Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge

CHAPTER 1 
TEACHING NOTES 
You have substantial latitude about what to emphasize in Chapter 1. I find it useful to talk about 
the economics of crime example (Example 1.1) and the wage example (Example 1.2) so that 
students see, at the outset, that econometrics is linked to economic reasoning, even if the 
economics is not complicated theory. 
I like to familiarize students with the important data structures that empirical economists use, 
focusing primarily on cross-sectional and time series data sets, as these are what I cover in a 
first-semester course. It is probably a good idea to mention the growing importance of data sets 
that have both a cross-sectional and time dimension. 
I spend almost an entire lecture talking about the problems inherent in drawing causal inferences 
in the social sciences. I do this mostly through the agricultural yield, return to education, and 
crime examples. These examples also contrast experimental and nonexperimental 
(observational) data. Students studying business and finance tend to find the term structure of 
interest rates example more relevant, although the issue there is testing the implication of a 
simple theory, as opposed to inferring causality. I have found that spending time talking about 
these examples, in place of a formal review of probability and statistics, is more successful (and 
more enjoyable for the students and me). 

SOLUTIONS TO PROBLEMS 
1.1 It does not make sense to pose the question in terms of causality. Economists would assume 
that students choose a mix of studying and working (and other activities, such as attending class, 
leisure, and sleeping) based on rational behavior, such as maximizing utility subject to the 
constraint that there are only 168 hours in a week. We can then use statistical methods to 
measure the association between studying and working, including regression analysis that we 
cover starting in Chapter 2. But we would not be claiming that one variable “causes” the other. 
They are both choice variables of the student. 
1.2 (i) Ideally, we could randomly assign students to classes of different sizes. That is, each 
student is assigned a different class size without regard to any student characteristics such as 
ability and family background. For reasons we will see in Chapter 2, we would like substantial 
variation in class sizes (subject, of course, to ethical considerations and resource constraints). 
 (ii) A negative correlation means that larger class size is associated with lower performance. 
We might find a negative correlation because larger class size actually hurts performance. 
However, with observational data, there are other reasons we might find a negative relationship. 
For example, children from more affluent families might be more likely to attend schools with 
smaller class sizes, and affluent children generally score better on standardized tests. Another 
possibility is that, within a school, a principal might assign the better students to smaller classes. 
Or, some parents might insist their children are in the smaller classes, and these same parents 
tend to be more involved in their children’s education. 
 (iii) Given the potential for confounding factors – some of which are listed in (ii) – finding a 
negative correlation would not be strong evidence that smaller class sizes actually lead to better 
performance. Some way of controlling for the confounding factors is needed, and this is the 
subject of multiple regression analysis. 
1.3 (i) Here is one way to pose the question: If two firms, say A and B, are identical in all 
respects except that firm A supplies job training one hour per worker more than firm B, by how 
much would firm A’s output differ from firm B’s? 
 (ii) Firms are likely to choose job training depending on the characteristics of workers. Some 
observed characteristics are years of schooling, years in the workforce, and experience in a 
particular job. Firms might even discriminate based on age, gender, or race. Perhaps firms 
choose to offer training to more or less able workers, where “ability” might be difficult to 
quantify but where a manager has some idea about the relative abilities of different employees. 
Moreover, different kinds of workers might be attracted to firms that offer more job training on 
average, and this might not be evident to employers. 
 (iii) The amount of capital and technology available to workers would also affect output. So, 
two firms with exactly the same kinds of employees would generally have different outputs if 
they use different amounts of capital or technology. The quality of managers would also have an 
effect.

Introductory Econometrics: A Modern Approach by Jeffrey M. Wooldridge