March 25, 2019

## Plan for Today:

### (1) Solutions for Bias

• design-based
• same-case over time
• similar cases, same time

## Design

design-based solutions to confounding:

• Do not identify and measure all confounding variables
• Choose a comparison that eliminates bias from many known/unknown measurable/unmeasurable confounding variables

• focus less on measuring known confounding variables to find comparisons among many cases
• choose fewer cases where confounding is plausibly less or absent

## Design

### Types of designs:

Designs using conditioning

• Compare same case over time
• Compare cases known to be similar at same time
• "Differences in Differences"

Designs using random exposure to $$X$$

• experiments
• "natural experiments"

## Design

### Designs using conditioning

Choice of comparison holds many confounding variables constant

• we condition, not by finding confounding variables and measuring
• we condition by choosing cases known to be similar

Holds constant many confounding variables

## Design: Same Case

### Same case over time

What is it?

• Compare the same case to itself before and after change in $$X$$

How does it work?

• This is a kind of conditioning:
• holds constant all unchanging attributes of the case

## Design: Same case

In 1956, Connecticut government responded to traffic deaths by increasing state police enforcement of speed limit and stronger fines/sentences

Did the speeding "crackdown" work?

We can compare Connecticut pre- and post- "crackdown"

## Design: Same case

• All unchanging attributes of Connecticut held constant, cannot confound

• What does this comparison not address?

## Design: Same case

• Other rapidly-changing variables not accounted for (weather, safety of vehicles)
• Does crackdown change measurement, but not value of variable? (Measurement bias)
• Why was the law passed?
• change in policy due to major events (did major events have an effect, not policy?)
• change in policy due to extreme event (low/high value of $$Y$$) then a return to normal?

## Design: Same case

all problems of confounding: other factors affect $$Y$$ (road deaths) and correlated over time with $$X$$.

## Design: Same case

Does removing on restrictions on gun ownership increase violent crime?

• If laws restricting gun ownership reduce violence, removing them should lead to rise in violence.

## Design: Same case

Correlation is weak: stronger gun laws not clearly related to lower or higher violent crime

possibility of confounding

• places with more gun laws may be different in many ways:
• urban vs. rural
• liberal political views
• quality of policing
• types of crime (organized crime vs not)
• etc.

Rather than conditioning on many possible variables… compare a case before and after change in the law

## Design: Same case

In 2007, US state of Missouri removed a permit-to-purchase (PTP) handgun law, which required all handgun purchasers to obtain a license verifying that they have passed a background check.

Did this repeal in the law change the level of violent crime?

• comparison of Missouri to itself holds constant many possible confounding factors

## Design: Same case

What are some possibly confounding variables does this comparison does not address?

## Design: Same Case

What is it?

• Compare the same case to itself before and after change in $$X$$

How does it work?

• This is a kind of conditioning:
• holds constant all unchanging attributes of the case

Assumes:

To infer causality

• No variables that affect $$Y$$ and change over time along with $$X$$.

## Design: Similar Cases

How do we deal with variables that change over time?

• We can look at cases that we expect to be similar on many attributes (usually due to spatial and temporal proximity)
• Compare provinces/states within countries, rather than different countries
• Compare districts/towns within provinces rather than different provinces
• Compares people within neighborhoods rather than across different areas

What does this do? Comparisons like this:

• Conditions on/eliminates all confounding variable that are the same across cases
• e.g. all confounding variables at country, province, neighborhood-level
• including things that might change over time and affect cases equally

## Similar Cases: Example

### Minimum Wage Laws

Do minimum wage laws cause higher unemployment?

• Could cause employers to employ fewer people
• Or could cause wages to rise, without a change in who is employed

### Naive comparison:

Correlate unemployment with minimum wage laws across countries

## Similar Cases: Example

Countries with different minimum wages likely differ in many ways:

• Political power of labor
• Unemployment insurance
• Health coverage
• Cultural/political institutions

### A better design?

Compare minimum-wage laws and unemployment across provinces within the same country

• Would keep country-level variables the same
• Fewer possible variables to condition/adjust for

## A better design?

Compare minimum-wage laws and unemployment across border-counties within the same country, on the same provincial border

Provinces/states might also differ from each other in many ways:

• Counties/districts on province/state borders probably similar in MORE ways
• Fewer differences between these counties, except for minimum wage law

## Design: Similar Cases

What is it?

• Compare the similar cases (due to geographic/cultural proximity) with different values of $$X$$

How does it work?

• This is a kind of conditioning:
• holds constant all variables that are the same across cases these cases, including things that change over time (similarly).

Assumes:

To infer causality

• No differences on variables that affect $$Y$$ between "similar" cases with different values of $$X$$