Now we will focus on some more specialized topics that are typically not covered in an introductory course. Some of these topics require a bit more specialized mathematical knowledge than the analysis of multiple regression in Parts 1 and 2.

In Chapter 13, we will show how to apply multiple regression to independently grouped stratifications. The topics addressed are very similar to classical stratified analysis, with the difference that we can study how relationships change over time by incorporating temporal pseudovariables.

We will also show how stratified time series data (panel data) can be analyzed within a regression framework. Chapter 14 examines more advanced methods for panel data that are still systematically used in applications.

Chapters 15 and 16 explore the problem of endogenous explanatory variables. In Chapter 15, we introduce the method of instrumental variables as a way to solve the problem of omitted variables, as well as the measurement error issue.

The two-stage least squares method is quite frequently used in empirical economics and is essential for estimating systems of equations models, a topic we will explore in Chapter 16.

Chapter 17 addresses some fairly advanced topics that are typically used in stratified analysis, including models for limited dependent variables and methods for correcting sample selection bias.

Chapter 18 shifts towards a different direction by examining some recent developments in time series econometrics that have proven useful for estimating dynamic relationships.

Chapter 19 may help students who need to write a paper in the field of social sciences. Suggestions are made on how to choose a topic, collect and analyze data, and write the paper.