Macroeconomics: The Labor Market, Wages, and Unemployment

Introduction to the Labor Market Supply-and-Demand

• The study of the labor market involves understanding how supply and demand interact to determine employment levels and wages.

• Key objectives of these notes include:

  • Analyzing how a supply-and-demand model helps explain labor market functions.

  • Examining how labor market distortions, such as taxes, affect long-run employment.

  • Exploring the "Bathtub model" of long-run unemployment.

  • Learning how to compute present discounted values (PDV).

  • Investigating the reasons behind the rising return to college education over the last half-century.

Labor Market Overview: United States and United Kingdom

• General US Trends:

  • Wages constitute two-thirds of per capita Gross Domestic Product (GDP).

  • Average wages have demonstrated a growth rate of $2\, \%$ per year for the past century.

• The Employment-Population Ratio:

  • Definition: This is the fraction of the civilian population over the age of 16 that is currently working.

  • Historical Trend: This ratio has generally been increasing over time, largely driven by female labor force participation.

  • Cyclical Changes: The ratio decreases significantly during recessions. For instance, during the COVID-19 pandemic, the US ratio dropped from $61\, \%$ to $53\, \%$.

• UK Trends:

  • The UK employment-population ratio is generally more stable compared to that of the US.

  • During the COVID-19 pandemic, the ratio decreased from $47\, \%$ to $46\, \%$, which is a less severe drop than observed in the US.

• Composition of the US Labor Force (January 2023):

  • Civilian population, aged 16 and over: $266\, \text{million}$.

  • Labor force (employed or actively seeking work): $166\, \text{million}$.

  • Employed: $160\, \text{million}$.

  • Unemployed: $5.7\, \text{million}$.

  • Not in the labor force: $100\, \text{million}$.

• Composition of the UK Labor Force (January-March 2019):

  • Total population: $66.4\, \text{million}$.

  • Population 16 and over: $53.2\, \text{million}$.

  • Labor force: $34.0\, \text{million}$.

  • Employed: $32.7\, \text{million}$.

  • Unemployed: $1.3\, \text{million}$.

Defining and Measuring Unemployment

• The Unemployment Rate: This is calculated as the fraction of the labor force that is currently unemployed.

• Definition of an Unemployed Person: To be classified as unemployed, an individual must meet three criteria:

  • They do not have a job that pays a wage or salary.

  • They have actively looked for work in the last 4 weeks.

  • They are currently available to work.

• Historical US Unemployment Data (1950–2023):

  • 1950s–1960s: Rates were typically between $4\, \%$ and $5\, \%$.

  • 1970s: Rates showed an increasing trend.

  • 1982: Reached a peak of $10.8\, \%$.

  • 1990s: Experienced decreasing rates.

  • 2009 (Great Recession): Reached $10\, \%$.

  • Pandemic peak: Reached $14.7\, \%$.

• UK Unemployment Trends: Like the US, UK unemployment is cyclical. However, an upward shift occurred starting in the 1970s, and rates have never returned to the lower levels seen in the 1950s and 1960s.

Dynamics and Social Safety Nets

• Unemployment Spells: For most individuals, periods of unemployment are relatively short. In the US, the majority of unemployment spells last less than 3 months, and approximately $25\, \%$ of unemployed individuals find a job each month.

• Social Safety Nets:

  • Unemployment Insurance (UI) Benefits: These vary significantly across regions. In the US and UK, the duration is typically up to 26 weeks.

  • Replacement Rates: The amount of income replaced by benefits varies by country.

  • Trade-off: Data suggests that more generous benefits tend to increase the average duration of unemployment as they may reduce the urgency to find new employment.

The Supply and Demand Model of the Labor Market

• Labor Demand:

  • Firms demand labor. The curve is downward-sloping due to the diminishing Marginal Product of Labor (MPL).

• Labor Supply:

  • Workers supply labor. The curve is upward-sloping because the price of leisure is higher when wages are higher (substitution effect).

• Equilibrium: The intersection of labor supply and demand determines both the wage rate and the level of employment ($L$). If $N$ is the population, this intersection also determines the employment-population ratio ($L/N$).

• Shifts in Supply (Taxes):

  • If the government increases income taxes on wages, workers receive less net income, causing the labor supply curve to shift left.

  • Firms must initially raise wages to reach a new equilibrium (Point B).

  • Effect: Employment falls, and market wages rise. The unemployment rate may rise initially but may fall if workers become discouraged and leave the labor force.

• Shifts in Demand:

  • If the price of a complementary input rises, firms demand fewer workers, shifting the labor demand curve to the left.

  • Effect: Wages and employment fall. The economy moves from Point A to Point B as wages adjust downwards.

• Wage Rigidity:

  • Definition: This occurs when wages fail to adjust downward following a shock to labor demand or supply.

  • Implication: If wages are "sticky" and do not fall during a demand shock, the labor market will not clear, resulting in a much larger fall in employment and higher unemployment.

  • Historical Note: John Maynard Keynes attributed the high unemployment during the Great Depression to wage stickiness.

Case Study: Historical Shocks in the US

• Rise in Employment-Population Ratio: Driven by an increase in female workers.

  • Supply Shocks: Changes in social norms and technological progress.

  • Demand Shock: Reduced discrimination against women.

• 1970s Unemployment Rise: Attributed to the Baby-boomer generation entering the workforce.

  • Supply Shock: Younger workers statistically have higher unemployment rates as they switch jobs more frequently.

The Bathtub Model of Unemployment

• The Bathtub model describes the flow of workers into and out of unemployment over time.

• Variables:

  • $\Delta U_{t+1}$: Change in the number of unemployed workers.

  • $s$: Job separation rate (fraction of employed people who lose jobs).

  • $f$: Job-finding rate (fraction of unemployed people who find jobs).

  • $E_t$: Number of employed individuals.

  • $U_t$: Number of unemployed individuals.

  • $\bar{L}$: Fixed labor force ($E_t + U_t = \bar{L}$).

• Equations:

  • The transition equation: $\Delta U_{t+1} = s E_t - f U_t$

• Steady State Calculation:

  • To find the long-term or steady-state unemployment rate ($U^*$), set $\Delta U_{t+1} = 0$.

  • $0 = s(\bar{L} - U^*) - f U^*$

  • $0 = s\bar{L} - sU^* - fU^*$

  • $U^*(f + s) = s\bar{L}$

  • $U^* = \frac{s\bar{L}}{f + s}$

• Natural Rate of Unemployment ($u^*$):

  • $u^* = \frac{U^*}{\bar{L}} = \frac{s}{f + s}$

  • To reduce the natural rate, one must either increase the job-finding rate ($f$) or decrease the job separation rate ($s$).

International Comparisons and Hours Worked

• Unemployment Rates: Prior to 1980, US unemployment was higher than Europe’s. Since 1980, European unemployment has remained significantly higher than both the US and Japan.

• Theories for Europe's High Unemployment:

  1. Changing labor market institutions.

  2. The interaction of existing institutions with economic shocks.

• Hours Worked per Person:

  • GDP per capita is lower in Europe than in the US primarily because Europeans work fewer average annual hours.

  • Welfare Impact: If working less is voluntary (leisure preference), welfare is improved. If it is due to labor market distortions (e.g., high taxes), welfare is not enhanced.

Human Capital and Present Discounted Value (PDV)

• Definition: Present Discounted Value tells how much a future flow of payments is worth in today's terms.

• Formula for a One-off Payment:

  • $PDV = \frac{\text{Payment}}{(1 + R)^t}$

  • Example: A prize of $\pounds 1,000$ in 5 years with an interest rate ($R$) of $10\, \%$.

  • $PDV = \frac{\pounds 1,000}{(1 + 0.10)^5} = \pounds 621$

• Formula for a Stream of Payments:

  • To calculate the value of $n$ constant payments ($P$):

  • $PDV = P \times \sum_{t=0}^{n-1} (\frac{1}{1+R})^t$

  • Using geometric series: $PDV = P \times \frac{1 - [\frac{1}{1+R}]^n}{1 - [\frac{1}{1+R}]}$

  • Example: $\pounds 100$ every year for 20 years at $10\, \%$ interest equals a PDV of $\pounds 936$.

• Human Capital Value Example:

  • Assume average income of $\pounds 50,000$, $R = 0.03$, and a 45-year work span.

  • $PDV = \pounds 50,000 \times \frac{1 - [\frac{1}{1.03}]^{45}}{1 - [\frac{1}{1.03}]} = \pounds 1.26\, \text{million}$.

The Rising Return to Education

• College Wage Premium: The extra income earned by having a degree compared to a high school diploma.

• PDV Comparison:

  • High School Graduate: Works 45 years. $PDV_{HS} \approx 25X$.

  • College Graduate: Earns $1.5X$ but starts 4 years later (works 41 years). $PDV_{UNI} \approx 32X$.

  • Result: A university degree yields an approximate $30\, \%$ higher PDV despite fewer working years.

• Explanations for Rising Demand for Skilled Workers:

  • Skill-biased technological change: Innovation (computers, internet) increases the demand for high-skilled workers who can use those tools.

  • Routine-biased technological change: Technology substitutes for routine, often middle-skill, tasks.

  • Globalization: Increases competition for low-skilled domestic workers from international markets.

Economic Growth and Income Inequality

• Inequality Drivers: Historically, inequality was tied to capital income. Recently, it is driven by differences in salaries and business income (education gap).

• Distribution of Growth in the US:

  • 1946–1980: Growth was evenly distributed at an average of $2\, \%$.

  • 1980–2014: Average growth dropped to $1.4\, \%$ and was unevenly distributed, with the top $1\, \%$ capturing gains above $2\, \%$.

• US vs France: Since 1980, the US has seen a sharp increase in the income share of the top $1\text{ in }1,000$, whereas France has remained more stable.

Minimum Wage and Efficiency Wages

• Microeconomic Model: Predictive models suggest a minimum wage set above the equilibrium wage causes unemployment.

• Efficiency Wages (The Henry Ford Case):

  • In 1914, Ford introduced a $\$5$-a-day minimum wage, doubling the previous rate.

  • Theory: Paying more than the market rate can increase profits by:

    • Improving worker health and productivity (via better nutrition).

    • Increasing worker effort (reducing the need for monitoring).

    • Attracting more productive, higher-quality job candidates.

• Modern Perspectives (Dube and Lindner 2024):

  • Evidence indicates that minimum wage policies have significantly raised the total earnings of low-wage groups because the positive effect on wages has outweighed the negative effect on employment levels.