Econ 3334: Introduction to Econometrics
What is this course about
• Econometrics: uses data to answer economic questions in a systematic way.
1) Test economic theories using real-world data
2) Forecast future economic variables
3) Measure causal relationships (e.g., policy → outcome)
4) Provide evidence for decision-making in business and public policy
• Outline of the introduction
– Examples of economic questions
– Causal effects and idealized experiments
– Causality vs forecast
– Data sources and types
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Economic questions
• Does reducing class size improve elementary school education?
– Common sense: small classes help learning
– Cost v. benefits
– Empirical evidence: small classes v. large classes, students learning outcomes
– Difficulty: isolate the effect of class size from other factors
• Is there racial discrimination in the market for home loans?
– During 1990s, mortgages denial rate: 28% black v. 9% white
– Isolate the effect of race from ability to repay loan
• Does healthcare spending improve health outcomes?
– Cross-country comparison: health care spending → mortality rates
• How well can we predict students’ performance based on schools’ characteristics?
– What variables predict students’ test scores better than others?
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Choosing predictors
Data: 3932 elementary schools in CA in 2013.
Predictors: 38 main variables and their transformations
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Causal analysis: fair comparison
• Does reducing class size improve elementary school education?
– Compare large and small classes with similar background, such as
• Students ability
• Learning resources
• Parents resources
• Is there racial discrimination in the market for home loans?
– Compare black and white with similar age, income, debt, wealth…
• Does healthcare spending improve health outcomes?
– Compare countries with similar income, age cohorts, habits…
• To investigate the causal effect of an intervention on outcomes, we must make a fair
comparison:
– Ceteris paribus or other things equal
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Hypothetical intervention
• An intervention is not always feasible in practice. To understand the causal effect in
such cases, we will conduct a “thought experiment” by using a “hypothetical
intervention”.
• For example, in the recent legal case against Harvard about possible racial
discrimination, we may think of race as the intervention, while admission rates or
evaluation scores as the outcomes.
• Of course, we cannot switch on and off an applicant’s race. However, we may still
imagine what could happen if the applicant is of a different race.
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Causal effects and randomized controlled experiments
• Randomized controlled experiment/trial (RCT)
– Control group v. treatment group
– Treatment is assigned randomly
• Causal effect: in an RCT, action/treatment → outcome
• Forecast/prediction: predictors → outcome
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Data source: experimental data
• Pfizer’s experimental data on Paxnovid; submitted to FDA for emergency approval.
• N = 1219.
• Treatment group (Paxlovid), control group (placebo)
• Double-blinded experiment: neither the patients nor the researchers know the group
membership of the patients until the experiment is over.
• Pills were given to patients within 5 days of Covid infection; results observed within
28 days of medication.
Effectiveness against Hosp. is defined as (6.7-1.0)/6.7 = 85%.
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Data source: observational data (1)
• In the experimental data, the treatment is randomly assigned.
• In the observational data, also called non-experimental data, the treatment is not
randomly assigned to individuals.
– Suppose we want to see how graduate school education affects income.
– We observe individuals with different educational background.
– Those who attend graduate school might prefer an academic job to working in
the private sector.
– Those who attend graduate school might have private information about the job
market outcomes of graduate students.
– Those who choose not to attend graduate school might be more ambitious about
private sector jobs and have private information about the value of work
experience.
– Comparing people with or without a graduate degree is not fair.
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Some jargons
• We will use the following notions while referring to a data set:
– Random variable: a variable that can take multiple possible values.
– Observation: the observed value of a random variable
• For example, we have 5 observations for two random variables “wage” ($/hour) and
“experience” (years) in year 2012:
• In this example, each observation denotes a person in a given period. For each
person, we observe his/her wage and experience in 2012.
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Data source: observational data (2)
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Observational data v. experimental (RCT) data
• In experimental data, the treatment is randomly assigned.
• In observational data, the treatment is not randomly assigned to individuals.
– Schools with small student-teacher ratios tend to be those with more resources.
– More learning resources tend to help students learning
– The outcome differences between small and large STR’s are due to a mixture of impacts
from class sizes and other learning resources
– Need to isolate the effects from class sizes and other learning resources.
• In sum, in the observational data, the control group and the treatment group differ in factors
other than the treatment.
– Such factors, if also affecting the outcome, are called “confounding factors”.
• In RCT data, the control group and the treatment group are similar in other factors
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Our objective
• Econ 3334 aims to isolate the effects of confounding factors from the treatment
effects, using observational data.
• We will design comparisons that mimick the scenario of “other things equal”.
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Review questions
• Describe a hypothetical RCT to study the effect of six hours of reading on the improvement
of the vocabulary of high school students.
– Suggest some impediments to implementing this experiment in practice.
• Describe a hypothetical RCT to study the effect of the consumption of alcohol on long-term
memory loss.
– Suggest some impediments to implementing this experiment in practice.
• You are asked to study the causal effect of hours spent on employee training (measured in
hours per worker per week) in a manufacturing plant on the productivity of its workers
(output per worker per hour). Describe:
– an ideal randomized controlled experiment to measure this causal effect;
– an observational cross-sectional data set with which you could study this effect;
– an observational time series data set for studying this effect;
– an observational panel data set for studying this effect.
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Causality vs forecast
• To “forecast” whether it is raining or not, just look outside your window and see if
pedestrians are using umbrellas.
– Using an umbrella does not cause it to rain.
• William Phillips in 1958 noted that low unemployment rate came hand-in-hand with
high inflation. Thus it seems we may forecast the inflation to be high when we
observe low unemployment rate, or the other way around.
– The Phillips curve (1958), Samuelson and Solow (1960)
– New evidence in recent decades.
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The Phillips curve: time series plot
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The Phillips curve: 1948Q1-1960Q4 (scatterplot)
Unemployment versus Inflation (with least squares fit)
7.5
Y = 4.86 - 0.411X
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Unemployment
6.5
6
5.5
5
4.5
4
3.5
3
2.5
-1
0
1
2
3
4
Inflation
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The Phillips curve: 1961Q1-1980Q4
Unemployment versus Inflation (with least squares fit)
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Y = 5.10 + 0.359X
Unemployment
8
7
6
5
4
3
0
0.5
1
1.5
2
2.5
3
3.5
4
Inflation
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The Phillips curve: 1981Q1-2020Q4
Actual and fitted Unemployment
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actual
fitted
13
12
Unemployment
11
10
9
8
7
6
5
4
3
-2
-1
0
1
2
Inflation
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The scatterplot
• Scatterplot is a diagram illustration of the data on two variables.
– Scatterplot provides a visual display of the relation between two variables.
– Scatterplot only shows “correlation”, but not a causal link.
• A causal link has a direction.
• The correlation has no direction.
• The horizontal and vertical axis of the scatterplot are interchangeable.
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Phillips Curve: explanations
• 1948Q2-1960Q4: demand shocks caused opposite movement of unemployment and
inflation
– A surge in demand → firms hire more workers → products are more expensive
due to higher demand.
• 1961Q1-1980Q4: supply shocks (oil markets disruptions) cause unemployment and
inflation to move in the same direction.
– A surge in energy prices → firms reduce production, hire fewer workers to
reduce cost → products are more expensive due to higher cost.
• 1981Q1-2020Q4: central bank became more determined to keep inflation stable, even
at the cost of high unemployment rates. Inflation became less responsive to
economic shocks.
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Importance of knowing the economic causal mechanism
• Data source: https://fred.stlouisfed.org/series/DEXJPUS
• Natural disaster: magnitude-9 earthquake and tsunami on March 11, 2011.
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Causality and forecast
• X forecasts Y does not imply X causes Y
• Understanding the causal link between X and Y is crucial for making forecast “outof-sample”.
– In the case of inflation and unemployment, it is usually a common factor Z that
drives X and Y together.
• Knowing the causal link among Z, X, Y helps us to make forecast about X and Y.
• Knowing the correlation between X and Y only helps “in-sample” forecast, but could
be misleading for “out-of-sample” forecast.
– In the case of natural disaster to FX rates, it depends on the specific channel how
X affects Y: (also short-term vs. long-term)
X→channel 1→Y
vs.
X→channel 2→Y.
“out-of-sample” means either
outside the time frame of the data
or predictor’s value being outside the coverage of the data.
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Data type: cross-sectional data
• Cross-sectional data: a sample of individuals within a specific period; timing
differences can be ignored.
– The individual can be a person, a firm, a country, a product, etc. (see Table 1.1 in p9)
• Repeated cross-sectional or pooled cross-sectional data
– Combine samples from different periods. Each period may include different individuals.
– The number of observations can be different across periods.
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Data type: time series data
• Time series data are data for a single entity (person, firm, country) collected at
multiple time periods
– Usually come with a given frequency, such as annually, quarterly, monthly,
weekly, daily, etc.
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Data type: panel data
• Panel data: (also called longitudinal data)
– Observations for the same set of individuals over multiple periods.
– The following data consist of three variables for 48 states observed over 11 years. There
are 48*11 = 528 observations in total.
Alabama in 1985 and Alabama in 1986 are regarded as two different observations.
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Summary
• Causality
– Ceteris Paribus / other things equal
– Confounding factors
– Intervention / treatment
• Experiment
– Randomized controlled experiment/trials (RCT)
• Forecast
• Scatterplot
• Data sources and types
– Experimental vs. observational data (non-experimental)
– Random variable
– Observation
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