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Transcript of Lec02
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Public Economics
Chikako YamauchiAssistant Professor, GRIPS
Lecture 2
Tools of Positive AnalysisRosen & Gayer, Ch. 2
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Todays topics
1. The Role of Theory2. Causation versus Correlation3. Experimental Studies4. Observational Studies5. Quasi-experimental Studies
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1. The Role of Theory
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Why is it so hard to tell whats going on?
The Bush administration reduced the income tax rate for high earners
In the 2008 election, John McCain supported keeping it; Obama did not
Conservatives think that lower tax rates provide incentives for people to work harder
Liberals think that tax rates do not matter
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Why is it so hard to tell whats going on?
What is the impact of tax rates on the number of work hours?
More generally, how can we estimate the impact of government programs on individual behavior?
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The Role of Theory
Theory provides a framework for thinking about the factors that might influence the behavior of interest
For example, suppose Roger derives utility from leisure, but he needs to earn income to buy goods
Suppose his wage rate is $10 per hour, and he finds a combination of income and leisure with which he feels the happiest
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The Role of Theory
Now suppose that 20% tax is imposed, and his net wage rate is $8. What happens?
Substitution effect: leisure is cheaper, so consume more of it, i.e., work less
Income effect: he earns only $8 by working one hour, loss in income induces him to consume less of goods and leisure, i.e., work more
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The Role of Theory
Thus, theory indicates the mechanism through which a policy might affects individual behavior
Sometimes it includes conflicting effects such as substitution and income effects
Under such circumstances, only empirical work can tell us the overall effect of a policy on individual behavior
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2. Causation versus Correlation
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Causation versus Correlation
To establish a causal relationship, The cause (X) must precede the effect (Y) X must be correlated with Y Other explanations for any observed
correlation must be eliminated
The last condition is difficult to pass
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Causation versus Correlation
Suppose we are interested in the effect of unemployment insurance (UI, payments to people who lost jobs) on unemployment spell
Those who received high benefits = treatment group
Those who received low benefits = control group Suppose the treatment group exhibited a shorter
spell of unemployment subsequently
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Causation versus Correlation
It could be because UI had an impact to shorten unemployment spell
However, a possible other explanation is that the treatment group were different in other ways High UI benefits are typically given to people
who had higher earnings in their previous jobs They might have greater motivation for work
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3. Experimental Studies
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Experimental Studies
The observed relationship between UI benefits and unemployment duration was due to a third influence, i.e., motivation level
Thus, the lower unemployment duration for the treatment group relative to the control was a biased estimate of the true causal impact of the higher benefits
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Experimental Studies
To rule out other factors, we want to know the counterfactual: what would have happened to members of the treatment group had they not received the treatment
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Experimental Studies
Golden standard = experimental study: a study in which individuals are randomly assigned to the treatment and control groups
Since the selection into the treatment group is out of individual control, it is less likely that factors, such as motivation level, differ between groups on average
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Conducting an Experimental Study
First, randomly assign a sample of unemployed people to receive high or low benefits
Second, check whether observed characteristics (age, education, gender) are similar on average
Third, compare the subsequent average unemployment duration
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Pitfalls of Experimental Studies
Ethical problem: can we force a certain group of people to be exposed to harmful treatment to measure its effect? pollution
No compliance: the treated may not participate, and the controlled may try to sneak in No compliance among the treated = Effect of Intent
to Treat No compliance among the controlled dilutes the
estimated effect of treatment Bias towards zero
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Pitfalls of Experimental Studies
Nonrandom attrition: disappearance of certain members from data Suppose we are interested in the effect of job-training
program on future wage rates Suppose the program actually increased the wage of
participants Suppose also that low-skilled workers in the control
group did not experience an increase in the wage and felt ashamed. They may not report their wages to researchers
This increases the average wage rate only among the controlled
The researchers may wrongly conclude that the treated and the controlled have the same wage rate
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Pitfalls of Experimental Studies Scope for generalization: true effect may differ
when a program is expanded indefinitely instead of temporarily
Effect of generous health insurance on frequency of doctor visits
If the treated receives generous health insurance for a year only under an experiment, they may increase doctor visits because they know that they will lose it next year
at the national, not local, level Effect of completing a college degree on the wage rate Suppose there was a shortage of college graduates initially New trained college graduates will be highly paid However, if the majority become college graduates, their
supply might exceed demand Then the effect is unlikely to be as high as the local
experiment suggests
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Experimental Studies Are Not Foolproof
Mechanism through which X resulted in Y is not clear This returns us to the role of theory. By assuming that
people rationally maximize utility, theory can help us explain particular experimental results, and generalize them to other contexts
Researchers have to check if original randomness is maintained and must be cautious about generalizing the results to other settings
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4. Observational Studies
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Observational Studies
Empirical studies can rely on observed data, which are not obtained from an experimental setting called observational studies
Why observational studies? Ethically or politically difficult to conduct an
experiment It is difficult to provide treatment without making
subjects aware that they are being evaluated once aware, they might change behavior to create the
outcome they want E.g., in the experiment to examine the effect of tax cuts on
labor supply, subjects might work hard only during the experiment to get tax cuts
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Observational Studies
Sources Telephone surveys of consumers Written surveys submitted by households Administrative records on economic
performance, demography, crime, etc.
Econometrics Statistical tools for analyzing economic data Regression analysis is used
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Conducting an Observational Study- Suppose that we are interested in the effect of a reduction of the income tax on annual hours of work, L
-Is there an observed correlation between changes in net wage rate, w, and changes in L?
-Independent variable = w
-Dependent variable = L
-Suppose we have data on the hours of work and the after-tax wages for a sample of people for a given year
-We can draw a scatter diagram looks like there is a positive correlation
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Conducting an Observational Study-How can we estimate the magnitude of the positive relationship?
-In regression analysis, we attempt to fit a regression line through these points
-The slope of the line is the regression coefficient, which indicates the relationship between w and L
-If the regression coefficient is 1.5, this suggests that an increase in the net wage by $10 is associated with an increase in labor supply by 15 hours per year
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Conducting an Observational Study-How do we judge whether the estimated coefficient is reliable?
-This regression line is identical with the previous one, but drawn through the scatter of points that is more diffuse -> less faith on the estimated coefficient
-In Econometrics, such reliability is measured by comparing the size of the coefficient to its standard error (SE): a statistical measure of how much an estimated coefficient might vary from its true value
-Coefficient is reliable if SE is small relative to coefficient
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Type of Data
Cross-section data Contain information on entities such as
individuals, firms, and countries at a given point in time
Time-series data Contain information on an entity at different
points in time Panel (longitudinal) data
Contain information on entities at different points in time
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Pitfalls of Observational Studies It is difficult to ensure that the control group forms a valid
counterfactural For example, the positive correlation between the net wage and
the hours of work may arise because highly ambitious people have higher wages and also work longer hours
In this case, we overestimate effect of net wage on work hours We might be able to hold the effect of other observed
characteristics constant in multiple regression analysis However, we may not be able to think of all the factors
which affect the hours of work, and may not be able to measure some of them
Nevertheless, observational studies are informative about possible causal effects. We just need to be careful in interpreting the results as there might be outside factors that might bias any causal inferences
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5. Quasi-experimental Studies
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Quasi-Experimental Studies
Experimental studies are good at eliminating bias, but difficult to perform
Observational studies have knotty problems with bias, but the data are easier to obtain
Quasi-experimental studies use observational data, but rely on circumstances outside of the researchers control that naturally lead to random assignment natural experiment
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An Early Example
The effect of water quality on cholera incidence by John Snow (1855)
Two water companies supplied water to households in London
One had its intake point upstream from the sewage discharges, while the other had it downstream from the discharges
Snow showed that households receiving water from the latter are more likely to be cholera victims
He also showed that households receiving water from the two companies do not differ much
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Conducting a Quasi-Experimental Study
Difference-in-Difference Instrumental Variables Regression Discontinuity
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Difference-in-Differences
Suppose we are interested in the effect of raising the tax on beer on teen traffic fatalities
A group of U.S. states increased their tax rates on beer between 1989 and 1992, and teen traffic fatalities declined by 5.2 per 100,000 teens
Can we use this information to conclude that higher taxes on beer lower teen traffic fatalities?
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No! teen traffic fatalities might have lowered without the tax rate change
We can compare changes in teen traffic fatalities in states which did not change the tax rate on beer
Dee (1999) found that in the control group the fatalities declined by 8.1 per 100,000 teems
Thus, the tax increases did not reduce teen traffic deaths
If we can assume that the control group provides a valid counterfactual for the trend/change, this Diff-in-Diff achieves unbiased results
Difference-in-Differences
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Instrumental Variables Method
Sometimes assignment into a treatment group may not be random E.g., states that did not introduce beer tax
might have had a increasing state budget, which enabled better infrastructure, thus reducing accidents
If trends differ, we cannot use DD IV = variable that affects entry into the
treatment group, but in itself is not correlated with the outcome of interest
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Instrumental Variables Method Suppose we are interested in the effect of class
size on childrens test scores An experiment to investigate this issue would
randomly assign students to different class sizes Done by Krueger (1999), but the assignment was only
temporary. Unclear if the results reflect the true effect An observational analysis might use regression
analysis to estimate whether students in smaller classes score higher than students in larger classes
However, what types of parents choose to send their children to schools with small class size? Bias is likely to be an issue
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Instrumental Variables Method
Hoxby (2000) observed that kindergarten class size varies across years because the timings of births fluctuate randomly
The random fluctuations in enrollment year-to-year is correlated with class size, but does not directly influence test scores. Thus, it satisfies the conditions to be an instrumental variable
Based on this strategy, she found that class size does not have a discernible effect on test scores
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Regression Discontinuity Eligibility for some policy programs is determined by
whether a measurable characteristic of a person is above or below a specific cut-off point E.g., public insurance is available to people whose incomes are
below $20,000 People who earn more than $20,000 and people who
earn less than $20,000 are likely to be not comparable However, people who earn $20,001 and people who
earn $19,999 are likely to be similar to each other RD relies on such a strict cut-off criterion for eligibility of
the intervention under study to approximate an experimental design
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Regression Discontinuity Suppose we are interested in the effect of mandatory
summer school for poorly performing students on their test scores
Experiment: most likely politically infeasible Observational studies: most likely the treatment group
(poorly performing students) is not comparable to the control group (well-performing students)
RD: In Chicago Public Schools, students who scored below a cut-off on the test were required to attend summer school
Jacob and Lefgren (2004) compared students who got scores just above and below the cut-off
As a result, they found a jump in follow-up reading and math scores for 3rd graders, but not for 6th graders. This suggests the existence of a positive effect at least for some grade levels
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Pitfalls of Quasi-Experimental Studies
It may not truly mimic random assignment to the treatment group DD: the two groups of states might have had
different trends in teen traffic fatalities IV: across-year variation in birth cohort size
might have been correlated with child cognitive skills (not random)
RD: students whose score were just above and below the cut-off might have been different
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Pitfalls of Quasi-Experimental Studies
Quasi-experiments approach cannot be used to address questions which involve the national- or global-level changes E.g., if the government does not provide pensions,
would people save more? If the pension system is introduced for everyone at
the same time in one country, there is no control group
How much can we generalize the results based on quasi-experiments? Specific to the intervention being studied Mechanism through which the estimated effect has
arisen is not always clear