Statistics Unit 8: Difference-in-Difference

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Questions and Answers

What does the Difference-in-Difference (DID) estimator primarily estimate?

The variation in outcomes due to random assignments

The causal effect of a treatment in a controlled setup (correct)

The total effect of treatment over time

The impact of external factors on outcomes

In the context of interactions between independent variables, how might class size reduction be more effective?

In larger classes with more diverse learners

In classes with many English learners needing more attention (correct)

In classes that have a higher student-to-teacher ratio

In classes with advanced students requiring less attention

What is a key aspect to consider when modeling interactions between independent variables?

The binary nature of the variables involved

The potential confounding variables that might influence outcomes

Only the means of each variable

How the effect of one variable depends on the level of another variable (correct)

In the classical example of Difference-in-Difference by Card and Krueger, what was the primary focus of their study?

The effects of minimum wage increases on employment rates Signup and view all the answers

How does age or potential experience influence wages differently based on gender?

It may reveal proficiency differences leading to wage variance Signup and view all the answers

What was identified as a significant barrier to education prior to the Free Primary Education program in Kenya?

High school fees Signup and view all the answers

How did the Free Primary Education program affect public and private school attendance?

Increased in public schools but decreased in private schools Signup and view all the answers

What methodological approach was used to identify the effect of the Free Primary Education program?

Difference-in-differences strategy Signup and view all the answers

What does the variable `intensityjt` represent in the identification equation?

The effective intensity based on dropout rates Signup and view all the answers

What was one of the main findings regarding the demographic most positively impacted by the FPE program?

Children from disadvantaged backgrounds Signup and view all the answers

According to the findings, what was the impact of the Free Primary Education program on school quality?

School quality remained the same Signup and view all the answers

Which of the following does not describe one of the goals behind the implementation of free primary education in Kenya?

Eliminate dropout rates entirely Signup and view all the answers

What was the primary concern that the Free Primary Education program aimed to address?

Access to education Signup and view all the answers

What does the value −2.89 in Row 3 Column (iii) represent?

The difference in FTE employment before the treatment between NJ and PA Signup and view all the answers

What is the DID estimate indicated in Row 3 Column (iii)?

2.76 Signup and view all the answers

What does the binary treatment Di indicate for NJ?

Di = 1 Signup and view all the answers

Which statement is true about the FTE employment after the treatment?

FTE employment in PA is higher than in NJ Signup and view all the answers

What does the change of 2.76 signify in this context?

The change in mean FTE employment between two states Signup and view all the answers

How many sample averages of the outcome are mentioned?

Three Signup and view all the answers

Which row presents the FTE employment in NJ before the treatment?

Row 1 Signup and view all the answers

What is the difference in mean FTE employment in PA before and after the treatment?

−2.16 Signup and view all the answers

What does the R-squared value of 0.1911 indicate in the regression analysis?

The model explains 19.11% of the variance in the dependent variable. Signup and view all the answers

What is the significance of the coefficient for the variable 'bachelor' in the regression output?

It shows a significant positive effect on the dependent variable. Signup and view all the answers

What does the 'parallel trends' assumption pertain to in Difference-in-Differences analysis?

Treatment groups must have the same trend in outcomes prior to treatment. Signup and view all the answers

Which variable has a statistically significant negative coefficient in the regression analysis?

bachelor_female Signup and view all the answers

In the example of Card and Krueger (1994), what economic phenomenon was being analyzed?

Effect of minimum wage increase on employment. Signup and view all the answers

What is the purpose of the 'no anticipation' assumption in difference-in-differences?

Participants should not anticipate any changes due to treatment. Signup and view all the answers

What does a p-value of 0.000 for the variable 'age' suggest?

There is strong evidence against the null hypothesis. Signup and view all the answers

How many observations were used in the regression model overview?

7,092 Signup and view all the answers

What does the term 'Di' represent in the regression model described?

A dummy variable related to a specific group Signup and view all the answers

In the regression equation $y_i = \beta_0 + \beta_1 D_i + \beta_2 x_i + \beta_3 (D_i \times x_i) + u_i$, what does $\beta_3$ represent?

The interaction effect of D and x Signup and view all the answers

When evaluating the regression line for observations with $D = 1$, which equation is used?

$y_i = (\beta_0 + \beta_1) + (\beta_2 + \beta_3)x_i + u_i$ Signup and view all the answers

How does the regression model handle different intercepts and slopes?

By allowing different intercepts and different slopes for different groups Signup and view all the answers

What does the expression $\Delta y = \beta_2 \Delta x + \beta_3 D \Delta x$ illustrate?

An interaction effect that changes with D Signup and view all the answers

What will happen to the intercept and slopes if D = 0 in the regression model?

The regression line is based only on $\beta_0$ and $\beta_2$ Signup and view all the answers

What does a regression model with different intercepts and slopes signify?

A response variable affected differently by predictor variables across groups Signup and view all the answers

Which of the following statements about the regression model is true?

The model can analyze interactions between binary and continuous variables. Signup and view all the answers

What does β1 represent in the regression equation yi = β0 + β1 D1i + β2 D2i + ui?

Effect of changing D1 from 0 to 1 regardless of D2 Signup and view all the answers

How is the interaction term D1i × D2i identified in the regression model?

It allows the effect of D1 to depend on the value of D2 Signup and view all the answers

What is the formula for the expected outcome when D1i = 1 and D2i = d2?

E(yi | D1i = 1, D2i = d2) = β0 + β1 + β2d2 + β3d2 Signup and view all the answers

What does the term β3 represent in the regression model?

Increment to the effect of D1 when D2 equals 1 Signup and view all the answers

Which of the following represents the difference in expected outcomes based on changing D1?

E(yi | D1i = 1, D2i = d2) - E(yi | D1i = 0, D2i = d2) = β1 + β3d2 Signup and view all the answers

In the given regression example, what does R-squared measure?

The proportion of variance explained by the model Signup and view all the answers

What does the value of Prob > F indicate in regression analysis?

The significance level of the model overall Signup and view all the answers

What is the implication of having a large Root MSE value in a regression output?

There is a high level of variance in prediction errors Signup and view all the answers

Study Notes

Unit 8: Difference-in-Difference

This unit covers the difference-in-differences (DID) estimator
DID is used to analyze the causal effect of a treatment by comparing the changes in outcomes across a treatment and a control group before and after the treatment.

Interactions between Independent Variables

Interactions between independent variables are relationships where the effect of one variable on the dependent variable depends on the value of another variable.
Binary interactions involve two binary variables, examining how the effect of one binary variable depends on another.
Binary-continuous interactions examine how the effect of a binary variable depends on a continuous variable.
Example: Test scores and student-to-teacher ratios; wages and education, age/experience.

Difference-in-Difference

The DID estimator examines changes in the difference between groups over time.
The classical example of DID is Card and Krueger (1994). This study examined the effect of the minimum wage increase.
This model analyses how a treatment affects different groups over time.
The model is estimated with two periods.

Interpreting Coefficients

The coefficients in a DID model show the effect of the treatment.
The effect of one variable depends on the value of another (interaction term).
This is done through comparing different cases.

Binary-Continuous Interactions

The regression model has an interaction term between a binary and a continuous variable.
The effect of the continuous variable is different for different levels of the binary variable.
The effect of X depends on D.

Example: Wages

This example uses a regression analysis of wages.
Variables like bachelor, female, bachelor_female, and age are used in the model.
Data and statistics from the table are used to analyze the example model.

Application: School Program in Kenya (Lucas and Mbiti, 2012)

This study examines the short-run effects of free primary education in Kenya.
The study explores the effect of free education on various criteria.
The results show suggestive evidence that FPE increased attendance in public schools but decreased it in private schools.

What is the DID Estimator Estimating?

The DID estimator calculates the average treatment effect on the treated (ATT).
It estimates how a treatment has affected outcomes compared to a control group that did not receive the treatment.
The estimator considers potential outcomes: the outcome if the treatment was received vs the outcome if the treatment was not received.

Sufficient Assumptions (1): No Anticipation

This assumption states that outcomes aren't affected by the impending treatment before implementation.

Sufficient Assumptions (2): Parallel Trends

The assumption is that outcomes in the treatment and control groups would've followed parallel trends in the absence of the treatment.

DID is Unbiased for ATT

The DID estimator is unbiased for the average treatment effect on the treated (ATT).

Regression Representation with Two Periods

The DID estimator can be implemented using a regression model.

Grouped Data and Repeated Cross Sections

The regression representation of the DID estimator is helpful for non-panel datasets.
Data can be collapsed and group-level panel data can be obtained.
The OLS estimates are the same as the DID estimates.

Two-Way Fixed Effects (TWFE)

TWFE regression is a common method used to implement DID.

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Description

Explore the Difference-in-Difference (DID) estimator in this quiz, focusing on its application in causal analysis. Understand interactions between independent variables and how they influence dependent variables through various examples. Test your knowledge on the foundational concepts and techniques used in the DID framework.