The Econometric Framework

• Pages: 25-43

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CHAPTER 3

THE ECONOMETRIC FRAMEWORK

The first two chapters so far described why and how econometrics

can be useful in an antitrust analysis. To understand and better appreciate

the “how and why” of econometrics, the following discussion takes a

step back to provide a short history of econometrics, starting with its

roots in statistics.

A. Brief History of Statistics and Econometrics: Drawing Inferences

about Causal Relationships from Data

In 1919, a young R.A. Fisher—soon to be recognized as one of the

founders of the field of statistics—went to work at Rothamsted

Experimental Station in Harpenden, UK. His job was quite practical: he

was to study the determinants of crop yields. Fisher was, first and

foremost, a scientist. He sought to make inferences about the nature of

the world based on observations and insights drawn from data, a process

he called inductive inference:

[E]veryone who . . . habitually attempt[s] the d ifficult tas k of making

sense of [data] is, in fact, essaying a logical process of the kind we call

inductive, in that he is attempting to draw inferences from the particular

to the general; or , as we more usually say in statistics, from the sample

to the po pulation. Such in ferences we recognize to be uncerta in

inferences, but it does not follow from this t hat they are not

mathematically rigorous inferences.

1

Statistics is concerned with the methods used to make inductive

inferences from data. These inferences are inherently uncertain, as Fisher

wrote, because they are based on a sample of data, rather than the entire

population of interest, and thus are subject to sample varia bility, or

differences between the particular sample being utilized for the analysis

and the entire population. Statistical methods seek to maximize the

1

. R.A. Fisher, The Logic of Inductive Inference, 98 J. ROY. STAT. SOC. 39

(1935).

26 Econometrics

precision of the inferences that can be drawn from available data, and

provide an assessment as to the level of precision attained.

As the discussion below will elaborate further, econometricians have

expanded upon statistical methods to account for particular issues that

arise when the data have been generated by individuals and companies

making choices in an economic environment.

1.

Statistics and Randomized Experimental Design

Imagine Fisher, having arrived on the scene at Rothamsted,

considering how to evaluate whether the application of a particular

fertilizer would improve crop yields. One approach would be to compare

average crop yields between (1) plots of land that had been treated with

the fertilizer (the treated group) and (2) plots that received no fertilizer

treatment (the control group) to obtain an estimate of the effect of the

fertilizer on crop yields. Such a comparison would be rendered “fuzzy”

by “errors” resulting from differences among the plots used in the

analysis in terms of unmeasured characteristics of their soil (Fisher called

the variation in soil quality “soil heterogeneity”). The crop yield for a

particular plot of land depended upon, not only the amount of fertilizer

applied to that plot, but also these unmeasured characteristics of the soil

(Fisher summarized the effects of these characteristics with the term “soil

fertility”). Because the differences in soil fertility among plots of land

were unobserved and unmeasured, they could not be accounted for

directly in the analysis. Accordingly, the differences in soil fertility

induced “noise” into the comparison between the treated and untreated

plots. This noise reduced the precision with which Fisher could estimate

the effect of the fertilizer on crop yields.

However, the “errors” associated with soil fertility potentially caused

a deeper and more subtle problem than mere imprecision. If the

researchers’ assignment of a given plot to the treatment or control group

was somehow correla ted with the plot’s soil fertility, the comparison

between treated and untreated plots would produce a bia sed estimate of

the effect of the fertilizer on crop yields. For example, if researchers

assigned plots thought to have low soil fertility to the treatment group,

the comparison between treated plots (those with low soil fertility and

fertilizer treatment) and untreated plots (those with high soil fertility)

would understate the effect of the fertilizer. Thus, for the comparison

between treated and untreated plots to provide an unbiased estimate of