Advanced Macroeconomic Formulas and Policy Concepts

Posted on Oct 8, 2025 in Economy

Core Macroeconomic Identities and Inflation

The Quantity Identity of Money

The Quantity Identity of Money is expressed as: M × V = P × Y

  • M = Money Supply
  • V = Velocity of Money
  • P = Price Level
  • Y = Real GDP
  • P × Y = Nominal GDP

Calculating Inflation and Growth Rates

To calculate inflation, multiply new prices by the total number of old goods.

The growth rate form of the Quantity Identity is: m + v = π + y

  • m = Money supply growth rate
  • v = Velocity growth rate
  • π (pi) = Inflation rate
  • y = Real GDP growth rate

Assuming v = 0 in the long run, the inflation rate is: π = m – y (Inflation equals money supply growth minus real GDP growth).

Central Banking, Interest Rates, and the Zero Lower Bound

Inflation makes it easier for central banks to respond to economic shocks with lower real interest rates, since the real interest rate is calculated as: r = i – π (Real rate = Nominal rate – Inflation rate). This is why raising expectations of inflation can help overcome the zero lower bound.

The Zero Lower Bound (ZLB)

The ZLB occurs when the central bank cannot lower the Interest on Reserves (IOR) further because it is already at or near zero. This is usually the first exhausted tool. To circumvent the ZLB, central banks use:

  1. Forward Guidance: A promise to keep short-term rates lower for longer, thereby reducing long-term rates.
  2. Quantitative Easing (QE): Targeting long-term rates directly through large-scale asset purchases.

Defining and Measuring GDP and GNP

Gross Domestic Product (GDP)

GDP measures the total value of goods and services produced within a country’s borders. It can be measured in three equivalent ways: Production = Expenditure = Income.

  • Production Approach: Measure each firm’s value added to a good (sales revenue minus purchase of intermediate goods).
  • Expenditure Approach: C + I + G + (X – M)
    • C = Consumption
    • I = Investment (new physical capital bought by households or firms)
    • G = Government spending (excluding transfer payments and interest on debt)
    • (X – M) = Net Exports (Exports minus Imports)
  • Income Approach: Labor income paid for work + Capital income realized by owners of physical or financial capital (e.g., dividends, interest, earnings retained by corporations, rent received by landlords, benefits of living in your own home).

Gross National Product (GNP)

GNP measures the output of all factors of production (labor and capital) owned by residents of a country, regardless of where the production takes place.

The GDP Deflator

The GDP Deflator is calculated as: (Nominal GDP / Real GDP) × 100. It measures how much prices have risen since the base year. The percentage change in the GDP deflator is another measure of inflation. It uses the GDP basket of goods, which is very similar to the CPI basket.

Labor Market Definitions and Unemployment Types

Potential Workers and Labor Force Status

Potential workers are the civilian non-institutional population aged 16 years or older. They fall into three categories:

  1. Employed: Currently holding a paid job.
  2. Unemployed: No paid job, but currently available to work and have looked for work in the past four weeks.
  3. Not in Labor Force: No paid job and not looking for work. This includes discouraged workers who want a job but have given up seeking one.

Types of Unemployment

Official unemployment statistics include:

  • Voluntarily Unemployed: Individuals who want work but only at a wage higher than the market rate.
  • Frictional Unemployment: Unemployment caused by imperfect information about jobs and the time required for the search process.
  • Cyclical Unemployment: Deviation from the long-run rate due to booms or recessions.
  • Structural Unemployment: Occurs when the number of labor supplied persistently exceeds labor demand.

Involuntary Unemployment occurs only if wages are rigid. It refers to individuals willing to work at the market wage but unable to find a job.

Causes of High Structural Unemployment

High structural or natural rates of unemployment can be caused by:

  • A rigid labor market.
  • Unsupportive market structures (e.g., lack of paid leave, apprenticeships, or job search assistance).
  • Poor education or skills mismatch.
  • High minimum wages or inflexible unions.

Okun’s Law

Okun’s Law links changes in GDP growth to changes in the unemployment rate:

Δ GDP Growth Rate = 3% – 2 × (Δ Unemployment Rate)

Asset Valuation and Bond Pricing Formulas

Present Value of a Growing Dividend

For an annual dividend D that grows at rate g each year, discounted by interest rate i, the present value P is:

P = D/(1+i) + D(1+g)/(1+i)² + D(1+g)²/(1+i)³ + … = D / (i – g)

The price-to-dividend ratio is: P/D = 1 / (i – g)

Pricing a Three-Year Maturity Bond

For a three-year maturity bond with face value F and coupon rate C, the price P is:

P = (C × F) / (1 + i) + (C × F) / (1 + i)² + (C × F) / (1 + i)³ + F / (1 + i)³

Interest Rate Expectations

The rule of thumb linking interest rates on short- and long-term bonds is to average the expected short-term rates. If the short-term rate is expected to rise, arbitrage will make the long-term rate higher, and vice versa.

Non-Fundamental Trading Methods

Methods of trading that are not based on fundamental economic value include:

  1. Guessing based on market sentiment (often called animal spirits).
  2. Pump and dump schemes (misleading investors to inflate the price, then selling at the peak).

Financial Stability and Key Policy Rules

Recessions and Financial Crises

A recession is a short-run decrease in GDP growth, though it can have effects on the long-term growth rate. Recessions are usually caused by leftward shifts in labor demand (and sometimes supply).

The Great Recession (2007-2009), compared to the Great Depression (1929-1939), had lower unemployment at its peak and GDP recovered more quickly. Both crises were precipitated by financial crises and neither was highly predictable.

Bank Runs and Deposit Insurance

An institutional bank run occurs when banks withdraw their deposits and short-term loans from other banks or firms.

Deposit insurance, introduced in 1933, reduced the amount of retail bank runs and failures but did not prevent institutional bank runs or the failure of some financial intermediaries.

The Fed as Lender of Last Resort

The Federal Reserve takes assets as collateral when acting as the lender of last resort. However, for riskier interventions, the Fed needs funding and permission from the Treasury, and any losses are borne by the Treasury.

The Taylor Rule

The Taylor Rule is used to set the Federal Funds Rate (FFR):

FFR = Long-Run FFR Target + 1.5(π – π Target) + 0.5(Output Gap)

Where the Output Gap is calculated as: (GDP – Trend GDP) / Trend GDP. As inflation (π) and the output gap rise, the Fed raises the FFR (a contractionary policy).

Essential Macroeconomic Concepts

Functions of Money

Money serves three primary functions:

  1. Medium of exchange.
  2. Store of value (temporally transferring purchasing power).
  3. Unit of account.

Social Security

More income generally leads to a higher payout from Social Security. However, the replacement ratio (the percentage of income given back) is much higher for low-income people.