Interpreting Regression Results

• Pages: 89-116

89

CHAPTER 6

INTERPRETING REGRESSION RESULTS

You have gathered the data (as described in Chapter 4) and estimated

your econometric model (as described in Chapter 5). Now what? This

chapter will cover how to interpret the results of the model, evaluate the

reliability of those results, and use the results for applications such as

liability or damages analyses.

Regression analysis can be used to determine both whether an event

had a statistically significant effect as well as the magnitude of the effect.

For example, regression analysis can be used to determine whether there

is statistical evidence of a pricing conspiracy and the amount of an

overcharge, if such a conspiracy is found to exist. However, the

regression analysis only gives meaningful results if the regression is

correctly specified and the results are reliable. A misspecified regression

can give misleading, or incorrect, results.

This chapter will cover some of the problems that can arise in

interpreting regression results, and how to avoid them. Topics covered

include: hypothesis testing, significance of results, goodness of fit,

specification testing, omitted variables, various data problems, and how

to use the results of a regression.

A. Understanding Regression Results

1.

Evaluating the Specification of the Regression Model

As a practical matter, the set of explanatory variables included in a

regression equation almost never accounts for all of the factors that affect

the dependent variable. When there are many economic factors at work,

generally there will be some factors that cannot be identified or

measured, and thus cannot be included as explanatory variables in the

model. These factors are summarized in an error term, which represents

variation in the dependent variable that is not explained by the

explanatory variables included in the model.

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1

. The fitted model is expressed as:

90 Econometrics

As discussed in Chapter 5, Ordinary Least Squares (“OLS”) is a

widely used regression technique that fits the model by finding the

parameter estimates that minimize the sum of squares of the error terms,

that is, that minimize the unexplained portion of the variation in the data.

Because of statistical noise, these estimates will not exactly equal the

true underlying coefficients. However, under certain conditions, these

estimates are unbiased (that is, their expected value is equal to the true

parameter) and efficient (that is, the parameters are estimated with

precision in the sense that the variance of the estimated parameters is

minimized).

Among the conditions that must be met for OLS to provide unbiased

estimates is that the regression model must be correctly specified. If the

regression model is misspecified, the regression will produce coefficient

estimates that are biased and unreliable. Misspecification can arise from,

among other reasons, the omission of important explanatory variables

from the model or the imposition of incorrect restrictions on the

regression coefficients.

2

2.

Interpreting Regression Coefficients in an OLS Regression

Model

The first step in evaluating and interpreting regression results is

simply assessing the estimated coefficients to ensure that they appear to

be reasonable, logical, and consistent with economic theory. An

econometric model typically is constructed to explain variation in the

dependent variable as a function of the independent variables, and

economic theory provides guidance on the expected sign (positive or

negative) and perhaps also the magnitude of the coefficients. As

discussed in Chapter 5, the parameter coefficients in a linear regression

model indicate how the average value of the dependent variables changes

in response to a small change in the independent variable.

An initial assessment of the regression results begins by verifying

that the estimated parameters conform to basic economic intuition. For

where is the estimate of the intercept, the s are the esti mates of the

coefficients, and is the estimate of the error term.

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. See Section D.2 below for additional discussion.

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