Using spreadsheets to conduct Monte Carlo experiments for teaching introductory econometrics.

• Author: Craft, R. Kim
• Position: Targeting Teaching

1. Introduction

   In recent years a number of authors have begun to use Monte Carlo simulation to help explain elementary concepts in statistics and econometrics (e.g., Gujarati 1999, pp. 79-81 and 159-161; Albright, Winston, and Zappe 2000, pp. 191-194; Studenmund 2001, pp. 101-102). Furthermore, Kennedy (1998a, b) has argued that the Monte Carlo experiment is an indispensable pedagogical tool for the undergraduate econometrics course. In particular, he believes that Monte Carlo methods can be used to illuminate the idea of a sampling distribution, a fundamental concept that is often difficult for students to grasp. Kennedy maintains that because the notion of a sampling distribution is the "statistical lens" that makes other statistical concepts clear, and because Monte Carlo methods provide a superior vehicle for acquiring this lens, introductory students should be required to describe a Monte Carlo experiment related to "every major topic in the course" (Kennedy 1998b, p. 148). Kennedy further contends, however, that intro ductory students should not be asked to conduct their own Monte Carlo experiments because of the high opportunity cost of learning to program standard econometric software.

   I concur with Kennedy's assertion that teaching statistical concepts in the context of a Monte Carlo study is an enormously valuable pedagogical technique. I also agree that the marginal benefit derived from requiring students to program Monte Carlo experiments with standard econometric software, rather than to only demonstrate their ability to conceptualize the experiment, probably exceeds the marginal cost for most undergraduates. Nevertheless, it is clear that students can derive substantial learning benefits from conducting their own Monte Carlo experiments. It is well known that many students learn best through experiencing and experimenting, and even students with strong abstract reasoning abilities usually find experiential learning exercises helpful. The process of developing and experimenting with a simulation model can provide such experiential learning opportunities with otherwise very abstract statistical concepts; but the opportunity cost is a problem.

   I have found that the benefit can substantially exceed the cost when introductory students use spreadsheets to perform their own Monte Carlo experiments. As I hope to demonstrate below, the opportunity cost of learning associated with conducting a Monte Carlo experiment with a spreadsheet can be relatively low. Nearly all of my econometrics students (juniors and seniors in finance and economics, most of whom have had a prior course in spreadsheet modeling) are familiar with spreadsheets and find the environment very natural. Thus, they learn the necessary spreadsheet commands quickly and are then able to focus on the purpose of the exercise rather than on programming. In addition, instructors can control the cost to some degree by supplying spreadsheet templates and directions tailored to the background of the students and the goals of the exercise (see Cahill and Kosicki 2001 for a useful discussion of this point). The use of spreadsheets to conduct Monte Carlo experiments in introductory courses can therefo re overcome the high-opportunity-cost problem to a large extent.

   The use of spreadsheets to teach Monte Carlo simulation offers additional learning benefits because the environment is especially intuitive and user friendly. For instance, the spreadsheet setting invites exploration: Once a model is created, the effects of changing a parameter value can be investigated by simply entering a new number in a cell and pressing a key. Spreadsheet models can also be superior teaching tools because of the way data are displayed. Realizations of random events can be organized, annotated, and presented in a tabular form that undergraduates can easily relate to. With a well-designed spreadsheet model, students can almost see samples being drawn and estimates being created. As opposed to the "black box" nature of standard econometric software, these models can be very explicit, with each step connected in a straightforward way.

   Finally, there are important positive externalities associated with the use of spreadsheets to teach Monte Carlo methods. Most of the spreadsheet techniques needed for a Monte Carlo study are useful in a variety of other modeling situations, ranging from economic theory (e.g., Cahill and Kosicki 2000) to personal finance (e.g., Holden and Womack 2000). Students therefore learn practical spreadsheet modeling skills along with econometrics. Moreover, since spreadsheet software is widely available, students are more likely to later use their knowledge of spreadsheets and Monte Carlo methods in a work environment. Because they recognize these benefits (with help from the instructor), most students are quite willing to invest in learning the necessary spreadsheet skills.

   Along with the numerous authors who have promoted the use of spreadsheets in teaching economic theory, Judge (1999) introduced a simple method for conducting Monte Carlo experiments with spreadsheets. The approach proposed in this paper differs from Judge's approach in at least three important ways. First, the method outlined here allows for random regressors. Although it is not useful for most research applications, sampling from a population of regressors adds an element of realism (for cross-sectional analysis) that facilitates student comprehension--my students are able to get a better grasp of the meaning and significance of the "fixed in repeated samples" assumption when I contrast fixed regressors with random regressors in a Monte Carlo context. Another distinguishing feature of the approach presented here involves the method of sampling. I believe it is both more intuitive and more efficient than that used with Judge's approach; in particular, it is easier to draw larger samples and to repeat experime nts under alternative scenarios. Finally, because it is easier to repeat experiments under alternative scenarios, the approach proposed here facilitates student...