Dynamic Latent Variable Models-Likelihood Evaluation

自20世纪70年代以来，对潜在变量模型的兴趣又有了很大的复苏。潜变量模型被广泛定义为进入计量经济模型的公式，但不是（直接）可观察的变量。潜在变量被广泛认为是经济主体行为的主要组成部分。对于包括跨期优化、搜索或持续过程、纠错机制、习惯形成或持久性、理性预期和状态依赖在内的广泛模型来说，它们本质上是动态的。动态潜变量模型的似然函数在分析上大多是难以处理的，主要是因为潜变量的消除需要高维的相互依赖的积分，而附加的复杂性是潜变量在可观测值上的实际分布很少能被看到。没有似然函数，就不可能用真实世界的数据严格而准确地检验经济理论，因为人们无法回答这样的问题：观察结果是偶然的，而不反映被检验的理论的概率有多大？许多蒙特卡罗模拟技术已经被开发出来并用于估计这些似然函数的特征。主要问题源于这样一个事实，即“蛮力”MC估计似然函数通常需要大量的迭代，除了小样本量。目前有许多加速技术可用。这些技术可以产生相当显著的效率提高（提高1000倍或更多），但是它们远不能满足实际需要，从而使MC似然评估适用于中等到较大的样本量。该项目的贡献来自于开发一种新的通用加速技术，该技术在一项试点研究中取得了计量经济学文献中闻所未闻的结果。所有迹象都表明，这项新技术很可能构成蒙特卡罗技术的一次重大飞跃。该项目在广泛的动态潜在变量模型的背景下操作新的加速技术。通过消除动态潜变量模型分析的一个关键障碍，这项新技术在广泛的重要经济应用中开辟了有趣的新研究途径。在本项目中，该技术被应用于一系列从金融市场、非均衡模型和住房市场的最新文献中提取的实质性现实应用。与其他技术下得出的结果进行系统比较，从从业者的角度对新技术的优点进行评估。使用这项新技术所需的软件将提供给其他研究人员。

Since the 1970's there has been a major resurgence of interest in the topic of latent variable models. Latent variable models are broadly defined as variables which enter the formulation of an econometric model and yet are not (directly) observable. Latent variables are widely recognized to be major components of the behavior of economic agents. They are inherently dynamic for a broad class of models including intertemporal optimization, search or duration processes, error correction mechanisms, habit formation or persistence, rational expectations and state dependence. The likelihood functions of dynamic latent variable models are mostly analytically intractable, largely because the elimination of the latent variables require high dimensional interdependent integration with the additional complication that the actual distribution of the latent variables conditional on the observables can rarely be seen. Without likelihood functions, it is impossible to rigorously and accurately test economic theories with real-world data because one can not answer the question what is the probability that the observations are due to chance and do not reflect the theory being tested. A number of Monte Carlo simulation techniques have been developed and used to estimate the characteristics of these likelihood functions. The main problem arises from the fact the "brute force" MC estimates of likelihood functions typically take a prohibitively large number of iterations for all but small sample sizes. A number of acceleration techniques are currently available. These techniques can produce fairly dramatic efficiency gains (by a factor of 1,000 or more), but they come nowhere close to what is actually required in order to render MC likelihood evaluation practical for moderate to large sample sizes. The contribution of this project comes from developing a new generic acceleration technique that in a pilot study achieved results unheard of in the econometric literature. All indications are that the new technique might well constitute a major leap in Monte Carlo technology. This project operationalizes the new acceleration technique within the context of a broad range of dynamic latent variable models. By removing a key stumbling block to the analysis of dynamic latent variable models, the new technique opens intriguing new avenues of research across a broad range of important economic applications. In this project the technique is applied it to a set of substantive real-life applications drawn from the recent literature on financial markets, disequilibrium models and housing markets. Systematic comparisons with results derived under alternative techniques provide an assessment of the merits of the new techniques from a practitioner's viewpoint. Software needed to use the new technique will be made available to other researchers.