### 商科代写|计量经济学代写Econometrics代考|ECON 7204

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 商科代写|计量经济学代写Econometrics代考|Estimation Method

Since we have some unobserved variables, the starting point is to write the model using a state-space representation. The parameters and unknown variables are then estimated using Kalman filter method. The state-space representation of the model is as follows:
\begin{aligned} X_{t} &=A X_{t-1}+Z_{t}+F_{t} W_{t}: \text { state equation } \ Y_{t} &=\mu_{t}+C_{t}^{\prime} X_{t}+V_{t}: \text { measurement equation } \end{aligned}
$X_{t}$ is the vector of $k_{1}$ state variables (unobserved), $Y_{t}$ is the vector of $k_{2}$ observed variables, A is a $k_{1} \times k_{1}$ matrix, $Z_{I}$ is a $k_{1} \times 1$ vector of deterministic terms, $W_{t}$ is a $r_{1} \times 1$ vector of residuals, $F_{t}$ is a $k_{1} \times r_{1}$ matrix, $\mu_{t}$ is the product of a $k_{2} \times n e x p l$ matrix of coefficients by a vector of nexpl explanatory variables. $C_{t}$ is a matrix of dimension $k_{2} \times k_{1}$ and $V_{t}$ is a vector of $r_{2}$ residual terms.
To estimate the model, we adopt a sequential approach based on five steps.
Step 1: we estimate the model with three state variables: $y_{t}^{}, y_{t-1}^{}, y_{t-2}^{*}$ and three observed variables $y_{t}, \pi_{t}, \tilde{u}_{t}$.

The influence of the import prices and oil prices on inflation in Eq. (9) is assumed to be measured by the average impact over two lagged quarters. In Eq. (11) $u_{t}^{*}$ is assumed to be a constant (exogenous). In the IS curve, the financial variables are assumed to be exogenous and the influence of world demand is captured by the average of the impacts of current and previous quarters $\left(D_{c}^{p_{c}}(L)=0.5 a_{31}\left(L+L^{2}\right.\right.$, $\left.D_{s}^{p_{x}}(L)=0.5 a_{32}\left(L+L^{2}\right), D_{w}^{p_{w}}(L)=0.5(1+L)\right)$. Moreover, we do not consider the influence of the interest rate. Finally potential growth rate is assumed to be a constant (exogenous)

Denoting $\Theta$ the set of parameter to estimate, we, therefore, search for $\hat{\Theta}, \hat{X}{t}$ that minimizes the following loss function: $$\sum{t=1}^{T}\left{\frac{1}{\sigma_{\tilde{y}}^{2}}\left(y_{t}-y_{t}^{*}\right)^{2}+\frac{1}{\sigma_{y *}^{2}}\left(\epsilon_{t}^{y *}\right)^{2}+\frac{1}{\sigma_{\pi}^{2}}\left(\epsilon_{t}^{\pi}\right)^{2}+\frac{1}{\sigma_{\tilde{u}}^{2}}\left(\epsilon^{\tilde{u}}\right)^{2}\right}$$
The estimates depends upon the values of the following weights (scaling factors): $\lambda_{1}=\frac{\sigma_{y}^{2}}{\sigma_{y y}^{2}}, \lambda_{2}=\frac{\sigma_{i}^{2}}{\sigma_{\pi}^{2}}, \lambda_{3}=\frac{\sigma_{y}^{2}}{\sigma_{v}^{2}}$. As has been evidenced in the literature, there is no clear guidance about the choice of particular values for these scaling factors. Even the conventional value of 1600 usually chosen for $\lambda_{1}$ would not be appropriate here as the cyclical properties of the output-gap depend upon all the scaling factors. We leave those scaling be estimated by the data. This first-step estimation, with constant $g$ aims at generating some first guess values for the output-gap and the coefficients of the Phillips, IS and Okun equations.

## 商科代写|计量经济学代写Econometrics代考|The Theoretical Concept of Rational Bubbles

The main objective of this study is to review statistical methods, but it is still important to understand the underlying economic theory of financial bubbles in order to specify a composition of statistical models. As discussed, recent research casts doubt on the rationality of investors, but many economic analyses maintain this assumption and it is often explained using the present value model (PVM). The rationality assumption prevails in academic research largely for convenience; it is easier to model rational behaviors than irrational ones. Survey data on investors’ expectations are the best source of information about investors’ expectations, but in the absence of survey data for a comprehensive number of countries and infrequent dissemination of survey data, we also maintain the rationality assumption.

According to the PVM, rational bubbles are defined as sizable and persistent deviations from economic fundamentals and follow a non-stationary process in a statistical sense. Based on the definition of asset returns or returns on real estate $\left(r_{t+1}=\left(P_{t+1}+D_{t+1}\right) / P_{t}-1\right)$, the PVM suggests that the contemporaneous prices $\left(P_{t}\right)$ will be determined by the expected value of future economic fundamentals $(D)$ and prices:
$$P_{t}=E_{t}\left[\frac{P_{t+1}+D_{t+1}}{1+r_{t+1}}\right]$$
where $t$ denotes time $(t=1, \ldots, T)$ and $E$ is an expectation operator. $D$ is an economic fundamental, such as dividend payments in equity analyses or rental costs in housing analyses. Solving Eq. (1) forwardly and using the law of iterated expectations, we can obtain Eq. (2):
$$P_{t}=E_{t}\left[\sum_{h=0}^{\infty}\left(\prod_{k=0}^{h}\left(\frac{1}{1+r_{t+k}}\right)\right) D_{t+h}+\lim {h \rightarrow \infty} \prod{k=0}^{h}\left(\frac{1}{1+r_{t+k}}\right) P_{t+h}\right]$$ When $P$ and $D$ are cointegrated, and when the transversality condition holds (i.e., $\left.E_{t}\left[\lim {h \rightarrow \infty} \prod{k=0}^{h}\left(\frac{1}{1+r_{i+k}}\right) P_{t+h}\right] \rightarrow 0\right)$, then the result shows no evidence of bubbles. Therefore, in this case, asset prices tend to move along with the economic fundamentals. On the other hand, when these conditions do not hold, then the results indicate evidence of bubbles. For this reason, prior studies frequently investigated rational bubbles using integration methods.

## 商科代写|计量经济学代写Econometrics代考|Econometric Methods

Econometricians proposed many statistical methods, with statistical hypotheses that seem designed to be suitable from their perspectives. Consequently, some approaches were developed to look for tranquil periods, while others investigate financial bubbles. Unlike previous studies, we make a clear distinction between statistical approaches to determine tranquil and bubble periods. This distinction is important since differences in the statistical hypotheses can explain the different results from these two approaches. In this section, we will clarify these two approaches using popular statistical specifications in studies of bubbles.

To investigate the theoretical model and predictions in Eq. (2) quantitatively, previous studies often focused on a single market utilizing time series methods. These statistical methods are one-tailed tests, but can be broadly categorized into left- and right-tailed approaches according to their alternative hypotheses. The lefttailed test is classical and is designed to look for cointegration between prices and economic fundamentals, and thus revealing tranquil periods. As an extension, we also propose a nonlinear approach that can be classified into a group of left-tailed tests. On the other hand, the right-tailed test, which has become popular, is an approach to identify explosive bubbles.

## 商科代写|计量经济学代写Econometrics代考|Estimation Method

X吨=一个X吨−1+从吨+F吨在吨: 状态方程  是吨=μ吨+C吨′X吨+在吨: 测量方程
X吨是向量ķ1状态变量（未观察到），是吨是向量ķ2观察到的变量，A 是ķ1×ķ1矩阵，从我是一个ķ1×1确定性术语的向量，在吨是一个r1×1残差向量，F吨是一个ķ1×r1矩阵，μ吨是一个产品ķ2×n和Xpl由 nexpl 解释变量向量组成的系数矩阵。C吨是一个维度矩阵ķ2×ķ1和在吨是一个向量r2剩余条款。

\sum{t=1}^{T}\left{\frac{1}{\sigma_{\tilde{y}}^{2}}\left(y_{t}-y_{t}^{*} \right)^{2}+\frac{1}{\sigma_{y *}^{2}}\left(\epsilon_{t}^{y *}\right)^{2}+\frac{1 }{\sigma_{\pi}^{2}}\left(\epsilon_{t}^{\pi}\right)^{2}+\frac{1}{\sigma_{\tilde{u}}^ {2}}\left(\epsilon^{\tilde{u}}\right)^{2}\right}\sum{t=1}^{T}\left{\frac{1}{\sigma_{\tilde{y}}^{2}}\left(y_{t}-y_{t}^{*} \right)^{2}+\frac{1}{\sigma_{y *}^{2}}\left(\epsilon_{t}^{y *}\right)^{2}+\frac{1 }{\sigma_{\pi}^{2}}\left(\epsilon_{t}^{\pi}\right)^{2}+\frac{1}{\sigma_{\tilde{u}}^ {2}}\left(\epsilon^{\tilde{u}}\right)^{2}\right}

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。