Section 2 PoEA

• T is the independent variable, also known as the "treatment" or variable of interest.
• Y is the dependent variable, also known as the outcome variable.

Limits of Randomized Controlled Trials (RCTs)

• RCTs can be costly and unethical.
• RCTs are not helpful when studying historical questions or understanding market level phenomena.
• Observational data and clever designs enable researchers to study causal questions without needing a specific experiment.
• Observation data is data collected as part of how societies and institutions normally function.
• Observational studies draw inferences from a sample of populations where the independent variable is not controlled by the researcher.

Selection on Observables vs. Unobservables

• Selection on observables means that treatment (T) and control groups (C) differ from each other only with respect to observable characteristics.
• Selection on unobservables means that T and C groups differ from each other in unobservable characteristics.
• This may happen when something unexpected affects some people almost randomly.
• An exogenous variable can induce a variation in treatment, which is an instrumental variable (IV).
• The selection mechanism can be known (Regression Discontinuity Design, RDD).
• Treatment and controls are observed before and after treatment (Difference in Differences, DiD).

Natural/Quasi-Experiments

• Natural/quasi-experiments occur when an unexpected event, like a government policy or natural event, affects some households similarly to an experiment.
• They provide both a treatment and a control group.
• Segregation by income occurs in cities, where rich people live in the city and poor people in the suburbs, stemming from income inequality, neighbourhood quality and optimizing behavior.
• Neighbourhood effects are direct or indirect impacts on socio-economic outcomes based on where you live.

Isolating the effect of treatment

• To isolate the effect of treatment, control for observable differences by comparing people with similar, measurable characteristics.
• Unobservable differences arise when similar families make different residential location choices because some invest more resources in parenting.

Public housing demolition

• Public housing demolition provides low-income households with resources to move to different residential areas.
• Being forced to relocate due to demolition results in receiving housing vouchers.
• Treatment and control occur naturally without planning, which qualifies as a quasi-experiment.
• Compare outcomes of young adults displaced and non-displaced from the same public housing project where T is displaced and C is non-displaced.

Key Assumptions

• Key assumption I: the decision to demolish buildings is unrelated to tenant characteristics and households and children are similar in treatment and control groups.
• If groups are similar in observable characteristics, it's plausible they are similar in unobservable characteristics too.
• Balance tests can assess this.
• Key assumption II: Demolition has no effect on children who were not displaced or there is no treatment effect on the control group.
• Balance test is used to assess if treatment and control groups are comparable across observable characteristics.
• Balance tests are crucial as quasi-experiments rely on non-random assignment methods.

Effects

• Heterogeneous effects describe how the outcome variable differs by subgroup.

Instrumental Variable

• An exogenous variable induces variation in treatment creating an instrumental variable
• Imperfect compliance is when some randomized into treatment do not receive treatment, and some randomized into control receive treatment

Groups

• Always-takers are people who get the treatment even if randomized into the control group.
• Compliers are people whose treatment status is decided by randomization.
• Never-takers are people who will not take the treatment even when randomized into the treatment group.
• Randomization ensures shares of each group is equally large in the treatment and control groups.
• Comparing everyone randomized into treatment to everyone randomized into control group is a valid comparison.
• Intention to treat (ITT) is the impact of being assigned to the treatment group versus being assigned to control, regardless of compliance.
• Local average treatment effect (LATE) estimates treatment effect on compliers in treatment and control groups although we cannot directly observe the compliers.
• The share of compliers can be estimated using the Wald Estimator

Wald estimator

• The Wald estimator formula: BLATE = (E[Y|Z = 1] - E[Y|Z = 0]) / (E[D|Z = 1] - E[D|Z = 0])
• Y is the outcome.
• Z indicates randomization into the treatment group.
• D indicates if treatment was actually received.
• For LATE with IV, ITT is the expected value for the outcome variable for T and C and calculates the ITT.
• Share compliance is the proportion of participants in each group that actually received treatment, it measures compliance rate.
• BLATE = E[Y1 - Yo|complier] is the local average treatment effect, where the treatment impact may differ from the impact on never-takers and always-takers.

Instrument Variables

• Answers the causal question: does T affect Y?
• Instruments are exogenous factors that only affect T and whose effect on Y is to be estimated.
• Instrument relevance condition: the instrument should be correlated with the variable of interest and have causal effects on it.
• Exogeneity means that the instrument is randomly assigned and unrelated to omitted variables.
• Exclusion restriction states the instrument affects outcomes only through the treatment variable.

Using Instrument Variable

• First stage is the relationship between the IV and the explanatory variable where the IV is the winning lottery and the explanatory variable is likely to attend.
• Second stage concerns outcome Y and treatment T which is attending.
• The causal effect of attending school is isolated, by controlling for cofounding factors correlated with attendance and grades.
• Relevance Condition: winning the lottery is tied to likelihood to attend.
• Exogeneity stipulates unrelated connection between winning the lottery not correlated with motivation/grades because the lottery is randomly assigned.
• Exclusion restriction states winning the lottery has no impact on grades other than attending school.
• Starting point: estimate the effect of T on the outcome, however there are factors correlating with treatment status and outcome.
• Possible solutions involve finding exogenous random variation in treatment where IV should not affect outcome directly and cannot be correlated with confounding factors.

Testing

• First stage regression to check IV and the variable of interest (T).
• Exogeneity cannot be fully tested because correlation of IV with unobservables cannot be checked, but correlation between IV and observable confounding factors can be checked.
• Exclusion restriction cannot be tested, but provide arguments in favour of it, and suggest and address exclusion restriction threats.
• The treatment is correlated with unobservables which also affect outcome.

Endogeneity issues

• IV is exogenous variable that only affects Y through treatment.
• Creating exogenous variation in treatment allows in isolate causal effect from treatment.
• There is an estimated treatment affect because treatment status changes.
• Economic shock T, conflict Y, rainfall shock Z.
• Relevancy Condition: rainfall and economic correlated.
• Exogeneity: rainfall and conflict do not have correlating unobserved factors.
• Exclusion Restriction: rainfall and conflict don't affect each other expect by effect of rainfall on economic shock.

Instrumental Variable (IV) requirements

• Potential omitted variable bias (OVB) affecting both T and Y.
• The IV should be correlated with the variable T which affects Y.
• IV should not directly affect Y.
• IV must be randomly assigned.
• IV must be strongly correlated with T and relevance must be tested in the first stage.
• Reduced form equation: effect of Z on Y, and since Z is exogenous then the only factor affecting Y is T.
• First stage: how IV affects treated people. Reduced form/first stage = causal effect in treatment units.

Regression Discontinuity Design (RDD)

• RDD isolates the causal effect of T in situations when individuals become treated after crossing some cutoff.
• Sharp RDD: treatment received one probability above cutoff, and zero below.
• Fuzzy RDD: probability of receiving treatment increases discontinuously at threshold with imperfect compliance.
• Smooth evolution across cutoff assumption.
• Observations should be very similar, to have a valid control group.
• Units cannot be above or below the cutoff.
• Absence of common support cannot see the outcome when units are not cut off.
• Treatment effect is within cutoff- treatment groups.
• There are controls and units.
• A key assumption is that units are comparable except the treatment.
• Conditions should mimic conditions of random experiment with units being equally assigned. Continuity of the cutoff, where outcomes are known.

Running the Variable

• Units should be not manipulate variables, and do not sort themselves depending on the running variable.
• Without manipulation, the # of observations should be = for each group.
• With signs of sorting, it should have jump the treat group, the transition should be smooth for the other.

Test

• Near cutoff treatment is near controls in observable characteristics.
• Placebo: the replacement should be replaced with a fake cutoff if significant treatment, it will show only at constant cutoffs. If not the treatment will equal zero.
• The alternate option is that the outcome should be affected by treatment, so it will show the other side of the cutoff and will not.

RDD Limitations

• It can be randomized near the cutoff. Can segment narrow for the results from it.
• The smaller it is the more data it should to work
• RDD means, that data should be below and above, which means it needs bandwidth data (how far away from the cutoff we can utilize)
• Different Bandwidths can be used.

Sharp and Fuzzy RDD

• Fuzzy RDD is when a treatment is switched off or completely instead of assigning to control when passing the cutoff.
• The cutoff determines a treatment, and use the cutoff to the rule, we can use without RCT.
• If units have similar characteristics then variables cannot be manipulated.
• Need extra lot of data/hard to extrapolate data of effects form cutoff.

Difference-in-Differences (DID)

• Treatment/controls shows before and after treatment.
• DID = two groups with two time periods
• Groups of timer the group is the same for all.
• The control group captures changes

Common effect

• Same trend lines that impact with treatment
• Treated = 1 if treatment, O if not.
• after = observations

parallel

• Follow trends = the outcome after treatment and control should follow the same trend
• Parallel pre-trends in similar manners.
• Check the shocks during the same period and impact on the groups.
• Research information depending on reform.