## 经济代写|计量经济学代写Econometrics代考|MTH250

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

## 经济代写|计量经济学代写Econometrics代考|Goodness-of-Fit

So far, we have no way of measuring how well the explanatory or independent variable, $x$, explains the dependent variable, $y$. It is often useful to compute a number that summarizes how well the OLS regression line fits the data. In the following discussion, be sure to remember that we assume that an intercept is estimated along with the slope.
Assuming that the total sum of squares, SST, is not equal to zero-which is true except in the very unlikely event that all the $y_i$ equal the same value-we can divide (2.36) by SST to get $1=$ SSE/SST + SSR/SST. The R-squared of the regression, sometimes called the coefficient of determination, is defined as
$$R^2=\mathrm{SSE} / \mathrm{SST}=1-\mathrm{SSR} / \mathrm{SST} .$$
$R^2$ is the ratio of the explained variation compared to the total variation, and thus it is interpreted as the fraction of the sample variation in $y$ that is explained by $x$. The second equality in (2.38) provides another way for computing $R^2$.

From (2.36), the value of $R^2$ is always between zero and one, since SSE can be no greater than SST. When interpreting $R^2$, we usually multiply it by 100 to change it into a percent: $100 \cdot R^2$ is the percentage of the sample variation in $y$ that is explained by $x$.
If the data points all lie on the same line, OLS provides a perfect fit to the data. In this case, $R^2=1$. A value of $R^2$ that is nearly equal to zero indicates a poor fit of the OLS line: very little of the variation in the $y_i$ is captured by the variation in the $\hat{y}_i$ (which all lie on the OLS regression line). In fact, it can be shown that $R^2$ is equal to the square of the sample correlation coefficient between $y_i$ and $\hat{y}_i$. This is where the term ” $R$-squared” came from. (The letter $R$ was traditionally used to denote an estimate of a population correlation coefficient, and its usage has survived in regression analysis.)

## 经济代写|计量经济学代写Econometrics代考|UNITS OF MEASUREMENT AND FUNCTIONAL FORM

Two important issues in applied economics are (1) understanding how changing the units of measurement of the dependent and/or independent variables affects OLS estimates and (2) knowing how to incorporate popular functional forms used in economics into regression analysis. The mathematics needed for a full understanding of functional form issues is reviewed in Appendix A.

The Effects of Changing Units of Measurement on OLS Statistics
In Example 2.3, we chose to measure annual salary in thousands of dollars, and the return on equity was measured as a percent (rather than as a decimal). It is crucial to know how salary and roe are measured in this example in order to make sense of the estimates in equation (2.39).

We must also know that OLS estimates change in entirely expected ways when the units of measurement of the dependent and independent variables change. In Example 2.3 , suppose that, rather than measuring salary in thousands of dollars, we measure it in dollars. Let salardol be salary in dollars (salardol $=845,761$ would be interpreted as $\$ 845,761$.). Of course, salardol has a simple relationship to the salary measured in thousands of dollars: salardol$=1,000 \cdot$salary. We do not need to actually run the regression of salardol on roe to know that the estimated equation is: $$\text { salârdol }=963,191+18,501 \text { roe. }$$ (2.40) We obtain the intercept and slope in (2.40) simply by multiplying the intercept and the slope in (2.39) by 1,000. This gives equations (2.39) and (2.40) the same interpretation. Looking at$(2.40)$, if roe$=0$, then salârdol$=963,191$, so the predicted salary is$\$963,191$ [the same value we obtained from equation (2.39)]. Furthermore, if roe increases by one, then the predicted salary increases by $\$ 18,501$; again, this is what we concluded from our earlier analysis of equation (2.39). Generally, it is easy to figure out what happens to the intercept and slope estimates when the dependent variable changes units of measurement. If the dependent variable is multiplied by the constant$c$– which means each value in the sample is multiplied by$c$-then the OLS intercept and slope estimates are also multiplied by$c$. (This assumes nothing has changed about the independent variable.) In the CEO salary example,$c=$1,000 in moving from salary to salardol. # 计量经济学代考 ## 经济代写|计量经济学代写Econometrics代考|Goodness-of-Fit 到目前为止，我们还没有办法衡量解释变量或自变量$x$如何很好地解释因变量$y$。计算一个数字来总结OLS回归线与数据的拟合程度通常是有用的。在下面的讨论中，一定要记住，我们假设截距是与斜率一起估计的。 假设总平方和SST不等于零(除非在非常不可能的情况下，所有的$y_i$都等于相同的值)，我们可以用(2.36)除以SST得到$1=$SSE/SST + SSR/SST。回归的r平方，有时称为决定系数，定义为 $$R^2=\mathrm{SSE} / \mathrm{SST}=1-\mathrm{SSR} / \mathrm{SST} .$$$R^2$是被解释的变异与总变异的比值，因此它被解释为$y$中被$x$解释的样本变异的比例。(2.38)中的第二个等式提供了计算$R^2$的另一种方法。 由式(2.36)可知，$R^2$的值总是在0到1之间，因为SSE不能大于SST。在解释$R^2$时，我们通常将其乘以100以将其转换为百分比:$100 \cdot R^2$是$x$解释的$y$中样本变化的百分比。 如果数据点都在同一条线上，则OLS提供了与数据的完美拟合。在本例中为$R^2=1$。接近于零的$R^2$值表明OLS线的拟合不佳:$\hat{y}_i$的变化捕获了$y_i$的很少变化(它们都位于OLS回归线上)。实际上，可以证明$R^2$等于$y_i$与$\hat{y}_i$之间样本相关系数的平方。这就是“$R$-平方”这个词的由来。(字母$R$传统上用来表示对总体相关系数的估计，它的用法在回归分析中保留了下来。) ## 经济代写|计量经济学代写Econometrics代考|UNITS OF MEASUREMENT AND FUNCTIONAL FORM 应用经济学中的两个重要问题是:(1)理解因变量和/或自变量的测量单位的变化如何影响OLS估计;(2)知道如何将经济学中常用的函数形式纳入回归分析。在附录a中回顾了全面理解函数形式问题所需的数学。 计量单位变化对OLS统计的影响 在例2.3中，我们选择以千美元为单位来衡量年薪，并且以百分比(而不是小数)来衡量股本回报率。为了理解公式(2.39)中的估计，在这个例子中如何衡量工资和股本回报率是至关重要的。 我们还必须知道，当因变量和自变量的测量单位发生变化时，OLS估计会以完全预期的方式变化。在例2.3中，假设我们不是以千美元来衡量工资，而是以美元来衡量工资。设salardol为美元工资(salardol$=845,761$将被解释为$\$845,761$ .)。当然，salardol与以千美元为单位的工资有一个简单的关系:salardol $=1,000 \cdot$工资。我们不需要实际运行salardol对roe的回归就知道估计方程是:
$$\text { salârdol }=963,191+18,501 \text { roe. }$$
(2.40)

## Matlab代写

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

## 经济代写|计量经济学代写Econometrics代考|ECON255

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

## 经济代写|计量经济学代写Econometrics代考|MECHANICS OF OLS

In this section, we cover some algebraic properties of the fitted OLS regression line. Perhaps the best way to think about these properties is to realize that they are features of OLS for a particular sample of data. They can be contrasted with the statistical properties of OLS, which requires deriving features of the sampling distributions of the estimators. We will discuss statistical properties in Section 2.5.

Several of the algebraic properties we are going to derive will appear mundane. Nevertheless, having a grasp of these properties helps us to figure out what happens to the OLS estimates and related statistics when the data are manipulated in certain ways, such as when the measurement units of the dependent and independent variables change.

Fitted Values and Residuals
We assume that the intercept and slope estimates, $\hat{\beta}_0$ and $\hat{\beta}_1$, have been obtained for the given sample of data. Given $\hat{\beta}_0$ and $\hat{\beta}_1$, we can obtain the fitted value $\hat{y}_i$ for each observation. [This is given by equation (2.20).] By definition, each fitted value of $\hat{y}_i$ is on the OLS regression line. The OLS residual associated with observation $i, \hat{u}_i$, is the difference between $y_i$ and its fitted value, as given in equation (2.21). If $\hat{u}_i$ is positive, the line underpredicts $y_i$; if $\hat{u}_i$ is negative, the line overpredicts $y_i$. The ideal case for observation $i$ is when $\hat{u}_i=0$, but in most cases every residual is not equal to zero. In other words, none of the data points must actually lie on the OLS line.

## 经济代写|计量经济学代写Econometrics代考|Algebraic Properties of OLS Statistics

There are several useful algebraic properties of OLS estimates and their associated statistics. We now cover the three most important of these.
(1) The sum, and therefore the sample average of the OLS residuals, is zero.
Mathematically,
$$\sum_{i=1}^n \hat{u}i=0 .$$ (2.30) This property needs no proof; it follows immediately from the OLS first order condition (2.14), when we remember that the residuals are defined by $\hat{u}_i=y_i-\hat{\beta}_0-\hat{\beta}_1 x_i$. In other words, the OLS estimates $\hat{\beta}_0$ and $\hat{\beta}_1$ are chosen to make the residuals add up to zero (for any data set). This says nothing about the residual for any particular observation $i$. (2) The sample covariance between the regressors and the OLS residuals is zero. This follows from the first order condition (2.15), which can be written in terms of the residuals as $$\sum{i=1}^n x_i \hat{u}_i=0 .$$
The sample average of the OLS residuals is zero, so the left hand side of (2.31) is proportional to the sample covariance between $x_i$ and $\hat{u}_i$.
(3) The point $(\bar{x}, \bar{y})$ is always on the OLS regression line. In other words, if we take equation (2.23) and plug in $\bar{x}$ for $x$, then the predicted value is $\bar{y}$. This is exactly what equation (2.16) shows us.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Algebraic Properties of OLS Statistics

OLS估计及其相关统计有几个有用的代数性质。我们现在讨论其中最重要的三个。
(1) OLS残差的和为零，因此OLS残差的样本平均值为零。

$$\sum_{i=1}^n \hat{u}i=0 .$$(2.30)该财产无需证明;当我们记得残差由$\hat{u}_i=y_i-\hat{\beta}_0-\hat{\beta}_1 x_i$定义时，它立即从OLS一阶条件(2.14)中得出。换句话说，选择OLS估计值$\hat{\beta}_0$和$\hat{\beta}_1$使残差相加为零(对于任何数据集)。这并没有说明任何特定观测值的残差$i$。(2)回归量与OLS残差之间的样本协方差为零。这是由一阶条件(2.15)得出的，它可以用残差的形式写成$$\sum{i=1}^n x_i \hat{u}_i=0 .$$
OLS残差的样本平均值为零，因此(2.31)的左侧与$x_i$和$\hat{u}_i$之间的样本协方差成正比。
(3)点$(\bar{x}, \bar{y})$始终在OLS回归线上。换句话说，如果我们采用公式(2.23)并将$\bar{x}$代入$x$，那么预测值就是$\bar{y}$。这正是式(2.16)告诉我们的。

## Matlab代写

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

## 经济代写|计量经济学代写Econometrics代考|ECMT1020

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

## 经济代写|计量经济学代写Econometrics代考|Time Series Data

A time series data set consists of observations on a variable or several variables over time. Examples of time series data include stock prices, money supply, consumer price index, gross domestic product, annual homicide rates, and automobile sales figures. Because past events can influence future events and lags in behavior are prevalent in the social sciences, time is an important dimension in a time series data set. Unlike the arrangement of cross-sectional data, the chronological ordering of observations in a time series conveys potentially important information.

A key feature of time series data that makes it more difficult to analyze than crosssectional data is the fact that economic observations can rarely, if ever, be assumed to be independent across time. Most economic and other time series are related, often strongly related, to their recent histories. For example, knowing something about the gross domestic product from last quarter tells us quite a bit about the likely range of the GDP during this quarter, since GDP tends to remain fairly stable from one quarter to the next. While most econometric procedures can be used with both cross-sectional and time series data, more needs to be done in specifying econometric models for time series data before standard econometric methods can be justified. In addition, modifications and embellishments to standard econometric techniques have been developed to account for and exploit the dependent nature of economic time series and to address other issues, such as the fact that some economic variables tend to display clear trends over time.

Another feature of time series data that can require special attention is the data frequency at which the data are collected. In economics, the most common frequencies are daily, weekly, monthly, quarterly, and annually. Stock prices are recorded at daily intervals (excluding Saturday and Sunday). The money supply in the U.S. economy is reported weekly. Many macroeconomic series are tabulated monthly, including inflation and employment rates. Other macro series are recorded less frequently, such as every three months (every quarter). Gross domestic product is an important example of a quarterly series. Other time series, such as infant mortality rates for states in the United States, are available only on an annual basis.

## 经济代写|计量经济学代写Econometrics代考|Pooled Cross Sections

Some data sets have both cross-sectional and time series features. For example, suppose that two cross-sectional household surveys are taken in the United States, one in 1985 and one in 1990. In 1985, a random sample of households is surveyed for variables such as income, savings, family size, and so on. In 1990, a new random sample of households is taken using the same survey questions. In order to increase our sample size, we can form a pooled cross section by combining the two years. Because random samples are taken in each year, it would be a fluke if the same household appeared in the sample during both years. (The size of the sample is usually very small compared with the number of households in the United States.) This important factor distinguishes a pooled cross section from a panel data set.

Pooling cross sections from different years is often an effective way of analyzing the effects of a new government policy. The idea is to collect data from the years before and after a key policy change. As an example, consider the following data set on housing prices taken in 1993 and 1995, when there was a reduction in property taxes in 1994. Suppose we have data on 250 houses for 1993 and on 270 houses for 1995 . One way to store such a data set is given in Table 1.4.

Observations 1 through 250 correspond to the houses sold in 1993, and observations 251 through 520 correspond to the 270 houses sold in 1995 . While the order in which we store the data turns out not to be crucial, keeping track of the year for each observation is usually very important. This is why we enter year as a separate variable.
A pooled cross section is analyzed much like a standard cross section, except that we often need to account for secular differences in the variables across the time. In fact, in addition to increasing the sample size, the point of a pooled cross-sectional analysis is often to see how a key relationship has changed over time.

# 计量经济学代考

## Matlab代写

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

## 经济代写|计量经济学代写Econometrics代考|Domestic and Global Productivity

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

## 经济代写|计量经济学代写Econometrics代考|Domestic and Global Productivity

In this section, we apply the Glick-Rogoff model to the fast-growing emerging economies, namely the BRICS countries, Brazil, China, India, Russia, and South Africa. The key determinants of current account change in the Glick-Rogoff model are global and country-specific productivity shocks. To account for the severe negative shocks experienced during the global financial crisis, we estimate the model in two sample periods; one ending in 2008 and the other ending in 2017. In the second subsection, we also apply the extended model with additional macroeconomic variables after we obtain the base results from the original Glick-Rogoff model. In next section, we apply the same model to developed countries, namely Canada, France, Germany, Italy, Japan, the UK, and the USA. We discuss similarities and differences in current account determinants between the BRICS and G7 countries.

Estimation Results of the Basic Glick–Rogoff Model

Global productivity is constructed from the weighted average of the productivities of the G7 countries, namely Canada, France, Germany, Italy, Japan, the UK, and the USA. Alternatively, the first principal component of the productivities of the G7 countries is also used as a measure of global productivity. ${ }^5$ The regression model of Eq. (10) is restated here.
$$\Delta C A_t=\gamma_1 I_{t-1}+\gamma_2 \Delta A_t^c+\gamma_3 \Delta A_t^W+\varepsilon_t,$$
From the Glick-Rogoff model, the expected sign of the past investment is positive, that of the first difference of each country’s productivity is negative, and that of the first difference of worldwide productivity is zero; that is, $\gamma_1>0, \gamma_2<0$, and $\gamma_3=$ 0 . The dynamic optimization model of Glick and Rogoff (1995) integrates the endogenous decisions of producers and consumers; therefore, the derived parameters of the model are affected by several sources. However, if we simply decompose the dependent variable, which is the first difference of the current account in terms of private saving and investment, and leave aside the government role, we can observe (in the first equality) the first-degree importance of the current investment and the past investment on the dependent variable. Adjusted for marginal production with respect to investment and capital stock, i.e., $\alpha_I$ and $\alpha_K$, and the impact of past investment shock on the current investment, i.e., $\beta_1$, the coefficient of unity in the equation remains positive, $\gamma_1$, as shown in Eq. (8).
$$\Delta C A_t \equiv C A_t-C A_{t-1}=\left(S_t-I_t\right)-\left(S_{t-1}-I_{t-1}\right)=\Delta S_t-\Delta I_t$$
It is also clear that a change in a country’s productivity negatively affects a change in its current account, $\gamma_2$, via a change in investment through the second equality.

## 经济代写|计量经济学代写Econometrics代考|Extended Models with Other Macroeconomic Variables

Not all empirical models of current account movements emphasize productivity shocks. The advantage of the Glick-Rogoff regression model is its concrete derivation based on the theoretical dynamic model. However, many researchers have continued to explore the possibility of many other macroeconomic variables to explain current account movements, frequently without theoretical models.

Chinn and Prasad (2003) investigated the medium-term determinants of current accounts for a large sample of developed and developing countries. They find that current account balance is positively correlated with government budget balance and the initial level of net foreign assets. Among developing countries, financial deepening is positively associated with current account balance, while trade openness is negatively correlated with current account balance.

Cudre and Hoffmann (2017) and Romelli et al. (2018) also showed that trade openness is a significant driver of current accounts. Romelli et al. (2018) investigated the impact of trade openness on the relationship between the current account and the real exchange rate. They find that during the balance of payment distress episodes, currency depreciations are associated with larger improvements in the current accounts of countries that are more open to trade, and the magnitude of exchange rate depreciations over the adjustment process of current accounts is related to the degree of openness to trade. Cudre and Hoffmann (2017) also find that trade openness is an important factor even across regions within a nation.

Following the recent development of the empirical current account literature, we extended the Glick-Rogoff model with five macroeconomic variables: financial deepening, old dependency ratio, young dependency ratio, net foreign assets, and trade openness. ${ }^8$ First, the fitness of regression substantially improved for Brazil, India, and China. In the shorter sample between 1983 and 2008, the adjusted Rsquared increased from 0.29 to 0.60 for Brazil, from 0.60 to 0.69 for India, and from 0.58 to 0.68 for China. In the longer sample that included the post-crisis period, the adjusted R-squared values were 0.31 for Russia, 0.21 for Brazil, and 0.24 for China; all of these values increased from zero or even negative values of the adjusted R-squared in the basic model estimations.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Domestic and Global Productivity

Glick-Rogoff基本模型的估计结果

$$\Delta C A_t=\gamma_1 I_{t-1}+\gamma_2 \Delta A_t^c+\gamma_3 \Delta A_t^W+\varepsilon_t,$$

$$\Delta C A_t \equiv C A_t-C A_{t-1}=\left(S_t-I_t\right)-\left(S_{t-1}-I_{t-1}\right)=\Delta S_t-\Delta I_t$$

## 经济代写|计量经济学代写Econometrics代考|Extended Models with Other Macroeconomic Variables

Cudre和Hoffmann(2017)以及Romelli等人(2018)也表明，贸易开放是经常账户的重要驱动因素。Romelli等人(2018)研究了贸易开放对经常账户与实际汇率关系的影响。他们发现，在国际收支困难时期，货币贬值与对贸易更开放的国家经常账户的较大改善有关，而汇率贬值在经常账户调整过程中的幅度与对贸易的开放程度有关。Cudre和Hoffmann(2017)还发现，即使在一个国家的各个地区，贸易开放程度也是一个重要因素。

## 经济代写|计量经济学代写Econometrics代考|Autoregressive Conditional Betas

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## 经济代写|计量经济学代写Econometrics代考|Autoregressive Conditional Betas

An alternative to the state space model presented above that also allows a direct specification of dynamic conditional betas has recently been proposed by Darolles et al. (2018). Their model, called CHAR, is a multivariate GARCH model based on the Cholesky decomposition of the $m \times m$ (with $m=N+1$ ) conditional covariance matrix $\Sigma_t$ of $\left(\mathbf{x}_t, y_t\right)^{\prime}$.

As Pourahmadi (1999), let us consider the Cholesky decomposition of $\Sigma_t$, i.e.,
$$\boldsymbol{\Sigma}t=\boldsymbol{L}_t \boldsymbol{G}_t \boldsymbol{L}_t^{\prime},$$ where $\boldsymbol{G}_t=\operatorname{diag}\left(g{11, t}, \ldots, g_{m m, t}\right)$ and $\boldsymbol{L}t$ is a lower unitriangular matrix (i.e., triangular with 1 ‘s on the diagonal and 0 ‘s above the diagonal) with element $\ell{i j, t}$ at the row $i$ and column $j$ for $i>j$.

Let us now illustrate this decomposition for $m=3$.
$$\boldsymbol{L}=\left[\begin{array}{ccc} 1 & 0 & 0 \ l_{21, t} & 1 & 0 \ l_{31, t} & l_{32, t} & 1 \end{array}\right] \quad \boldsymbol{G}=\left[\begin{array}{ccc} g_{11, t} & 0 & 0 \ 0 & g_{22, t} & 0 \ 0 & 0 & g_{33, t} \end{array}\right]$$
and
$$\boldsymbol{\Sigma}=\left[\begin{array}{ccc} g_{11, t} & l_{21, t} g_{11, t} & l_{31, t} g_{11, t} \ l_{21, t} g_{11, t} & l_{21, t}^2 g_{11, t}+g_{22, t} & l_{21, t} l_{31, t} g_{11, t}+l_{32, t} g_{22, t} \ l_{31, t} g_{11, t} & l_{21, t} h_{31, t} g_{11, t}+l_{32, t} g_{22, t} & l_{31, t}^2 g_{11, t}+l_{32, t}^2 g_{22, t}+g_{33, t} \end{array}\right] .$$
Darolles et al. (2018) show that if $\boldsymbol{w}t \equiv\left(\mathbf{x}_t, y_t\right)^{\prime}$ has mean $\mathbf{0}$, \begin{aligned} w{i, t} & =\sum_{j=1}^{i-1} \ell_{i j, t} \varepsilon_{j, t}+\varepsilon_{i, t}=\sum_{j=1}^{i-1} \ell_{i j, t}\left(w_{j, t}-\sum_{k=1}^{j-1} \ell_{j k, t} v_{k, t}\right)+\varepsilon_{i, t} \ & =\sum_{j=1}^{i-1} \beta_{i j, t} w_{j, t}+\varepsilon_{i, t} . \end{aligned}
Interestingly, for $i=m$, the $m$ th equation of the CHAR model is
$$y_t=\sum_{j=1}^{m-1} \beta_{i j, t} x_{j, t}+\varepsilon_{i, t}$$
which corresponds to Eq. (35) when $\alpha_t=0, N=m-1$ and $\varepsilon_t=\varepsilon_{i, t}$.

## 经济代写|计量经济学代写Econometrics代考|Empirical Application on REITs

Real Estate Investment Trusts ${ }^{23}$ (REITs), which are publicly traded real estate companies that own and manage commercial or residential real estate, are attractive alternatives to the mainstream investment choice (e.g., stocks and bonds) since they allow investors to easily access real estate investments without directly owning or managing the underlying assets. ${ }^{24}$ Moreover, the literature on real estate has shown that the inclusion of REITs within one’s portfolio improves the risk-return profile of the portfolio. Compared to other asset classes such as bonds and stocks, they have the characteristics of offering more stable returns and a lower volatility historically. For the purpose of portfolio diversification, it is important to know how the level of exposure of REITs to both the bond market risk and to the stock market risk varies over time. The aim of this section is thus to perform a comparative analysis of the three most advanced modeling techniques (state space, DCB, and ACB) used in estimating the sensitivity of REIT indices to changes in both the bond market and the stock market. Van Nieuwerburgh (2019) argues that a model with a bond market and stock market factor is both the most basic and most natural model of risk for REITs as the bond market beta measures how sensitive REITs are to changes in interest rates and the stock market beta measures how sensitive REITs are to changes in economic activity. ${ }^{25}$ A similar model is used by Allen et al. (2000). Moreover, we note that the addition of three Fama-French risk factors (size, value, and momentum) to the original two-factor model in the study of Van Nieuwerburgh (2019) leaves the bond and stock market betas almost unchanged. As a consequence, we follow Van Nieuwerburgh (2019) and choose to perform our analysis on the following parsimonious two-factor model:
$$\tilde{r}{\mathrm{REIT}, t}=\alpha_t+\beta{B, t} \tilde{r}{B, t}+\beta{M, t} \widetilde{r}{M, t}+\varepsilon_t,$$ where $\widetilde{r}{\text {REIT }}$ is the excess return on the REIT market, measured by the daily excess return on the FTSE EPRA Nareit index, $\widetilde{r}B$ is the excess return on the bond market, measured by the daily excess return on the sovereign bond index and $\widetilde{r}_M$ is the excess return on the stock market, measured by the daily excess return on the stock market index. Equation (66) corresponds to the conditional risk factor model that we use to estimate conditional betas on day $t$ from a regression of the daily excess REIT index returns on the excess stock market and bond market returns. In the special case where $\boldsymbol{\beta}_t=\left(\beta{B, t}, \beta_{M, t}\right)^{\prime}=\boldsymbol{\beta}$, the betas are restricted to be constant. Note also that for some models, the alpha is allowed to be time-varying as well. However, empirical results (not reported here to save space) suggest that $\alpha_t=\alpha(\forall t)$ once allowing the conditional betas of this two-factor model to be time-varying.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Autoregressive Conditional Betas

Darolles等人(2018)最近提出了上述状态空间模型的替代方案，该模型也允许直接规范动态条件beta。他们的模型称为CHAR，是一个基于$\left(\mathbf{x}_t, y_t\right)^{\prime}$的$m \times m$(与$m=N+1$)条件协方差矩阵$\Sigma_t$的Cholesky分解的多元GARCH模型。

$$\boldsymbol{\Sigma}t=\boldsymbol{L}t \boldsymbol{G}_t \boldsymbol{L}_t^{\prime},$$，其中$\boldsymbol{G}_t=\operatorname{diag}\left(g{11, t}, \ldots, g{m m, t}\right)$和$\boldsymbol{L}t$是一个较低的单角矩阵(即三角形，对角线上有1，对角线上有0)，元素$\ell{i j, t}$位于行$i$，列$j$为$i>j$。

$$\boldsymbol{L}=\left[\begin{array}{ccc} 1 & 0 & 0 \ l_{21, t} & 1 & 0 \ l_{31, t} & l_{32, t} & 1 \end{array}\right] \quad \boldsymbol{G}=\left[\begin{array}{ccc} g_{11, t} & 0 & 0 \ 0 & g_{22, t} & 0 \ 0 & 0 & g_{33, t} \end{array}\right]$$

$$\boldsymbol{\Sigma}=\left[\begin{array}{ccc} g_{11, t} & l_{21, t} g_{11, t} & l_{31, t} g_{11, t} \ l_{21, t} g_{11, t} & l_{21, t}^2 g_{11, t}+g_{22, t} & l_{21, t} l_{31, t} g_{11, t}+l_{32, t} g_{22, t} \ l_{31, t} g_{11, t} & l_{21, t} h_{31, t} g_{11, t}+l_{32, t} g_{22, t} & l_{31, t}^2 g_{11, t}+l_{32, t}^2 g_{22, t}+g_{33, t} \end{array}\right] .$$
Darolles et al.(2018)表明，如果$\boldsymbol{w}t \equiv\left(\mathbf{x}t, y_t\right)^{\prime}$有平均$\mathbf{0}$, \begin{aligned} w{i, t} & =\sum{j=1}^{i-1} \ell_{i j, t} \varepsilon_{j, t}+\varepsilon_{i, t}=\sum_{j=1}^{i-1} \ell_{i j, t}\left(w_{j, t}-\sum_{k=1}^{j-1} \ell_{j k, t} v_{k, t}\right)+\varepsilon_{i, t} \ & =\sum_{j=1}^{i-1} \beta_{i j, t} w_{j, t}+\varepsilon_{i, t} . \end{aligned}

$$y_t=\sum_{j=1}^{m-1} \beta_{i j, t} x_{j, t}+\varepsilon_{i, t}$$

## 经济代写|计量经济学代写Econometrics代考|Empirical Application on REITs

$$\tilde{r}{\mathrm{REIT}, t}=\alpha_t+\beta{B, t} \tilde{r}{B, t}+\beta{M, t} \widetilde{r}{M, t}+\varepsilon_t,$$其中$\widetilde{r}{\text {REIT }}$为房地产投资信托基金市场的超额收益，以富时EPRA Nareit指数的每日超额收益衡量;$\widetilde{r}B$为债券市场的超额收益，以主权债券指数的每日超额收益衡量;$\widetilde{r}M$为股票市场的超额收益，以股票市场指数的每日超额收益衡量。式(66)对应于条件风险因子模型，我们使用该模型从超额股票市场和债券市场回报的每日超额REIT指数回报的回归中估计day $t$的条件贝塔。在$\boldsymbol{\beta}_t=\left(\beta{B, t}, \beta{M, t}\right)^{\prime}=\boldsymbol{\beta}$的特殊情况下，beta被限制为常数。还要注意，对于某些模型，alpha也允许时变。然而，实证结果(为了节省篇幅，这里没有报道)表明$\alpha_t=\alpha(\forall t)$一旦允许这个双因素模型的条件贝塔是时变的。

## 经济代写|计量经济学代写Econometrics代考|Futures Prices and Hedging Demand

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

## 经济代写|计量经济学代写Econometrics代考|Futures Prices and Hedging Demand

Most studies relating CIT trade positions to commodity prices presume that CIT (demand side) initiate the trades and Granger causes the futures price rises. However, CIT positions also reflect producers’ hedging needs (supply side). We need here an identification strategy designed to identify a CIT demand shock in view to assess the genuine contribution of CIT investors to the price evolution. Cheng et al. (2015) used fluctuations in the VIX to isolate trades initiated by CITs and found a positive correlation between CIT position changes and futures prices. Henderson et al. (2015) used commodity-linked note (CLN) issuances to similarly identify trade initiated by financial traders. They found that financial traders “have significantly positive and economically meaningful impacts on commodity futures prices around the pricing dates of the CLNs when the hedge trades are executed and significantly negative price impacts around the determination dates when the hedge trades are unwounded.”
4.4.2 Spot Prices and Macro-Driven Boom
If large inflows of institutional investors on commodity markets can affect the commodity futures prices, the reverse is also true. Indeed, rising commodity prices also attract institutional investors. Most papers based on correlation measures are subject to this endogeneity concern.

Tang and Xiong (2012) studied the correlation of non-energy commodity returns with oil returns and propose a solution. They analyze separately the commodities included in the S\&P GSCI and DJ-UBSCI (treatment group) and the commodities excluded from these indices (control group). They found that the commodities of the treatment group, which are presumed to be subject to commodity index traders’ purchases, had a rise in their correlation with oil returns significantly larger than the one of the commodities in the control group.

As an alternative, Kilian and Murphy (2014) deal with reverse causality by relying on structural VAR modelling and sign restrictions as identification strategy. They use monthly “the percent change in global oil production, a measure of cyclical variation in global real activity, the real price of crude oil, and the change in above-ground global crude oil inventories. The model is identified based on a combination of sign restrictions and bounds on the short-run price elasticities of oil demand and oil supply.”

## 经济代写|计量经济学代写Econometrics代考|De-Financialization

Weekly futures open interest as reported in CFTC’s CoT fell by $50 \%$ in 2008 but has then recovered and is currently far above its pre-crisis levels. However, all indicators do not support the belief of a constantly rising financialization. The BIS notional value of outstanding OTC commodity derivatives has collapsed from USD 14.1 trillion in 2008 to USD 2.1 trillion in 2019, now stable for more than five years. In addition, the composition of the open interest (in terms of producer, swap dealer, money managers, pother reportable) has remained remarkably stable since 2006 (see Fig. 9 in Bhardwaj et al. 2015).

Further, the presumed effects on financialization on inter-commodity correlation and equity-commodity correlations have vanished as documented via simple rolling correlations in Bhardwaj et al. (2015) and via the explanatory power of multifactor models in Christoffersen et al. (2019). Zhang et al. (2017) explicitly raise the question of “de-financialization,” measured as correlation between equity market and oil and gas markets. Based on a variance-threshold dynamic correlation model, they conclude that financialization persists since 2008.

Discussion
The literature on financialization of commodity markets is challenged by the difficulty to identify the exogenous contribution of financial investors to commodity prices. A clear rise of correlation among commodity prices and between commodity and equity prices has been documented by many from 2004 to around 2010, but only few papers were explicitly accounting for reverse causality (rising prices attract investors) or for hedging supply-demand determination (do financial investors go long because commodity hedgers are on the rise). Those that develop original identification strategy (Tang and Xiong (2012), Cheng et al. (2015), Henderson et al. (2015) among others) show that the debate on the persistent effects of financialization ten years after the financial crisis remains open.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Futures Prices and Hedging Demand

4.4.2现货价格与宏观经济繁荣

Tang and Xiong(2012)研究了非能源商品收益与石油收益的相关性，并提出了解决方案。他们分别分析了纳入S\&P GSCI和DJ-UBSCI的商品(治疗组)和未纳入这些指数的商品(对照组)。他们发现，假设受商品指数交易员购买影响的实验组的商品，其与石油收益的相关性上升幅度明显大于对照组的商品。

## 经济代写|计量经济学代写Econometrics代考|De-Financialization

CFTC的CoT报告的每周期货未平仓合约在2008年下跌了50%，但随后有所回升，目前远高于危机前的水平。然而，并非所有指标都支持金融化持续上升的观点。国际清算银行未结算场外商品衍生品的名义价值已从2008年的14.1万亿美元暴跌至2019年的2.1万亿美元，目前已稳定五年多。此外，自2006年以来，未平仓合约的构成(就生产商、掉期交易商、资金经理、其他可报告方而言)保持了非常稳定(见Bhardwaj et al. 2015的图9)。

## 经济代写|计量经济学代写Econometrics代考|How to Measure the Real Exchange Rate

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## 经济代写|计量经济学代写Econometrics代考|How to Measure the Real Exchange Rate

Similar to nominal exchange rates, real exchange rates can be computed on a bilateral or on an effective basis.

In their seminal contribution, Chen and Rogoff (2003) studied commodity currencies with exchange rates expressed in USD. One obvious limit of bilateral exchange rates is that it does not isolate from factors that are specific to the reference currency area, namely the dollar zone. Checking the robustness of the results on alternative currencies is a necessity when working with bilateral exchange rates. Chen and Rogoff therefore compared their results with those obtained with exchange rates expressed in GBP.

Most studies on commodity currencies (Cashin et al. 2004; Bodart et al. 2012, 2015; Coudert et al. 2011) rely on the effective version of the exchange rate, defined as trade-weighted multilateral real exchange rate, where the weights are specific to each country trade network, as set out in Eq. (7)
$$\mathrm{RER}{i t}=\sum{j=1}^J w_{i j} \mathrm{RER}{i j t}$$ where $\mathrm{RER}{i t}$ is the real effective exchange rate of country $i, \operatorname{RER}{i j t}$ is the real bilateral exchange of country $i$ with country $j$, where $w{i j}$ is the weight associated to $\mathrm{RER}_{i j t}$, and where $J$ is the number of countries considered in the real effective exchange rate formula of country $i$. Such series are available from IMF-IFS database, or alternatively from Darvas (2012).

The strength of effective rates is that real exchange rates are measured in terms of a basket of currencies, thereby diluting the fluctuations due to country $j$ shocks. The weakness is that the basket is country specific, that is, $w_{i j}$ depends on $i$. Using countryspecific trade weights is mainly justified for studies focusing on competitiveness. An alternative is to use a fixed basket of currencies (in the vein of special drawing rights or of the Libra), set identically for all investigated countries, that is, $w_{i j}=w_j$ in Eq. (7). Chen and Rogoff (2003) took this option by replicating their analysis on Canada, Australia, and New Zealand by looking at the exchange rate with the socalled broad index, a composite of over 30 non-US-dollar currencies. Surprisingly, this interesting practice has not been much followed.

## 经济代写|计量经济学代写Econometrics代考|Real Versus Nominal

As discussed by Chinn (2006), we often face a trade-off between using the most appropriate real exchange rate measure conceptually, and the most readily available data.

In practice, one only has a choice of a few price deflators. At the monthly frequency, they include the consumer price index (CPI), producer price index (PPI), wholesale price index (WPI), and export price index. At lower frequencies, such as quarterly, the set of deflators increases somewhat, to include the GDP deflator, unit labor costs, and price indices for the components of GDP, such as the personal consumption expenditure (PCE) deflator.

Typically, the CPI is thought of as weighting fairly heavily non-traded goods such as consumer services. Similarly, the GDP deflator and the CPI weigh expenditures on non-tradables in proportion to their importance in the aggregate economy. In contrast, the PPI and WPI exclude retail sales services that are likely to be non-traded.

Due to availability constraints for long periods and the need of a large enough set of developing countries, most studies use CPI-real exchange rates (Chen and Rogoff 2003; Cashin et al. 2004; Bodart et al. 2012, 2015), as provided by the IMF-IFS database for a wide set of countries and years.

Clearly, for purposes of calculating the relative price of goods and services that are tradable, the preferred measure would have been the exchange rate deflated by PPIs or WPIs were the data available. It is worth noting that a recent empirical paper of Ahn, Mano, and Zhou (2017), compared CPI, GDP, and ULC deflators in the context of the expenditure switching mechanism studies. It supports Chinn (2006) statement that the choice of the deflator may have considerable effects on the empirical conclusions.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|How to Measure the Real Exchange Rate

Chen和Rogoff(2003)在其开创性贡献中研究了以美元表示汇率的商品货币。双边汇率的一个明显限制是，它没有与参考货币区(即美元区)特有的因素隔离开来。在处理双边汇率时，检查替代货币结果的稳健性是必要的。因此，Chen和Rogoff将他们的结果与以英镑表示的汇率得到的结果进行了比较。

$$\mathrm{RER}{i t}=\sum{j=1}^J w_{i j} \mathrm{RER}{i j t}$$ 在哪里 $\mathrm{RER}{i t}$ 一国的实际有效汇率是多少 $i, \operatorname{RER}{i j t}$ 真正的双边交流是国家的吗 $i$ 有国家 $j$，其中 $w{i j}$ 重量与 $\mathrm{RER}_{i j t}$，在哪里? $J$ 国家的实际有效汇率公式中是否考虑了国家的数量 $i$． 这些序列可从IMF-IFS数据库获得，也可从Darvas(2012)获得。

## 有限元方法代写

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

## MATLAB代写

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

## 经济代写|计量经济学代写Econometrics代考|Deterministic Trends

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

## 经济代写|计量经济学代写Econometrics代考|Deterministic Trends

First, let us assume that the relative commodity price series is generated by a trendstationary (TS) data process as follows
$$\mathrm{COMP}_{\mathrm{t}}=\alpha+\beta t+\varepsilon_t$$
where $\mathrm{COMP}_t$ is the logarithm of the commodity price indice, where $t$ is an annual deterministic trend, where $\varepsilon_t$ is a stationary process with mean equal to zero, an ARMA for example, and where the sign and significance of $\beta$ lead to conclusions on the PSH. Most studies based on this methodology (Sapsford 1985; Grilli and Yang 1988) found support to the PSH, in other words $\beta$ was found to be significantly negative.

Of course, these conclusions are subject to the validity of the stationarity assumption. Non-stationarity of the error terms could lead to spurious rejection of the null $\beta=0$ and to spurious support of the PSH. Cuddington and Urzua (1989) were the first to carry out unit-root tests on the Grilli-Yang commodity price dataset. Similarly, Kim et al. (2003) showed that the 24 commodity price series contained in the standard Grilli-Yang commodity price index are characterized by unit-root behaviors (18 commodities) or quasi-unit roots ( 6 commodities). Similar results were reported by Cuddington (1992) and Newbold et al. (2005).

## 经济代写|计量经济学代写Econometrics代考|Stochastic Trends

Consequently, we can assume that the relative commodity price series are generated by a difference-stationary (DS) process as follows
$$\Delta \mathrm{COMP}_t=\beta+u_t$$
where $\Delta P_t$ is the differenced logarithm of the commodity price index, where $u_t$ is a stationary process, an ARMA for example, with mean equal to zero, and where the sign and significance of $\beta$ leads to conclusions on the PSH. Kim et al. (2003) accounted for non-stationarity and find much less support to the PSH. Indeed, using the same 24 commodity prices of the Grilli-Yang database, they observe that the null hypothesis of $\beta=0$ is much less frequently rejected with a non-stationary process specification than in stationary models.

The finding that most commodity price series largely behave like random walks is not anodine. A shock to the price of, say, copper today would thus be permanent. Copper price would no longer revert to any stable, long-run values/trends. As a consequence, stabilization mechanism as the one implemented by Chile, whereby asset accumulation is conditioned on copper prices being above a long-term level, would theoretically no longer be sustainable as it relies on the concept of a stable level/trend.

Detection of unit roots remains subject to some caution. It might be spuriously derived from a bad specification of the data-generating process or due to the wellknown lack of power of standard non-stationary tests (Schwert 1987). We now consider extensions related to these two possibilities and see that the conclusions supporting the PSH lose their strength.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Deterministic Trends

$$\mathrm{COMP}_{\mathrm{t}}=\alpha+\beta t+\varepsilon_t$$

## 经济代写|计量经济学代写Econometrics代考|Stochastic Trends

$$\Delta \mathrm{COMP}_t=\beta+u_t$$

## 有限元方法代写

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

## MATLAB代写

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

## 经济代写|计量经济学代写Econometrics代考|Structural Generalized Impulse-Response Function (SGIRF) Analysis of US Productivity Shocks

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

## 经济代写|计量经济学代写Econometrics代考|Structural Generalized Impulse-Response Function (SGIRF) Analysis of US Productivity Shocks

The identification of shocks has been a major issue in GVAR models. In order to conduct dynamic analysis, the vast majority of research papers using GVAR models rely on the GIRF proposed by Koop et al. (1996) and further developed by Pesaran and Shin (1998). The identification of shocks in a GVAR model is complicated due to the cross-country interactions and high dimensionality of the model.

The identification in a traditional VAR analysis is usually achieved by using the orthogonalized impulse-response functions (OIRFs) that require a certain ordering of variables. This approach is often not suitable for GVAR models, as it requires ordering not only of the variables, but also countries. As a result, when a large number of variables and countries are included in the model, it becomes difficult to justify such ordering based on economic theory and empirical findings. The advantage of GIRFs is that they are invariant to the ordering of countries and variables. This is very convenient for models like GVAR that involve many countries and variables. However, it comes at a cost. Critics often argue that in GIRFs, the error terms are not orthogonal and it allows correlation among them. This, in turn, makes economic interpretation of shocks difficult.

We take this into account by using SGIRFs instead of GIRFs. The SGIRF allows the most dominant economy in the model to be ordered first and also its variables to have certain ordering. Since the main aim of this paper is to investigate spillover effects of productivity shocks arising in the USA, the largest economy in the model, the USA and its variables are ordered first. This means that the identifying scheme for the model of the USA is based on a lower-triangular Cholesky decomposition and has the following ordering: [R\&D, TFP, capital, GDP]’. Thus, for the USA, R\&D is ordered first, followed by TFP because greater expenditure on R\&D could increase TFP. This assumes that R\&D spending affects TFP contemporaneously, but not vice versa. TFP is then followed by capital and GDP. This ordering system assumes that GDP is the most endogenous variable, which is a realistic assumption to make. Other countries and their variables are kept unrestricted. More about the GIRF and SGIRF is discussed in the appendix.

## 经济代写|计量经济学代写Econometrics代考|Productivity Shocks in the EU, Non-OECD, and Others

Figures 4, 5 and 6 show the response of the same variables to one standard deviation (SD) positive shock in ‘the EU,’ ‘non-OECD,’ and ‘Others’ country groups, respectively. The first row of each figure shows the response of GDP to a TFP shock. The EU’s TFP shock does have some positive and significant effects on GDP of the EU and the other country groups. Compared to the US TFP shock, these reactions are smaller in magnitude. EU’s TFP shock also increases US R\&D and has a further positive effect on its own TFP. Such reactions are, however, significant for a very short period of time. A shock to the non-OECD group’s TFP has some positive significant effect on its own GDP, but spillover effects are not highly significant. A shock to the final group ‘Others’ has no significant effect on the GDP of any country groups either. In terms of the effect on other variables, results are not very significant.

Interestingly, a positive TFP shock is associated with increases in R\&D spending for the USA and other country groups. This might be due to the size of the US R\&D and the fact that US multinational firms are much more global in terms of investing in other country groups. According to the Forbes Global 2000 that lists top 2000 companies in the world, the USA was ranked first in terms of the number of firms included in this list. An increase in productivity in the rest of the world creates greater incentives for them to expand their business by spending more on R\&D. Put it differently, productivity improvements in other country groups are dependent upon productivity advances in the USA. On the contrary, R\&D spending in the EU decreases when there is a positive TFP shock in ‘Non-OECD’ and ‘Others’ country groups. These results might explain why the EU is still lagging behind the USA in terms of research and innovation and are in line with findings of Miller and Atkinson (2014). While the USA is able to make best use of productivity improvements in other countries, the rest of the world fails to do so.

# 计量经济学代考

## 有限元方法代写

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

## MATLAB代写

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

## 经济代写|计量经济学代写Econometrics代考|Time-Varying VECM Specification for Wealth Effects

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

## 经济代写|计量经济学代写Econometrics代考|Time-Varying VECM Specification for Wealth Effects

This specification is more original as it enables both the long-run relationship (cointegration relationship) and the ECM to exhibit nonlinearity. ${ }^8$ This novel specification allows a generalization of both first and second specifications and offers a more original econometric framework to investigate complex wealth effects.

Formally, following Bierens and Martins (2010), we first compute the multivariate time-varying cointegration. Bierens et Martins (2010) explained that long-run coefficients of the $\operatorname{VAR}(\mathrm{p})$ are allowed to change with time and can be approximated by a finite sum of Chebyshev polynomials. In this way, the Bierens and Martins methodology considers a multivariate VECM framework for which the Johansen (1991) model is a special case.
Thus we start with the following TV-VECM of order $p$ :
$$\Delta Z_t=\mu+\alpha \beta_t^{\prime} Z_{t-1}+\sum_{j=1}^{p-1} \Gamma_j \Delta Z_{t-j}+\varepsilon_t, \varepsilon_t \sim \text { i.i.d. } N_k(0, \Omega), t=1, \ldots, T .$$
With $Z_t=\left(C_t, T W_t\right.$, Income $\left._t\right)$ for the model with aggregate data or $Z_t=$ $\left(C_t, F W_t, H W_t\right.$, Income $\left._t\right)$ when considering the disaggregate data. $\mu, \alpha$ and $\beta$ are $3 \times 1$ fixed coefficients vectors.

Contrary to the standard VECM from Johansen (1991), the coefficients may be time-varying. Assuming that the function of discrete time $\beta_t$ is smooth in line with Bierens and Martins (2010), we thus have the following: $\beta_t=\beta_m\left(\frac{t}{T}\right)=$ $\sum_{i=0}^m \xi_{i, T} P_{i, T}(t)$ where the orthonormal Chebyshev time polynomials $P_{i, T}(t)$ are defined by $P_{0, T}(t)=1, P_{i, T}(t)=\sqrt{2} \cos \left(\frac{i \pi(t-0.5)}{T}\right), t=1,2, \ldots, T, i=$ $1,2, \ldots, m$ and $\xi_{i, T}=\frac{1}{T} \sum_{t=1}^T \beta_t P_{i, T}(t)$ are unknown $k \times r$ matrices with $k$ the number of variables and $r$ the rank.

## 经济代写|计量经济学代写Econometrics代考|Data and Preliminary Analysis

Data are quarterly and cover the period 1987Q1 to 2011Q4. They concern France and are obtained from financial and non-financial national accounts. Consumption is defined as the household’s total expenditures, while Income corresponds to the flow of human wealth and is measured by disposable income net of property and imputed rents. Financial wealth consists in the household’s financial assets net of debts, whereas Housing wealth consists in tangible assets (land and housing). Our study extended the one by Chauvin and Damette (2011), who used similar data over the period 1987-2008, by focusing on nonlinearity in the wealth-consumption relationship. It also extended their study through the use of more recent data to outline the effect of the subprime crisis on the Consumption/Wealth relationship. More details about the data are reported in Fig. 1.

First, the analysis of Fig. 1-which reports consumption, income, total wealth, HW and $\mathrm{FW}$ in logarithms-shows that series are a priori non-stationary in level. Furthermore, consumption and $\mathrm{HW}$ indicate some smoothness and seem less volatile than income, FW and Total Wealth (TW). We also plot the dynamics of the FW/Income and HW/Income ratios, using the disposable income net of property and imputed rents. These ratios show some French stylized facts associated with the preference of French householders for real estate investments to financial investments. This fact is more marked after the 2000 dotcom bubble.

Second, we tested for the presence of a unit root in the data. To this end, we performed both the usual unit root tests-ADF of Dickey-Fuller (1979) and DFGLS of Elliot, Rothenberg, Stock (1996)_and also a unit root test with structural breaks of Zivot and Andrews (1992) and Kapetanios et al. (2003) in the nonlinear STAR framework. Accordingly, all series are integrated of order one, noted I(1). ${ }^9$ We focused thereafter on the variables in first difference.

# 计量经济学代考

## 经济代写|计量经济学代写Econometrics代考|Time-Varying VECM Specification for Wealth Effects

$$\Delta Z_t=\mu+\alpha \beta_t^{\prime} Z_{t-1}+\sum_{j=1}^{p-1} \Gamma_j \Delta Z_{t-j}+\varepsilon_t, \varepsilon_t \sim \text { i.i.d. } N_k(0, \Omega), t=1, \ldots, T .$$

## 有限元方法代写

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

## MATLAB代写

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