ECO 420
Advanced Empirical Methods
1
Instructor
• Jing Li
• Second year at Miami
• Taught undergraduate and graduate
econometrics before
• Married with two kids
2
Books
• Required: Introductory Econometrics, a
Modern Approach by Jeffrey M. Wooldridge
• http://www.amazon.com/s/ref=nb_sb_noss?u
rl=search-alias%3Daps&fieldkeywords=Introductory+Econometrics%2C+a+
Modern+Approach+by+Jeffrey+M.+Wooldridg
e
• Recommended: Mostly Harmless
Econometrics: An Empiricist's Companion
3
Webpage
• http://fsb.muohio.edu/lij14/
• Notes, data and codes will be posted
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Critical Thinking
• Example: someone tries to show Canadians
like girls more than boys
• How? He shows that the number of baby girls
born in 2011 is greater than boys. Ok?
• Next, he shows that the number of girls
adopted in 2011 is greater than boys. Ok?
• What do you think?
5
Critical Thinking
• A president of a private high school wants to
prove that private school is worth the money.
• How? He shows that the more students of his
schools go to Ivy League than the best public
school in town.
• What do you think?
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Causality
• How to interpret regression?
• Regression can show association
• Under stricter assumption (ceteris paribus),
regression can prove causality
• Econometrics focuses on causality
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Two Examples
• Does wearing safety belt cause fewer deaths?
• Does the great recession in 2007-2009 cause
fewer marriages?
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Ceteris Paribus
• It means all other things being equal
• Ideally, causality can be proved if Ceteris
Paribus holds
• The president of the private school is wrong
because the family backgrounds of students in
private and public schools are not equal, so
Ceteris Paribus fails.
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Key Issues
• How to design experiment to ensure ceteris
paribus?
• How to find natural experiment?
• How to deal with non-experimental data?
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STATA
• Available at FSB computer lab Room 2037
• Do file puts commands together. Click File--Do, and then choose the do file.
• Log file puts results (no graphs) together. The
text format is recommended. You can use any
text editor to open the file.
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A Typical Do File
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•
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Clear
Capture log close
Log using logfilename.txt, text replace
Insheet using datafilename.csv, clear
…
Log close
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Most Important Commands
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Insheet: read data into memory
List: display data on screen
Sort: sort data
Des: summarize quantitative variable
Tab: summarize qualitative variable
Reg: run regression
Gen: generate new variable
Egen: generate fancy thing
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Tips for Reading Data
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•
•
•
Double check the following items
The variable names (letter and number only)
The missing values (NA, space, a dot)
Dollar sign, comma, etc
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Tips for Summarizing Data
• Pay attention to min, max, obs
• Median (the 50% percentile) is more robust to
extreme values than mean
• Skewness is zero for symmetric distribution
• Kurtosis is three for normal distribution
• Variance and standard deviation measure the
dispersion of the distribution
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Tips for Plotting
• Help twoway
• A scatter plot only shows association, not
causality
• Pay attention to scale
• It is not uncommon to plot the log of data
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Tips for Running Regression
• In general, regression shows association, not
causality
• Pay attention to following:
• Outliers
• Structural Change
• Omitted Variables
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Review
• Mean is good guess by minimizing errors
• Conditional mean is better guess than
unconditional mean
• Conditional mean is random variable
• Law of iterated expectation
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STATA
• Unconditional Mean:
sum y
• Conditional Mean:
by x: sum y
You need to sort data by x first
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Compare Means
• Example: Are the exam scores in section B
greater than section C?
• If there are two groups and x is the group
indicator, using
ttest y, by(x)
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Regression with Dummy Variables
• Alternatively, we can run regression using
dummies to compare means. This approach is
better than ttest
gen d1 = (x == 1), gen d2 = (x == 2), …
reg y d1 d2…
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Question (Optional, Just for fun)
• Suppose we draw 𝑍~𝑈𝑛𝑖𝑓𝑜𝑟𝑚(0,1). After we
know 𝑍 = 𝑧 we draw 𝑌|(𝑍 = 𝑧)
~𝑈𝑛𝑖𝑓𝑜𝑟𝑚(𝑧, 1). Find E𝑌?
• Solve this problem using Law of Iterated
Expectation.
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Answer
• 𝐸 𝑌 = 𝐸 𝐸 𝑌|𝑍
= 0.75
=𝐸
1+𝑍
2
=
1+𝐸𝑍
2
=
1+0.5
2
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Simulation
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•
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•
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help uniform
set obs 10000
gen z = uniform()
gen y = z+(1-z)*uniform()
sum y
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Mean and Sample Mean
• We use sample mean (estimator) to estimate
the population mean (parameter)
• The sample mean has nice properties of (1)
unbiasedness; (2) consistency
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Unbiasedness
• E𝑥 = 𝐸
=𝜇
1
𝑛
𝑛
𝑖=1 𝑥𝑖
=
1
𝑛
𝑛
𝑖=1 𝐸𝑥𝑖
=
1
𝑛
𝑛
𝑖=1 𝜇
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Law of Large Number (Consistency)
• If 𝑥𝑖 ~𝑖𝑖𝑑(𝜇, 𝜎 2 ), then as 𝑛 → ∞,
𝑛
1
𝑥=
𝑥𝑖 → 𝜇
𝑛
𝑖=1
In words, the sample mean gets closer and
closer to the true population mean as the size of
random sample rises
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Simulation (Show Consistency)
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clear
set obs 1000
gen y = 4 + 2*invnormal(uniform())
sum y in 1/10
sum y in 1/100
sum y in 1/1000
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Discuss
• How to use simulation to show unbiasedness?
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Answer
• We need to generate many samples.
• Compute sample mean for each sample.
• Unbiasedness means the average of those
sample means should be close (or in theory
identical) to the population mean
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Causality
• Most often, an economist goal is to infer that
one variable (x) has a causal effect on another
variable (y)
• Example 1: x = price, y = quantity demanded
• Example 2: x = wearing safety belt, y = death
rate
• Example 3: x = hosting Olympics Game, y =
GDP
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Ceteris Paribus
• By definition, inferring causality requires
ceteris paribus (CP)
• CP means all other factors being equal (fixed,
constant)
• Without CP, we are not sure the change in Y is
due to the change in X.
• Exercise: what does CP mean when x = price, y
= quantity demanded?
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Real Problem
• Someone thinks that driving on left (passing)
lane causes more accidents
• How to prove?
• One (bad) answer: let’s pick an interstate, say
I275. Consider I275 between exit 33 and exit
41. Each day between 8 am and 10 am we
record the number of accidents that happen
on the right lane and left lane. Then we do the
mean-comparison test.
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Discuss
• Is I275 representative?
• Is traffic between exit 33 and exit 41
representative?
• Does the time (rush hour, night time) matter?
• How to run a regression?
• How about using the percentage (# accident /
# traffic) rather than the number of accidents?
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Fundamental Drawback
• CP fails since the bad answer uses the
observed data
• Reckless drivers (W) tend to drive on left lane
(X), and reckless driving causes more
accidents (Y).
• The observed association between X and Y
tells nothing about causality since W is not
held constant (CP fails).
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Solutions
• (I) use an experiment: randomly assign reckless
drivers to left and right lanes. Then compare the
mean using the experimental data.
• (2) still use observed data, but run a multiple
regression which includes as regressor the
number of reckless drivers on the left lane.
• (3) use fancy econometric models such as
instrumental variable regression if the number of
reckless drivers on left lane is unobserved.
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Discrimination Paper
• (Race) Discrimination means that someone is
treated unfairly just because of his skin color
(even if he has high ability)
• Using observed data cannot ensure ceteris
paribus
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Experimental Data
• Obtained by using the fake resumes
• Factors (characteristics) other than names
(signal for skin colors) are made comparable
• In other words, the name (skin color) is
independent of ability.
• E(xu)=0, so the key regressor is exogenous
• Ceterius Paribus is ensured by using
experimental data
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Policy Implications
• The punch line of this research is that job
training program may help little for AfricanAmerican, because the program may improve
their skill, but cannot change their skin color.
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Discuss
• This is a very smart paper, why?
• How about using observed data? Can we draw
conclusion based on the observed salary
difference between black and white?
• How about market heterogeneity? Can we
generalize the finding to other markets such
as the market for college faculty? Why?
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Tax Paper
• Supply-Side Economics says that people work
more (and so GDP rises) after tax cut
• So the theory implies a causal effect of tax cut
on labor supply
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Discuss
• Consider using the observed data, and run the
regression of
Labor hours = 𝛽0 + 𝛽1 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 + 𝑢
What does 𝑢 represent?
Is E(xu)=0, or is 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 exogenous?
What is the consequence of using observed
data?
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Natural Experiment
• There is a tax reform (natural experiment)
• In 1987-1988, Iceland moved from a system
under which taxes were paid on previous
year's income to a pay-as-you-earn system.
• So the tax rate for 1987 income became zero
in an exogenous manner (has nothing to do
with 𝑢)
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Policy Implications
• Figure 1 shows that cutting tax leads to higher
employment
• Figure 2 shows a hike in GDP in 1987-1988
• Another paper that uses natural experiment:
HOME-EQUITY LENDING AND RETAIL
SPENDING: EVIDENCE FROM A NATURAL
EXPERIMENT IN TEXAS
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Discuss
• Where is natural experiment? Reform, Law
Change, Natural Event…
• Q: how to show the causal effect of the
number of children on labor hours of women?
How to design a pure experiment? How about
natural experiment?
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