ECO 375: Introduction to Econometrics · 2020-01-30 · ECO375: Introduction to EconometricsBrian...

Dependence Structure between Random VariablesMoving from Correlation to Causation

ECO 375: Introduction to EconometricsMoving from Correlation to Causation

Brian PhelanDePaul University

January 12, 2020

Brian Phelan DePaul University ECO 375: Introduction to Econometrics 1 / 40


Statistics vs. Econometrics

Statistics Emphasizes...Properties of Random VariablesDependence Structure of Random Variables

A random variable is a variable whose outcome determinedin part by chance.

Econometrics Emphasizes...Understanding the causal relationship between randomvariablesUses include:

test economic theoriesestimate economic parameters (e.g. elasicities)Predict economic aggregates (GDP, unemployment, etc)Measure efficacy and distortions of policies (e.g. taxes,minimum wages)



Statistics and Econometrics are both interested in...

The relationship between variables

Dependence over time

If it rains today is it more likely to rain tomorrow?

Dependence across variables:

How are height and weight related?

How is the IQ of one twin related to the IQ of the other twin?



Scatter Plot

A scatter plot is a good way to see the relationshipbetween random variables

Sample of N observations with the following information:

Individual, Age, Education, Height, Weight, etc.

For each observation, 2 pieces of data (X,Y)

Plot each point for all observations in sample

For example, Height vs. Weight



Scatter Plot: Height and Weight of Adult FemalesScatter Plot: Height and Weight of Adult Females

ECO375: Introduction to Econometrics Moving from Correlation 28 / 79Brian Phelan DePaul University ECO 375: Introduction to Econometrics 5 / 40


Scatter Plot: Cigarette Consumption and TaxesScatter Plot: Cigarette Consumption and Taxes



Scatter Plot: Wins and Home Attendance in BaseballScatter Plot: Wins and Home Attendance in Baseball



Scatter Plot: IQ of Twins Raised ApartScatter Plot: IQ of Twins Raised Apart



Correlation: An ExampleCorrelation: An Example



Limitation

Correlation coefficient is a convenient way to measure astatistical relationship between two variables

It does not however signify anything more than statisticalrelationship

It does not get us any closer to saying whether two thingsare causally related

Correlation does not equal causation



Births to Unwed Mothers

Risen from 5% in 1960 to 37% in 2006

Predictive of many child outcomes

Low birth weight, increased mortality, poor performance inschools, etc.

Many potential explanations

Poor performance of male wages & employment, risingdivorce

Is there a magic bullet explanation?



What is Correlated to Births to Unwed Mothers?What is Correlated to Births to Unwed Mothers?

Figure:ECO375: Introduction to Econometrics Moving from Correlation 50 / 79Brian Phelan DePaul University ECO 375: Introduction to Econometrics 17 / 40


Correlation Does Not Equal CausationCorrelation Does Not Equal Causation

ECO375: Introduction to Econometrics Moving from Correlation 55 / 79



Correlation Does Not Equal CausationCorrelation Does Not Equal Causation

ECO375: Introduction to Econometrics Moving from Correlation 56 / 79



Correlation Does Not Equal Causation

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Conflating Correlation and Causation

Above examples purposely silly, but distinguishingcausation from correlation can be very difficult.

For example, there is a very strong correlation betweengraduating college and earning more money later in life(we saw the same with economics in particular), is this acausal relationship?

Why might this be causal?Why might this be spurious correlation?Why does knowing the difference matter?

What about pro-Marriage policies



Ceteris Paribus Condition

We want to know what happens to some variable, Y, whenwe increase the variable X by one unit – holding all otherrelevant factors/variables fixed (i.e. ceteris paribus).

If ceteris paribus condition holds, we can estimate causaleffects.

Why does the correlation between college graduation andearnings violate the ceteris paribus condition?The SI program at DePaul claims that students that attendsix or more SI sessions have a 90% pass rate.

This is a conditional mean.Is it causal? Why or why not?

Is there some way to get the ceteris paribus condition tohold?

Multivariate regression will help, but it is not a silver bullet.This will continuously be a challenge.



How to measure Causal Effect?

Ideal approach to measuring causality based on thescientific method.

Build two identical worldsVary one thing in the “experimental” world, but not in the“control” worldCompare outcomes between the two worlds. The differenceis the causal effect due to varying the one variable.

This works in many areas in the natural sciences, is thisfeasible for economic applications?

No, not really. No way to make two exact worlds.So, what can be done?



Measuring Causal Effects in Economics

If the scientific method is not feasible in economics, how dowe move forward with understanding causality?Many ways, but the Randomized Control Trial (RCT) is thebest possible way.How does a RCT work?

1 Draw a large sample of individuals2 Randomly assign half to get a treatment and half to not get

it3 Compare outcomes between treated and control groups

How does randomization overcome the ceteris paribuscondition?

new heart drugBecoming more common in economics, but randomizationnot possible in most econ applications

Very expensiveOften unethical



Econometrics

Seeks to uncover CAUSAL relationships betweenvariables.

Understand strength of relationship b/t variablesTest TheoriesPredict Aggregates (GDP, Inflation, etc)

Try to replicate random assignment approach, but for manyeconomic applications, cannot randomly assign many“treatments”

teen birth and outcomes of childrenmore education and earningsobesity and health

Standard comparisons of people in different treatmentgroups will not work. What to do?

Multivariate RegressionUse TheoryLook for “Natural Experiments”



Using Theory to Organize Empirical Models

Economic theory helps frame question: what affects what?

People/firms/organizations are purposefulFirms maximize profitsPeople maximize happiness/utility

Economic agents maximize objectives subject toconstraints

Consumers have limited budgets, firms must paywages/rent to produce, etc.

Econ theory has strong ideas about what consumers andfirms choose and what affects those choices.

Comparative statics also “predicts” how behavior changeswhen parameters change.



Theory of Demand

Model set up (Intermediate Micro)Consumers derive utility from consumption of 2 goods (x, y)

U = u (x, y)x = f (px, py, I);y = f (px, py, I)

Predictions from the model

How demand changes when prices rise(

∂Y∂py

)This model is very clear about what affects what, i.e. thedirection of causality. That’s a start.



Building a Model

Before building a statistical model that will allow us topredict the changes in outcomes, we need to assume adirection of causation

What happens to quantity demanded when priceincreases?Hours of study impact gradesYears of education alter earnings ability

Our model will only accurately measure the impact of “x ony” if this assumption is correct



Break Variables into 2 Groups

Exogenous (external conditions)

Constraints on behavior“Treatments” Factors that can be altered“Independent” variables

Endogenous outcomesChoice variablesOutcomes of systems“Dependent” variables



Optimal Decision Making Guiding Empirical Analyses

In economics, all optimal decisions can be boiled down tomarginal thinking with economic agents taking all actionswhere the marginal benefit exceeds the marginal costs.

So, an empirical analysis of crime (a choice variable)should take into account:

the marginal benefits of crimethe marginal costs of crime (implicit and explicit costs)

What do you think should be included in each?

Gary Becker’s model of crime, has crime a function of:“Wage” for time spent in criminal activity, probability ofgetting caught, probability of getting convicted, penalty ifconvicted, income, wage for time spent in legal work, andage.



An Economic Example

Public finance economists are interested in the productivityof government spending

Two largest components of local spending are schools andpublic safety

Will hiring more police reduce crime?Let y = crime rate (crime per person)Let x = police employed per person

Interested in estimating the slope Dy/Dx how will crimechange when a city hires more police



An Economic Example

Collect data on a cross section of cities

61 cities with populations in excess of 250K

Estimate a simple linear modelYi = β0 + Xiβ1 + εi

In words: b1 will measure relationship between police percapita (X) and crime (Y)

Predict: What is the sign (+ or -) of β1?



Police and Violent CrimePolice and Violent Crime



Highest Violent Crime Rates

Does a positive coefficient mean that more police causesmore crime?Only if the ceteris paribus condition holds, which means...?

As you go from the cities with the most police to the leastpolice, nothing else about the city changes. Is that likely tobe true?

Who are the highest crime cities?Rank of Police

Crime Rate Force Size1 Detroit 102 Memphis 273 Baltimore 64 Nashville 25



USNWR, October 2009

Children fed candy and sweets on a daily basis are morelikely to be convicted of violent crimes as adults, a newstudy finds.

Researchers . . . . looked at data on 17,415 children born in1970 in the United Kingdom.

69% of those who committed violent acts also reportedeating candy daily at age 10 (vs. 42% of those who did notcommit a violent act)

What is the mechanism here?Is the ceteris paribus condition violated?



Basic Statistical Model: OLS

Ordinary least squares (OLS) regression

This model is the base for a vast majority of statisticalanalysis in social sciences

Highly stylized models with tremendous power

Power comes from assumptionsIf assumptions are wrong, model is wrong



OLS: Problem

Can always estimate the basic modelYi = β0 + Xiβ1 + εi

But, this does not mean the estimate for β1 is any good (foreither model)

Biggest problem in empirical work is that people generateestimates – assume they are causal – when there aregood reasons to believe they are not


ECO 375: Introduction to Econometrics · 2020-01-30 · ECO375: Introduction to EconometricsBrian...

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