Mixtures of G-Priors for Bayesian Model Averaging with Economic Application
Mixtures of G-Priors for Bayesian Model Averaging with Economic Application
复制标题
贝叶斯模型平均的 G 先验混合及其经济应用
DOI：
10.1016/j.jeconom.2012.06.009
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Steel
中科院分区：
文献类型：
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作者：
E. Ley;M. Steel
我们研究线性回归模型中的变量选择问题，在线性回归模型中，我们有大量可能的协变量，经济理论对如何选择适当的子集提供了不足的指导。在这种情况下，贝叶斯模型平均提出了一个正式的贝叶斯解决方案来处理模型的不确定性。我们的主要兴趣是先验对结果的影响，例如回归量的后验包含概率和预测性能。我们结合联合收割机的二项式贝塔先验模型的大小与g先验的系数，每个模型。此外，我们为g分配了一个超先验，因为g的选择对结果有很大的影响。对于g的先验，我们研究了Zellner-Siow先验和一类Beta收缩先验，它们涵盖了最近文献中的大多数选择。我们提出了一个基准测试之前，灵感来自早期的研究结果与固定的g，并显示它导致一致的模型选择。这种先前的结构的复杂性和缺乏适合的处罚的影响进行了详细描述。通过马尔可夫链蒙特卡罗采样器在模型空间和g上进行推理。我们研究的各种先验的模拟和真实的数据的背景下的性能。对于后者，我们考虑了经济学中的两个重要应用，即跨国增长回归和学校教育回报。提供了对应用用户的建议。
We examine the issue of variable selection in linear regression modelling, where we have a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset. In this context, Bayesian Model Averaging presents a formal Bayesian solution to dealing with model uncertainty. Our main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. We combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, we assign a hyperprior to g, as the choice of g has been found to have a large impact on the results. For the prior on g, we examine the Zellner-Siow prior and a class of Beta shrinkage priors, which covers most choices in the recent literature. We propose a benchmark Beta prior, inspired by earlier findings with fixed g, and show it leads to consistent model selection. The effect of this prior structure on penalties for complexity and lack of fit is described in some detail. Inference is conducted through a Markov chain Monte Carlo sampler over model space and g. We examine the performance of the various priors in the context of simulated and real data. For the latter, we consider two important applications in economics, namely cross-country growth regression and returns to schooling. Recommendations to applied users are provided.