ECON 2504 - 统计代写答疑辅导

标签： ECON 2504

商科代写|计量经济学代写Econometrics代考|ECON 2504

Posted on 2022年7月1日2022年7月1日 by statistics-lab

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计量经济学，对经济关系的统计和数学分析，通常作为经济预测的基础。这种信息有时被政府用来制定经济政策，也被私人企业用来帮助价格、库存和生产方面的决策。

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我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Some Examples

Each of the loss functions that we discuss in this subsection corresponds to a machine learning algorithm, as thoroughly explained in Bühlmann and Hothorn (2007), Sect. 3. We refer to this article for more properties of these losses and for issues regarding their practical implementation.

A first canonical example, in the regression setting, is to let $\psi(x, y)=(y-x)^{2}$ (squared error loss), which is 2 -strongly convex in its first argument (Assumption $\mathbf{A}{\mathbf{2}}$ ) and satisfies Assumption $\mathbf{A}{\mathbf{1}}$ as soon as $\mathbb{E} Y^{2}<\infty$. It also satisfies $\mathbf{A}{\mathbf{3}}^{\prime}$, with $\partial{x} \psi(x, y)=2(x-y)$ and $L=2$.
Another example in regression is the loss $\psi(x, y)=|y-x|$ (absolute error loss), which is convex but not strongly convex in its first argument. Whenever strong convexity of the loss is required, a possible strategy is to regularize the objective via an $L^{2}$-type penalty, and take
$$
\psi(x, y)=|y-x|+\gamma x^{2},
$$
where $\gamma$ is a positive parameter (possibly function of the sample size $n$ in the empirical setting). This loss is (2 ) -strongly convex in $x$ and satisfies $\mathbf{A}{\mathbf{1}}$ and $\mathbf{A}{\mathbf{2}}$ whenever $\mathbb{E}|Y|<\infty$, with $\xi(x, y)=\operatorname{sgn}(x-y)+2 \gamma x$ (with $\operatorname{sgn}(u)=2 \mathbb{1}{[u>0]}-1$ for $u \neq 0$ and $\operatorname{sgn}(0)=0$ ). On the other hand, the function $\psi(\cdot, y)$ is not differentiable at $y$, so that the smoothness Assumption $\mathbf{A}{3}^{\prime}$ is not satisfied. However,
$$
\begin{aligned}
\mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)=& \int\left(\operatorname{sgn}\left(x_{1}-y\right)-\operatorname{sgn}\left(x_{2}-y\right)\right) \mu_{Y \mid X}(\mathrm{~d} y)+2 \gamma\left(x_{1}-x_{2}\right) \
=& \mu_{Y \mid X}\left(\left(-\infty, x_{1}\right)\right)-\mu_{Y \mid X}\left(\left(-\infty, x_{2}\right)\right)+2 \gamma\left(x_{1}-x_{2}\right) \
&-\mu_{Y \mid X}\left(\left(x_{1}, \infty\right)\right)+\mu_{Y \mid X}\left(\left(x_{2}, \infty\right)\right) .
\end{aligned}
$$
Thus, if we assume for example that $\mu_{Y \mid X}$ has a density (with respect to the Lebesgue measure) bounded by $B$, then
$$
\left|\mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)\right| \leq 2(B+\gamma)\left|x_{1}-x_{2}\right|,
$$
and Assumption $\mathbf{A}{3}$ is therefore satisfied. Of course, in the empirical setting, assuming that $\mu{Y \mid X}$ has a density precludes the use of the empirical measure $\mu_{n}$ for $\mu_{X, Y}$. A safe and simple alternative is to consider a smoothed version $\tilde{\mu}{n}$ of $\mu{n}$ (based,
for example, on a kernel estimate; see Devroye and Györfi 1985), and to minimize the functional
$$
C_{n}(F)=\int|y-F(x)| \tilde{\mu}{n}(\mathrm{~d} x, \mathrm{~d} y)+\gamma \int F(x)^{2} \tilde{\mu}{n}(\mathrm{~d} x)
$$
over the linear combinations of functions in $\mathscr{F}$.

商科代写|计量经济学代写Econometrics代考|Two Algorithms

Let $\operatorname{lin}(\mathscr{F})$ be the set of all linear combinations of functions in $\mathscr{F}$, our collection of base predictors in $L^{2}\left(\mu_{X}\right)$. So, each $F \in \operatorname{lin}(\mathscr{F})$ has the form $F=\sum_{j=1}^{J} \beta_{j} f_{j}$. where $\left(\beta_{1}, \ldots, \beta_{J}\right) \in \mathbb{R}^{J}$ and $f_{1}, \ldots, f_{J}$ are elements of $\mathscr{F}$. Finding the infimum of the functional $C$ over lin $(\mathscr{F})$ is a challenging infinite-dimensional optimization problem, which requires an algorithm. The core idea of the gradient boosting approach is to greedily locate the infimum by producing a combination of base predictors via a gradient-descent-type algorithm in $L^{2}\left(\mu_{X}\right)$. Focusing on the basics, this can be achieved by two related yet different strategies, which we examine in greater

mathematical details below. Algorithm 1 appears in Mason et al. (2000), whereas Algorithm 2 is essentially due to Friedman (2001).

It is implicitly assumed throughout this paragraph that Assumption $\mathbf{A}{\mathbf{1}}$ is satisfied. We recall that under this assumption, the convex functional $C$ is locally bounded and therefore continuous. Thus, in particular, $$ \inf {F \in \operatorname{lin}(\mathscr{F})} C(F)=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F), $$ where $\varlimsup \overline{\operatorname{lin}(\mathscr{F})}$ is the closure of lin( $\mathscr{F})$ in $L^{2}\left(\mu{X}\right)$. Loosely speaking, looking for the infimum of $C$ over $\overline{\operatorname{lin}(\mathscr{F})}$ is the same as looking for the infimum of $C$ over all (finite) linear combinations of base functions in $\mathscr{F}$. We note in addition that if Assumption $\mathbf{A}{2}$ is satisfied, then there exists a unique function $\bar{F} \in \overline{\operatorname{lin}(\mathscr{F})}$ (which we call the boosting predictor) such that $$ C(\bar{F})=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F)
$$
Algorithm 1. In this approach, we consider a class $\mathscr{F}$ of functions $f: \mathscr{X} \rightarrow \mathbb{R}$ such that $0 \in \mathscr{F}, f \in \mathscr{F} \Leftrightarrow-f \in \mathscr{F}$, and $|f|_{\mu_{X}}=1$ for $f \neq 0$. An example is the collection $\mathscr{F}$ of all $\pm$-binary trees in $\mathbb{R}^{d}$ using axis parallel cuts with $k$ terminal nodes (plus zero). Each nonzero $f \in \mathscr{F}$ takes the form $f=\sum_{j=1}^{k} \beta_{j} \mathbb{1}{A{j}}$, where $\left|\beta_{j}\right|=1$ and $A_{1}, \ldots, A_{k}$ is a tree-structured partition of $\mathrm{R}^{d}$ (Devroye et al. 1996, Chap. 20). The parameter $k$ is a measure of the tree complexity. For example, trees with $k=d+1$ are such that $\overline{\operatorname{lin}(\mathscr{F})}=L^{2}\left(\mu_{X}\right)$ (Breiman 2000). Thus, in this case,
$$
\inf {F \in \operatorname{lin}(\mathscr{F})} C(F)=\inf {F \in L^{2}\left(\mu_{X}\right)} C(F)
$$

商科代写|计量经济学代写Econometrics代考|Algorithm 1

The convergence of this algorithm rests upon the choice of the step size sequence $\left(w_{t}\right){t}$, which needs to be carefully specified. We take $w{0}>0$ arbitrarily and set
$$
w_{t+1}=\min \left(w_{t},-(2 L)^{-1} \mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X)\right), \quad t \geq 0,
$$
where $L$ is the Lipschitz constant of Assumption $\mathbf{A}{\mathbf{3}}$. Clearly, the sequence $\left(w{t}\right){t}$ is nonincreasing. It is also nonnegative. To see this, just note that, by definition, $$ f{t+1} \in \arg \max {f \in \mathscr{F}}-\mathbb{E} \xi\left(F{t}(X), Y\right) f(X),
$$
and thus, since $0 \in \mathscr{F},-\mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X) \geq 0$. The main result of this section is encapsulated in the following theorem.

Theorem 1 Assume that Assumptions $\mathbf{A}{\mathbf{1}}$ and $\mathbf{A}{\mathbf{3}}$ are satisfied, and let $\left(F_{t}\right){t}$ be defined by Algorithm 1 with $\left(w{t}\right){t}$ as in (8). Then $$ \lim {t \rightarrow \infty} C\left(F_{t}\right)=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F) . $$ Proof See Supplementary Material Document. Observe that Theorem 1 holds without Assumption $\mathbf{A}{2}$, i.e., there is no need here to assume that the function $\psi(x, y)$ is strongly convex in $x$. However, whenever Assumption $\mathbf{A}_{2}$ is satisfied, there exists as in (4) a unique boosting predictor $\bar{F} \in \overline{\operatorname{lin}(\mathscr{F})}$ such that $C(\bar{F})=\inf {F \in \operatorname{lin}(\mathscr{F})} C(F)$, and the theorem guarantees that $\lim {t \rightarrow \infty} C\left(F_{t}\right)=C(\bar{F})$

The proof of the theorem relies on the following lemma, which states that the sequence $\left(C\left(F_{t}\right)\right){t}$ is nonincreasing. Since $C(F)$ is nonnegative for all $F$, we concludê thât $C\left(F{t}\right) \downarrow \inf {k} C\left(F{k}\right)$ â $t \rightarrow \infty$. This is thé kêy argumént tó prové thé convergence of $C\left(F_{t}\right)$ toward inf $F \in \operatorname{lin}(\mathscr{F}) C(F)$.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|Some Examples

我们在本小节中讨论的每个损失函数都对应于机㕷学习算法，如 Bühlmann 和 Hothorn (2007), Sect. 3. 我们参考这篇文章来了解这些损失的更多属性以及关于它们的实际实现的问题。

第一个典型的例子，在回归设置中，是让 $\psi(x, y)=(y-x)^{2}$ (平方误差损失)，它的第一个参数是 2 – 强凸 (假设 $\mathbf{A} 2$ ) 并满足假设 $\mathbf{A 1}$ 立刻 $\mathbb{E} Y^{2}<\infty$. 也满足 $\mathbf{A} \mathbf{3}^{\prime}$ ，和 $\partial x \psi(x, y)=2(x-y)$ 和 $L=2$.
回归中的另一个例子是损失 $\psi(x, y)=|y-x|$ (绝对误差损失)，它是凸的，但在其第一个参数中不是强凸的。每当需要损失的强凸性时，一种可能的策略是通过 $L^{2}$-型惩罚，并采取
$$
\psi(x, y)=|y-x|+\gamma x^{2},
$$
在哪里 $\gamma$ 是一个正参数 (可能是样本量的函数 $n$ 在经验设置中) 。这种损失是 (2) – 在 $x$ 并满足 $\mathbf{A} 1$ 和 $\mathbf{A} 2$ 每当 $\mathbb{E}|Y|<\infty$ ，和 $\xi(x, y)=\operatorname{sgn}(x-y)+2 \gamma x($ 和 $\operatorname{sgn}(u)=21[u>0]-1$ 为了 $u \neq 0$ 和 $\operatorname{sgn}(0)=0$ ) 。另一方面，函数 $\psi(\cdot, y)$ 不可微分 $y$, 使平滑假设 $\mathbf{A} 3^{\prime}$ 不满意。然而，
$$
\mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)=\int\left(\operatorname{sgn}\left(x_{1}-y\right)-\operatorname{sgn}\left(x_{2}-y\right)\right) \mu_{Y \mid X}(\mathrm{~d} y)+2 \gamma\left(x_{1}-x_{2}\right)=
$$
因此，如果我们假设例如 $\mu_{Y \mid X}$ 有一个密度（相对于 Lebesgue 测度) 为界 $B$ ，然后
$$
\left|\mathbb{E}\left(\xi\left(x_{1}, Y\right)-\xi\left(x_{2}, Y\right) \mid X\right)\right| \leq 2(B+\gamma)\left|x_{1}-x_{2}\right|,
$$
和假设 $\mathbf{A} 3$ 因此感到满意。当然，在经验设置中，假设 $\mu Y \mid X$ 有一个密度排除了经验测量的使用 $\mu_{n}$ 为了 $\mu_{X, Y}$. 一个安全且简单的替代方案是考虑平滑版本 $\tilde{\mu} n$ 的 $\mu n$ (基于，
例如，在核估计上；参见 Devroye 和 Györfi 1985)，并最小化函数
$\$ \$$
C_{n}(F)=|int $|y F(x)| \backslash$ tilde ${\backslash m u}{n}(\backslash \operatorname{mathrm}{\sim d} x$, \mathrm ${\sim d} y)+\backslash$ gamma $\backslash$ int $F(x)^{\wedge}{2} \backslash t \mathrm{~ i l d e {}$ (数学 ${\sim d} x)$
\$\$
在函数的线性组合上 $\mathscr{F}$.

商科代写|计量经济学代写Econometrics代考|Two Algorithms

让 $\operatorname{lin}(\mathscr{F})$ 是函数的所有线性组合的集合 $\mathscr{F}$ ，我们收集的基础预测变量在 $L^{2}\left(\mu_{X}\right)$. 所以，每个 $F \in \operatorname{lin}(\mathscr{F})$ 有形式 $F=\sum_{j=1}^{J} \beta_{j} f_{j}$. 在哪里 $\left(\beta_{1}, \ldots, \beta_{J}\right) \in \mathbb{R}^{J}$ 和 $f_{1}, \ldots, f_{J}$ 是元素 $\mathscr{F}$. 寻找泛函的下确界 $C$ 过林 $(\mathscr{F})$ 是一个具有挑战性的无限维优化问题，需要一个算法。梯度提升方法的核心思想是通过梯度下降型算法生成基本预测变量的组合来贪婪地定位下确界。 $L^{2}\left(\mu_{X}\right)$. 专注于基础，这可以通过两种相关但不同的策略来实现，我们将在更大的
下面的数学细节。算法 1 出现在 Mason et al. (2000 年)，而算法 2 主要归功于 Friedman（2001 年)。
在本段中隐含地假设假设 $\mathbf{A 1}$ 很满意。我们记得在这个假设下，凸泛函 $C$ 是局部有界的，因此是连续的。因此，特别是，
$$
\inf F \in \operatorname{lin}(\mathscr{F}) C(F)=\inf F \in \operatorname{lin}(\mathscr{F}) C(F),
$$
在哪里 $\overline{\lim } \overline{\operatorname{lin}(\mathscr{F})}$ 是 $\operatorname{lin}(\mathscr{F})$ 在 $L^{2}(\mu X)$. 松散地说，寻找下确界 $C$ 超过 $\overline{\operatorname{lin}(\mathscr{F}) \text { 和寻找下确界一样 } C \text { 基函数的所 }$ 有 (有限) 线性组合 $\mathscr{F}$. 我们还注意到，如果假设 $\mathbf{A} 2$ 满足，则存在唯一函数 $\bar{F} \in \overline{\operatorname{lin}(\mathscr{F})}$ (我们称之为提升预测器) 使得
$$
C(\bar{F})=\inf F \in \operatorname{lin}(\mathscr{F}) C(F)
$$
算法 1. 在这种方法中，我们考虑一个类 $\mathscr{F}$ 功能 $f: \mathscr{X} \rightarrow \mathbb{R}$ 这样 $0 \in \mathscr{F}, f \in \mathscr{F} \Leftrightarrow-f \in \mathscr{F}$ ，和 $|f|{\mu{X}}=1$ 为了 $f \neq 0$. 一个例子是集合 $\mathscr{F}$ 其中 $\pm$ – 二叉树 $\mathbb{R}^{d}$ 使用轴平行切割 $k$ 终端节点 (加零) 。每个非零 $f \in \mathscr{F}$ 采取形式 $f=\sum_{j=1}^{k} \beta_{j} 1 A j$ ，在哪里 $\left|\beta_{j}\right|=1$ 和 $A_{1}, \ldots, A_{k}$ 是一个树形结构的分区 $\mathrm{R}^{d}$ (Devroye 等人，1996 年，第 20 章) 。参数 $k$ 是树复杂度的度量。例如，树与 $k=d+1$ 是这样的 $\overline{l i n}(\mathscr{F})=L^{2}\left(\mu_{X}\right)$ (布雷曼 2000) 。因此，在这种情况下，
$$
\inf F \in \operatorname{lin}(\mathscr{F}) C(F)=\inf F \in L^{2}\left(\mu_{X}\right) C(F)
$$

商科代写|计量经济学代写Econometrics代考|Algorithm 1

该算法的收敛取决于步长序列的选择 $\left(w_{t}\right) t$, 这需要仔细指定。我们采取 $w 0>0$ 任意设置
$$
w_{t+1}=\min \left(w_{t},-(2 L)^{-1} \mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X)\right), \quad t \geq 0,
$$
在哪里 $L$ 是假设的 Lipschitz 常数 $\mathbf{A 3}$. 显然，序列 $(w t) t$ 是非增加的。它也是非负的。要看到这一点，请注意，根据定义，
$$
f t+1 \in \arg \max f \in \mathscr{F}-\mathbb{E} \xi(F t(X), Y) f(X),
$$
因此，由于 $0 \in \mathscr{F},-\mathbb{E} \xi\left(F_{t}(X), Y\right) f_{t+1}(X) \geq 0$. 本节的主要结果封装在以下定理中。
定理 1 假设假设 $\mathbf{A} 1$ 和 $\mathbf{A} 3$ 满意，让 $\left(F_{t}\right) t$ 由算法 1 定义 $(w t) t$ 如（8)。然后
$$
\lim t \rightarrow \infty C\left(F_{t}\right)=\inf F \in \operatorname{lin}(\mathscr{F}) C(F) .
$$
证明见补充材料文件。观察定理 1 在没有假设的情况下成立 $\mathbf{A} 2$ ，即这里不需要假设函数 $\psi(x, y)$ 是强凸的 $x$. 然而，每当假设 $\mathbf{A}{2}$ 满足，如（4) 中存在一个唯一的提升预测器 $\bar{F} \in \overline{\operatorname{lin}(\mathscr{F}) \text { 这样 } C(\bar{F})=\inf F \in \operatorname{lin}(\mathscr{F}) C(F) \text {, 该 }$ 定理保证 $\lim t \rightarrow \infty C\left(F{t}\right)=C(\bar{F})$
定理的证明依赖于以下引理，它表明序列 $\left(C\left(F_{t}\right)\right) t$ 是非增加的。自从 $C(F)$ 对所有人都是非负的 $F$ ，我们真的得出结论 $C(F t) \downarrow \inf k C(F k)$ 一个 $t \rightarrow \infty$. 这是证明收敛性的论证 $C\left(F_{t}\right)$ 朝着inf $F \in \operatorname{lin}(\mathscr{F}) C(F)$.

商科代写|计量经济学代写Econometrics代考请认准statistics-lab™

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金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

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，工具箱允许您学习和应用专业技术。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。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECON 7204

Posted on 2022年7月1日2022年7月1日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Simulation and Comparisons with Other Estimators

In this section, we compare the LSE with the Simple Score Estimator (SSE), the Efficient Score Estimator (ESE), the Effective Dimension Reduction (EDR) estimate, the spline estimate, the MAVE estimate, and the EFM estimate. We take part in the simulation settings in Balabdaoui et al. (2019a), which means that we take the dimension $d$ equal to 2 . Since the parameter belongs to the boundary of a circle in this case, we only have to determine a one-dimensional parameter. Using this fact, we use the parameterization $\alpha=\left(\alpha_{1}, \alpha_{2}\right)=(\cos (\beta), \sin (\beta))$ and determine the angle $\beta$ by a golden section search for the SSE, ESE, and spline estimate. For EDR, we used the $\mathrm{R}$ package edr: the method is discussed in Hristache et al. (2001). The spline method is described in Kuchibhotla and Patra (2020), and there exists an $R$ package simest for it, but we used our own implementation. For the MAVE method, we used the R package MAVE; for theory, see Xia (2006). For the EFM estimate (see Cui et al. 2011), we used an $\mathrm{R}$ script, due to Xia Cui and kindly provided to us by her and Rohit Patra. All runs of our simulations can be reproduced by running the $R$ scripts in Groeneboom $2018 .$

In simulation model 1 , we take $\alpha_{0}=(1 / \sqrt{2}, 1 / \sqrt{2})^{T}$ and $X=\left(X_{1}, X_{2}\right)^{T}$, where $X_{1}$ and $X_{2}$ are independent Uniform $(0,1)$ variables. The model is now
$$
Y=\psi_{0}\left(\alpha_{0}^{T} \boldsymbol{X}\right)+\varepsilon
$$
where $\psi_{0}(u)=u^{3}$ and $\varepsilon$ is a standard normal random variable, independent of $\boldsymbol{X}$.
In simulation model 2 , we also take $\alpha_{0}=(1 / \sqrt{2}, 1 / \sqrt{2})^{T}$ and $\boldsymbol{X}=\left(X_{1}, X_{2}\right)^{T}$, where $X_{1}$ and $X_{2}$ are independent Uniform $(0,1)$ variables. This time, however, the model is (Table 1)
$$
Y=\operatorname{Bin}\left(10, \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}\right)
$$
see also Table 2 in Balabdaoui et al. (2019a). This means $$
Y=\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)+\varepsilon $$ where $$ \psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)=10 \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}, \quad \varepsilon=N{n}-\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right), $$ and $$ N{n}=\operatorname{Bin}\left(10, \frac{\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right.}{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)}\right)
$$
Note that indeed $\mathbb{E}{\varepsilon \mid \boldsymbol{X})=0$, but that we do not have independence of $\varepsilon$ and $\boldsymbol{X}$, as in the previous example.

商科代写|计量经济学代写Econometrics代考|Concluding Remarks

We replaced the “crossing of zero” estimators in Balabdaoui et al. (2019b) with profile least squares estimators. The asymptotic distribution of the estimators was determined and its behavior illustrated by a simulation study, using the same models as in Balabdaoui et al. (2019a).

In the first model, the error is independent of the covariate and homoscedastic and in this case, four of the estimators were efficient. In the other (binomial-logistic) model, the error was dependent on the covariates and not homoscedastic. It was shown that the Simple Score Estimate (SSE) had in fact a smaller asymptotic variance in this model than the other estimators for which the asymptotic variance is known, although the difference is very small and does not really show up in the simulations.
There is no uniformly best estimate in our simulation, but the EDR estimate is clearly inferior to the other estimates, including the LSE, in particular for the lower sample sizes. On the other hand, the LSE is inferior to the other estimators except for the EDR. All simulation results can be reproduced by running the $R$ scripts in Groeneboom (2018).

商科代写|计量经济学代写Econometrics代考|Mathematical Context

We assume to be given a sample $\mathscr{D}{n}=\left{\left(X{1}, Y_{1}\right), \ldots,\left(X_{n}, Y_{n}\right)\right}$ of i.i.d. observations, where each pair $\left(X_{i}, Y_{i}\right)$ takes values in $\mathscr{X} \times \mathscr{Y}$. Throughout, $\mathscr{X}$ is a Borel subset of $\mathbb{R}^{d}$, and $\mathscr{Y} \subset \mathbb{R}$ is either a finite set of labels (for classification) or a subset of $\mathbb{R}$ (for regression). The vector space $\mathbb{R}^{d}$ is endowed with the Euclidean norm $|\cdot|$.
Our goal is to construct a predictor $F: \mathscr{X} \rightarrow \mathbb{R}$ that assigns a response to each possible value of an independent random observation distributed as $X_{1}$. In the context of gradient boosting, this general problem is addressed by considering a class $\mathscr{F}$ of functions $f: \mathscr{X} \rightarrow \mathbb{R}$ (called the weak or base learners) and minimizing some empirical risk functional
$$
C_{n}(F)=\frac{1}{n} \sum_{i=1}^{n} \psi\left(F\left(X_{i}\right), Y_{i}\right)
$$
over the linear combinations of functions in $\mathscr{F}$. The function $\psi: \mathbb{R} \times \mathscr{Y} \rightarrow \mathbb{R}{+}$, called the loss, is convex in its first argument and measures the cost incurred by predicting $F\left(X{i}\right)$ when the answer is $Y_{i}$. For example, in the least squares regression problem, $\psi(x, y)=(y-x)^{2}$ and
$$
C_{n}(F)=\frac{1}{n} \sum_{i=1}^{n}\left(Y_{i}-F\left(X_{i}\right)\right)^{2} .
$$
However, many other examples are possible, as we will see below. Let $\delta_{z}$ denote the Dirac measure at $z$, and let $\mu_{n}=(1 / n) \sum_{i=1}^{n} \delta_{\left(X_{i}, Y_{j}\right)}$ be the empirical measure associated with the sample $\mathscr{D}{n}$. Clearly, $$ C{n}(F)=\mathbb{E} \psi(F(X), Y),
$$
where $(X, Y)$ denotes a random pair with distribution $\mu_{n}$ and the symbol $\mathbb{E}$ denotes the expectation with respect to $\mu_{n}$. Naturally, the theoretical (i.e., population) version of $C_{n}$ is
$$
C(F)=\mathbb{E} \psi\left(F\left(X_{1}\right), Y_{1}\right),
$$
where now the expectation is taken with respect to the distribution of $\left(X_{1}, Y_{1}\right)$. It turns out that most of our subsequent developments are independent of the context,whether empirical or theoretical. Therefore, to unify the notation, we let throughout $(X, Y)$ be a generic pair of random variables with distribution $\mu_{X, Y}$, keeping in mind that $\mu_{X, Y}$ may be the distribution of $\left(X_{1}, Y_{1}\right)$ (theoretical risk), the standard empirical measure $\mu_{n}$ (empirical risk), or any smoothed version of $\mu_{n}$.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|Simulation and Comparisons with Other Estimators

在本节中，我们将 LSE 与简单分数估计 (SSE)、有效分数估计 (ESE)、有效降维 (EDR) 估计、样条估计、MAVE 估计和 EFM 估计进行比较。我们参与了 Balabdaoui 等人的模拟设置。(2019a)，这意味着我们取维度d等于 2 。由于在这种情况下参数属于圆的边界，我们只需要确定一个一维参数。利用这个事实，我们使用参数化一个=(一个1,一个2)=(因⁡(b),罪⁡(b))并确定角度b通过黄金分割搜索 SSE、ESE 和样条估计。对于 EDR，我们使用Rpackage edr：Hristache 等人讨论了该方法。（2001 年）。样条方法在 Kuchibhotla 和 Patra (2020) 中有描述，并且存在R最适合它的包，但我们使用了自己的实现。对于 MAVE 方法，我们使用了 R 包 MAVE；理论见Xia (2006)。对于 EFM 估计（参见 Cui et al. 2011），我们使用了R剧本，感谢夏翠，由她和 Rohit Patra 提供给我们。我们模拟的所有运行都可以通过运行RGroeneboom 中的脚本2018.

在仿真模型 1 中，我们取一个0=(1/2,1/2)吨和X=(X1,X2)吨，在哪里X1和X2是独立的制服(0,1)变量。模型现在

是=ψ0(一个0吨X)+e
在哪里ψ0(在)=在3和e是标准正态随机变量，独立于X.
在仿真模型 2 中，我们还取一个0=(1/2,1/2)吨和X=(X1,X2)吨，在哪里X1和X2是独立的制服(0,1)变量。然而，这一次，模型是（表 1）

Y=\operatorname{Bin}\left(10, \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\粗体符号{\alpha}{0}^{T} \boldsymbol{X}\right)\right}\right)Y=\operatorname{Bin}\left(10, \exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) /\left{1+\exp \left(\粗体符号{\alpha}{0}^{T} \boldsymbol{X}\right)\right}\right)
另见 Balabdaoui 等人的表 2。（2019a）。这表示

是=ψ0(一个0吨X)+e在哪里

\psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)=10 \exp \left(\boldsymbol{\alpha}{0}^{T} \ boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}, \quad \varepsilon=N{ n}-\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right),\psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)=10 \exp \left(\boldsymbol{\alpha}{0}^{T} \ boldsymbol{X}\right) /\left{1+\exp \left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right}, \quad \varepsilon=N{ n}-\psi_{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right),和

ñn=垃圾桶⁡(10,经验⁡(一个0吨X1+经验⁡(一个0吨X))
注意确实 $\mathbb{E}{\varepsilon \mid \boldsymbol{X})=0,b在吨吨H一个吨在和d○n○吨H一个在和一世nd和p和nd和nC和○F\伐普西隆一个nd\boldsymbol{X}$，如上例所示。

商科代写|计量经济学代写Econometrics代考|Concluding Remarks

我们替换了 Balabdaoui 等人的“过零”估计量。（2019b）具有轮廓最小二乘估计器。使用与 Balabdaoui 等人相同的模型，确定了估计量的渐近分布，并通过模拟研究说明了其行为。（2019a）。

在第一个模型中，误差与协变量和同方差无关，在这种情况下，四个估计量是有效的。在另一个（二项式逻辑）模型中，误差取决于协变量而不是同方差。结果表明，与已知渐近方差的其他估计量相比，简单分数估计 (SSE) 实际上在该模型中具有更小的渐近方差，尽管差异非常小并且并未真正显示在模拟中。
在我们的模拟中没有统一的最佳估计，但 EDR 估计明显不如其他估计，包括 LSE，特别是对于较小的样本量。另一方面，LSE 不如 EDR 以外的其他估计量。所有模拟结果都可以通过运行RGroeneboom (2018) 中的脚本。

商科代写|计量经济学代写Econometrics代考|Mathematical Context

我们假设给定一个样本\mathscr{D}{n}=\left{\left(X{1}, Y_{1}\right), \ldots,\left(X_{n}, Y_{n}\right)\right}\mathscr{D}{n}=\left{\left(X{1}, Y_{1}\right), \ldots,\left(X_{n}, Y_{n}\right)\right}独立同分布观察，其中每一对(X一世,是一世)取值X×是. 始终，X是一个 Borel 子集Rd，和是⊂R是一组有限的标签（用于分类）或R（用于回归）。向量空间Rd被赋予欧几里得范数|⋅|.
我们的目标是构建一个预测器F:X→R将响应分配给独立随机观察的每个可能值，分布为X1. 在梯度提升的背景下，这个一般问题是通过考虑一个类来解决的F功能F:X→R（称为弱学习器或基础学习器）并最小化一些经验风险函数

Cn(F)=1n∑一世=1nψ(F(X一世),是一世)
在函数的线性组合上F. 功能ψ:R×是→R+，称为损失，在其第一个参数中是凸的，并衡量通过预测所产生的成本F(X一世)当答案是是一世. 例如，在最小二乘回归问题中，ψ(X,是)=(是−X)2和

Cn(F)=1n∑一世=1n(是一世−F(X一世))2.
但是，许多其他示例也是可能的，我们将在下面看到。让d和表示狄拉克测度和，然后让μn=(1/n)∑一世=1nd(X一世,是j)是与样本相关的经验度量Dn. 清楚地，

Cn(F)=和ψ(F(X),是),
在哪里(X,是)表示具有分布的随机对μn和符号和表示相对于的期望μn. 自然地，理论（即人口）版本Cn是

C(F)=和ψ(F(X1),是1),
现在的期望是关于分布的(X1,是1). 事实证明，我们随后的大部分发展都独立于背景，无论是经验的还是理论的。因此，为了统一符号，我们让通篇(X,是)是具有分布的通用随机变量对μX,是，请记住μX,是可能是分布(X1,是1)（理论风险），标准经验测量μn（经验风险），或任何平滑版本μn.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECOM20001

Posted on 2022年7月1日2022年7月1日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|General Conditions and the Functions ψˆ n,αˆ and ψα

We give general conditions that we assume to hold in the remainder of the paper here and give graphical comparisons of the functions $\hat{\psi}{n, \alpha}$ and $\psi{\alpha}$, where $\psi_{\alpha}$ is defined in Definition $1 .$

Example 1 As an illustrative example, we take $d=2, \psi_{0}(x)=x^{3}, \alpha_{0}=(1 / \sqrt{2}$, $1 / \sqrt{2})^{T}, Y_{i}=\psi_{0}\left(\alpha_{0}^{T} X_{i}\right)+\varepsilon_{i}$, where the $\varepsilon_{i}$ are i.i.d. standard normal random variables, independent of the $\boldsymbol{X}{i}$, which are i.i.d. random vectors, consisting of two independent Uniform $(0,1)$ random variables. In this case, the conditional expectation function (5) is a rather complicated function of $\alpha$ which we shall not give here but can be computed by a computer package such as Mathematica or Maple. The loss functions: $L^{\mathrm{LSE}}: \alpha{1} \mapsto \mathbb{E}\left{Y-\psi_{\alpha}\left(\alpha^{T} \boldsymbol{X}\right)\right}^{2} \quad$ and $\quad \widehat{L}{n}^{\mathrm{LSE}}: \alpha{1} \mapsto n^{-1} \sum_{i=1}^{n}\left{Y_{i}-\hat{\psi}{n, \alpha}\left(\alpha^{T} \boldsymbol{X}{i}\right)\right}^{2}$
where the loss function $\widehat{L}{n}^{L S E}$ is for sample sizes $n=10,000$ and $n=100,000$, and $\alpha=\left(\alpha{1}, \alpha_{2}\right)^{T}$. For $\alpha_{1} \in[0,1]$ and $\alpha_{2}$ equal to the positive root $\left{1-\alpha_{1}^{2}\right}^{1 / 2}$, we get Fig. 1. The function $L^{\mathrm{LSE}}$ has a minimum equal to 1 at $\alpha_{1}=1 / \sqrt{2}$, and $\widehat{L}{n}^{\mathrm{LSE}}$ has a minimum at a value very close to $1 / \sqrt{2}$ (furnishing the profile LSE $\hat{\alpha}{n}$ ), which gives a visual evidence for consistency of the profile LSE.

In order to show the $\sqrt{n}$-consistency and asymptotic normality of the estimators in the next sections, we now introduce some conditions, which correspond to those in Balabdaoui et al. (2019b). We note that we do not need conditions on reparameterization.
(A1) $\boldsymbol{X}$ has a density w.r.t. Lebesgue measure on its support $\mathcal{X}$, which is a convex set $\mathcal{X}$ with a nonempty interior, and satisfies $\mathcal{X} \subset\left{x \in \mathbb{R}^{d}:|x| \leq R\right}$ for some $R>0$.
(A2) The function $\psi_{0}$ is bounded on the set $\left{u \in \mathbb{R}: u=\alpha_{0}^{T} \boldsymbol{x}, \boldsymbol{x} \in \mathcal{X}\right}$.
(A3) There exists $\delta>0$ such that the conditional expectation $\tilde{\psi}{\alpha}$, defined by (5), is nondecreasing on $I{\alpha}=\left{u \in \mathbb{R}: u=\alpha^{T} \boldsymbol{x}, x \in \mathcal{X}\right}$ and satisfies $\bar{\psi}{\alpha}=\psi{\alpha}$, so minimizes $$
\left|\mathbb{E}\left{Y-\psi\left(\boldsymbol{\alpha}^{T} \boldsymbol{X}\right)\right} \boldsymbol{X}\right|^{2}
$$
over nondecreasing functions $\psi$, if $\left|\boldsymbol{\alpha}-\boldsymbol{\alpha}_{0}\right| \leq \delta$.

商科代写|计量经济学代写Econometrics代考|The Limit Theory for the SSE

In this section, we derive the limit distribution of the SSE introduced above. In our derivation, the function $\psi_{\alpha}$ of Definition 1 plays a crucial role. Below, we will use the following assumptions, additionally to $(\mathrm{A} 1)-(\mathrm{A} 6)$.
(A7) There exists a $\delta>0$ such that for all $\alpha \in\left(\mathcal{B}\left(\alpha_{0}, \delta\right) \cap \mathcal{S}{d-1}\right) \backslash\left{\alpha{0}\right}$, the random variable
$$
\operatorname{cov}\left(\left(\boldsymbol{\alpha}{0}-\boldsymbol{\alpha}\right)^{T} \boldsymbol{X}, \psi{0}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) \mid \boldsymbol{\alpha}^{T} \boldsymbol{X}\right) $$ is not equal to 0 almost surely. (A8) The matrix $$ \mathbb{E}\left[\psi{0}^{\prime}\left(\boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right) \operatorname{cov}\left(\boldsymbol{X} \mid \boldsymbol{\alpha}{0}^{T} \boldsymbol{X}\right)\right]
$$
has rank $d-1$.
We start by comparing (3) with the function
$$
\alpha \mapsto\left|\mathbb{E}\left{Y-\psi_{\alpha}\left(\alpha^{T} \boldsymbol{X}\right)\right} \boldsymbol{X}\right|^{2}
$$ As in Sect. 1, the function $\hat{\psi}_{n, \alpha}$ is just the (isotonic) least squares estimate for fixed $\alpha$.

商科代写|计量经济学代写Econometrics代考|The Limit Theory for ESE and Cubic Spline Estimator

The proofs of the consistency and asymptotic normality of the ESE and spline estimator are highly similar to the proofs of these facts for the SSE in the preceding section. The only extra ingredient is the occurrence of the estimate of the derivative of the link function. We only discuss the asymptotic normality.
In addition to the assumptions (A1)-(A7), we now assume the following:
(A8′) $\psi_{\alpha}$ is twice differentiable on $\left.\inf {x \in \mathcal{X}}\left(\alpha^{T} \boldsymbol{x}\right), \sup {x \in \mathcal{X}^{\prime}}\left(\boldsymbol{\alpha}^{T} \boldsymbol{x}\right)\right)$.
(A9) The matrix
$$
\mathbb{E}\left[\psi_{0}^{\prime}\left(\alpha_{0}^{T} \boldsymbol{X}\right)^{2} \operatorname{cov}\left(\boldsymbol{X} \mid \alpha_{0}^{T} \boldsymbol{X}\right)\right]
$$
has rank $d-1$.
An essential step is again to show that
$$
\begin{aligned}
&\int \boldsymbol{x}\left{y-\hat{\psi}{n, \hat{\alpha}{n}}\left(\hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{x}\right)\right} \hat{\psi}{n \hat{\boldsymbol{\alpha}}{n}}^{\prime}\left(\hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{x}\right) d \mathbb{P}{n}(\boldsymbol{x}, y) \ &=\int\left{\boldsymbol{x}-\mathbb{E}\left(X \mid \hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{X}\right)\right}\left{y-\hat{\psi}{n, \hat{\alpha}{n}}\left(\hat{\boldsymbol{\alpha}}{n}^{T} \boldsymbol{x}\right)\right} \hat{\psi}{n \hat{\alpha}{n}}^{\prime}\left(\hat{\alpha}{n}^{T} \boldsymbol{x}\right) d \mathbb{P}{n}(\boldsymbol{x}, y) \ &+o{p}\left(n^{-1 / 2}\right)+o_{p}\left(\hat{\alpha}{n}-\boldsymbol{\alpha}{0}\right)
\end{aligned}
$$
For the ESE, this is done by defining the piecewise constant function $\bar{\rho}{n, \alpha}$ for $u$ in the interval between successive jumps $\tau{i}$ and $\tau_{i+1}$ ) of $\hat{\psi}{n \alpha}$ by $$ \bar{\rho}{n, \alpha}(u)= \begin{cases}\mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=\tau_{i}\right] \psi_{\alpha}^{\prime}\left(\tau_{i}\right) & \text { if } \psi_{\alpha}(u)>\hat{\psi}{n \alpha}\left(\tau{i}\right) \text { for all } u \in\left(\tau_{i}, \tau_{i+1}\right) \ \mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=s\right] \psi_{\alpha}^{\prime}(s) & \text { if } \psi_{\alpha}(s)=\hat{\psi}{n \alpha}(s) \text { for some } s \in\left(\tau{i}, \tau_{i+1}\right) \ \mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=\tau_{i+1}\right] \psi_{\alpha}^{\prime}\left(\tau_{i+1}\right) & \text { if } \psi_{\alpha}(u)<\hat{\psi}{n \alpha}\left(\tau{i}\right) \text { for all } u \in\left(\tau_{i}, \tau_{i+1}\right)\end{cases}
$$ see Appendix E in the supplement of Balabdaoui et al. (2019b). The remaining part of the proof runs along the same lines as the proof for the SSE. For additional details, see Appendix E in the supplement of Balabdaoui et al. (2019b).

The corresponding step in the proof for the spline estimator is given by the following lemma.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|General Conditions and the Functions ψˆ n,αˆ and ψα

我们给出了我们假设在本文的其余部分中持有的一般条件，并给出了函数的图形比较 $\hat{\psi}, \alpha, \alpha$ 和 $\psi \alpha$ ，在哪里 $\psi_{\alpha}$ 在定义中定义 1 .
例 1 作为一个说明性的例子，我们取 $d=2, \psi_{0}(x)=x^{3}, \alpha_{0}=(1 / \sqrt{2}, 1 / \sqrt{2})^{T}, Y_{i}=\psi_{0}\left(\alpha_{0}^{T} X_{i}\right)+\varepsilon_{i}$ ，其中 $\varepsilon_{i}$ 是独立同分布的标准正态随机变量，独立于 $\boldsymbol{X} i$ ，它们是 iid 随机向量，由两个独立的 Uniform 组成 $(0,1)$ 随机变量。在这种情况下，条件期望函数 (5) 是一个相当复杂的函数 $\alpha$ 我们不会在这里给出，但可以通过诸如 Mathematica 或 Maple 之类的计算机包来计算。损失函数: 和
$\mathrm{~ I q u a d ~ I w i d e h a t { { \ { n }}$ 其中损失函数 $\widehat{L} n^{L S E}$ 适用于样本量 $n=10,000$ 和 $n=100,000$ ，和 $\alpha=\left(\alpha 1, \alpha_{2}\right)^{T}$. 为了 $\alpha_{1} \in[0,1]$ 和 $\alpha_{2}$ 等于正根 $\mathrm{~ l e f t { 1 – l a l p h a _ { 1 } へ { 2 } \ r i g h t }}$ $\widehat{L} n^{\mathrm{LSE}}$ 最小值非常接近 $1 / \sqrt{2}$ (提供简介 LSE $\left.\hat{\alpha} n\right)$ ，这为配置文件 LSE 的一致性提供了视觉证据。
为了显示 $\sqrt{n}$-在下一节中估计量的一致性和渐近正态性，我们现在介绍一些条件，这些条件对应于 Balabdaoui 等人的条件。(2019b)。我们注意到我们不需要重新参数化的条件。
(A1) $\boldsymbol{X}$ 在其支持上有一个密度 wrt Lebesgue 度量 $\mathcal{X}$ ，这是一个凸集 $\mathcal{X}$ 具有非空的内部，并且满足
$\mathrm{~ I m a t h c a l { X } }}$
(A2) 功能 $\psi_{0}$ 有界在集合上
\eft ${u \backslash$ in $\backslash \mathrm{~ m a t h b b b { R } : ~ u =}$
(A3) 存在 $\delta>0$ 使得条件期望 $\tilde{\psi} \alpha$ ，由 (5) 定义，在
I{\alpha $}=\backslash 1$ eft $\left{u \backslash\right.$ in $\backslash$ mathbb ${R}: u=\backslash a \mid p h a^{\wedge}{T} \backslash$ boldsymbol ${x}, x \backslash \mathrm{~ i n ~}$
Veft $\backslash \backslash$ mathbb ${$ E $} \backslash$ eft ${Y \mathrm{~ – ~ \ p s i V l e f t (}$
过非减函数 $\psi$ ，如果 $\left|\boldsymbol{\alpha}-\boldsymbol{\alpha}_{0}\right| \leq \delta$.

商科代写|计量经济学代写Econometrics代考|The Limit Theory for the SSE

在本节中，我们推导出上面介绍的 SSE 的极限分布。在我们的推导中，函数 $\psi_{\alpha}$ 定义 1 起着至关重要的作用。下面，我们将使用以下假设，此外 $(\mathrm{A} 1)-(\mathrm{A} 6)$.
(A7) 存在一个 $\delta>0$ 这样对于所有人
$\mathrm{~ \ a l p h a ~ \ i n \ l e f t ( \ m a t h c a l { B }}$
变量
$$
\operatorname{cov}\left((\boldsymbol{\alpha} 0-\boldsymbol{\alpha})^{T} \boldsymbol{X}, \psi 0\left(\boldsymbol{\alpha} 0^{T} \boldsymbol{X}\right) \mid \boldsymbol{\alpha}^{T} \boldsymbol{X}\right)
$$
几乎肯定不等于 0 。 (A8) 矩阵
$$
\mathbb{E}\left[\psi 0^{\prime}\left(\boldsymbol{\alpha} 0^{T} \boldsymbol{X}\right) \operatorname{cov}\left(\boldsymbol{X} \mid \boldsymbol{\alpha} 0^{T} \boldsymbol{X}\right)\right]
$$
有等级 $d-1$.
我们首先将 (3) 与函数进行比较
\alpha \mapsto\left } \backslash \backslash \text { mathbb } { E } \backslash l e f t { Y \mathrm { ~ –
就像在教派中一样。1、功能 $\hat{\psi}_{n, \alpha}$ 只是固定的 (等渗的) 最小二乘估计 $\alpha$.

商科代写|计量经济学代写Econometrics代考|The Limit Theory for ESE and Cubic Spline Estimator

ESE 和样条估计量的一致性和渐近正态性的证明与上一节中 SSE 的这些事实的证明非常相似。唯一的额外因素是链接函数导数估计的出现。我们只讨论渐近正态性。
除了假设（A1 ) – (A7)，我们现在假设以下:
(A8′) $\psi_{\alpha}$ 是两次可微的 $\left.\inf x \in \mathcal{X}\left(\alpha^{T} \boldsymbol{x}\right), \sup x \in \mathcal{X}^{\prime}\left(\boldsymbol{\alpha}^{T} \boldsymbol{x}\right)\right)$.
(A9) 矩阵
$$
\mathbb{E}\left[\psi_{0}^{\prime}\left(\alpha_{0}^{T} \boldsymbol{X}\right)^{2} \operatorname{cov}\left(\boldsymbol{X} \mid \alpha_{0}^{T} \boldsymbol{X}\right)\right]
$$
有等级 $d-1$.
一个重要的步骙是再次证明
\begin } { \text { 对齐 } } \text { \& Int } \backslash \text { boldsymbol } { x } \backslash l e f t { y \mathrm { ~ – ~
对于 ESE，这是通过定义分段常数函数来完成的 $\bar{\rho} n, \alpha$ 为了 $u$ 在连续咷跃之间的间隔 $\tau i$ 和 $\tau_{i+1} ）$ 的 $\hat{\psi} n \alpha$ 经过 $\bar{\rho} n, \alpha(u)=\left{\mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=\tau_{i}\right] \psi_{\alpha}^{\prime}\left(\tau_{i}\right) \quad\right.$ if $\psi_{\alpha}(u)>\hat{\psi} n \alpha(\tau i)$ for all $u \in\left(\tau_{i}, \tau_{i+1}\right) \mathbb{E}\left[\boldsymbol{X} \mid \alpha^{T} \boldsymbol{X}=s\right.$ 请参阅 Balabdaoui 等人的补充资料中的附录 $E_{。}$ (2019b) 。证明的其余部分与 SSE 的证明相同。有关详细信息，请参阅 Balabdaoui 等人的补充资料中的附录 $E_{0}$ (2019b)。
样条估计器证明中的相应步骙由以下引理给出。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECON2515

Posted on 2022年6月20日2022年6月20日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|A Time-Varying Parameter Model for the M3 Velocity

In modern economies, neglecting what happens to money velocity leads to large relative errors in estimating inflation and output. Moreover, velocity, or its twin sibling, the demand for money, turns out to be highly volatile, difficult to model and hard to measure. Hence, movements in $P$ end up being dominated by unexplained movements in $V$ rather than in $M$.

Traditional theories of money demand identify income as the principal determinants of velocity. As highlighted in Friedman and Schwartz (1963), if money demand elasticity to income is greater than one, then economic growth would induce a secular downward trend in velocity, inflation and interest rates. The theoretical literature (see Orphanides and Porter 2000) also posits that velocity fluctuates with the opportunity cost of money, driven by inflation and interest rates.

A benchmark regression representing the traditional theories of money demand is presented in Bordo and Jonung (1987), updated in Bordo and Jonung (1990) and revisited using cointegration techniques by Bordo et al. (1997). This formulation is described in Hamilton (1989) using an equation such as:
$$
\log V_{i, t}=\beta_{0, i}+\xi_{i, t}+\lambda_{i} f_{t}+\beta_{1, i} i_{t}+\beta_{2, i} \pi_{t}^{e}+\beta_{3, i} \log Y_{p c_{i, t}}+\beta_{4, i} \log Y_{p c i, t}^{p}+\varepsilon_{i, t}
$$
The above model expresses the log of velocity $\left(V_{t}\right)$ as a function of the opportunity cost of holding money halances in terms of an appropriate nominal interest rate ( $\left.i_{t}\right)$, expected inflation $\left(\pi_{t}^{e}\right)$, proxied by the fitted values of a univariate autoregression for actual inflation, the log of real GNP per capita $\left(Y_{\mathrm{pc}{t}}\right)$ and its smoothed version $\left(Y{\text {pct }}^{p}\right)$ interpreted as permanent real GNP per capita. The velocity formulation is strongly based on economic theory of permanent income hypothesis (Friedman and Schwartz 1963). We expect a positive sign for permanent income as any increase in it will rise the number of transactions in the economy affecting the velocity positively. Transitory income with a positive coefficient but less than one would indicate that velocity moves pro-cyclically, which would be in line with Friedman’s permanent income hypothesis. Over the cycle, the transitory income would increase the demand for money, because cash balances serve as buffer stock, and therefore, in the long run these transitory balances would disappear, returning the coefficient to unity. As for the real interest rate, it is expected to have a positive sign as an increase in it would decrease the demand for real money balances and thus a raise in the velocity for a given level of income. Finally, the impact of inflation on velocity is ambiguous depending upon its relative influence on money balances and income growth.

商科代写|计量经济学代写Econometrics代考|Univariate Properties of the Data

Trend breaks appear to be prevalent in macroeconomic time series, and unit root tests therefore need to make allowance for these if they are to avoid the serious effects that unmodeled trend breaks have on power. ${ }^{16}$ Consequently, when testing for a unit

root it has become a matter of regular practice to allow for this kind of deterministic structural change.

In order to avoid this pitfall, we run tests to assess whether structural breaks are present in the series. This testing problem has been addressed by Perron and Yabu (2009), who define a test statistic that is based on a quasi-GLS approach using an autoregression for the noise component, with a truncation to 1 when the sum of the autoregressive coefficients is in some neighborhood of 1 , along with a bias correction. For given break dates, one constructs the $F$-test (Exp $-W_{F S}$ ) for the null hypothesis of no structural change in the deterministic components. The final statistic uses the Exp functional of Andrews and Ploberger (1994). Perron and Yabu (2009) specify three different models depending on whether the structural break only affects the level (Model I), the slope of the trend (Model II) or the level and the slope of the time trend (Model III). The computation of these statistics, which are available in Table 1 , shows that we find more evidence against the null hypothesis of no structural break with Model III.

The analysis shows instabilities in the money velocity for all the countries with two exceptions, Spain and France. Therefore, in a second step, we have computed the unit root test statistics in Carrion-i Silvestre et al. (2009). The unit root tests in Carrion-i Silvestre et al. (2009) allow for multiple structural breaks under both the null and alternative hypotheses which make especially suitable for our purpose, since we have obtained evidence in favor of the presence of structural breaks regardless of their order of integration. The results of all these statistics are reported in Table 3 . As can be seen, the unit root tests proposed by Carrion-i Silvestre et al. (2009) led to the non-rejection of the null hypothesis of a unit root in most of cases at the $5 \%$ level of significance. ${ }^{17}$ Our conclusion is that the income velocity variable for the countries considered has unit roots with breaks both in levels and in most of the cases.

商科代写|计量经济学代写Econometrics代考|Linear Cointegration Specification for Wealth Effects

First, we specify the consumption-wealth relationship differently while assessing for the effect of total wealth (Eq. 1) and that of disaggregate wealth (Eq. 2) since households might react differently to shocks on financial assets or on property prices. Indeed, in line with the theoretical framework from Lettau and Ludvigson $(2001$, 2004), we can write the following log-linear model:
$$
\begin{gathered}
c_{t}=\alpha+\beta_{1} T W_{t}+\beta_{2} y_{t}+\varepsilon_{t} \
c_{t}=\alpha+\beta_{1} F W_{t}+\beta_{2} H W_{t}+\beta_{3} y_{t}+\varepsilon_{t}
\end{gathered}
$$
where: $c_{t}, W_{t}, \mathrm{FW}{t}, \mathrm{HW}{t}$ and $y_{t}$ refer to consumption, total wealth (TW), financial wealth (FW), housing wealth (HW) and disposable income respectively. All variables are in logarithm.

Considering Lettau and Ludvigson (2001, 2004) in line with the life-cycle approach of wealth effects, Eqs. (1) and (2) are estimated in a cointegration framework. Indeed, Lettau and Ludvigson (2001) used the Campbell and Mankiw (1989) micro-funded model of consumption to show that consumption tends to a stationary fraction of wealth. The so-called cointegration-based approach from Lettau and Ludvigson $(2001,2004)$ lead directly to the estimations of wealth effects elasticities.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|A Time-Varying Parameter Model for the M3 Velocity

在现代经济中，忽视货币流通速度会导致在估计通货膨胀和产出时出现较大的相对误差。此外，速度，或者它的孪生兄弟，对货币的需求，被证明是高度波动的，难以建模和衡量。因此，在磷最终被无法解释的运动所支配在而不是在米.

传统的货币需求理论将收入确定为流通速度的主要决定因素。正如 Friedman 和 Schwartz（1963）所强调的，如果货币需求对收入的弹性大于 1，那么经济增长将导致速度、通货膨胀和利率的长期下降趋势。理论文献（参见 Orphanides 和 Porter 2000）还假设，在通货膨胀和利率的驱动下，流通速度随货币的机会成本而波动。

Bordo 和 Jonung (1987) 提出了代表传统货币需求理论的基准回归，在 Bordo 和 Jonung (1990) 中进行了更新，并由 Bordo 等人使用协整技术重新审视。(1997)。该公式在 Hamilton (1989) 中使用如下等式进行了描述：

日志⁡在一世,吨=b0,一世+X一世,吨+λ一世F吨+b1,一世一世吨+b2,一世圆周率吨和+b3,一世日志⁡是pC一世,吨+b4,一世日志⁡是pC一世,吨p+e一世,吨
上述模型表示速度的对数(在吨)作为以适当名义利率持有货币差额的机会成本的函数（一世吨), 预期通货膨胀(圆周率吨和)，由实际通货膨胀的单变量自回归的拟合值代表，实际人均国民生产总值的对数(是pC吨)及其平滑版本(是百分比 p)解释为永久实际人均国民生产总值。速度公式强烈基于永久收入假设的经济理论（弗里德曼和施瓦茨，1963 年）。我们预计永久收入将出现积极迹象，因为它的任何增加都会增加经济中对速度产生积极影响的交易数量。具有正系数但小于 1 的暂时性收入表明速度呈顺周期性移动，这与弗里德曼的永久收入假设一致。在这个周期中，暂时性收入会增加对货币的需求，因为现金余额作为缓冲存量，因此，从长远来看，这些暂时性余额会消失，使系数恢复为一。至于实际利率，预计它会有一个积极的迹象，因为它的增加会减少对实际货币余额的需求，从而提高给定收入水平的流通速度。最后，通货膨胀对流通速度的影响是模棱两可的，这取决于它对货币余额和收入增长的相对影响。

商科代写|计量经济学代写Econometrics代考|Univariate Properties of the Data

趋势中断似乎在宏观经济时间序列中很普遍，因此，如果要避免未建模的趋势中断对功率的严重影响，单位根检验需要考虑这些因素。16因此，当测试一个单元时

根，允许这种确定性的结构变化已成为常规做法。

为了避免这个陷阱，我们运行测试来评估系列中是否存在结构性中断。Perron 和 Yabu (2009) 已经解决了这个测试问题，他们定义了一个基于准 GLS 方法的测试统计量，使用噪声分量的自回归，当自回归系数的总和在1 的某个邻域，以及偏差校正。对于给定的休息日期，构建F-测试（经验−在F小号) 对于确定性成分没有结构变化的原假设。最终统计使用 Andrews 和 Ploberger (1994) 的 Exp 函数。Perron 和 Yabu (2009) 指定了三种不同的模型，具体取决于结构性断裂是仅影响水平（模型 I）、趋势斜率（模型 II）还是时间趋势的水平和斜率（模型 III）。表 1 中提供的这些统计数据的计算表明，我们发现了更多证据反对模型 III 没有结构中断的零假设。

分析显示，除西班牙和法国这两个国家外，所有国家的货币流通速度都不稳定。因此，在第二步中，我们计算了 Carrion-i Silvestre 等人的单位根检验统计量。（2009 年）。Carrion-i Silvestre 等人的单位根检验。（2009）允许在特别适合我们的目的的零假设和替代假设下存在多个结构中断，因为我们已经获得了支持结构中断存在的证据，而不管它们的整合顺序如何。所有这些统计的结果报告在表 3 中。可以看出，Carrion-i Silvestre 等人提出的单位根检验。（2009）导致在大多数情况下不拒绝单位根的原假设5%显着性水平。17我们的结论是，所考虑国家的收入速度变量具有单位根，在水平和大多数情况下都有中断。

商科代写|计量经济学代写Econometrics代考|Linear Cointegration Specification for Wealth Effects

首先，我们在评估总财富（等式 1）和分解财富（等式 2）的影响时，以不同的方式指定了消费与财富的关系，因为家庭可能对金融资产或房地产价格的冲击做出不同的反应。确实，符合 Lettau 和 Ludvigson 的理论框架(2001, 2004)，我们可以写出以下对数线性模型：

C吨=一个+b1吨在吨+b2是吨+e吨 C吨=一个+b1F在吨+b2H在吨+b3是吨+e吨
在哪里：C吨,在吨,F在吨,H在吨和是吨分别指消费、总财富（TW）、金融财富（FW）、住房财富（HW）和可支配收入。所有变量均为对数。

考虑 Lettau 和 Ludvigson (2001, 2004) 与财富效应的生命周期方法一致，方程式。(1) 和 (2) 在协整框架中进行估计。事实上，Lettau 和 Ludvigson (2001) 使用 Campbell 和 Mankiw (1989) 的小额消费模型来表明消费趋向于财富的固定部分。Lettau 和 Ludvigson 所谓的基于协整的方法(2001,2004)直接导致财富效应弹性的估计。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECON 2517

Posted on 2022年6月20日2022年6月20日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|The Inflation Puzzle and Money Velocity in the EA

The quantity theory of money (QTM) predicts a positive relationship between monetary growth and inflation. However, even if inflation truly were a monetary phenomenon in the long run, as stated in Friedman (1963) seminal book, a conventional vector cointegration approach does not necessarily identify the long-run relation between money and prices correctly, because it neglects the structural development of the velocity of money. Since excess supply and demand of money are captured by transitory movements of velocity in a world where real and nominal rigidities

prevail, the identification of excess liquidity that endangers price stability is tied to the identification of equilibrium velocity.

In general, evidence from cross-country studies strongly supports the one-to-one correlation of average money growth and average inflation. However, the impact of money on prices is hard to identify within one country. De Grauwe and Polan (2005) have argued that the long-run link between nominal money growth and inflation might be much looser than commonly assumed in countries which have operated in moderate inflation environments as it is the case of the EA.

Flexible inflation targeting implies that the central bank attempts to reach the target gradually in the medium term and not in the immediate period. As recently stressed by Cochrane (2017), existing theories of inflation make straight predictions. The Keynesian school argues that velocity is a highly fluctuating variable which is significantly affected by economic policies. As a result, changes in velocity could nullify the effects of monetary policy. They stress that the velocity of money is severely affected by demand management policies; hence, it is a non-stationary yariable. Furthermore, they argue that the movements of velocity are the opposite of the movement of money supply. Interest rate is also regarded as one of the variables influencing velocity. The opposite forecast is made by monetarist models, who predict that, as provided the velocity is “stable” in the long run, a massive increase in reserves must lead to galloping inflation. Yet, none of these predictions have proved right. This issue was already central to the debates of the 1950 s and 1960 setween Keynesians and monetarists. Keynesians thought that at the zero rates of the Great Depression, money and bonds were perfect substitutes, so monetary policy could do nothing, and advocated fiscal stimulus instead. On the contrary, monetarists held that additional money, even at zero rates, would be stimulative; therefore, the failure to provide additional money was the big monetary policy mistake of that time. The view that inflation is always a monetary phenomenon has a long tradition based on the quantity theory of money. In its simplest form, the QTM states that changes in money supply growth are followed by equal changes in the inflation rate and, through the force of the Fisher effect, in the nominal interest rate.
According to the monetarist doctrine:
$$
M V=P Y
$$

商科代写|计量经济学代写Econometrics代考|State-Space Models and Time-Varying Parameter Models

State-space representation of a linear system constitutes a statistical framework for modeling the dynamics of a $(n \times 1)$ vector of variables observed at regular time intervals $t, y_{t}$, in terms of a possibly unobserved (or state) $(r \times 1)$ vector $\xi_{t}{ }^{10}$ The origin of state-space modeling is intimately linked with the Kalman filter, a recursive algorithm for generating minimum mean square error forecasts in state-space models.
The measurement equation models the dynamics of the observable variables $y_{t}$, possibly measured with noise, that are assumed to be related to the state vector, providing information on $\xi_{t}$. It takes the following general form:
$$
\underset{(n \times 1)}{y_{t}}=\underset{(n \times k)}{\mathbf{A}{(k \times 1)}^{\top}} x{t}+\underset{(n \times r)}{\mathbf{H}^{\top}} \xi_{(r \times 1)}+\underset{(n \times 1)}{w_{t}}
$$
where $y_{t}$ represents an $(n \times 1)$ vector of variables that are observed at date $t$ and $x_{t}$ represents a $(k \times 1)$ vector of exogenous determinants, their coefficients being included in the $(k \times n)$ matrix $A . H$ is an $(r \times n)$ matrix of coefficients for the $(r \times 1)$ vector of unobserved components $\xi_{r}$. Finally, the measurement or observational error, $w_{t}$, is an $(n x 1)$ vector assumed to be i.i.d. $N(0, R)$, independent of $\xi_{t}$ and $\nu_{t}$ and for $t=1,2, \ldots$, where $$
E\left(w_{t} w_{t}^{\top}\right)=\underset{(n \times n)}{R}
$$
and variance covariance equal to
$$
E\left(w_{t} w_{\tau}^{\top}\right)= \begin{cases}\mathrm{R} & \text { for } t=\tau \ 0 & \text { for } t \neq \tau\end{cases}
$$
The state-transition equation describes the evolution of the underlying unobserved states that determine the time series behavior, generated by a linear stochastic difference representation through a first-order Markov process, such as in 11 :
where $F$ denotes an $(r \times r)$ state-transition matrix, which applies the effect of each system state parameter at time $t-1$ on the system state at time $t, \xi_{t}$, and $Z_{t}$ is a $(s \times 1)$ vector containing any control inputs, either deterministic (drift and/or deterministic trend) or stochastic. If present, control inputs affect the state through the $(r \times s)$ control input matrix, $B$, which applies the effect of each control input parameter in the vector on the state vector.

The introduction of stochastic control inputs is common practice in the literature on control engineering where this concept was coined. Basically, the idea is to simulate the effect of changes in the control variable on a system, namely the state vector. ${ }^{11}$ Despite their many potential uses, empirical economic research generally has employed simple state-transition equations, where the unobserved component evolves as a random walk process and no control inputs are present.

商科代写|计量经济学代写Econometrics代考|A Panel Time-Varying State-Space Extension

In this subsection, we extend the previous time-varying parameter model to a panel setting. Our main goal is to explore the use of the state-space modelization and the Kalman filter algorithm as an effective method for combining time series in a panel. This flexible structure allows the model specification to be affected by different potential sources of cross-sectional heterogeneity. This approach can be a superior alternative to the estimation of the model in unstacked form, commonly employed when there is a small number of cross sections.
The general model can be written as follows:
$$
y_{i, t}=x_{i, t}^{\top} \bar{\beta}+x_{i, t}^{\top} \xi_{i, t}+\omega_{t}
$$
or in matrix form:
$$
\underset{(n \times i)}{y}=\underset{(n \times n * k)}{\mathbf{A}^{\top}} \times \underset{(n \times k \times t)}{x}+\underset{(n \times r)}{\mathbf{H}^{\top}(x) \times} \underset{(r \times i)}{\xi}+\underset{(n \times i)}{w}
$$
representing the measurement equation for a $y_{t} \in \mathbb{R}^{n}$ vector containing the dependent variable for a panel of countries. $x_{t} \in \mathbb{R}^{k \times n}$ is a vector of $k$ exogenous variables, including either (or both) stochastic or deterministic components. The unobserved vector $\xi_{t} \in \mathbb{R}^{r}$ influences the dependent variable through a varying $H^{\top}\left(x_{t}\right)(n \times r)$ matrix, whose simplest form is $H^{\top}\left(x_{t}\right)=x_{t}$. Finally, $w_{t} \in \mathbb{R}^{n}$ represents the $(n \times 1)$ vector of $N$ measurement errors.

The specification of the model in Eq. (19) relies on a mean-reverting-type modelization of the measurement equation, which also allows for the inclusion of fixed parameters, in matrix $\mathbf{A}$. Each of the fixed parameters can be modeled, either as a common parameter for all the agents in the panel, $\bar{\beta}$, or, alternatively, as a countryspecific coefficient, $\bar{\beta}{i}$. The model also includes time-varying parameters $\left(\xi{t}\right)$ for some of the regressors that eventually can be interpreted as deviations from the mean parameters $\left(\left(\beta_{i t}-\bar{\beta}{i}\right)=\xi{t}\right)$.

The measurement equation for each $i$ th element in the $t$ th period $\left(y_{i, t}\right)$ in the vector of the dependent variable can be expressed as follows:
$y_{i, t}=\sum_{\mathrm{ks}=\mathrm{ksmin}}^{\mathrm{ksmax}} \bar{\beta}{\mathrm{ks}, i} x{\mathrm{ks}, i, t}+\sum_{\mathrm{kc}=\mathrm{kcmin}}^{\mathrm{kmmax}} \bar{\beta}{\mathrm{kc}} x{\mathrm{kc}, i, t}$
$+\sum_{\mathrm{kv}=\mathrm{kvmin}}^{\operatorname{kvmax}} \xi_{\mathrm{kv}, i t} x_{\mathrm{kv}, i, t}+h_{i} \xi_{r, i t}+w_{(n \times 1)}$

计量经济学代考

商科代写|计量经济学代写Econometrics代考|The Inflation Puzzle and Money Velocity in the EA

货币数量论 (QTM) 预测货币增长与通货膨胀之间存在正相关关系。然而，即使从长远来看，通货膨胀确实是一种货币现象，正如弗里德曼（1963）的开创性著作中所述，传统的向量协整方法不一定能正确识别货币与价格之间的长期关系，因为它忽略了结构货币流通速度的发展。由于在一个真实和名义刚性存在的世界中，货币的过度供求是由速度的短暂运动捕获的

普遍认为，对危及价格稳定的过剩流动性的识别与对均衡速度的识别是联系在一起的。

一般来说，跨国研究的证据强烈支持平均货币增长和平均通货膨胀的一对一相关性。然而，货币对价格的影响在一个国家内很难确定。De Grauwe 和 Polan (2005) 认为，名义货币增长与通胀之间的长期联系可能比在温和通胀环境中运行的国家通常假设的要宽松得多，就像 EA 一样。

灵活的通胀目标意味着央行试图在中期而不是短期内逐步达到目标。正如 Cochrane (2017) 最近强调的那样，现有的暴胀理论做出了直接的预测。凯恩斯学派认为，速度是一个高度波动的变量，受经济政策的影响很大。因此，速度的变化可能会抵消货币政策的影响。他们强调货币流通速度受到需求管理政策的严重影响；因此，它是一个非平稳的 yariable。此外，他们认为速度的运动与货币供应的运动相反。利率也被视为影响速度的变量之一。货币主义模型做出了相反的预测，他们预测，只要速度从长远来看是“稳定的”，储备的大量增加必然会导致通货膨胀的迅猛发展。然而，这些预测都没有被证明是正确的。这个问题已经成为 1950 年代和 1960 年代凯恩斯主义者和货币主义者之间争论的核心。凯恩斯主义者认为，在大萧条的零利率下，货币和债券是完美的替代品，货币政策无能为力，反而提倡财政刺激。相反，货币主义者认为，即使是零利率，额外的货币也会具有刺激作用。因此，未能提供额外的货币是当时的重大货币政策错误。基于货币数量论的通货膨胀始终是一种货币现象的观点由来已久。以最简单的形式，
根据货币主义学说：

米在=磷是

商科代写|计量经济学代写Econometrics代考|State-Space Models and Time-Varying Parameter Models

线性系统的状态空间表示构成了用于建模动态的统计框架(n×1)以固定时间间隔观察到的变量向量吨,是吨，就可能未观察到的（或状态）而言(r×1)向量X吨10状态空间建模的起源与卡尔曼滤波器密切相关，卡尔曼滤波器是一种用于在状态空间模型中生成最小均方误差预测的递归算法。
测量方程模拟可观察变量的动态是吨，可能与噪声一起测量，假设与状态向量有关，提供关于X吨. 它采用以下一般形式：

是吨(n×1)=一个(ķ×1)⊤(n×ķ)X吨+H⊤(n×r)X(r×1)+在吨(n×1)
在哪里是吨代表一个(n×1)在日期观察到的变量向量吨和X吨代表一个(ķ×1)外生行列式的向量，它们的系数包含在(ķ×n)矩阵一个.H是一个(r×n)的系数矩阵(r×1)未观察到的分量的向量Xr. 最后，测量或观察误差，在吨，是一个(nX1)假定为 iid 的向量ñ(0,R)，独立于X吨和ν吨并且对于吨=1,2,…，在哪里

和(在吨在吨⊤)=R(n×n)
和方差协方差等于

和(在吨在τ⊤)={R 为了吨=τ 0 为了吨≠τ
状态转移方程描述了确定时间序列行为的潜在未观察状态的演变，由线性随机差异表示通过一阶马尔可夫过程生成，例如在 11 中
：F表示一个(r×r)状态转移矩阵，它在时间应用每个系统状态参数的影响吨−1在当时的系统状态吨,X吨，和从吨是一个(s×1)包含任何控制输入的向量，无论是确定性的（漂移和/或确定性趋势）还是随机的。如果存在，控制输入通过(r×s)控制输入矩阵，乙，它将向量中每个控制输入参数的影响应用于状态向量。

在创造这个概念的控制工程文献中，引入随机控制输入是常见的做法。基本上，这个想法是模拟控制变量的变化对系统的影响，即状态向量。11尽管它们有许多潜在的用途，但实证经济学研究通常采用简单的状态转移方程，其中未观察到的部分演变为随机游走过程，并且不存在控制输入。

商科代写|计量经济学代写Econometrics代考|A Panel Time-Varying State-Space Extension

在本小节中，我们将之前的时变参数模型扩展到面板设置。我们的主要目标是探索使用状态空间建模和卡尔曼滤波器算法作为在面板中组合时间序列的有效方法。这种灵活的结构允许模型规范受到横截面异质性的不同潜在来源的影响。这种方法可以更好地替代以非堆叠形式估计模型，通常在横截面数量较少时使用。
一般模型可以写成如下：

是一世,吨=X一世,吨⊤b¯+X一世,吨⊤X一世,吨+ω吨
或以矩阵形式：

是(n×一世)=一个⊤(n×n∗ķ)×X(n×ķ×吨)+H⊤(X)×(n×r)X(r×一世)+在(n×一世)
表示 a 的测量方程是吨∈Rn包含一组国家的因变量的向量。X吨∈Rķ×n是一个向量ķ外生变量，包括（或两者）随机或确定性成分。未观察到的向量X吨∈Rr通过变化影响因变量H⊤(X吨)(n×r)矩阵，其最简单的形式是H⊤(X吨)=X吨. 最后，在吨∈Rn代表(n×1)向量ñ测量误差。

方程式中模型的规格。(19) 依赖于测量方程的均值回复型建模，它还允许在矩阵中包含固定参数一个. 每个固定参数都可以建模，或者作为面板中所有代理的公共参数，b¯，或者，作为一个国家特定的系数，b¯一世. 该模型还包括时变参数(X吨)对于最终可以解释为与平均参数的偏差的一些回归量((b一世吨−b¯一世)=X吨).

每个测量方程一世中的第一个元素吨期(是一世,吨)在因变量的向量中可以表示为：
$y_{i, t}=\sum_{\mathrm{ks}=\mathrm{ksmin}}^{\mathrm{ksmax}}\bar{\beta} {\mathrm{ks}, i} x {\mathrm{ks},i,t}+\sum_{\mathrm{kc}=\mathrm{kcmin}}^{\mathrm{kmmax}} \bar{\beta } {\math{kc}} x {\math{kc}, i, t}+\sum_{\mathrm{kv}=\mathrm{kvmin}}^{\operatorname{kvmax}} \xi_{\mathrm{kv}, it} x_{\mathrm{kv}, i, t}+h_{ i} \xi_{r, it}+w_{(n \times 1)}$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECOM30002

Posted on 2022年6月20日2022年6月20日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|T-ARDL Model

Finally, as an extension to the classical approach, we propose the T-ARDL model. ${ }^{4}$ The linear ARDL is a classical method used to capture persistence in time series data, and Pesaran et al. (2001) proposed a bounds test to detect cointegration based on the ARDL. An advantage of this method is its ability to determine the presence of cointegration without prior knowledge of the explanatory variables being stationary $(I(0))$ or non-stationary $(I(1))$. This is a useful feature in studies of bubbles, as economies often experience periods of tranquility and mild bubbles.

Pesaran et al. (2001) proposed five specifications of the ARDL with a different combination of deterministic terms. Here, we use the most popular model in financial research, with an unrestricted constant and no trend. For asset prices $(y)$, we can express this as
$$
\Delta y_{t}=a+c y_{t-1}+\boldsymbol{b} \boldsymbol{x}{t-1}+\sum{i=1}^{p-1} \boldsymbol{d}{i} \Delta z{t-i}+\boldsymbol{f}^{\prime} \Delta \boldsymbol{x}{t}+u{t}
$$
where $a, c, \boldsymbol{b}, \boldsymbol{d}$, and $\boldsymbol{f}$ are the parameters to estimate by the ordinary least squares (OLS) for time $(t=1, \ldots, T)$, and $u_{t}$ is the residual $\left(u_{t} \sim N\left(0, \sigma^{2}\right)\right)$. $x$ is a matrix of explanatory variables and $z=[y, x]$. The appropriate lag length $(p)$ is determined such that it captures the data generating process of $y$. We can study the cointegrated relationship between $y$ and $\boldsymbol{x}$ by analyzing the time series properties of $c y_{t-1}+\boldsymbol{b} \boldsymbol{x}_{t-1}$, known as the ECM. We can test the null hypothesis of no ECM $(c=0$ and $\boldsymbol{b}=\mathbf{0})$ by the $F$ test or $c=0$ the $t$ test.

As the conventional asymptotic distribution is invalid here, Pesaran et al. (2001) provided critical values based on Monte Carlo simulations for a different dimension of $x$. Because economic variables may be $I(0)$ or $I(1)$, the critical values for these tests have both lower and upper bounds. For the $F$ tests, the lower bound is determined when the data are $I(0)$, and the latter when they are $I(1)$. Test statistics above the upper bound imply evidence of cointegration, and those below the lower bound suggest the absence of cointegration. Test statistics between these bounds are inconclusive. For the $t$ tests, the lower bound is determined when the data are $I(1)$, as the test statistics are expected to he negative. The urper hound is designed for $I(0)$ data.

Howcver, this bounds tssting approach is inappropriate for a study of bubblcs because it investigates the possibilities of both negative and positive bubbles. That is, like the standard unit root tests, it considers bubbles even when housing prices are low. To treat bubbles as high price phenomena, we introduce nonlinearity into the ARDL as follows:
$$
\begin{aligned}
\Delta y_{t} &=\alpha_{1} g+\alpha_{2} \tilde{g}+c_{1} g y_{t-1}+c_{2} \tilde{g} y_{t-1}+b_{1} g \boldsymbol{x}{t-1}+b{2} \tilde{g} \boldsymbol{x}{t-1}+\sum{i=1}^{p-1} d_{i} \Delta z_{t-i} \
& \boldsymbol{f} \Delta \boldsymbol{x}{t}+u{t}
\end{aligned}
$$
where $g$ and $\tilde{g}$ are dummy variables that distinguish the regimes, and Eq. (15) has two (upper $(g)$ and lower $(\widetilde{g})$ ) regimes. When these regimes are determined by a certain threshold point $(w)$, the dummies are defined as follows:
$$
g=\left{\begin{array}{ll}
1 & \text { if } y>w \
0 & \text { otherwise }
\end{array} \text { and } \tilde{g}= \begin{cases}1 & \text { if } y \leq w \
0 & \text { otherwise }\end{cases}\right.
$$

商科代写|计量经济学代写Econometrics代考|Classical Test Approaches

We use three left-tailed unit root tests (the ADF, Phillips-Perron, and DF-GLS) that are popular univariate tests in economic and financial research. These tests investigate the null hypothesis that the price-to-rent ratio in levels follows the unit root process $(I(1))$, and a rejection of this null provides evidence of stationarity in this ratio, and thus cointegration between housing prices and rents. Therefore, a failure to reject

this null hypothesis indicates that rents cannot explain the long-term housing price movements, thereby suggesting the presence of mild bubbles. We conduct these tests for the ratios in levels and first differences in order to check the order of integration.
Table 3 summarizes the test statistics for the Euro area, Japan, the UK, and the USA. The results suggest that these ratios follow the unit rovl process. Using the $5 \%$ critical values, we often fail to reject the null hypothesis for the data in levels, but can do so for the differenced data. Therefore, we conclude that mild bubbles existed in all countries, suggesting that rental increases are not always associated with housing price inflation, and there must be some periods when housing prices deviate substantially from the trend in rentals. Obviously, these tests preclude a possibility of explosive bubbles, and moreover, we need to pay attention to the composition of economic fundamentals. However, these outcomes are consistent with our expectations that all housing markets experienced chaotic moments during our sample period.
The potential non-stationary periods identified by the classical method are shaded in Fig. 3. We present two graphs for each country, and the upper figures (denoted as OLS estimates) are obtained from the classical method. As explained earlier, a drawback of this approach is the lack of statistical power to differentiate between hypotheses and that it allows for negative bubbles. For consistency with the standard phenomenon of financial bubbles, we should consider only the positive bubbles (above the horizontal line) as relevant to financial bubbles. Thus, only positive bubble periods are highlighted in gray in this figure and are potential bubble periods because these classical tests are not designed to identify the exact periods of bubbles while they give us evidence of mild bubbles during the sample period. ${ }^{5}$

商科代写|计量经济学代写Econometrics代考|Explosive Test Approaches

Next, we conduct explosive unit root tests for each country and for a group of countries. From the classical tests, we already know that the price-to-rent ratio is nonstationary and, in fact, implies the presence of mild bubbles. However, when it is not known, we propose the following general steps to reach a conclusion. In short, explosive unit root tests should be conducted if and only if the classical approaches show the data $(y)$ to be a non-stationary process.

Failing to reject the null hypothesis that price-to-rent ratios are $I$ (1) by the classical tests, we eliminated the possibility of market tranquility and thus conduct explosive unit root tests for each market. Table 4 summarizes the results from the right-tailed tests (RADF, SADF, and GSADF) for each country. The null hypothesis of these tests is consistent with our finding of a random walk price-to-rent ratio from the classical tests. The explosive test results differ somewhat by test type, but the null hypothesis is rejected frequently using the $p$-values obtained from 1000 replications, which is evidence in favor of explosive bubbles in all markets. The results from the GSADF are also depicted in Fig. 4. GSADF statistics greater than $95 \%$ critical values suggest the presence of explosive bubbles, which are also shaded in this figure, and generally

identify explosive bubble periods when housing prices are high. The timing and duration of explosive bubbles differ among countries, but many countries seemed to experience explosive bubbles before the Lehman Brothers collapse in September 2018. The presence of real estate markets is consistent with the results from the classical approaches, but here we have evidence of explosive bubbles, which the classical approach cannot capture.

Given the cross-sectional dependence in international housing markets, we also conduct a multi-country analysis using two methods. First, we calculate panel GSADF statistics using the data of 12 countries: Canada, Denmark, Finland, France, Germany, Ireland, Italy, Japan, the Netherlands, Switzerland, the UK, and the USA. Second, in order to check the robustness of the findings from the panel explosive tests, we conduct the explosive unit root tests for a price-to-rent index that covers OECD countries. ${ }^{6}$ These analyses help us identify explosive bubbles in the global housing market.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|T-ARDL Model

最后，作为经典方法的扩展，我们提出了 T-ARDL 模型。4线性 ARDL 是用于捕获时间序列数据中持久性的经典方法，Pesaran 等人。(2001) 提出了一个边界检验来检测基于 ARDL 的协整。这种方法的一个优点是它能够确定协整的存在，而无需事先知道解释变量是固定的(我(0))或非固定(我(1)). 这在泡沫研究中是一个有用的特征，因为经济体经常经历平静和温和泡沫的时期。

佩萨兰等人。(2001) 提出了五种 ARDL 规范，它们具有不同的确定性术语组合。在这里，我们使用了金融研究中最流行的模型，具有不受限制的常数，没有趋势。对于资产价格(是), 我们可以表示为
$$
\Delta y_{t}=a+c y_{t-1}+\boldsymbol{b} \boldsymbol{x} {t-1}+\sum {i=1}^{ p-1} \boldsymbol{d} {i} \Delta z {ti}+\boldsymbol{f}^{\prime} \Delta \boldsymbol{x} {t}+u {t}
$$
其中一个,C,b,d，和F是通过普通最小二乘法 (OLS) 估计时间的参数(吨=1,…,吨)，和在吨是残差(在吨∼ñ(0,σ2)). X是解释变量的矩阵，并且和=[是,X]. 适当的滞后长度(p)被确定为它捕获的数据生成过程是. 我们可以研究两者之间的协整关系是和X通过分析时间序列属性C是吨−1+bX吨−1，称为 ECM。我们可以检验没有 ECM 的原假设(C=0和b=0)由F测试或C=0这吨测试。

由于传统的渐近分布在这里无效，Pesaran 等人。（2001）基于蒙特卡罗模拟提供了不同维度的临界值X. 因为经济变量可能我(0)或者我(1)，这些测试的临界值都有下限和上限。为了F测试，下限在数据被确定时确定我(0)，而后者当它们是我(1). 高于上限的检验统计量暗示协整的证据，低于下限的检验统计量表明不存在协整。这些界限之间的测试统计数据是不确定的。为了吨测试，下限在数据被确定时确定我(1)，因为测试统计量预计为负。urper 猎犬专为我(0)数据。

但是，这种边界测试方法不适合研究气泡，因为它研究了负气泡和正气泡的可能性。也就是说，就像标准的单位根检验一样，即使房价很低，它也会考虑泡沫。为了将泡沫视为高价现象，我们将非线性引入 ARDL，如下所示：

Δ是吨=一个1G+一个2G~+C1G是吨−1+C2G~是吨−1+b1GX吨−1+b2G~X吨−1+∑一世=1p−1d一世Δ和吨−一世 FΔX吨+在吨
在哪里G和G~是区分这些制度的虚拟变量，方程式。(15) 有两个（上(G)和更低(G~)) 制度。当这些制度由某个阈值点确定时(在)，假人定义如下：
$$
g=\left{

1 如果是>在 0 否则 \text { 和 } \tilde{g}=

{1 如果是≤在 0 否则 \正确的。
$$

商科代写|计量经济学代写Econometrics代考|Classical Test Approaches

我们使用三个左尾单位根检验（ADF、Phillips-Perron 和 DF-GLS），它们是经济和金融研究中流行的单变量检验。这些检验调查了水平价格租金比遵循单位根过程的原假设(我(1))，并且拒绝该零值提供了该比率的平稳性的证据，从而证明了房价和租金之间的协整。因此，拒绝失败

这个零假设表明租金不能解释长期房价变动，从而表明存在温和泡沫。我们对水平比率和一阶差分进行这些测试，以检查积分顺序。
表 3 总结了欧元区、日本、英国和美国的测试统计数据。结果表明，这些比率遵循单位 rovl 过程。使用5%临界值时，我们经常无法拒绝水平数据的原假设，但可以拒绝差异数据。因此，我们得出结论，所有国家都存在温和的泡沫，这表明租金上涨并不总是与房价上涨相关，一定存在房价大幅偏离租金趋势的时期。显然，这些测试排除了爆发泡沫的可能性，此外，我们还需要关注经济基本面的构成。然而，这些结果与我们的预期是一致的，即所有房地产市场在我们的样本期间都经历了混乱的时刻。
经典方法确定的潜在非平稳期在图 3 中用阴影表示。我们为每个国家提供了两个图表，上面的数字（表示为 OLS 估计值）是从经典方法中获得的。如前所述，这种方法的一个缺点是缺乏区分假设的统计能力，并且它允许出现负泡沫。为了与金融泡沫的标准现象保持一致，我们应该只考虑正泡沫（水平线以上）与金融泡沫相关。因此，在该图中，只有积极的泡沫期以灰色突出显示，并且是潜在的泡沫期，因为这些经典测试并非旨在识别泡沫的确切时期，而它们在样本期间为我们提供了轻度泡沫的证据。5

商科代写|计量经济学代写Econometrics代考|Explosive Test Approaches

接下来，我们对每个国家和一组国家进行爆炸单位根检验。从经典测试中，我们已经知道房价租金比是非平稳的，实际上意味着存在温和的泡沫。但是，当未知时，我们提出以下一般步骤来得出结论。简而言之，当且仅当经典方法显示数据时，才应进行爆炸单位根检验(是)是一个非平稳过程。

未能拒绝房价租金比为我(1)通过经典检验，我们排除了市场平静的可能性，从而对每个市场进行爆炸单位根检验。表 4 总结了每个国家的右尾检验（RADF、SADF 和 GSADF）的结果。这些测试的零假设与我们从经典测试中发现的随机游走价格租金比一致。爆炸性检验结果因检验类型而有所不同，但零假设经常被拒绝使用p- 从 1000 次重复中获得的值，这是支持所有市场都存在爆炸性泡沫的证据。图 4 还描述了 GSADF 的结果。 GSADF 统计量大于95%临界值表明存在爆炸性气泡，在该图中也有阴影，通常

确定房价高企时的爆炸性泡沫时期。爆发泡沫的时间和持续时间因国家而异，但许多国家似乎在 2018 年 9 月雷曼兄弟倒闭之前经历了爆发泡沫。房地产市场的存在与经典方法的结果一致，但这里我们有证据表明爆炸性气泡，经典方法无法捕获。

鉴于国际房地产市场的横截面依赖性，我们还使用两种方法进行了多国分析。首先，我们使用 12 个国家的数据计算面板 GSADF 统计数据：加拿大、丹麦、芬兰、法国、德国、爱尔兰、意大利、日本、荷兰、瑞士、英国和美国。其次，为了检查面板爆炸测试结果的稳健性，我们对涵盖经合组织国家的房价租金指数进行了爆炸单位根测试。6这些分析有助于我们识别全球房地产市场的爆炸性泡沫。

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非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

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MATLAB代写

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MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
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EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECON 2504

Posted on 2022年6月20日2022年6月20日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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
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Foundations of Data Science 数据科学基础

商科代写|计量经济学代写Econometrics代考|Classical Approaches

Left-tailed integration tests are classical approaches. Indeed, the majority of previous analyses used this conventional approach; in particular, the relationship between housing prices and their economic fundamentals was investigated by a cointegration method (Engle and Granger 1987). The concept of cointegration is widely accepted by economists who established a theoretical framework to identify economic equilibrium conditions and led to Prof. Granger receiving a Nobel Prize (2003). Today, many applied studies used this concept to analyze housing markets worldwide (Hendry 1984; Meese and Wallace 2003; McGibany and Nourzad 2004; Gallin 2006; Adams and Fuss 2010; Oikarinen 2012; De Wit et al. 2013). Because most economic and financial data, including real estate prices and their economic fundamentals, follow a non-stationary process (e.g., Nelson and Plosser (1982), cointegration was considered appropriate to test their long-run relationship and bubbles.

The concept of cointegration can be summarized by rewriting it as a dynamic bivariate relationship. More specifically, to derive the long-run relationship between housing prices $(y)$ and covariates $(x)$, for the period $(t=1, \ldots, T)$, consider the following dynamic equation:
$$
y_{t}=\alpha_{0}+\rho_{1} y_{t-1}+\beta_{0} x_{t}+\beta_{1} x_{t-1}+u_{t}
$$
where the residual $u$ is normally distributed $\left(u_{t} \sim N\left(0, \sigma^{2}\right)\right)$. Both $x$ and $y$ are in natural the logarithmic form and are assumed to exhibit persistence, in line with many economic and financial variables. Then, we can transform Eq. (7) as follows:
$$
\Delta y_{t}=\alpha_{0}+\beta_{0} \Delta x_{t}+\left(\rho_{1}-1\right)\left(y_{t-1}+\frac{\beta_{0}+\beta_{1}}{\alpha_{1}-1} x_{t-1}\right)+u_{t}
$$
or simply
$$
\Delta y_{t}=a+b \Delta x_{t}+c_{1}\left(y_{t-1}+f x_{t-1}\right)+u_{t}
$$
where $\Delta$ is the difference parameter and $c_{1}=\rho_{1}-1$. When $y$ is a housing price, $\Delta y_{t}=y_{t}-y_{t-1}$ represents housing price inflation. Parameters $a, b, c_{1}$, and $f$ need to be estimated. The parameter $b$ measures the short-term sensitivity of $y$ to $x$, and $c_{1}$ measures the speed of the return to the long-run path. The parameter $f$ is a vector of cointegrating parameters that summarize the long-run relationship between $x$ and $y$, and $y_{t-1}+f x_{t-1}$ is the error correction mechanism (ECM). It is stationary, $I(0)$, in the presence of cointegration; in this case, the adjustment parameter $c_{1}$ will be $-1<c_{1}<0$ according to the Granger representation theorem (Engle and Granger 1987). A value of parameter $c_{1}$ close to $-1$ indicates a quick return to the long-run path, and a value close to 0 indicates a slow adjustment. In contrast, when there is no cointegration, $c_{1}$ will not lie within this theoretical range, which implies that there are significant deviations of prices from economic fundamentals, which provides evidence of a bubble. Because financial bubbles are unobservable and are considered leftover (i.e., residuals) in Eq. (9), bubble analyses are sensitive to what comprises economic fundamentals.

商科代写|计量经济学代写Econometrics代考|Explosive Unit Root Tests

Financial bubbles are expected to occur occasionally and be recurrent (Blanchard and Watson 1982); furthermore, housing prices may be more chaotic and integrated of an order higher than one. In these cases, the classical unit root and cointegration tests possess only a weak statistical power for detecting bubbles (Evans 1991). To address these shortcomings, Phillips and Yu (2011) proposed conceptually different statistical methods based on Bhargava (1986) and Diba and Grossman (1998). Their tests are right-tailed and aim to examine a high level of a non-stationary process based on Eq. (11). They are designed to trace the orientation and collapse of bubbles, and thus to find chaotic moments (i.e., explosive bubbles) in financial markets. These statistical tests do not aim to determine tranquil periods.

Phillips et al. (2011) is based on the right-tailed test. Their motivation is (Phillips et al. 2011, p. 206), who state that “In the presence of bubbles, $p_{t}$ is always explosive and hence cannot comove or be integrated with $d_{t}$ if $d_{t}$ is itself not explosive.” Here, $p_{t}$ is the log price, and $d_{t}$ represents the log economic fundamentals. This is a subtle difference from the view of economists who pay most attention to cointegration between prices and economic fundamentals. Whether or not prices and economic fundamentals follow a unit root or explosive process is not their major interest. Economists claim evidence of tranquility as long as prices and economic fundamentals are cointegrated, regardless of the order of integration for each variable.
This can be seen in the alternative hypotheses of statistical tests. With the same null hypothesis as that of the classical $\operatorname{ADF}\left(c_{2}=0\right)$, Phillips and Yu (2011) suggested evaluating the right-tailed alternative of an explosive unit $\left(c_{2}>0\right)$. Therefore, compared with the classical unit root tests that define bubbles as $I(1)$ under the null hypothesis, this alternative hypothesis has an implication for stronger bubbles. Thus, the explosive unit root test is conceptually different from the traditional test that looks for cointegration, that is, tranquil periods, and assumes the prevalence of financial bubbles in the market.

商科代写|计量经济学代写Econometrics代考|Panel Approach

A single-country analysis can be extended to a study of financial bubbles in a multivariate context. Panel data estimation approaches often exploit cross-sectional information and increase statistical power. A multi-country analysis may be more appropriate because housing prices are highly correlated, particularly among advanced countries (see next section).

Pavlidis et al. (2016) extended the GADF statistics originally developed for singlecountry analyses by following Im et al. (2003), who proposed a left-tailed panel unit root test by extending the conventional univariate ADF test. In their approach, test statistics calculated for each country are pooled to create a single statistic that can be used to assess the statistical hypotheses in a panel context. For country $k$ $(k=1, \ldots, K)$, we can express the panel data version of Eq. (11) as follows:
$$
\Delta y_{k, t}=\alpha_{k}+c_{k} y_{k, t-1}+\sum_{i=1}^{p} \theta_{k, i} \Delta y_{k, t-i}+\epsilon_{k, t}
$$
where $\epsilon_{k, t} \sim N\left(0, \sigma_{\epsilon_{k}}^{2}\right)$. The null hypothesis is $c_{k}=0, \forall k$ against the alternative of explosive behaviors, $c_{k}>0$ for some $k$. The noble feature of this approach is that it allows heterogeneity (i.e., $c$ ). However, a conclusion from this test becomes somewhat unclear, as the alternative hypothesis states. In other words, a rejection of the null does not necessarily mean that financial bubbles existed in all countries under investigation, but did in at least one country. To obtain a country-specific conclusion, country-wise analyses are required, as we summarized in the previous subsections.
For example, the panel GSADF can be constructed as the supremum of the panel backward SADF (BSADF). The panel BSADF is in turn obtained as the average of the SADF calculated backwardly for individual countries.
$$
\begin{aligned}
\text { Panel GSADF }\left(r_{0}\right)=& \text { sub } \quad \text { Panel } \operatorname{BSADF}{\mathrm{r}{2}}\left(\mathrm{r}{0}\right) \ \mathrm{r}{2} \in\left[\mathrm{r}_{0}, 1\right]
\end{aligned}
$$
Given the possible cross-country dependence, we follow the calculation method in Pavlidis et al. (2016) closely and use a sieve bootstrap approach. The panel approach using cross-sectional information may be useful to understand a general trend in real estate prices in global markets.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|Classical Approaches

左尾集成测试是经典方法。事实上，以前的大多数分析都使用了这种传统方法。特别是，通过协整方法研究了房价与其经济基本面之间的关系（Engle and Granger 1987）。协整的概念被经济学家广泛接受，他们建立了一个理论框架来确定经济均衡条件，并导致格兰杰教授获得诺贝尔奖（2003 年）。今天，许多应用研究使用这个概念来分析全球房地产市场（Hendry 1984；Meese 和 Wallace 2003；McGibany 和 Nourzad 2004；Gallin 2006；Adams 和 Fuss 2010；Oikarinen 2012；De Wit 等 2013）。因为大多数经济和金融数据，包括房地产价格及其经济基本面，都遵循一个非平稳过程（例如，

协整的概念可以通过将其重写为动态二元关系来概括。更具体地说，推导出房价之间的长期关系(是)和协变量(X)，该期间(吨=1,…,吨)，考虑以下动态方程：

是吨=一个0+ρ1是吨−1+b0X吨+b1X吨−1+在吨
其中残差在是正态分布的(在吨∼ñ(0,σ2)). 两个都X和是自然是对数形式，并假定表现出持久性，与许多经济和金融变量一致。然后，我们可以变换方程。(7) 如下：

Δ是吨=一个0+b0ΔX吨+(ρ1−1)(是吨−1+b0+b1一个1−1X吨−1)+在吨
或者干脆

Δ是吨=一个+bΔX吨+C1(是吨−1+FX吨−1)+在吨
在哪里Δ是差异参数和C1=ρ1−1. 什么时候是是房价，Δ是吨=是吨−是吨−1代表房价通胀。参数一个,b,C1，和F需要估计。参数b衡量短期敏感性是至X，和C1衡量回归长期路径的速度。参数F是一个协整参数的向量，总结了两者之间的长期关系X和是，和是吨−1+FX吨−1是纠错机制（ECM）。它是静止的，我(0), 在存在协整的情况下; 在这种情况下，调整参数C1将会−1<C1<0根据格兰杰表示定理（Engle and Granger 1987）。参数值C1相近−1表示快速返回长期路径，接近 0 的值表示调整缓慢。相反，当没有协整时，C1不会在这个理论范围内，这意味着价格与经济基本面存在显着偏差，这提供了泡沫的证据。因为金融泡沫是不可观察的，在方程式中被认为是剩余的（即残差）。(9)，泡沫分析对构成经济基本面的内容很敏感。

商科代写|计量经济学代写Econometrics代考|Explosive Unit Root Tests

预计金融泡沫会偶尔发生并反复出现（Blanchard 和 Watson 1982）；此外，房价可能会更加混乱和综合，高于一阶。在这些情况下，经典的单位根检验和协整检验对检测气泡仅具有微弱的统计能力（Evans 1991）。为了解决这些缺点，Phillips 和 Yu (2011) 在 Bhargava (1986) 和 Diba 和 Grossman (1998) 的基础上提出了概念上不同的统计方法。他们的测试是右尾的，旨在检查基于方程式的高水平非平稳过程。(11)。它们旨在追踪泡沫的方向和破裂，从而发现金融市场中的混乱时刻（即爆炸性泡沫）。这些统计测试的目的不是确定平静期。

菲利普斯等人。（2011）基于右尾检验。他们的动机是（Phillips et al. 2011, p. 206），他们说“在存在泡沫的情况下，p吨总是爆炸性的，因此不能与d吨如果d吨本身没有爆炸性。” 这里，p吨是对数价格，并且d吨代表对数经济基本面。这与最关注价格与经济基本面协整的经济学家的观点存在细微差别。价格和经济基本面是否遵循单位根或爆炸过程并不是他们的主要兴趣。经济学家声称，只要价格和经济基本面是协整的，无论每个变量的整合顺序如何，都可以证明是平静的。
这可以从统计检验的替代假设中看出。与经典的零假设相同ADF⁡(C2=0), Phillips 和 Yu (2011) 建议评估爆炸装置的右尾替代方案(C2>0). 因此，与将气泡定义为的经典单位根检验相比我(1)在原假设下，这个替代假设暗示了更强的泡沫。因此，爆炸单位根检验在概念上不同于寻找协整（即平静期）并假设市场上普遍存在金融泡沫的传统检验。

商科代写|计量经济学代写Econometrics代考|Panel Approach

单一国家分析可以扩展到多变量背景下的金融泡沫研究。面板数据估计方法通常利用横截面信息并增加统计能力。多国分析可能更合适，因为房价高度相关，尤其是在发达国家之间（见下一节）。

帕夫利迪斯等人。(2016) 遵循 Im 等人扩展了最初为单一国家分析开发的 GADF 统计数据。(2003)，他通过扩展传统的单变量 ADF 检验提出了左尾面板单位根检验。在他们的方法中，为每个国家/地区计算的测试统计数据汇集在一起，以创建一个单一的统计数据，可用于评估面板上下文中的统计假设。对于国家ķ (ķ=1,…,ķ)，我们可以表示方程的面板数据版本。(11) 如下：

Δ是ķ,吨=一个ķ+Cķ是ķ,吨−1+∑一世=1pθķ,一世Δ是ķ,吨−一世+εķ,吨
在哪里εķ,吨∼ñ(0,σεķ2). 原假设是Cķ=0,∀ķ反对爆炸性行为的替代方案，Cķ>0对于一些ķ. 这种方法的崇高特征是它允许异质性（即，C）。然而，正如替代假设所述，该测试的结论变得有些不清楚。换句话说，拒绝零值并不一定意味着所有接受调查的国家都存在金融泡沫，但至少存在一个国家。正如我们在前面的小节中总结的那样，为了获得针对特定国家的结论，需要进行国家分析。
例如，面板 GSADF 可以构造为面板后向 SADF (BSADF) 的上确界。反过来，面板 BSADF 是作为单个国家的反向计算的 SADF 的平均值获得的。

面板 GSADF (r0)= 子控制板 BSADF⁡r2(r0) r2∈[r0,1]
鉴于可能存在跨国依赖性，我们遵循 Pavlidis 等人的计算方法。（2016）密切并使用筛引导方法。使用横截面信息的面板方法可能有助于了解全球市场房地产价格的总体趋势。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECON 7204

Posted on 2022年6月20日2022年6月20日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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.

计量经济学代考

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

由于我们有一些未观察到的变量，因此起点是使用状态空间表示来编写模型。然后使用卡尔曼滤波器方法估计参数和未知变量。模型的状态空间表示如下：

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。
为了估计模型，我们采用基于五个步骤的顺序方法。
第 1 步：我们用三个状态变量估计模型：是吨,是吨−1,是吨−2∗和三个观察到的变量是吨,圆周率吨,在~吨.

方程中进口价格和石油价格对通货膨胀的影响。(9) 假设通过两个滞后季度的平均影响来衡量。在等式。(11)在吨∗假定为常数（外生的）。在 IS 曲线中，假设金融变量是外生的，世界需求的影响由当前和前几个季度的平均影响来捕捉(DCpC(大号)=0.5一个31(大号+大号2, DspX(大号)=0.5一个32(大号+大号2),D在p在(大号)=0.5(1+大号)). 此外，我们不考虑利率的影响。最后假设潜在增长率是一个常数（外生的）

表示θ要估计的参数集，因此，我们搜索θ^,X^吨最小化以下损失函数：

\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}
估计值取决于以下权重（比例因子）的值：λ1=σ是2σ是是2,λ2=σ一世2σ圆周率2,λ3=σ是2σ在2. 正如文献中所证明的，对于这些比例因子的特定值的选择没有明确的指导。即使是通常选择的 1600 的常规值λ1在这里不合适，因为输出差距的周期性属性取决于所有比例因子。我们让这些缩放由数据来估计。第一步估计，常数G旨在为输出间隙和 Phillips、IS 和 Okun 方程的系数生成一些初步猜测值。

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

本研究的主要目的是回顾统计方法，但理解金融泡沫的基本经济理论以指定统计模型的组成仍然很重要。正如所讨论的，最近的研究对投资者的理性提出了质疑，但许多经济分析都维持了这一假设，并且通常使用现值模型 (PVM) 来解释。理性假设在学术研究中盛行，主要是为了方便。对理性行为进行建模比对非理性行为进行建模更容易。投资者预期的调查数据是投资者预期信息的最佳来源，但在缺乏全面的国家调查数据和不经常发布的调查数据的情况下，我们也维持理性假设。

根据 PVM，理性泡沫被定义为与经济基本面相当大且持续存在的偏差，并且在统计意义上遵循非平稳过程。基于资产收益或房地产收益的定义(r吨+1=(磷吨+1+D吨+1)/磷吨−1), PVM 表明同期价格(磷吨)将由未来经济基本面的预期值决定(D)和价格：

磷吨=和吨[磷吨+1+D吨+11+r吨+1]
在哪里吨表示时间(吨=1,…,吨)和和是期望算子。D是经济基础，例如股权分析中的股息支付或住房分析中的租金成本。求解方程。(1) 向前并使用迭代期望定律，我们可以得到方程。(2):

磷吨=和吨[∑H=0∞(∏ķ=0H(11+r吨+ķ))D吨+H+林H→∞∏ķ=0H(11+r吨+ķ)磷吨+H]什么时候磷和D是协整的，并且当横向条件成立时（即，和吨[林H→∞∏ķ=0H(11+r一世+ķ)磷吨+H]→0)，则结果显示没有气泡的迹象。因此，在这种情况下，资产价格往往会随着经济基本面而波动。另一方面，当这些条件不成立时，结果表明存在泡沫。出于这个原因，先前的研究经常使用积分方法研究理性气泡。

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

计量经济学家提出了许多统计方法，其统计假设似乎从他们的角度来看是合适的。因此，开发了一些方法来寻找平静时期，而另一些方法则研究金融泡沫。与以前的研究不同，我们明确区分了确定平静期和泡沫期的统计方法。这种区别很重要，因为统计假设的差异可以解释这两种方法的不同结果。在本节中，我们将使用气泡研究中流行的统计规范来阐明这两种方法。

研究方程式中的理论模型和预测。(2) 在数量上，以往的研究往往侧重于利用时间序列方法的单一市场。这些统计方法是单尾检验，但可以根据其替代假设大致分为左尾方法和右尾方法。左尾检验是经典的，旨在寻找价格和经济基本面之间的协整，从而揭示平静时期。作为扩展，我们还提出了一种非线性方法，可以分为一组左尾测试。另一方面，流行的右尾测试是一种识别爆炸气泡的方法。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|ECOM20001

Posted on 2022年6月20日2022年6月20日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|Using Disaggregated Data: Accounting for the Good

To complement our previous country-level results, let us now estimate ERPT into import prices at a disaggregated level, using the two-digit level of disaggregation in the SITC classification. Analyzing ERPT at the good level allows us to account for the fact that the shift in the composition of imports towards goods whose prices are less sensitive to exchange rate changes has contributed to the “seemingly” pass-through decline. The corresponding results are reported in Table $5.9$

As shown, ERPT is found to be quite high or even complete in most sectors. These findings again illustrate the importance of controlling for intra-EU trade in assessing the effect of exchange rate changes to import prices. ${ }^{10}$ However, the estimates strongly vary depending on the type of goods. The highest ERPT coefficients are generally obtained for goods belonging to SITC 8, SITC 7 and SITC 2 which are the sectors the most commodity-intensive. On the whole, the exchange rate effect on the prices of imported goods comes principally through its indirect effect on commodity prices: in commodity-intensive sectors, foreign producers have strong market power and face very weak domestic competition, and, consequently, the world price passed on when the exchange rate fluctuates. The declining share of commodity-intensive goods for which ERPT is higher than for other goods, may thus explain the declining pass-through reported in several studies (see, e.g. López-Villavicencio and Mignon (2017) and the references therein). For some industries, such as those concerned with manufactured goods (SITC 6), the pass-through strongly differs between countriesthe value of ERPT degree for Belgium being about two times that of France. ${ }^{11}$ This can be explained by the fact that these industries are more oriented towards product differentiation, leading to distinct ERPT degrees in different countries.

商科代写|计量经济学代写Econometrics代考|Accounting for Globalization at the Good Level

Tables $6,7,8,9$ and 10 display the estimation results at the disaggregated level of Eq. (2). $\Lambda s$ shown, there is no clear-cut evidence regarding how global factors affect the way foreign exporters pass-through increasing costs to their prices. Indeed, when significant, the interactive term mostly indicates that higher trade openness or lower

tariffs increase the ERPT in some cases. However, higher intra-industry trade and, above all, more regional trade reduce the ERPT. Chinese import share, in turn, seems to play no major role in the pricing decisions of foreign exporters.

More in detail, regarding trade openness, the interactive term is positive and significant for goods belonging to SITC 2 (crude materials, inedible, except fuels) for all the countries, SITC 4 (animal and vegetable oils) except in France, and SITC 7 (machinery and transport equipment) for France. In those cases, greater competition is thus associated with higher ERPT, in line with the arguments developed by Dornbusch (1987) and Benigno and Faia (2016).

Turning to intra-industry trade, when significant, the associated coefficient is mostly negative. This means that for the concerned sectors, higher intra-industry trade tends to lower ERPT. This result is consistent with the fact that for sectors characterized by high levels of intra-industry trade, firms react in terms of product differentiation, leading to lower ERPT. A typical example is given by the German case for which machinery and transport equipment sector plays a central role worldwide in the sense that the negative sign reflects the aim of Germany to preserve its market shares.
Our findings also illustrate that Chinese firms’ market penetration has not caused a structural change in ERPT, the interactive coefficient being rarely significant, except in some special cases such as manufactured goods and miscellaneous manufactures in France and Germany, which correspond to sectors in which China is highly competitive. $^{12}$ This means that an increase in the share of China tends to weaken ERPT, reflecting a threat from competition with China in these sectors. Those findings may reflect the wish of domestic firms to preserve their market power and protect against foreign competition in these particular sectors.

商科代写|计量经济学代写Econometrics代考|The General Model

The model embodies several theoretical ideas from the Keynesian tradition of an economic equilibrium determined by demand factors, from the Wicksellian view of a link between the interest rate gap and the business cycle, and Minsky’s approach ö the rolé ơf the financial cyclẻ in determining the business cyclé.

A natural interest rate is considered as a benchmark for monetary policy and is determined by both potential growth and short-term determinants. A short-term determinant is, for instance, consumer’s rate of preference, while long-run determinants refer, for example, to technological changes or demographic factors, which are both key determinants of potential growth. Unlike the original suggestion by Wicksell, the natural rate is not considered here as a direct determinant of the inflation gap. In the author’s reasoning, the economy was assumed to be permanently at its steady-state level and, therefore, any gap between the central bank’s nominal interest rate and the natural rate of interest caused inflationary pressure or deflation. As is known, the Wicksell approach was extended by the Stockholm school during the $1930 s$ and the natural rate was conceptualized to build a theory of the business cycle. Differences between the nominal and natural rates cause a credit expansion or restriction and this in turn cause increases or decreases in output through changes in private demand. The impact to inflation comes then through a Phillips curve. In some recent models of potential growth, the interest rate gap directly enters as an explanatory variable of the output-gap [see Laubach and Williams (2003)]. Here, we adopt the Minsky’s view of cumulative processes in the credit sector as a key source of output fluctuations. Banks and lenders’ behavior, through changes in the interest rates of loans tighten or loose credit availability. The interest rate gap also induces speculative investment. Therefore, our model attempts to capture the Minsky’s financial instability hypothesis as follows. The output-gap (defined as the gap between the observed GDP and potential GDP) depends upon monetary and financial sector imbalances, and these imbalances are related to the interest rate gap.

We consider a simple model with backward looking expectations. This assumption can be criticized given the importance of inflation expectations in the determi-nation of the real interest rates and with regards to the fact that interest rate rules with forward looking output-gap and inflation-gap have been extensively used in the literature. Further, one may argue that a forward looking Phillips curve better fits the new Keynesian theories of price determination. We are aware of these limits to our framework. Though these views have many advocates, we motivate the use of backward looking expectations models as follows.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|Using Disaggregated Data: Accounting for the Good

为了补充我们之前的国家级结果，现在让我们使用 SITC 分类中的两位数分解水平，将 ERPT 估算为分解水平的进口价格。在良好水平上分析 ERPT 使我们能够解释这样一个事实，即进口构成向价格对汇率变化不太敏感的商品的转变导致了“看似”的传递下降。相应的结果见表5.9

如图所示，大多数行业的 ERPT 都相当高甚至完整。这些发现再次说明了在评估汇率变化对进口价格的影响时控制欧盟内部贸易的重要性。10但是，估计值因商品类型而异。最高的 ERPT 系数通常来自 SITC 8、SITC 7 和 SITC 2 的商品，它们是商品最密集的部门。总体而言，汇率对进口商品价格的影响主要来自其对商品价格的间接影响：在商品密集型行业，外国生产商具有强大的市场力量，面临非常弱的国内竞争，因此，世界价格当汇率波动时传递。因此，ERPT 高于其他商品的商品密集型商品的份额下降可能解释了几项研究报告的传递率下降（参见例如 López-Villavicencio 和 Mignon（2017 年）及其参考文献）。对于某些行业，11这可以通过以下事实来解释：这些行业更倾向于产品差异化，导致不同国家/地区的 ERPT 学位不同。

商科代写|计量经济学代写Econometrics代考|Accounting for Globalization at the Good Level

表6,7,8,9和 10 显示了在等式的分类级别的估计结果。(2)。Λs如图所示，没有明确的证据表明全球因素如何影响外国出口商将增加的成本转嫁到价格上的方式。实际上，当交互项显着时，主要表明贸易开放度较高或较低

在某些情况下，关税会增加 ERPT。然而，更高的行业内贸易，尤其是更多的区域贸易会降低 ERPT。反过来，中国的进口份额似乎在外国出口商的定价决策中没有发挥重要作用。

更详细地说，关于贸易开放，交互项对于所有国家属于 SITC 2（原油，不可食用，燃料除外）、除法国以外的 SITC 4（动物和植物油）和 SITC 7 的商品是积极且显着的（机械和运输设备）为法国。在这些情况下，更大的竞争与更高的 ERPT 相关，这与 Dornbusch (1987) 和 Benigno 和 Faia (2016) 提出的论点一致。

转向产业内贸易，当显着时，相关系数大多为负。这意味着对于相关行业而言，较高的行业内贸易往往会降低 ERPT。这一结果与以下事实一致：对于以高水平的行业内贸易为特征的行业，企业会根据产品差异化做出反应，从而导致较低的 ERPT。一个典型的例子是德国的案例，机械和运输设备行业在全球范围内发挥着核心作用，因为负号反映了德国保持其市场份额的目标。
我们的研究结果还表明，中国企业的市场渗透并没有引起 ERPT 的结构性变化，交互系数很少显着，除了在一些特殊情况下，例如法国和德国的制成品和杂项制造，它们对应于中国的行业。具有很强的竞争力。12这意味着中国份额的增加往往会削弱 ERPT，反映出在这些领域与中国竞争的威胁。这些调查结果可能反映了国内公司希望在这些特定领域保持其市场力量并防止外国竞争。

商科代写|计量经济学代写Econometrics代考|The General Model

该模型体现了凯恩斯主义传统的由需求因素决定的经济均衡、利率差距与商业周期之间联系的威克塞尔观点以及明斯基的金融周期在决定商业活动中的作用的方法的若干理论思想。循环。

自然利率被视为货币政策的基准，由潜在增长和短期决定因素共同决定。例如，短期决定因素是消费者的偏好率，而长期决定因素是指技术变革或人口因素等，它们都是潜在增长的关键决定因素。与 Wicksell 最初的建议不同，这里没有将自然利率视为通胀差距的直接决定因素。在作者的推理中，经济被假定为永久处于稳态水平，因此，中央银行名义利率与自然利率之间的任何差距都会导致通胀压力或通货紧缩。众所周知，维克塞尔方法在斯德哥尔摩学派中得到了扩展。1930s自然利率被概念化以建立商业周期理论。名义利率和自然利率之间的差异会导致信贷扩张或限制，进而通过私人需求的变化导致产出增加或减少。然后通过菲利普斯曲线对通货膨胀产生影响。在最近的一些潜在增长模型中，利率缺口直接作为产出缺口的解释变量出现 [参见 Laubach 和 Williams (2003)]。在这里，我们采用明斯基关于信贷部门累积过程的观点，将其作为产出波动的关键来源。银行和贷方的行为，通过贷款利率的变化收紧或放宽信贷供应。利差也引发投机性投资。所以，我们的模型试图捕捉明斯基的金融不稳定假设如下。产出缺口（定义为观察到的 GDP 与潜在 GDP 之间的缺口）取决于货币和金融部门的失衡，而这些失衡与利率缺口有关。

我们考虑一个具有回溯期望的简单模型。考虑到通胀预期在确定实际利率中的重要性，以及考虑到具有前瞻性产出缺口和通胀缺口的利率规则已在文献中广泛使用这一事实，这一假设可能会受到批评。此外，有人可能会争辩说，前瞻性的菲利普斯曲线更符合新的凯恩斯价格决定理论。我们知道我们框架的这些限制。尽管这些观点有很多拥护者，但我们鼓励使用如下回溯预期模型。

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广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

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MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

商科代写|计量经济学代写Econometrics代考|A. López-Villavicencio and V. Mignon

Posted on 2022年6月20日2022年6月20日 by statistics-lab

如果你也在怎样代写计量经济学Econometrics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

我们提供的计量经济学Econometrics及其相关学科的代写，服务范围广, 其中包括但不限于:

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|A. López-Villavicencio and V. Mignon

商科代写|计量经济学代写Econometrics代考|Indicators of Globalization

Let us now describe our five indicators of globalization. First, at the aggregated and disaggregated levels, trade openness is defined as the sum of extra-EU exports and imports over GDP. Overall and disaggregated trade values are collected from the Comext database. Note that, according to our previous discussion (see Sect. 1), the sign of the ERPT coefficient can be positive or negative. Indeed, following Benigno and Faia (2016), $\theta^{C}$ should be positive and significant if we expect that higher trade openness implies that there are more foreign firms competing in the destination market. In this case, globalization affects the dynamics of imported inflation through its effect on ERPT into import prices, the rise in the share of foreign products in the domestic market increasing the pass-through degree. However, in case of strategic complementarity in setting prices, a foreign exporter does not want its price to deviate too far from its competitors. Thus, the foreign exporter’s price becomes more responsive to the prices of its competitors as its markup increases. As a consequence, it is optimal for a firm to vary its markup more and its price less in response to an exchange rate change. Accordingly, we should observe a reduction of the passthrough of exchange-rate changes to import prices with higher trade integration $\left(\theta^{C}\right.$ should be negative and significant).

Second, we also evaluate how China’s presence in total imports may have affected the pricing decisions of exporters from other countries. We, therefore, consider China’s imports share over total imports as well as China’s share in each SITC sector [see Marazzi et al. (2005)]. Our third global indicator is a measure of intraindustry trade. Here, the underlying hypothesis is that increasing levels of intraindustry trade reflect higher product differentiation with respect to foreign competitors. Indeed, as shown by Caves (1998), product differentiation leads to increasing levels of intra-industry trade among countries, providing opportunities to develop new market-niches. To test for this hypothesis, we employ the Grubel-Lloyd index of intra-industry trade $I I T$ [see Lipsey (1976)], which is computed as follows:
$$
M I_{t}=2 \times \frac{\min \left(M_{t} ; X_{s}\right)}{\left(M_{t}+X_{t}\right)}
$$
where $M$ denotes extra-EU imports, and $X$ stands for extra EU-exports (of each SITC sector in the disaggregated analysis) in the considered country. The index ranges between zero (no intra-industry trade) and one (perfect intra-industry trade), and captures the level of product heterogeneity and trade complementarity between each sector-country pair and the trading partners. We interpret an increase in intra-industry trade as an adjustment to trade liberalization. Indeed, as suggested by Colantone et al.

商科代写|计量经济学代写Econometrics代考|Descriptive Statistics

Tables 1 and 2 provide some descriptive statistics referring to our five different globalization indicators and their growth over the period under study. At the country level (Table 1), Belgium is the country displaying the highest degree of trade openness. However, the level of trade exposure is increasing everywhere, particularly in Germany in addition to Belgium. France is the less opened economy and is the country that exhibits the lowest trade exposure growth. At the industry level (Table 2 ), openness is relatively higher for chemicals and related products (SITC 5), machinery and transport equipment (SITC 7) and miscellaneous manufactured articles (SITC 8), and it has especially increased for animal and vegetable oils (SITC 4) in France and Germany and miscellaneous manufactured articles (SITC 8) in all countries.

Looking at the figures in Table 2 another trend seems to emerge: Chinese imports account for about $35 \%$ in miscellaneous manufactured articles and, while being much lower in other sectors such as chemicals, they have been increasing over time in all panels. This is particularly the case in machinery, even though the average tariff rate increased slightly over the period. Intra-industry trade, in turn, is very heterogeneous among the different sectors in the three countries but, as it is known in the literature, it tends to be higher for manufactured goods than for raw materials or primary goods [see, e.g., Deese (2016)]. Finally, it is interesting to note that intra-EU imports represent more than $70 \%$ in several sectors. However, regional trade has decreased in sectors such as manufacturing or chemicals (except in Germany).

商科代写|计量经济学代写Econometrics代考|Accounting for Globalization

To assess the role of globalization at the country level, Table 4 reports the estimation results of Eq. (2). We consider the five aforementioned indicators in favor of globalization, namely: (i) an increase in the degree of trade openness, (ii) a higher intra-industry trade, (iii) a higher presence of Chinese imports over total imports, (iv) lower import tariffs, and (v) higher intra-EU trade as a regional globalization measure.

As shown, the interactive effect between exchange rate changes and globalization is mostly non-significant. This means that an increase in product differentiation with respect to foreign competitors, in the share of products from China in total imports and in the share of intra-UE imports, as well as a decline in import tariffs do not contribute to explaining the ERPT to import prices, at least at the aggregate level. The sole significant interactive terms are obtained when considering growth in trade openness and intra-industry trade for Germany and a higher presence of Chinese imports over total imports in France, suggesting that globalization tends to slightly increase the ERPT degree. Regarding Germany, these findings can be related to the fact that the German economy has known an important rise in trade openness over the period under study, leading to greater competition. In line with the argument developed by Benigno and Faia (2016), this growing competition due to the increase in the share of foreign products pushes up the degree of ERPT. In other words, there is slight evidence that the impact of firms’ entry on pass-through outweighs the effect of markup adjustments at the intensive margin.

While overall evidence regarding the pass-through effect of global factors is quite weak, it is worth noticing that their impact can operate through other channels. For instance, as recalled by Marazzi and Sheets (2007), pricing decisions of exporters from other countries may have been affected by the efforts made to remain competitive against China. The Chinese economy has also proven its high capacity to win market share, making credible the threat of its potential competition and constraining other exporters from passing through exchange rate shocks. Besides and at a more general level, if there is heterogeneity prevailing at the industry level, results based on aggregated import prices present aggregation bias, suggesting the importance of assessing ERPT degree at the sectoral level with disaggregated data.

计量经济学代考

商科代写|计量经济学代写Econometrics代考|Indicators of Globalization

现在让我们描述一下全球化的五个指标。首先，在综合和分类层面上，贸易开放度被定义为欧盟以外的进出口总额与 GDP 之和。从 Comext 数据库收集总体和分类的贸易价值。请注意，根据我们之前的讨论（参见第 1 节），ERPT 系数的符号可以是正数或负数。事实上，在 Benigno 和 Faia（2016 年）之后，θC如果我们预期更高的贸易开放度意味着有更多的外国公司在目的地市场竞争，那么应该是积极的和显着的。在这种情况下，全球化通过其对进口价格的ERPT的影响来影响输入性通货膨胀的动态，国外产品在国内市场份额的上升增加了传递度。但是，如果在定价方面存在战略互补性，外国出口商不希望其价格与竞争对手相差太远。因此，随着加价的增加，外国出口商的价格对其竞争对手的价格更加敏感。因此，对于一家公司来说，最好的做法是根据汇率变化增加其加价幅度和减少其价格。因此，(θC应该是负的和显着的）。

其次，我们还评估了中国在进口总额中的存在可能如何影响其他国家出口商的定价决策。因此，我们考虑中国在总进口中的进口份额以及中国在每个 SITC 部门中的份额 [参见 Marazzi 等人。（2005 年）]。我们的第三个全球指标是衡量产业内贸易的指标。这里的基本假设是，行业内贸易水平的提高反映了产品相对于外国竞争对手的更高差异化。事实上，正如 Caves (1998) 所表明的，产品差异化导致国家之间产业内贸易水平的提高，为开发新的市场利基提供了机会。为了检验这一假设，我们采用了行业内贸易的 Grubel-Lloyd 指数我我吨[参见 Lipsey (1976)]，其计算如下：

米我吨=2×分钟(米吨;Xs)(米吨+X吨)
在哪里米表示欧盟以外的进口，并且X代表所考虑国家的额外欧盟出口（分类分析中的每个 SITC 部门）。该指数介于零（无行业内贸易）和一（完美的行业内贸易）之间，反映了每个部门-国家对与贸易伙伴之间的产品异质性和贸易互补性水平。我们将产业内贸易的增加解释为对贸易自由化的调整。事实上，正如 Colantone 等人所建议的那样。

商科代写|计量经济学代写Econometrics代考|Descriptive Statistics

表 1 和表 2 提供了一些描述性统计数据，涉及我们的五个不同的全球化指标及其在研究期间的增长。在国家层面（表 1），比利时是贸易开放程度最高的国家。然而，世界各地的贸易风险水平都在增加，特别是在德国和比利时。法国是开放程度较低的经济体，是贸易风险增长最低的国家。在行业层面（表2），化学品及相关产品（SITC 5）、机械和运输设备（SITC 7）和杂项制成品（SITC 8）的开放度相对较高，尤其是动植物油开放度更高（SITC 4）在法国和德国，杂项制成品（SITC 8）在所有国家。

从表 2 中的数字来看，似乎出现了另一个趋势：中国进口约占35%在杂项制成品中，虽然在化学品等其他部门中的比例要低得多，但随着时间的推移，所有面板中的比例都在增加。机械行业尤其如此，尽管在此期间平均关税税率略有上升。反过来，这三个国家的不同部门之间的产业内贸易差异很大，但正如文献中所知，制成品的贸易往往高于原材料或初级商品 [例如，参见 Deese （2016）]。最后，有趣的是，欧盟内部的进口量超过70%在几个部门。然而，制造业或化工等行业的区域贸易有所下降（德国除外）。

商科代写|计量经济学代写Econometrics代考|Accounting for Globalization

为了评估全球化在国家层面的作用，表 4 报告了等式的估计结果。(2)。我们考虑上述五个有利于全球化的指标，即：（i）贸易开放程度的提高，（ii）更高的产业内贸易，（iii）中国进口占总进口的比例更高，（iv ) 降低进口关税，以及 (v) 提高欧盟内部贸易作为区域全球化措施。

如图所示，汇率变化与全球化之间的交互作用大多不显着。这意味着相对于外国竞争对手的产品差异化增加、中国产品在总进口中的份额和 UE 内部进口的份额以及进口关税的下降并不能解释 ERPT进口价格，至少在总体水平上。考虑到德国的贸易开放和产业内贸易的增长以及中国进口高于法国的总进口，获得了唯一重要的交互项，这表明全球化倾向于略微提高 ERPT 程度。关于德国，这些发现可能与德国经济在研究期间贸易开放度显着上升的事实有关，导致更大的竞争。与 Benigno 和 Faia (2016) 提出的论点一致，由于外国产品份额的增加，这种日益激烈的竞争推高了 ERPT 的程度。换句话说，有少量证据表明公司进入对传递的影响超过了集约边际加价调整的影响。

虽然关于全球因素传递效应的总体证据相当薄弱，但值得注意的是，它们的影响可以通过其他渠道发挥作用。例如，正如 Marazzi 和 Sheets (2007) 所回忆的那样，其他国家的出口商的定价决策可能会受到为保持对中国的竞争力所做的努力的影响。中国经济也证明了其赢得市场份额的强大能力，使其潜在竞争的威胁变得可信，并限制了其他出口商通过汇率冲击。此外，在更一般的层面上，如果行业层面普遍存在异质性，基于汇总进口价格的结果存在汇总偏差，这表明使用分类数据在行业层面评估 ERPT 程度的重要性。

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