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The numerical approximation for the integrability problem and the measure of welfare changes, and its applications.

机译：可积性问题和福利变化测度的数值逼近及其应用。

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摘要

This dissertation mainly studied on numerical approximation methods as a solution of the integrability problem and the measure of welfare changes, and demonstrated how numerical algorithms can be applied in empirical studies as a solution method.;In general, the integrability problem is described as a system of the partial differential equations (PDE) in terms of the expenditure function, and the measure of welfare changes is defined by the difference between the expenditure function at two different time periods. Both problems can be solved using the same method since solutions for these questions mainly relied on how to recover the compensated income (expenditure) from the ordinary demand function.;In order to investigate whether numerical approximation methods can be applied to the integrability problem and the measure of welfare changes, first, we studied the integrability problem mainly focusing on how to transform the system of the partial differential equations to the system of the ordinary differential equation since this transform possibility provides a way to solve the integrability problem using the numerical method. Second, several numerical methods were investigated as a possible solution of both problem including the Vartia, the RK-4th order algorithm, and the Adams Fourth-Order Predictor-Corrector algorithm. In addition, the Rotterdam and Almost Ideal demand system were investigated since the demand system played an important role on recovering the expenditure.;Two empirical studies are performed. In the first application, using both the U.S consumer expenditure (CE) data and the consumer price index (CPI), the AI and Rotterdam demand system were estimated, and the expenditure was recovered from the estimated demand system using numerical approximation methods. From this, we could demonstrate the power and the applicability of numerical algorithms. In the second application, we paid attention to analyze the welfare effect on the U.S elderly population when prices changed. The burden index and the compensating variation were calculated using the numerical algorithm. From the evaluation, we could confirm that the welfare changes and consumer welfare losses of the elderly population were larger than that of the general U.S population.
机译：本文主要研究数值逼近方法作为可积性问题的解决方案和福利变化的测度，并论证了数值算法如何在实证研究中作为一种求解方法。一般而言，可积性问题被描述为一个系统偏微分方程（PDE）在支出函数方面的差异，福利变化的度量由两个不同时间段内支出函数之间的差定义。这两个问题都可以使用相同的方法解决，因为针对这些问题的解决方案主要取决于如何从普通需求函数中恢复补偿收入（支出）。为了研究数值逼近方法是否可以应用于可积性问题和衡量福利变化的方法，首先，我们研究可积性问题，主要集中在如何将偏微分方程组转换为常微分方程组，因为这种转换可能性提供了一种使用数值方法解决可积性问题的方法。其次，研究了几种数值方法来解决这两个问题，包括Vartia，RK-4阶算法和Adams四阶Predictor-Corrector算法。此外，由于需求系统在收回支出方面起着重要作用，因此对鹿特丹和几乎理想的需求系统进行了研究。进行了两个实证研究。在第一个应用程序中，使用美国消费者支出（CE）数据和消费者物价指数（CPI），估算了AI和鹿特丹的需求系统，并使用数值近似方法从估算的需求系统中回收了支出。由此，我们可以证明数值算法的强大功能和适用性。在第二个应用程序中，我们关注分析价格变化时对美国老年人口的福利影响。使用数值算法计算负担指数和补偿偏差。通过评估，我们可以确定老年人口的福利变化和消费者福利损失大于美国总人口的福利变化和消费者福利损失。

著录项

  • 作者

    Lim, Sung Jin.;

  • 作者单位

    University of Kansas.;

  • 授予单位 University of Kansas.;
  • 学科 Economics General.
  • 学位 Ph.D.
  • 年度 2012
  • 页码 123 p.
  • 总页数 123
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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