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Introduction to Econometrics
What is econometrics? Econometrics means different things to different people. Most
economists, however, would agree econometrics is the application of statistical and mathematical
methods to economic problems. Problems addressed using econometrics are almost endless. As
such, econometrics has become the basis for economic and business analysis and forecasting.
Students with a working knowledge of econometrics are a step ahead of other students in the job
market. After college, knowledge of econometric techniques may help in job advancement.
Beginning classes in econometrics are inevitably a source of frustration and concern for
students. Very few students pick up the concepts without putting a sizable productive effort into
the class. Why is econometrics a source of frustration and concern? From experience, it appears
several reasons contribute to this source of frustration. First, econometrics is usually the first
class most students take that integrates components and theory from various disciplines, namely,
mathematics, statistics, and economics, along with minor components from other disciplines.
Second, econometrics is usually taught assuming a basic knowledge of prerequisites. Although,
the prerequisite knowledge necessary is small, students tend to focus on the need to remember
prerequisite material from classes taken several semesters earlier. Experience has suggested by
focusing attention on prerequisites, students have highly over estimated the prerequisite material
necessary to understand econometric techniques. Comments such as “we needed to understand
high level economic theory and calculus that we do not have” are common. When the truth is
the high-level, economic theory the student was referring to is “demand curves slope
downward.” Calculus required at the time of this comment was taking the derivative of a
squared term. Only basic concepts are used in beginning econometrics. An unnecessary mental
block is created even before the student is introduced to the material. Students who are not able
to overcome this mental block perform poorly in econometric classes. Students want to place the
blame on their lack understanding the prerequisites rather than on themselves for the lack of
trying. Third, econometrics notation is different than notation used in previous classes. Learn
the nomenclature, but do not use the new notation as an excuse for lack of understanding.
Fourth, students do not put forth the effort at the beginning of the class to understand the initial
problem setup. Failure to put forth this effort at the beginning of the class has consequences later
in the class. Econometrics is a subject, there is no substitute for keeping current with the
material and lectures. Students cannot comprehend the material by cramming the night before a
test or doing their homework at the last minute. Fifth, econometrics lectures are not
entertainment. A common paradigm arising in education is students must be entertained to learn.
In reality, learning is hard work. Finally, giving the above reasons, students tend to fight the
material and notation. To quote George Davis of the Department of Agricultural Economics at
Texas A&M University, “Don’t fight it.”
Don’t fall into the traps listed above. You will only get out of a beginning econometrics
class what you put into it. Not surprisingly, the best advice to learning econometrics is to work
hard, remain current on the lectures and homework, and ask questions.
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Econometric Analysis
Econometric analysis is an extremely powerful and versatile tool. However, like all
methodological techniques, it is subject to proper use, along with abuse and misuse. One
objective of this class is to introduce the statistical technique, ordinary least squares, and provide
the basis for it proper application.
Presented in table 1 (please note - for ease, most figures and tables are at the end of the
reading assignments), is data on gross state product and per capita income level for 1997. As an
economist, you are interested if there is a relationship between the gross state product and per
capita income level. That is, does increasing gross state product lead to an increase in per capita
income. If such a relationship exists, describing the relationship mathematically and statistically,
along with making inferences from the relationship, is usually the next step. Data on per capita
income and gross state product are graphed in figure 1. It appears that as gross state product
increases, per capita income increases, although the relationship is far from perfect. Two
questions are apparent. First, is the apparent relationship real or is it just a chance occurrence?
Second, if it is a “true” relationship, can a relationship be found that represents the relationship
between income and gross state product? The first question is usually answered using theory,
that is, what does theory suggest about any relationships between per capita income and gross
state product? Should one even be interested in this relationship? Econometric techniques can
be used to provide inference or statistical tests of the existence of a relationship. Statistical tests
although powerful cannot prove relationships exist. Instead, statistical tests indicate within an
acceptable probability of an error, a relationship exists. Econometric techniques can be used to
estimate the mathematical relationship, along with providing a foundation for statistical tests on
the existence of a relationship between income and gross state product.
As will be shown throughout this class, econometrics is used to turn observations on data
points, such as in table 1 and figure 1, into specific mathematical equations. These equations are
then used in economic modeling and forecasting. In addition, to obtaining specific equations,
econometrics allows for statistical testing and inference.
Components of an Econometric Analysis
In figure 2, linkages and interactions between the different components that comprise an
econometric analysis are illustrated. As illustrated, most of the linkages are two-way street.
That is the flow of information is not one directional, but rather feedbacks exist. Each
component is briefly described separately, but keep in mind the importance of the two-way
linkages.
Problem Identification. Before conducting an econometric analysis, a specific problem must be
identified. As noted earlier, a wide range of problems can be addressed using econometrics.
Examples of the types of problems econometrics can address include estimating and using price
elasticities to determine how a price change may impact quantity sold, to forecasting product
sales for next several years. In this class, it will be generally assumed the problem has been
identified. Once a specific problem has been identified, analysis is undertaken. This class
concentrates on the analysis and not identifying the problem.
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Starting Point for the Analysis. The starting point for any econometric analysis is theory,
economic theory or theory from other disciplines. For example, if you are interested in a demand
relationship, economic theory indicates which variables are important in the demand function.
Variables of interest would include own price, prices of substitutes and complements, income,
and taste and preferences. If you are interesting in obtaining a production function for corn,
agronomic theory provides information on important variables and how they might influence
corn yields. Integration of theory is an important component. A priori knowledge, previous
studies, and intuition are also important in conducting an econometric analysis. The role of these
three components is often overlooked in teaching econometrics, but their role in applied studies
is tremendous. Their role keeps analysts from reinventing the wheel. But, there is no substitute
for the role of theory plays in economic analysis. The role of theory, however, cannot be over
stressed.
Data Collection. As noted earlier, econometrics turns data observations into specific
mathematical equations for use in economic models and for statistical testing and inference.
From this statement, it is clear; observations of the kind illustrated in table 1 and figure 1 are
necessary for econometric analysis. Theory is the main source of information on data collection
that is what economic variables should be collected. Next, a prior knowledge, experience, and
prior studies contribute to determining which variables to collect. Finally, and unfortunately,
availability of data ultimately determines which variables will be collected. Although an
important component, data collection is not the main subject area for this course.
Model Specification. Model specification involves which economic variables to include in the
model and how they should be included. Obviously, the variables included in the model are
related to the previous sections, staring point and data collection. The second issue how should
the variable be included in the model will be covered in some detail in this class. This issue is
often referred to as determining the functional form. Should the model be a linear equation? Or,
should the model feature curvature, such as being a quadratic equation?
To illustrate the importance of functional form, consider the following examples.
Suppose you decide to estimate a demand equation. If you estimate a linear demand equation,
the price elasticity of demand changes from elastic to inelastic as the quantity demanded
increases. One could estimate a Cobb-Douglas type demand equation. Price elasticity of
demand is constant over the entire range of the Cobb-Douglas demand equation. Conclusions
drawn from these two different demand equations may be quite different.
As a second example, consider estimating a production function. If a linear production
function is estimated, the calculated marginal product is a constant. A constant marginal product
indicates each additional unit of input provides the same amount of output. This contradicts
economic theory of the “law of diminishing marginal returns.” One may be better off estimating
a quadratic production function, which can provide diminishing marginal returns to the inputs.
However, a quadratic production function introduces other problems. Trade-offs exist between
the different functional forms.
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These two examples illustrate the importance of determining the functional form.
Further, the examples illustrate the interaction between the different components of an
econometric analysis. As illustrated in the above examples, theory is important in helping
determine the functional form. Another important determinate of the functional form is the use
of the estimated model. Unfortunately, there is no silver bullet when it comes to the “proper”
functional form. The reality is we do not know the proper functional form. Further, each
functional form has pros and cons. This class examines some functional form issues.
Estimation Procedures. At this point, you have identified a problem, collected data, and
specified a functional form. This issue becomes how do you covert the data collected into a
mathematical equation using all the data collected. That is, you do not want to throw away
information contained in the data. In this class, considerable amount of time is devoted to
deriving and using one econometric / statistical procedure, ordinary least squares (OLS), which
converts data into a mathematical relationship. OLS is one of the most powerful and widely
used econometric techniques. In deriving the OLS estimator, necessary assumptions and
statistical properties are discussed.
One often asked question is “because ‘canned’ programs exit that easily perform OLS,
why should students learn how to derive the OLS estimator?” The most important response to
this question is that because of the power and ease of using OLS it is often misused. Without
knowing the background of OLS it is easy to violate the assumptions necessary to derive the
estimator and its statistical properties. Inference derived from equations / data which violate the
assumptions are suspect or possibly outright wrong. Do you want to make business decisions on
wrong inference? Do you want your employment to hinge on such estimations? Further, by
understanding the assumptions and possible violations, the student is making a large step forward
to correction the problems by using advanced statistical techniques. Advanced techniques are
beyond the scope of this class, but the basis is provided to understand these procedures.
Along these lines, a statement often made by students is “I don’t need to know where it
came from, just how to perform the estimation.” University’s are in the business of education
and not vocational training. If a student only wants to learn how to do something, they should
enroll in vocational school. Education involves much more than just doing, but also
understanding where procedures come from and how to extend the procedures.
Model Inference and Use. The main purpose for estimating an econometric model is to provide
information concerning the original problem. Econometric models range from a single equation
with a single variable for simple forecasting to very large policy models with tens of equations
and hundreds of variables. Any student who has taken beginning economics has experienced
economic model use and inference. Several simple examples are discussed.
In your introductory economics classes, supply and demand equations were graphed. Did
you ever wonder where the supply and demand equations came from? Econometric methods are
used to estimate these equations. Once estimated, inference such as downward or upward supply
equations can be made. Further use of the models was to find equilibrium price and quantity.
Another use of such equations is to estimate price and income elasticities. Policy analysis can
also be under taken to provide information on how changing some policy will impact the
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equilibrium price and quantity. Most introductory classes also provide a discussion of
production relationships. Econometric methods are used to estimate production functions. From
the estimated functions, marginal product, average product, elasticities, etc. can be determined.
The key here is econometrics provides the link from general theoretical concepts (i.e. just
drawing a supply and demand graph) to specific mathematical equations that can be used in both
academics and the business world.
Statistics also plays an important role in the use and inference made from econometric
models. Although statistics cannot prove any statement (recall there is always the chance of a
type I or type II error), statistics are used to provide information concerning the fit of the
estimated model to the data and provide inference on the estimated coefficients. Statistical
inference will receive considerable attention in this class; as such it is not discussed further here.
Statistical inference is highly interconnected to the estimation procedure. Discussion on
inference and estimation is intermixed in this class.
Conclusions
The goal of this introduction was to introduce the idea of econometrics and provide
motivation for understanding econometric basics. Econometrics provides one link from the
general theoretical aspects discussed in introductory classes to applying the theory in business
and economic settings. Three key aspects were discussed as they related to students in
introductory econometric classes 1) econometric classes are different from other classes, 2)
econometric classes are inherently tough, and 3) students must apply themselves and stay current
with the material in order to understand the basics. There is no substitute for hard work. Several
frequently encountered questions from students were answered.
Important Terms / Concepts
Econometrics
Inference
Estimation
Why learn econometric basics?
What is contained in each steps of an econometric analysis?
What are some of the key concerns of beginning econometric students?
Econometrics combines subject material from what subjects?
Econometrics provides the link between what areas?
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Table 1. State-Level Data on Gross State Product and per Capita Income for 1997.
Gross State Per Capita
Gross State Per Capita
State
Product
Income
State
Product
Income
Alabama
104213
20899
Missouri
155811
23926
Alaska
26575
26898
Montana
18907
19920
Arizona
122273
21892
Nebraska
49275
24148
Arkansas
59141
19628
Nevada
59248
26789
California
1045254
26521
New Hampshire 37470
27238
Colorado
129575
27067
New Jersey
299986
31720
Connecticut
134968
34759
New Mexico
47829
19641
Delaware
31263
26807
New York
663377
29670
Florida
389473
24869
North Carolina
221629
23468
Georgia
235733
23911
North Dakota
15910
20520
Hawaii
38537
25765
Ohio
326451
24772
Idaho
29388
20534
Oklahoma
79423
20739
Illinois
400327
27950
Oregon
97510
24385
Indiana
162953
23418
Pennsylvania
347306
25635
Iowa
81695
23499
Rhode Island
29409
25643
Kansas
72998
24182
South Carolina
95447
20998
Kentucky
101535
20979
South Dakota
19767
21885
Louisiana
123549
20874
Tennessee
151738
22814
Maine
30409
22134
Texas
608622
23756
Maryland
154646
28857
Utah
55070
20613
Massachusetts 223571
30773
Vermont
15510
23026
Michigan
279503
25509
Virginia
212105
26385
Minnesota
152334
27086
Washington
175242
26469
Mississippi
58743
18580
West Virginia
38281
19351
Source: U.S. Department of Commerce.
Bureau of Economic Analysis.
http://www.bea.doc.gov/bea/regional/data.htm
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Per Capita Income (in dollars)
40000
35000
30000
25000
20000
15000
0
200000
400000
600000
800000
1000000
1200000
Gross State Product (in 1000's dollars)
Figure 1. Gross State Product and Per Capita Income
for 1997
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Theory, a priori
knowledge,
previous studies
Data Collection
Model Specification
Problem Formulation
Model Use and Inference
Model Estimation
Figure 2. A More Complicated Schematic of Econometric Analysis Showing Various
Directions and Information Flows.