Applied Statistics - Introduction

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Econometrics
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Applied Statistics for Economics
1. Introduction

SFC - juliohuato@gmail.com

Spring 2012

SFC - juliohuato@gmail.com Applied Statistics for Economics 1. Introduction

Outline
Econometrics
Illustrations
On method

Econometrics

Illustrations

On method


Outline
Econometrics
Illustrations
On method

Definitions

Statistics or statistical inference is the set of methods used in
science, technology, and industry to extract information from data.
Data is a set of records drawn from observations of the world.
When used in economics (and also business management, finance,
and a number of social sciences) and in policymaking,1 statistical
methods are often called econometrics. We will see that there is a
good reason for the terminological distinction. We will follow this
convention and refer to our course as introductory econometrics.

1
Policymaking means choosing rules of behavior (‘policies’). We usually
think of governments making (and implementing) policies, but this also applies
to any other organization (business, household, nonprofit, club) or individual. In
this sense, business managers or heads of household are “policymakers.”

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Econometrics
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Econometric applications
In practice, econometrics:
tests empirically whether theories2 about social or economic
behavior match observed facts,
forecasts the future values of interesting economic variables of
interest,
ﬁts economic models to real-world data, and
uses historical data to make quantitative policy
recommendations to policymakers.
2
By theory (or model), I mean a clear statement about the relationship
between at least two variables of interest. In very general terms, a theory is a
statement of the following type: “If x, then y .” Often, x is called the ‘premises’
and y the ‘conclusions.’ More speciﬁcally, a simple theory about cigarette
consumption would be a statement like this: “Other things equal, if cigarette
prices increase, the consumption of cigarettes will decline.”

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The econometrics approach

Ideally, as a scientiﬁc discipline, econometrics uses (1) statistics (a
branch of deductive mathematics), (2) probability theory (a theory
of uncertainty in the world), and (3) economics (a theory about
how economic variables are related) in response to the practical
concerns of policymakers.
Ultimately, it is the practical needs of policymakers that dictate
which theories to test empirically, which relationships to estimate,
and which variables to forecast.


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Illustrations

To illustrate the use of econometrics (and the reason why we call it
‘econometrics’ rather than just ‘statistics’), consider the following
examples:


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Class size and grades
Does reducing class size improve elementary school education?
The question cannot be answered well by looking at the data
casually. Suppose we do and note that smaller classes and higher
grades go together. This may be due to other advantages that
students in small classes may have over students in bigger classes.
E.g., students in smaller classes may have richer parents, greater
access to libraries, etc.
The data available don’t come from an experiment where
otherwise identical students are placed in classes of diﬀerent size
and then test their respective academic performance.3
Hence, we need special tricks to examine this kind of data and try
to answer the question.
3
In Latin, the word “data” is plural for the singular “datum.” However, we
may subsequently say “data is . . . ” rather than – awkwardly – “data are . . . .”

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Racial discrimination in mortgage lending

Is there racial discrimination in the market for home loans?
Again, a casual look at the data won’t do. If after looking at the
data, we say that black applicants are denied loans more often
than white applicants and the issue is race, a critic may object that
the correlation between race and mortgage approvals may be due
to other reasons. For instance, black people may be poorer and
have less property to use as collateral. Then the issue is not race,
but income or wealth.


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Again, the data don’t come from black and white people who are
otherwise similar. We need econometrics (not just statistics) to get
around the deficiency of the data. We need to isolate the race
effect from other effects. One cause doesn’t exclude the other.
Moreover, the causes may interact. Discrimination may result not
only from being black or only from being poor, but from being
both black and poor!


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Notice how important a test like this can be for policy
recommendations:
If the main reason why black people are more often denied loans
than whites is because they are black, then we need mainly the
enforcement of civil rights laws. But if the main reason is that they
are poor, then we mainly need actions and resources to fight
poverty, joblessness, etc. If the reason is the interaction between
race and economic condition, then the combination of policies
required to address the problem will also be different. The
recommended courses of action depend on the diagnosis. And
since the resources of a community to deal with its problems are
finite, you want to spend those limited resources in their most
effective uses.


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Taxes and cigarette smoking

How much do cigarette taxes reduce smoking?
Suppose you look at data on cigarette sales, prices, taxes, and
personal income for U.S. states in the 1980s and 1990s, and note
that states with low taxes and low prices have higher smoking
rates, and vice versa.
A problem here is double causality. Presumably, low taxes lead to
high demand. But also, because of high demand, there will be
many voters who smoke, and politicians may try to keep cigarette
taxes low to get reelected.
Econometrics methods, as opposed to regular statistical inference
that relies experimental data, has ways to get around this double
causality problem.


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Forecasting future inflation

What will the inflation rate be next year?
Nowadays, most central banks think of their mission as controlling
inflation (they used to think their mission was to help the economy
reach full employment). They set the interest rates based on their
inflation outlook in the future.
If they think inflation will increase, they may want to slow down
the economy by rising the rates. Or vice versa. If they guess
wrong, they can cause an unnecessary recession or they may enable
inflation to spin out of control.


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Required answers

To give quantitative answers to these questions, we use data. If we
use diﬀerent data sets, then we may get a diﬀerent answer. In a
way, our answer to the question is uncertain. The answer will
depend on the data we use. There’s uncertainty. What kind of
quantitative answers do we need?
Does reducing class size improve elementary school education? If
classes are reduced in 10%, holding constant other student
characteristics, the test scores of students increased in x%.


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Required answers

Is there racial discrimination in the market for home loans?
Holding constant all other characteristics of loan applicants and
possible applicants,4 being black reduces your chances of getting a
loan by x%.
How much do cigarette taxes reduce smoking? If the price of
cigarettes increases in 1%, holding constant the income of smokers
and possible smokers5 and all other variables, the smoking rate
declines in x%.

4
Potential applicants must be included in the data sample because it may
well be that some blacks don’t apply for loans because they believe they’ll be
denied loans. And loan discrimination is what we’re trying to measure.
5
Again, we include potential smokers who don’t currently smoke because a
hefty tax may discourage them to join the smoking club and vice versa.

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Required answers

To answer these questions, we need the multiple regression model
that we’ll introduce by the end of the course. However, because
this is an introductory course, we may not be able to get to the
topics where we can actually learn the tricks to get around all the
data deﬁciencies indicated above. Some, perhaps, but not all. But
at least we will know that these issues exist.


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Required answers

What will the inflation rate be next year? Here the type of answer
is obvious: The inflation rate next year will be x%.
In this course, we will not be able to study the econometric
methods required to answer this type of question. These methods
are called time-series econometrics, and they are heavily used in
macroeconomics and finance.


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Causality

An action causes an outcome if the outcome is the immediate
result or consequence of that action. Causality means that a
specific action (fertilizing tomatoes) leads to a specific measurable
consequence (more tomatoes).
How do we measure whether a specific action is the cause of
certain effects? We can run an experiment. For that we need many
plots with tomato plants. They must be, as far as possible,
identical except in the amount of fertilizer applied.
Moreover, the decision whether a plot should be fertilized or not
must be random to make sure that the only systematic difference
between the plots is whether they are fertilized or not. We record
the amount of fertilizer and count the tomatoes at the end of the
cycle.

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Causality

That’s a randomized controlled experiment. The non-fertilized
plots are called the controlled group. The other is the treatment
group. It is randomized because the treatment is assigned
randomly to eliminate the possibility of other systematic
differences among control and treatment groups. If the experiment
is conducted in a sufficiently large scale, then we may be able to
estimate the causal effect of fertilizing on tomato production.


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Causality

Our definition of causal effect: The effect on an outcome of a
given action or treatment as measured in a randomized controlled
experiment. The only systematic reason for differences in outcomes
between the controlled and treatment groups is the treatment
itself.
We cannot always conduct experiments in economic life. They’d
be too costly, unethical, or practically impossible. So a randomized
controlled experiment will be only a theoretical benchmark for us.


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Causality

Note that, to answer the fourth question, we do not require to
know the causes of inﬂation. All we need to know is how to make
a reliable forecast. We can forecast rain if we look through a
window and see people carrying their umbrellas, relying on the fact
that people tend to carry their umbrellas along when they expect
rain. But the use of umbrellas is not the cause of rain.6

6
Advanced time-series econometrics also has methods to estimate causes:
these methods fall under the rubric of ‘structural models.’

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Data sources

According to its origin or source, there are two basic types of data:
1. experimental data and
2. observational data
In economics (and to a large extent in business) we use
observational data. We need to use econometric tricks to estimate
causal effects from observational data. In the real world, the levels
of “treatment” are not assigned at random and it is therefore hard
to disentangle the effect of the “treatment” from the effects of
other causes.
That’s what econometrics is for. That’s why econometrics exists,
as opposed to mere statistical inference of the type used in the
physical and natural sciences.


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Data types

Types of data:
1. Cross-sectional data: Data on different entities (individuals,
firms, states, countries, etc.) for a single period of time.
2. Time-series data: Data for a single entity (individual, firm,
state, country, etc.) from different periods of time or at
different points in time.7
3. Longitudinal or panel data: Data for more than one entity in
which each entity is observed at two or more periods of time.

7
For more on this difference, see my review slides on flows, stocks, and
accounting.

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Wrap-up

1. Why do we need to give quantitative answers to some
questions?
2. What’s a causal effect?
3. What is a randomized controlled experiment?
4. What’s econometrics for?
5. Why do we need techniques different from those used in the
physical and natural sciences?
6. What is the difference between cross-sectional, time series,
and panel data?


Applied Statistics - Introduction

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