Core Course 7: Statistical Methods for Economics
This course provides the essential statistical foundation for empirical analysis in economics, preparing students for econometrics.
Course Content Details
1. Probability Theory and Distributions
This unit is the bedrock of statistical inference. It introduces the mathematical theory of probability, covering concepts like random variables, probability distributions, and expected values. We will study several common distributions that are frequently used to model economic phenomena, such as the Binomial, Poisson, and Normal distributions.
Key Topics:
- Random Variables and Probability Distributions (Discrete and Continuous)
- Measures of Central Tendency and Dispersion
- The Normal Distribution and its Properties
- The Central Limit Theorem
2. Sampling and Point/Interval Estimation
Since we can rarely observe an entire population, we rely on data from samples to make inferences. This unit discusses different sampling methods and introduces the concept of a sampling distribution. We will then learn how to use sample data to estimate unknown population parameters. This includes both point estimation (a single best guess) and interval estimation (a range of plausible values, i.e., confidence intervals).
Key Topics:
- Simple Random Sampling
- Sampling Distribution of the Sample Mean and Proportion
- Properties of Estimators: Unbiasedness, Efficiency, Consistency
- Confidence Intervals for Population Means and Proportions
3. Hypothesis Testing for Means and Proportions
Hypothesis testing provides a formal framework for using sample data to test claims about population parameters. This unit covers the logic of hypothesis testing, including setting up null and alternative hypotheses, calculating test statistics, and making decisions based on p-values or critical values. We will cover tests for a single population mean and proportion, as well as tests for comparing two populations.
Key Topics:
- The Logic of Hypothesis Testing: Null and Alternative Hypotheses
- Type I and Type II Errors
- Z-tests and t-tests for a Population Mean
- Tests for a Population Proportion
- Comparing Two Population Means (Independent and Paired Samples)
4. Correlation and Introduction to Simple Regression
The final unit introduces methods for analyzing the relationship between two variables. Correlation measures the strength and direction of a linear association. Simple linear regression goes a step further by modeling one variable as a linear function of another. This provides a gentle introduction to the core concepts of econometrics, which is the application of statistical methods to economic data.
Key Topics:
- Scatterplots and Correlation Coefficient
- The Simple Linear Regression Model
- Estimation of Regression Coefficients using Ordinary Least Squares (OLS)
- The Coefficient of Determination (R-squared)
- Hypothesis Testing for the Slope Coefficient