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?

<p>The effects of minimum wage increases on employment rates (A)</p> Signup and view all the answers

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

<p>It may reveal proficiency differences leading to wage variance (B)</p> Signup and view all the answers

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

<p>High school fees (C)</p> Signup and view all the answers

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

<p>Increased in public schools but decreased in private schools (B)</p> Signup and view all the answers

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

<p>Difference-in-differences strategy (D)</p> Signup and view all the answers

What does the variable intensityjt represent in the identification equation?

<p>The effective intensity based on dropout rates (A)</p> Signup and view all the answers

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

<p>Children from disadvantaged backgrounds (C)</p> Signup and view all the answers

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

<p>School quality remained the same (C)</p> 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?

<p>Eliminate dropout rates entirely (A)</p> Signup and view all the answers

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

<p>Access to education (C)</p> Signup and view all the answers

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

<p>The difference in FTE employment before the treatment between NJ and PA (C)</p> Signup and view all the answers

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

<p>2.76 (B)</p> Signup and view all the answers

What does the binary treatment Di indicate for NJ?

<p>Di = 1 (B)</p> Signup and view all the answers

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

<p>FTE employment in PA is higher than in NJ (A)</p> Signup and view all the answers

What does the change of 2.76 signify in this context?

<p>The change in mean FTE employment between two states (A)</p> Signup and view all the answers

How many sample averages of the outcome are mentioned?

<p>Three (B)</p> Signup and view all the answers

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

<p>Row 1 (A)</p> Signup and view all the answers

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

<p>−2.16 (C)</p> Signup and view all the answers

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

<p>The model explains 19.11% of the variance in the dependent variable. (A)</p> Signup and view all the answers

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

<p>It shows a significant positive effect on the dependent variable. (B)</p> Signup and view all the answers

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

<p>Treatment groups must have the same trend in outcomes prior to treatment. (C)</p> Signup and view all the answers

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

<p>bachelor_female (B)</p> Signup and view all the answers

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

<p>Effect of minimum wage increase on employment. (D)</p> Signup and view all the answers

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

<p>Participants should not anticipate any changes due to treatment. (A)</p> Signup and view all the answers

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

<p>There is strong evidence against the null hypothesis. (C)</p> Signup and view all the answers

How many observations were used in the regression model overview?

<p>7,092 (C)</p> Signup and view all the answers

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

<p>A dummy variable related to a specific group (C)</p> 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?

<p>The interaction effect of D and x (C), The increment to the effect of x when D = 1 (D)</p> Signup and view all the answers

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

<p>$y_i = (\beta_0 + \beta_1) + (\beta_2 + \beta_3)x_i + u_i$ (B)</p> Signup and view all the answers

How does the regression model handle different intercepts and slopes?

<p>By allowing different intercepts and different slopes for different groups (D)</p> Signup and view all the answers

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

<p>An interaction effect that changes with D (C)</p> Signup and view all the answers

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

<p>The regression line is based only on $\beta_0$ and $\beta_2$ (B)</p> Signup and view all the answers

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

<p>A response variable affected differently by predictor variables across groups (C)</p> Signup and view all the answers

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

<p>The model can analyze interactions between binary and continuous variables. (B)</p> Signup and view all the answers

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

<p>Effect of changing D1 from 0 to 1 regardless of D2 (A)</p> Signup and view all the answers

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

<p>It allows the effect of D1 to depend on the value of D2 (D)</p> Signup and view all the answers

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

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

What does the term β3 represent in the regression model?

<p>Increment to the effect of D1 when D2 equals 1 (D)</p> Signup and view all the answers

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

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

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

<p>The proportion of variance explained by the model (C)</p> Signup and view all the answers

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

<p>The significance level of the model overall (A)</p> Signup and view all the answers

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

<p>There is a high level of variance in prediction errors (D)</p> Signup and view all the answers

Flashcards

Interaction between variables

The effect of one independent variable on another can depend on the value of a third variable.

Binary-continuous interaction

An interaction between a binary variable (e.g., gender) and a continuous variable (e.g., education).

Difference-in-difference

A statistical method to estimate causal effects by comparing changes in a dependent variable over time between a treatment and a control group.

Card and Krueger (1994)

A famous example using the difference-in-difference estimation method, often studying the impact of minimum wage laws.

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DID Estimator

The estimator used in difference-in-difference analysis to measure the causal effect of the treatment.

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Binary variable interaction

An interaction term in a regression model where the effect of one binary variable (e.g. D1) depends on the value of another binary variable (e.g. D2).

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Interaction term (D1i × D2i)

A new regressor created by multiplying two binary variables (D1i and D2i) to represent their interaction.

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Effect of D1 independent of D2

The effect of changing D1 from 0 to 1, irrespective of the value of D2.

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Effect of D1 dependent on D2

The effect of changing D1 from 0 to 1, which changes based on the value of D2.

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β3 = increment to D1 effect

β3 quantifies the change in D1's effect when D2 changes from 0 to 1.

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Expected value (E(yi))

The average outcome (y) given specific values of the binary variables (D1, D2).

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Regression with interaction (Yi = β0 ... )

A regression model including binary variables, their interaction, and a general intercept.

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Interpreting regression coefficients

Comparing the outcomes when one or more binary variables change, assessing the significance of the interaction term.

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Binary-continuous interaction

An interaction between a categorical and a continuous variable, where the effect of the continuous variable depends on the category.

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Regression Line, D=0

The regression line for observations where the categorical variable (D) is zero.

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Regression Line, D=1

The regression line describing the relationship when the category variable equals one.

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β3

The coefficient of the interaction term (D × x). Indicates the effect change by the interaction effect.

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Effect of X, dependent on D

The impact of variable X varies depending on the categorical variable D.

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Different Intercepts, Same Slope

The regression lines in an interaction model with the same slope and separate intercept for different categories.

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Different Intercepts, Different Slopes

Regression lines have different slopes for different levels of a binary variable, in an interaction model.

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Same Intercept, Different Slopes

The regression lines share a common intercept value but have varied slopes corresponding to different categorical variables.

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Interaction Term

A term in a statistical model created by multiplying different independent variables, often used when the impact of one independent variable depends on another.

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Difference-in-Differences (DID)

A method to estimate causal effects by comparing changes over time between a treated and control group.

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No Anticipation Assumption (DID)

Treatment group's behavior isn't influenced by expectations of future treatment before the treatment actually happens.

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Parallel Trends Assumption (DID)

Absence of systematic changes in dependent variable for control and treatment groups prior to the treatment.

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Variable Interaction (Regression)

The effect of one independent variable depends on the level of another independent variable.

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Continuous vs. Binary variables

Variables like 'age' (continuous) measured against dummy variables such as 'bachelor' (binary).

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Regression Output Interpretation

Determining significance of coefficients (slope estimates) in explaining relationships.

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Card and Krueger (1994)

Used DID to examine the effect of a minimum wage increase on fast-food employment.

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Dummy Variables (0/1)

Categorical variables represented as 0 or 1, signifying presence or absence of a characteristic.

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DID Estimate (Card & Krueger)

The estimated change in employment between Pennsylvania (PA) and New Jersey (NJ) stores, after implementing a policy change, calculated using the difference-in-difference method.

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Difference-in-Difference (DID)

A statistical technique to measure the causal impact of a treatment (policy change) comparing changes in treatment and control groups over time.

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Control Group (DID)

The group (e.g., Pennsylvania stores) that did not receive the treatment (e.g., minimum wage increase), used to compare changes with the treatment group.

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Treatment Group (DID)

The group (e.g., New Jersey stores) that received the treatment (e.g., minimum wage increase), used to measure the change relative to the control group.

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FTE Employment Before

Full-time equivalent employment before a minimum wage change, used as a baseline measure for comparisons in Card & Krueger's data.

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FTE Employment After

Full-time equivalent employment after the minimum wage change, used to measure changes in employment compared to before.

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Change in Mean FTE Employment

Average change in full-time equivalent employment measured between NJ and PA stores, crucial to identify treatment impacts using Difference-in-Differences.

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Binary Variable (Di)

A variable taking on values 0 (PA) or 1 (NJ), used to identify treatment and control groups in the study.

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Free Primary Education (FPE) in Kenya

A policy in Kenya that aimed to provide free primary education, affecting access and enrollment.

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Increased Public School Attendance

Free primary education in Kenya led to more students attending public schools initially, but less attendance in private schools.

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Differentiated Impact of FPE

FPE's impact varied across Kenyan districts, linked to prior dropout rates. Regions with higher dropout rates initially showed a stronger positive response to FPE.

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Difference-in-Difference Strategy

A method used to evaluate the causal effect of FPE by comparing outcomes before and after the policy, while controlling for regional differences (dropout rates).

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Key Result of Kenyan FPE

Increased enrollment in schools, especially among disadvantaged children.

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Identification in Study

The study identified the FPE effect by leveraging how the program's influence varied across districts based on pre-existing dropout rates.

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Regression Model

A statistical model (ysjt = β0 + β1 (intensityjt × publics) + .....) used to analyze how educational intensity interacts with public/private school choices, controlling for other effects.

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School Quality Maintenance

The study suggested that FPE did not negatively affect overall school quality.

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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.
  • 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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Difference-in-Difference Analysis PDF

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.

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