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• Section A: Comparison of the Average Case and Observed Value Approaches

^ Marginal Effect Analysis to Determine the Difference Between the Average Effect Using the Observed Value Approach and the Effect for the Average Case

▪ Figure 1. Second Derivative of the Probit pdf by the Probability of Success for the Average Case

^ Discrete Difference Analysis

▪ Figure A2. Difference in the Second Derivative of the Probit CDF Changing From xk = 0 to xk = 1 for Various Values of βk by the Probability of Success for the Average Case When xk = 0

• Section B: NES Results

^ Table 1. Probability of Voting for George W. Bush vs. John Kerry In 2004

^ Table 2. Predicted Probability of Voting for George W. Bush vs. John Kerry in 2004, Using the Average Case and Observed Value Approaches, for Variables Not Shown in Figure 1

^ Table 3. Statistical Simulation Results for Predicted Probability of Voting for George W. Bush vs. John Kerry in 2004, Using the Observed Value Approach, with 95% Confidence Intervals

^ Table 4. Predicted Effect (First Difference) of Changes in Select Variables on the Probability of Voting for George W. Bush vs. John Kerry in 2004, Using the Observed Value Approach, with 95% Confidence Intervals

• Section C: Sample Stata Code (Version 10)

^ Stata Code for First Differences and Marginal Effects

^ Stata Code for Implementing the Observed Value Approach Via Simulation

• Tips for Other Models

• Section D: Additional Monte Carlo Simulation Results

^ Table 1. Monte Carlo Simulations Showing That the Average Case and Observed Value Approaches Do Not Converge as the Sample Size Increases (Using True Models)

▪ Panel a. Marginal Effects for x2 and x3 for True Models

▪ Panel b: Predicted Probability of Success Across Values of x1 for True Models

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