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Martin, Weidner ; Stéphane, Bonhomme ; St'Ephane, Bonhomme ; Martin, Weidner. (2021) Posterior Average Effects.
In: Papers. RePEc:arx:papers:1906.06360.
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To provide intuition about the magnitude of the bias, we simulate data where all latent components are independent, εj are standard normal, and α follows a skew-normal distribution (e.g., Azzalini, 2014) with zero mean, variance 1, and skewness ≈ .47 corresponding to the skew-normal parameter δ = .99. We take n = 1000, and run 100 simulations varying J from 1 to 30. We estimate means and variances using minimum-distance based on first and second moment restrictions. In the left panel of Figure D1 we show the results. We see that the model-based estimator is equal to zero irrespective of the number J of individual measurements. In contrast, the posterior estimator converges to the true skewness of α as J increases, although it is substantially biased for small J. Gini coefficient. We next focus on the Gini coefficient of α: G = 2Ef0 [exp (α)] ZZ | exp(α′ ) − exp(α)|f0(α)f0(α′ )dαdα′
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