Specifying and Estimating an Appropriate Econometric Model

• Pages: 65-88

65

CHAPTER 5

SPECIFYING AND ESTIMATING AN

APPROPRIATE ECONOMETRIC MODEL

In an econometric analysis, econometricians must make decisions

about the econometric model to use and how best to estimate the model.

Those decisions will be informed by the economic issues being modeled

and the available data. This chapter discusses some of the key

considerations that may factor into choosing the appropriate econometric

model for the task at hand and estimating the model.

The chapter begins by describing a variety of commonly used

econometric models. Then, the chapter discusses some common data and

modeling issues and how these issues may affect the specification and

estimation of the econometric models.

For a more detailed discussion of econometric models, and an

overview of the typical mathematical and statistical specifications used

in developing those models, please refer to the Appendix and Glossary of

this book.

A. Basics of an Econometric Model

In dealing with econometrics, it is important for lawyers to

understand the terms that economists often refer to, such as specifying

versus estimating an econometric model. When economists refer to the

task of “specifying” the model, they refer to the process of determining

the equations that would be most appropriate to estimate to help shed

light on the economic issues at hand. This involves making decisions

about the type of model, the variables to be included in the model, and

potentially other details about the model.

An econometric model uses a mathematical equation or equations to

describe the economic relationship between a variable of interest (e.g.,

price of the product or service that is the subject of an antitrust claim)

and one or more explanatory variables (e.g., various production costs, the

structure of the relevant market, and the contested or alleged conduct).

The variable of interest i s commonly referred to as the “dependent” or

“left-hand-side” variable. The set of explanatory variables are also

referred to as the “independent” or “right-hand-side” variables.

66 Econometrics

In an econometric equation, each explanatory variable is associated

with a “coefficient,” which characterizes how the variation in the

explanatory variable is statistically related to the variation in the

dependent variable, while controlling for the correlation between the

dependent variable and other explanatory variables included in the

model. For example, an econometric model may use the following

equation: Price = “Producer Coefficient” × Number of Producers + “Cost

Coefficient” × Cost + Other Explanatory Variables times their

corresponding Coefficients, to describe the relationship between the

market price of a good (the dependent variable) and the explanatory

variables such as the number of producers of the good, cost of producing

the good, etc. In the equation, the “Number of Producers” variable is

associated with a “Producer Coefficient,” the Cost variable is associated

with a “Cost Coefficient,” and so on.

When economists refer to the task of “estimating” the model, they

mean the process of actually using the data and a computer program to

estimate the “coefficients” for variables in the model (e.g., the “Producer

Coefficient” and “Cost Coefficient” in the above example) according to

some statistical criteria. For example, a commonly used criterion is to

select the coefficients that enable the explanatory variables to jointly

explain the maximum amount of variation in the variable of interest. The

coefficient of each explanatory variable reveals the average change in the

dependent variable when there is a change in that explanatory variable,

holding other explanatory variables unchanged. For example, in the

model above, a one-dollar increase in the firm’s costs might on average

be associated with a 95-cent increase in the firm’s price, when the other

explanatory variables included in the model are held constant. In that

case, 0.95 would be the estimated coefficient for the cost variable when

both price and cost are measure in dollars.

As described in the Appendix, the Ordinary Least Squares (“OLS”)

model, also known as the Classical Linear Regression Model, is the basic

and most commonly used econometric model. In OLS models, the

coefficients of the explanatory variables are estimated to minimize the

amount of variation in the dependent variable that is not explained by the

explanatory variables in the model, or equivalently, to maximize the

amount of variation in the dependent variable that is explained by the

explanatory variables. This process of minimizing the amount of

variation in the dependent variable not explained by the explanatory