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Inference and probability (due by 22 October 2020) 1

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Inference and probability (due by 22 October 2020)

1.1 David Hume was skeptic about interpreting empirical generalizations as causal relationships. Is his skepticism reconcilable with the practice of economics?

1.2 Using only the three Kolmogorov’s axioms (and nothing else!) prove:

• P(∅) = 0
• P(A) = 1−P(A¯)
• If A⊆B, then P(A) ≤P(B)
• If A = B (i.e. A⊆B and B⊆A), then P(A) = P(B)
  3. Prove Bayes theorem using definition of conditional probability.
  4. Discuss assignment of probability to the event “Head” in coin tossing in the classical, frequentist, and subjectivist (Bayesian) framework.
  5. Using the R script “Rscript economic methodology 20 21.R” repeat the ”Tea-Tasting Experiment” analysed by Imai (2017) using (i) 4 cups instead of 8; (ii) 10 cups instead of 8. Discuss the severity of the test in case (i) and (ii) in comparison with the case discussed by Imai (8 cups).

Explanation and causation (due by 12 November 2020)

1. 1. Take an economic phenomenon of your choice and try to sketch (just describe the general idea) an explanation following at least 2 of the 4 models of explanation treated in class (DN, SR, CM, unificationist). Highlight the obstacles that you encounter in complying with the chosen models.
   2. Causation as been defined in terms of (i) probabilistic dependence, (ii) counterfactual dependence, (iii) manipulability, (iv) and mechanistic dependence. Find a counterexample for each of these definitions.
   3. Consider the following causal structure: X −→Y −→Z ←−W. Which are the conditional independence relations (included conditioning on the empty set) implied by the Causal Markov Condition?

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2.4 Using the R script “Rscript economic methodology 20 21.R” and the data by Bertrand and Mullainathan (2004), consider whether perception of applicants’ gender affects callbacks for the job.

2.5 Comment or react to this claim “Randomized controlled experiments are the gold standard for

establishing causality.”