What You Did in Preparation for Today

• Chapter 2 Sections 2.5

Today's Agenda

• Review randomized controlled trials:

  • Role of randomization

  • Social pressure experiment (optional)

• Review Sections 2.5 and 2.6 of QSS:

  • Observational studies

  • Confounding bias

  • Cross-section, before-and-after, and difference-in-differences designs

  • Minimum wage study

Review of Randomized Control Trials

• Fundamental problem of causal inference:

  • Comparison between factual and counterfactual

  • Counterfactuals are not observed

• Solution: Randomized controlled trials (RCTs)

  • Treatment and control groups identical on average

  • Similar in all (observed and unobserved) characteristics

  • Difference in average outcome between the two groups, ˉY(1)−ˉY(0), is an estimate of

Sample Average Treatment Effect (SATE)=1nn∑i=1{Yi(1)−Yi(0)}

Examples of RCTs

• Causal effect of safe/locked box on health savings

• Causal effect of race on employment prospect

• Causal effect of naming-and-shaming on turnout

Social Pressure Experiment [Optional]

• August 2006 Primary Statewide Election in Michigan¹

• Send postcards with different (randomly assigned) messages

1. no message (control group)

2. civic duty message

3. “you are being studied” message (Hawthorne effect)

4. neighborhood social pressure message

Analysis

Turnout by Group:

SATE for each group:

• Randomization balances covariates across groups:

Primary 2004 for each group:

Observational Studies

• Often, we can’t randomize treatment for ethical and logistical reasons:

  • e.g., smoking and lung cancer

• Observational studies: naturally assigned treatment

• Better external validity for generalization beyond experiment

• Weaker internal validity:

  • pre-treatment variables may differ between treatment and control groups

  • confounding bias due to these differences

  • selection bias from self-selection into treatment

  • statistical control needed

  • unobserved confounding poses a threat

Confounding

• Key assumption “Unconfoundedness”: treatment and control groups comparable with respect to everything other than treatment

• How can we find a good comparison group?

Asthma in Children [Optional]

• New evidence for the role of microbes from farm animals in dust

• Comparison of Amish and Hutterites:

  • similar genetic backgrounds, large families, and a simple communal life style

  • diets are similar, little exposure to tobacco or pollution, both groups prohibit indoor pets, meticulously clean homes

• Rates of asthma in children: 2–4% (Amish) vs. 15–20% (Hutterites)

• Findings:

  • Amish do not use electricity, but Hutterites do

  • Amish kids play in animal barns

  • Amish kids have better immune system, leading to less allergic reaction

  • Giving Amish house dust to mice protected them from allergens whereas Hutterites house dust did not

Minimum Wage and Unemployment

• How does the increase in minimum wage affect employment?

• Current debate: federal minimum wage increase

• Many economists believe the effect is negative

  • especially for the poor

  • also for the whole economy

• Hard to randomize the minimum wage increase

• Two social scientists tested this using fast food chains in NJ and PA

  • In 1992, NJ minimum wage increased from $4.25 to $5.05

  • Neighboring PA stays at $4.25

• Observe employment in both states before and after increase

• NJ and (eastern) PA are similar

• Why limit to fast food chains?

Did the Minimum Wage Law Affect the Wages in NJ?

Before

After

Are the NJ and PA Restaurants Comparable?

Average wages before the increase in minimum wage:

Prior proportion of fulltime employment:

Cross-Section Comparison

• Compare NJ and PA using the data after the increase

• The treatment and control groups are assumed to be identical on average in terms of all confounders

• What confounders are missing from the data?

• Assumptions:

  • No cross-sectional contamination

  • No cross-sectional confounders

• Compute the proportion of fulltime employees after the increase:

ˉY(1)−ˉY(0)=ˉY(NJafter)−ˉY(PAafter)=0.0481

• Here, NJ (after the increase) is the treatment group and PA (after the increase in NJ) is the control group.

• This is our estimated SATE. Why "estimated"?

Before and After Comparison

• State-specific confounders for cross-section comparison

• Compare NJ before and after

• Assumptions:

  • No temporal contamination (treatment is exogenous)

  • No (temporal) confounders

• What might be time-varying confounders?

ˉY(1)−ˉY(0)=ˉY(NJafter)−ˉY(NJbefore)=0.0239

• Here, NJ (after the increase) is the treatment group and NJ (before the increase) is the control group.

Difference-in-Difference

• Key Idea: use PA before-and-after difference to figure out what would have happened in NJ without the increase

• NJ before-and-after difference addresses within-state confounding

• Assumptions:

  • Parallel time trends (how good is our control group)

  • Treatment is exogenous (no temporal or cross-sectional contamination)

• Estimate the sample average treatment effect for the treated (SATT), NOT SATE

ˉY(NJafter)−ˉY(NJbefore)−(ˉY(PAafter)−ˉY(PAbefore))=0.0616

Visualizing Difference-in-Difference

The Difference-in-Difference Design

• A natural experiment always has the control group (observations not affected by the change) and the treatment group (observations that are affected).

• Need data for two time periods (before and after the treatment).

• Thus, four groups of observations: control before, treatment before, control after, treatment after

• The difference between the two before groups helps account for the differences between the treatment and control groups that are not caused by the treatment.

Summary of 3 Identification Strategies

1. Cross-section comparison

   • Compare treated units with control units after the treatment

   • Assumption: the treated and control units are comparable

   • Possible unit-specific confounding

2. Before-and-after comparison

   • Compare the same units before and after the treatment

   • Assumption: no time-varying confounding

3. Difference-in-Differences

   • Assumption: parallel time trend

   • Under this assumption, it accounts for both unit-specific and time-varying confounding

• None of the approaches is best. They require different assumptions.

Incinerator and Home Prices [Optional]

Suppose we would like to study the effect of proximity to a garbage incinerator on home prices.

• Propose a cross-sectional natural experiment design to study this question. What is the key assumption for this design? Does it hold?

• Propose a before-and-after comparison design to study this question. What is the key assumption for this design? Does it hold?

• Propose a diff-in-diff design to study this question. What is the key assumption for this design? Does it hold?

• Which of the proposed design would work the best in this example?

Lab Questions

1. Download and open the data on housing prices, hprice3.

2. Create a binary variable, nearinc that equals to 1 if the house is within 3 miles of the incinerator.

3. How many houses are there in the data in each year?

4. Compare the average house price in 1978 between the houses near and far from the incinerator.

5. Compare the average house price in 1981 between the houses near and far from the incinerator.

6. Implement the diff-in-diff design.