Introduction and Review
This part contains three chapters on the fundamentals of econometrics, probability theory, and statistics. The chapters in this part provide the necessary background for understanding the material covered in the rest of the book. There are three chapters in this part:
- Chapter 8 Economic Questions and Data
- Chapter 9 Review of Probability
- Chapter 10 Review of Statistics
Chapter 8 defines econometrics and highlights the importance of providing quantitative answers to economic questions. It also introduces some basic concepts, including causal effect, randomized controlled experiment, estimation, prediction, and forecasting. We also discuss the difference between experimental and observational data and define different types of data used in econometric analysis.
In Chapter 9, we review the fundamentals of probability theory. We define the sample space associated with an experiment and introduce two functions defined on the sample space: the probability function and random variables. Next, we explore probability distributions for both discrete and continuous random variables and define key moments, such as the mean, variance, skewness, and kurtosis. We also examine multiple random variables and their joint and conditional probability distributions. We introduce commonly used continuous distributions in econometrics: the binomial, uniform, normal, chi-squared, Student t, and F distributions. The chapter concludes with an introduction to random sampling. Once we have a random sample from a population, we can define statistics, such as the sample mean, and discuss their sampling distribution. To study large sample properties of the sample mean, such as consistency and asymptotic distribution, we introduce the law of large numbers and the central limit theorem.
In Chapter 10, we provide a brief review of statistics. We introduce estimators and discuss related concepts, including unbiasedness, consistency, and efficiency. Next, we explain how to conduct hypothesis tests and construct confidence intervals for the population mean. We also cover hypothesis testing and confidence intervals for the difference between the means of two distinct populations. Finally, we introduce the sample covariance and the sample correlation coefficient as measures of the linear relationship between two random variables.
In Chapters 9 and 10, we cover the fundamentals of probability theory and mathematical statistics. Our review is not exhaustive; rather, it focuses on the key concepts that are essential for econometric analysis. For more detailed discussions of these topics, we recommend Wackerly, Mendenhall, and Scheaffer (2008) and Hansen (2022).