Introduction to Econometrics
Topic 1: The nature of econometrics and economic data
Konstantinos Tatsiramos
University of Luxembourg
February 2025
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Outline
▶ What is Econometrics?
▶ Steps in an Empirical Analysis
▶ The Structure of Economic Data
▶ Causality and the Notion of Ceteris Paribus
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What is Econometrics?
▶ Econometrics is the set of tools by which economists, and others in the social
sciences, analyze data.
▶ We can use econometrics to:
1. estimate economic relationships;
2. test economic theories;
3. evaluate government and business policies.
▶ For example, what if we are asked to study the effects of school spending on
student performance?
▶ A simple correlation analysis might not be sufficient because causality can be
difficult to infer.
▶ On average, schools that have more revenue per student may also have more
capable students.
▶ Econometrics is its own discipline (separate from statistics).
▶ Focuses on problems inherent in analyzing data generated by individuals, firms, and
other entities acting strategically, and interacting with one another.
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Data used (mostly) in Econometrics
▶ Experimental data: data from controlled experiments (less common in social
sciences compared to natural sciences)
▶ Non-experimental data: most frequent in economics (also known as observational
or retrospective data)
▶ Observational data are collected in a passive manner, after we observe outcomes on
individuals, firms, schools, and so on.
▶ We simply act as “observers” of what has happened and then try to learn from
what we observe.
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Why Study Econometrics?
▶ Bridge between theory and practice: apply economic theory to real world data.
▶ Policy analysis: assess the impact of policies.
▶ Forecasting economic variables: inflation, interest rates, housing starts, and so on.
▶ Fosters critical thinking and problem-solving skills: transferable skills to a wide range
of fields and professions.
▶ Preparation for Master degrees in economics or finance.
▶ Employment opportunities: employers value candidates with econometrics expertise in
fields such as finance, consulting, government, data analytics.
▶ Quantitative literacy: in a data-driven world econometrics enable you to critically
assess and interpret data-driven arguments and studies.
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Empirical Analysis
▶ In economics, theory and empirical analysis are both important.
▶ An empirical analysis uses data to:
▶ test a theory
▶ estimate an economic relationship
▶ determine the effects of a policy or intervention
▶ Econometrics allows us to analyze data using formal statistical methods.
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Steps in an Empirical Analysis
▶ Steps for a Successful Empirical Study
1. Be very precise in posing the question you hope to answer.
▶ Example: does attending lectures in college lead to better grades (on
average)?
2. Specify an economic model, or at least a conceptual model, to study the
phenomenon of interest.
▶ Formal economic modeling (such as utility maximizaton) is often used, but
can also proceed with careful economic reasoning that is less formal.
3. Turn the economic model into an econometric model.
4. Collect data on the variables and use statistical methods to:
▶ estimate the parameters of the econometric model
▶ construct confidence intervals for the parameters
▶ test hypotheses about the parameters
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Example 1 - Economic model of crime
▶ Gary Becker (a Nobel Prize winner), in 1968, wrote an influential article showing how
criminal behavior can be modeled in a utility maximizing framework.
▶ Crimes have rewards but have also costs (opportunity cost, probability to be caught,
punishment). The decision to undertake illegal activity is one of resource allocation
taking into account the costs and benefits of competing activities.
▶ The result is a supply function for time an individual spends in illegal activity
(including, of course, not spending any time) which can depend on:
▶ “wage” for an hour spent in criminal activity
▶ hourly wage in legal employment
▶ other income
▶ probability of getting caught
▶ probability of being convicted if caught
▶ expected sentence if convicted
▶ age
▶ Becker’s analysis helps one decide the kind of factors one would ideally include in a
study of factors that affect criminal behavior.
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Example 2 - Job training and worker productivity
▶ Question: What is the effect of job training on worker productivity?
▶ To answer this question, we can start with an equation describing the determinants
of productivity, where productivity is measured by the observed hourly wage
wage = f (educ, exper , training )
▶ educ is a measure of schooling (years of schooling)
▶ exper is a measure of workforce experience
▶ training is a measure of time spent in job training (the variable of most interest).
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Turn the economic model into an econometric model
▶ Our focus is on econometric models, which resolves certain difficulties and
ambiguities concerning an economic model.
▶ How should we measure the variables of interest?
▶ What is the exact functional relationship among economic variables?
▶ How do we account for unobserved factors that make relationships among
variables inexact?
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An econometric model of the wage/job training example
▶ We can specify an econometric model for the wage/job training example as
wage = β0 + β1 educ + β2 exper + β3 training + u
▶ The constants β0 , β1 , β2 , and β3 (“the betas”) are the parameters of the model,
and it is these (especially β3 in this example) that we hope to estimate.
▶ Ideally we will be able to collect data on wage, educ, exper , and training from a
large group of working people.
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The error term
wage = β0 + β1 educ + β2 exper + β3 training + u
▶ The last term in the equation, denoted by u, is called the error term or disturbance
and plays a very important role in econometrics.
▶ It represents all other factors that can affect someone’s wage, including intelligence,
motivation, and so on. The error term can also capture measurement problems in
one or more of the variables.
▶ We will use statistical methods and data to estimate and test hypotheses about the
parameters.
▶ For example, the hypothesis that job training has no effect on wages is β3 = 0.
▶ The hypothesis that one year of experience worths as much as one year of
education is β1 = β2 .
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The Structure of Economic Data
▶ Economic data come in several different forms. We will focus on cross-sectional
data.
▶ Cross-sectional data are collected on units (e.g. individuals, families, firms, schools)
at a given point in time.
▶ There are also other forms of data such repeated cross-sectional data, panel data,
time series.
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Random Sampling
▶ In this course, we will assume that a cross-sectional data set represents a random
sample.
▶ That is, each unit in the population has the same chance of appearing in the
sample, and the draws are statistically independent of one another.
▶ Random sampling (with replacement) generates observations that are independent
and identically distributed.
▶ Intuitively, a random sample is representative of the population of interest, and
gives us the best chance of learning about the population.
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Example of a cross-sectional data set -1
▶ The following is a list of variables in a cross-sectional data set. It contains information on
hourly wage, years of schooling (highest grade completed), gender, and workforce experience
among 871 individuals.
obs:
871
vars:
6
----------------------------------------------------------------------------------------------------------------storage display
value
variable name
type
format
label
variable label
----------------------------------------------------------------------------------------------------------------wage
float %9.0g
hourly wage
female
byte
%8.0g
=1 if female
educ
byte
%8.0g
years of schooling
exper
byte
%8.0g
years of workforce experience
lwage
float %9.0g
log(wage)
expersq
int
%8.0g
exper^2
-----------------------------------------------------------------------------------------------------------------
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Example of a cross-sectional data set -2
. list in 1/15
+---------------------------------------------------------+
| wage
female
educ
exper
lwage
expersq
|---------------------------------------------------------|
1. | 5.73
1
14
30
1.745715
900
2. | 4.28
1
12
28
1.453953
784
3. | 11.57
0
16
38
2.448416
1444
4. | 11.42
0
16
27
2.435366
729
5. | 3.91
1
12
20
1.363537
400
|---------------------------------------------------------|
6. | 8.76
0
16
12
2.170196
144
7. | 4.03
0
16
6
1.393766
36
8. | 5.14
0
17
19
1.637053
361
9. | 7.99
0
16
12
2.078191
144
10. | 6.01
0
16
17
1.793425
289
|---------------------------------------------------------|
11. | 5.16
0
17
7
1.640936
49
12. | 11.54
0
17
12
2.445819
144
13. | 7.69
1
16
7
2.039921
49
14. | 6.79
0
14
19
1.915451
361
15. | 6.87
0
12
33
1.927164
1089
+---------------------------------------------------------+
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Causality and the Notion of Ceteris Paribus
▶ The concept of causality is key in econometrics.
▶ How can we know that more spending causes better student performance (on
average)?
▶ How can we know that job training causes an increase in wages (on average)?
▶ Finding correlations in data might be suggestive but is rarely conclusive.
▶ Crucial to establishing causality is the notion of ceteris paribus, which means
all (relevant) factors equal.
▶ To establish that changes in one variable (job training) in fact ”cause” changes in
another variable (wages) we need to “hold fixed” other relevant factors.
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Correlation does not imply causation
▶ To determine if a job training program has a causal effect on wages it is tempting to
examine whether wages differ between those who participated in the program and
those who did not.
▶ However, the decision to participate in a program is a choice made by the
participants.
▶ We should expect those without jobs or with low-paying jobs to be more likely to
participate.
▶ So if we just compare the wages of participants and non-participants, we may find a
negative correlation even if the job training program might have a positive impact
on the incomes of participants.
▶ The problem is participants and non-participants differ in many other ways, so all
other factors are not held fixed.
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Ceteris paribus and counterfactual reasoning
▶ The notion of ceteris paribus can also be described through counterfactual
reasoning.
▶ The idea is to imagine a unit (an individual) in two (or more) different states of the
world.
▶ In the job training program example, we can imagine the wages of a single worker
under two states: one with job training and one without job training.
▶ By considering the counterfactual outcomes of a single worker, we easily hold other
factors fixed, since the counterfactual thought experiment applies to each individual
separately.
▶ Causality means that the outcome (wages in this case) in the two states of the
world differs for at least some individuals. In other words, receiving training causes
an increase in wages.
▶ Counterfactual reasoning is helpful in thinking about the kind of experiment we
would need to infer causality
▶ In reality, we only observing one of the two possible states of the world.
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Randomized Experiment
▶ One way to determine the causal effect of job training on wages is to conduct an
experiment:
▶ Assign randomly some members of the population to a treatment group who
then participate in the program
▶ Assign randomly other members of the population to a control group who do
not participate in the program
▶ This experiment does not hold other relevant factors fixed. For example, worker
quality might differ across workers (It is impossible to truly hold all other factors
fixed).
▶ The key point is that if participation in the job training program is determined
independently of other worker-related factors that affect wages, then we are able
to get a “good” estimate of the causal effect.
▶ Random assignment of the treatment ensures that the treatment and the control
group are similar in all aspects except that those in the treatment group received the
treatment.
▶ So any differences in the outcomes between the treatment and the control group are
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the causal effect of the treatment.
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Other Factors in Experimental vs. Non-Experimental data
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Experiments are not always feasible
▶ Question: What is the value of another year of education on one’s earnings?
▶ What is the type of experiment we would have to run to infer causality?
▶ At birth: each child is randomly given a highest grade that they must complete
(everyone complies).
▶ During adulthood: we record earnings and we compare them across the different
grades.
▶ This experiment is not feasible.
▶ For problems such as finding out the value of education, we must usually rely on
observational data.
▶ For a large random sample of people, we can collect information on education
and earnings and hold fixed all other relevant variables.
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Self-selection
▶ In the education example, the amount of schooling is not randomly assigned but
chosen by individuals and their parents (self selected).
▶ Probably (on average) those who are more capable choose to become better
educated.
▶ However, more capable individuals would earn more, on average, than less capable
individuals.
▶ So comparing the earnings of those with more education to those with less education
might reveal a positive correlation between earnings and education.
▶ However, this correlation does not imply that the higher earnings of those with more
education is due to schooling, because other factors are not held fixed (intelligence,
prior experience etc)
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