017\text{ Q1}$ ):
- M2 Money Supply ( $M$ ): $\$13{,}319\text{ billion}$
- M2 Monetary Velocity ( $V$ ): $1.431$
- GDP Deflator Price Level ( $P$ ): $1.1275$
- Real GDP Output ( $Q$ ): $\$16{,}903\text{ billion}$
- Computational Balance of the Equation of Exchange:
- Left-Hand Side (Nominal GDP via Price and Output):
  - P \times Q = 1.1275 \times \16{,}903\text{ billion} = \ $19{,}058\text{ billion}$
- Right-Hand Side (Nominal GDP via Money and Velocity):
  - M \times V = \13{,}319\text{ billion} \times 1.431 = \ $19{,}058\text{ billion}$
- Equilibrium Identity:
  - \19{,}058\text{ billion} = \ $19{,}058\text{ billion}$