Regression Discontinuity Design

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Regression Discontinuity Design

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Econometrics, buy green, regression, RDD Regression Discontinuity Design, auction

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At its core, endogeneity arises when an explanatory variable is correlated with the error term in a regression model. This can occur due to omitted variables, measurement errors, or simultaneity. This correlation biases OLS estimators, making causal interpretations problematic. The RDD offers a clever way to circumvent this issue by exploiting a "natural experiment" setting, which is created by an exogenously determined threshold or cut-off.
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The McCrary (2008) sorting test, often referred to as the "density test", addresses the continuity assumption in Regression Discontinuity Design (RDD). Specifically, it tests for the presence of manipulation around the cutoff or threshold. If there's no sorting (or manipulation) around the cutoff, then we would expect the density of observations to be continuous on both sides of the threshold.

Question 1. Boosting green public procurement
1. What are the incentives, for public servants, to buy green?
2. What do you think is the main (economic) barrier to buy green (as a public buyer)? Explain
3. What is the amount of money expended for public procurement in France?
4. Why the previous regression measures the probability to uptake GPP?
5. Discuss all the potential issues you might encounter estimating the previous relationship
6. Load the data, create a summary statistics table and describe it
7. Run the following regression and interpret the SA coefficient in terms of the previous equation. Store the regression, you will create a final table at the end
8. Explanation of How the Regression Discontinuity Design (RDD) Solves the Endogeneity Concern
9. In the context of this TD, why the threshold creates a discontinuity in the probability of choosing a simplified auction?
10. Use your intuition to explain whether the setting is sharp or fuzzy
11. Explain what the code does line by line. You might need to install the packages OneR and stringr
12. Based on your result on the previous regression, what is the probability of choosing a simplified auction at the threshold?
13. Based on both, the figure and the regression, do you think a fuzzy-RDD design is suitable in this case?
14. Estimate the reduce form and store it
Question 2 (Optional). Validation and robustness checks
1. What assumption is addressed by the McCrary (2008) sorting test?
2. Run the McCrary (2008) sorting test using the DCdensity from the rdd package and report the figure
3. Create figures to visually inspect the behavior of different controls (duration_years, small_supplier_n, and ln_Budget) around the threshold. Why do you think this test is important?
4. One typical issue with RDD is the bandwidth selection. Explain what it is and why it is relevant

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[...] The second graph seems to have less clear of a discontinuity but still suggests potential for RDD. In a fuzzy RDD, treatment assignment near the threshold is not strictly binary, meaning some entities right above the threshold might not get treated, and some just below might. Given the visual evidence and if there's some imprecision in how the threshold is assigned in your data, a fuzzy RDD would be suitable. m. Estimate the reduce form and store it. The reduced form would be estimated by regressing the outcome (GPP uptake) on the instrument (probability of choosing a simplified auction), the running variable kk, and the interaction of the two. [...]

[...] Inertia and Resistance to Change: Procurement processes that have been in place for years, if not decades, develop a certain inertia. Changing these processes to accommodate GPP requires effort, retraining, and sometimes even cultural shifts within the organization. Perceived Risk: There might be a perception that green products are newer, less tested, or might not meet the stringent requirements of public entities. Supplier Limitations: In many regions, the market for green products might not be as mature. This means fewer suppliers, less competition, and potentially higher prices. [...]

[...] Localized Comparisons: RDD primarily draws inferences from observations near the threshold. This localized comparison ensures that units on either side of the threshold are comparable, minimizing the risk of omitted variable bias. It's like comparing apples to apples. Endogeneity in the Forcing Variable: If there's endogeneity in the forcing variable itself (e.g., if students can manipulate their scores to be just above the scholarship threshold), this can be addressed in RDD by checking for discontinuities in the density of the forcing variable around the threshold. [...]

[...] The independent variables include an interaction between the predicted hat_sa values and and other control variables specified in the controls object. ? Again, the paste0 function concatenates to form a complete formula. 5. reg_iv lm(f2s, data = df_sa) ? A linear regression model is fit using the formula f2s created in the previous step. ? The data source for this regression model is df_sa. ? The result of this regression model, which represents the second stage of the 2SLS, is stored in the reg_iv object. Question 2 (Optional). Validation and robustness checks. [...]

[...] For example, the effect of being a small supplier might differ based on the auction type. - Measurement Error: If any of the new variables (like ln_Bprice or ln_Budget) are measured with error, it could bias the results. - Sample Selection Bias: If the dataset does not capture all procurement contracts or if there are systematic dropouts, the results may not be generalizable. - Multicollinearity: If the independent variables in the expanded model are highly correlated, it can make estimates unstable and difficult to interpret. [...]

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