Applied Econometrics

Course details

The course is offered in autumn. The class meets:

• Tuesday 08:30 - 11:30 (TBA)
• Wednesday 08:30 - 11:30 (room G.252)

Course aim

This course investigates the main econometric methods as a tool for the quantitative analysis of economic and financial phenomena. The application of econometric models allows measuring variables that are not directly observable, studying their relationships and behavior, testing and comparing alternative theories, as well as forecasting and simulating the effects of different policies. This course heavily emphasizes the importance of applications. A discussion of the main theoretical issues and a systematic analysis of econometric tools are intended as prerequisites for the investigation of a series of problems that are of particular relevance for economic and financial applications. For this reason, the theoretical lectures will be complemented by a systematic series of financial and economic applications through which the student will be in the position to autonomously develop econometric analysis, and perform empirical studies on financial and economic topics.

Course Outline

• Regression Models.
  
  A chapter containing a brief review of regressions, along with a few reminders of things from statistics and probability theory that will be needed later. Very important is the subsection of Section 1.3 entitled “Simulating Econometric Models”. The ideas in that subsection are essential for understanding the bootstrap and much else, and are not too easily found elsewhere. There are also sections dealing with various useful aspects of matrix algebra. You may find that this is well-known stuff, except perhaps for some of the material on partitioned matrices.
  • Working example: A bad day on Wall Street
  • Working example: How to simulate an econometric model
  
  
  
• The Geometry of Linear Regression.
  
  In this chapter, statistical issues are set aside in order to discuss ordinary least squares as a purely formal procedure. The chapter begins with some straightforward geometry, and introduces the concept of vector, or linear, spaces.
  • Working example: Estimating and Testing the Capital Asset Pricing Model
  
  
  
• The Statistical Properties of Ordinary Least Squares.
  
  In this chapter, the most fundamental concept of econometric theory is introduced, that of a data-generating process, or DGP. This concept allows us to define the almost equally important concept of a statistical or econometric model, and how such models are specified. Pretty much the simplest regression model is what we call the classical normal linear model, and this is introduced in this chapter. Much of the material in later chapters allows us to relax the very restrictive assumptions that are made in specifying this model. In this chapter, we also introduce some concepts, most importantly that of probability limits, needed for asymptotic theory, the approximate theory used for more general models, for which the exact classical results do not hold. Using this theory, we can show that the OLS estimator is consistent under much weaker conditions than the classical ones.
  • Working example: Explaining house prices
  
  
  
• Hypothesis Testing in Linear Regression Models.
  
  This chapter is devoted to inference. We develop tests for linear regressions. Tests can be exact if the assumptions of the classical normal linear model are satisfied, but otherwise asymptotic theory allows us to construct approximate tests. In many cases, we can do better than these approximate tests by using the bootstrap; the elements of bootstrap testing are covered in this chapter.
  • Working example: The determinants of the stock return
  
  
  
• Confidence Intervals.
  
  Confidence intervals provide another way to conduct statistical inference. At a rather deep level, there is an equivalence between hypothesis tests and confidence intervals. Like hypothesis tests, confidence intervals can be exact, under the strong assumptions of the classical normal linear model, for instance, or approximate. Approximate confidence intervals can be based on asymptotic theory or on the bootstrap. Another topic is heteroskedasticity-consistent inference.
  • Working example: Market cap and the oil price
  
  
  
• Generalized Least Squares and Related Topics.
  
  We continue the process of relaxing the restrictive classical assumptions by considering models in which the disturbances may have a more complicated specification, in particular by being heteroskedastic, or serially correlated, or both. In this chapter, we introduce some ideas related to time series that arise naturally from the study of serial correlation.
  • Working example: Food expenditure and income
  • Working example: Market cap and the oil price
  
  
  
• Instrumental Variable Estimation.
  
  In economics, typically “everything depends on everything else”. In econometric parlance, almost all economic variables are endogenous. Their endogeneity means that they cannot be used as explanatory variables in regression models estimated by least squares, and this is not something that asymptotic theory can get around. A new estimation method is needed, and we are led to the study of instrumental variables.
  • Working example: The Fulton Fish Market
  
  
  

Reading

• Econometric Theory and Methods, R. Davidson e J. MacKinnon, Oxford University Press, 2004.

Assessment

There is a blackboard test based on three sections:

• Six True or False questions
• Six Multiple choice questions
• Six questions on a proposed empirical analysis