Models and Data

Introduction to Economic Models

Economic models are simplified representations of reality that help economists analyze complex phenomena. They are essential tools for understanding how the world works and for making predictions about economic behavior.

• Model: A simplified description of reality used to explain and predict economic outcomes.

• Data: Empirical evidence used to evaluate the accuracy of models.

• Correlation vs. Causality: Correlation does not imply causality; just because two variables move together does not mean one causes the other.

• Experiments: Help economists measure cause and effect by testing hypotheses.

Evidence-Based Economics

Opportunity Cost and Returns to Education

Economists use data to answer practical questions, such as whether college is worth the investment. Opportunity cost is a key concept in evaluating such decisions.

• Opportunity Cost: The value of the next best alternative forgone. For college students, this often includes lost wages from not working full-time.

• Example: If minimum wage is $17.60/hour, working 50 hours/week for 28 weeks yields an opportunity cost of $24,640 per year (before tax).

The Scientific Method in Economics

Steps of the Scientific Method

The scientific method, also called empiricism, is the foundation of economic inquiry. It involves developing models and testing them against real-world data.

1. Developing models that explain some part of the world.

2. Testing those models using data to see how closely the model matches actual observations.

Application: The Wright Brothers Example

The Wright brothers succeeded in building a working airplane by using models and controlled experiments (wind tunnel tests) to refine their designs before building a real plane.

Returns to Education: An Evidence-Based Example

Economists often use models to estimate the returns to education. A common assumption is that each additional year of education increases future earnings by a fixed percentage.

• Assumption: One more year of education results in a 10% increase in future earnings.

• Formula: where is the initial wage and is the number of additional years.

• Example Calculations:

  • First year:

  • Second year:

  • Third year:

  • Fourth year:

  • General formula:

• Hypothesis: Getting a college degree (years 13-16) increases wages from rac{21.9615 - 15}{15} = 0.4641$).

Features of Economic Models

• Models are not exact; averages can mask variation among individuals.

• Models generate predictions that can be tested with data.

Empirical Wage Data

Average Canadian wage data for ages 30-34 in 2016 shows a positive relationship between education and earnings.

• Comparison: College graduates earn 43.5% more than high school graduates ().

• Model Prediction: 46% higher; empirical data is close to the model's prediction.

The Median and the Mean

Measures of Central Tendency

Understanding the difference between the mean and the median is important for interpreting economic data, especially when distributions are skewed.

• Median: The middle value in a data set.

• Mean: The average, calculated as the sum of all observations divided by the number of observations ().

Example: Three Samples of Five Incomes

• Sample B is more unequal; mean is much higher than median.

• Sample C has more variance (dispersion) than A, despite same mean and median.

• Comparing mean and median helps assess inequality and skewness in data.

• Variance: Measures dispersion, but is less commonly reported.

Causation and Correlation

Distinguishing Causation from Correlation

Economists must distinguish between causation (one variable directly affects another) and correlation (variables move together).

• Causation: Direct effect; e.g., pulling an all-nighter causes tiredness.

• Correlation: Statistical relationship; can be positive, negative, or spurious.

• Spurious Correlation: Variables are related statistically but not causally.

Types of Correlation

• Positive correlation: Both variables move in the same direction.

• Negative correlation: Variables move in opposite directions.

• Spurious correlation: No meaningful causal link.

Why Correlation Is Not Causality

• Omitted Variables: Missing factors can explain observed correlations.

• Reverse Causality: The direction of cause and effect may be opposite to what is assumed.

Experiments in Economics

• Controlled Experiments: Subjects are randomly assigned to treatment and control groups. Rare in economics due to practical constraints.

• Natural Experiments: Assignment to groups occurs due to external factors, not researcher intervention.

Example: UK School Drop-Out Age

• In 1947, UK raised minimum drop-out age from 14 to 15.

• Students just before 1947 = control group; students after = treatment group.

• Result: One more year of schooling increased earnings by 10% on average.

Appendix 1: Examples of Spurious Correlation

Illustrative Cases

Spurious correlations can arise between unrelated variables, highlighting the importance of careful analysis.

• US spending on science, space, and technology vs. suicides by hanging.

• Number of people who drowned in pools vs. films Nicolas Cage appeared in.

• Divorce rate in Maine vs. per capita consumption of margarine.

• Total revenue generated by arcades vs. computer science doctorates awarded.

• Other examples: Age of Miss America vs. murders by steam, points scored in Super Bowl vs. deaths by venomous spiders, etc.

Appendix 2: Equations and Graphs

Graphing Functions

Functions are used to represent relationships between variables in economics. Linear functions are commonly used for simplicity.

• General Form:

• Linear Example:

• Intercept (A): Value of Y when X = 0.

• Slope (B): Change in Y for a one-unit change in X ().

• Example: If and , then .

Problems (Practice Questions)

Algebraic and Graphical Solutions

• Problem 1: Find two numbers whose sum is 385 and whose difference is 97. Solution: Let and . Adding: Subtracting: Answers: 241 and 144.

• Problem 2: A fishing boat brings in cod and haddock. Cod sells for $2.00/lb, haddock for $1.50/lb. Total catch: 5,000 lbs, total revenue: $9,000. Let: = pounds of cod, = pounds of haddock. Solving: Answers: 3,000 lbs cod, 2,000 lbs haddock.

Additional info: These notes cover foundational concepts in microeconomics, including the use of models, the scientific method, empirical analysis, and the distinction between correlation and causation. The examples and problems are typical of introductory microeconomics courses.