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## 经济代写|计量经济学代写Introduction to Econometrics代考|Out-of-Sample Estimates

The aim of this section is to illustrate the usefulness of the competing models in a portfolio and risk management exercise. Since realized betas are not observed, it is impossible to judge the quality of the models by looking at the forecasting errors of the conditional betas.

Instead, following Engle (2016) and Darolles et al. (2018), we perform a tracking exercise that consists in taking a position at time $t$ in the two considered factors (bond and market) whose weights are the one-step ahead forecasts of the corresponding conditional betas.

For each model, the conditional betas forecasts are, therefore, used to construct a hedging portfolio. The returns on this portfolio are obtained using the conditional betas forecasts, i.e.,
$$Z_{\mathrm{REIT}, t+1 \mid t}=\beta_{B, t+1 \mid t} \widetilde{t}{B, t+1}+\beta{M, t+1 \mid t} \widetilde{r}_{M, t+1},$$

where $\tilde{r}{B, t+1}$ and $\tilde{r}{M, t+1}$ are the realized excess log-returns of the two factors at time $t+1$ while $\beta_{B, t+1 \mid t}$ and $\beta_{M, t+1 \mid t}$ are the one-step-ahead forecasts of the conditional betas obtained at the end of day $t$.

This hedging portfolio can be interpreted as a portfolio invested in the risk factors and which optimally tracks the corresponding REIT returns. It is a hedging portfolio in the sense that it can be sold short to hedge the main risks of a given portfolio. In this asset pricing context, expected returns on any asset are linear in the betas and only depend upon the risk premiums embedded in the factors. In other words, there is no alpha or intercept in (69).

For both the USA and developed Europe, we compute the ex-post tracking errors as follows:
$$T E_{t+1 \mid t}=\widetilde{r}{\text {REIT }, t+1}-Z{\text {REIT }, t+1 \mid t}$$
and we look for the model that has the smallest sample mean square error (MSE) and mean absolute deviation (MAD) over the 250 values of the tracking errors using the model confidence set approach of Hansen et al. (2011). Models are reevaluated every 25 steps so that estimated parameters are kept constant to produce 25 one-step-ahead forecasts of the conditional betas before being updated.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Glick–Rogoff Small-Country Model with Adjustment Costs to Investment

A small-country faces both country-specific productivity shocks and global productivity shocks. Global productivity shock can be mitigated by trading global bonds in the world capital market at the riskless gross world interest rate $r$. However, the representative agent in each country cannot diversify country-specific shocks. The representative firm chooses the path of investments to maximize the present discounted value of future profits under the given aggregate output (1). ${ }^3$ Taking a linear approximation to the first-order condition yields Eqs. (2) and (3).
$$\begin{gathered} Y_t=A_t^c K_t^\alpha\left[1-\frac{g}{2}\left(\frac{I_t^2}{K_t}\right)\right] \ Y_t \cong \alpha_I I_t+\alpha_K K_t+\alpha_A A_t^c \ I_t \cong \beta_1 I_{t-1}+\eta \sum_{s=1}^{\infty} \lambda^s\left(E_t A_{t+s}^c-E_{t-1} A_{t+s-1}^c\right) \end{gathered}$$
In Eq. (3), the first term captures the past investment (or lagged productivity shock) on the current investment, and the second term captures the impact of revisions in expectations about the future path of productivity.

The representative agent chooses the path of consumption to maximize the present discounted utility (4).
$$\mathrm{E}t \sum{s=0}^{\infty} \beta^s U\left(C_{t+s}\right), \text { where } U_t=C_t-\frac{h}{2} C_t^2, \text { s.t. } F_{t+1}=r F_t+Y_t-I_t-C_t,$$

where $r$ is assumed to be equal to $\beta$. The solution to the maximization for consumer yields (5), and the ex-post rate of change of consumption depends only on the unanticipated movement in permanent net income (6).
$$\begin{gathered} C_t=\frac{r-1}{r}\left(F_t+E_t \sum_{s=0}^{\infty} \frac{Y_{t+s}-I_{t+s}}{r^s}\right)=\frac{r-1}{r} F_t+\bar{Y}t-\bar{I}_t \ \Delta C_t=\left(E_t-E{t-1}\right) \frac{r-1}{r}\left(E_t \sum_{s=0}^{\infty} \frac{Y_{t+s}-I_{t+s}}{r^s}\right)=\left(\bar{Y}t-\bar{I}_t\right)-E{t-1}\left(\bar{Y}_t-\bar{I}_t\right) \end{gathered}$$
Differencing the accounting identity for the current account, we obtain the following equation.
$$\Delta C A_t=(r-1) \Delta F_t+\Delta Y_t-\Delta I_t-\Delta C_t$$
Combining the equations obtained from maximization for $\Delta I_t, \Delta Y_t, \Delta C_t$ with Eq. (7) yields the estimating equation for the current account ${ }^4$.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Out-of-Sample Estimates

$$Z_{\mathrm{REIT}, t+1 \mid t}=\beta_{B, t+1 \mid t} \widetilde{t}{B, t+1}+\beta{M, t+1 \mid t} \widetilde{r}_{M, t+1},$$

$$T E_{t+1 \mid t}=\widetilde{r}{\text {REIT }, t+1}-Z{\text {REIT }, t+1 \mid t}$$

## 经济代写|计量经济学代写Introduction to Econometrics代考|Glick–Rogoff Small-Country Model with Adjustment Costs to Investment

$$\begin{gathered} Y_t=A_t^c K_t^\alpha\left[1-\frac{g}{2}\left(\frac{I_t^2}{K_t}\right)\right] \ Y_t \cong \alpha_I I_t+\alpha_K K_t+\alpha_A A_t^c \ I_t \cong \beta_1 I_{t-1}+\eta \sum_{s=1}^{\infty} \lambda^s\left(E_t A_{t+s}^c-E_{t-1} A_{t+s-1}^c\right) \end{gathered}$$

$$\mathrm{E}t \sum{s=0}^{\infty} \beta^s U\left(C_{t+s}\right), \text { where } U_t=C_t-\frac{h}{2} C_t^2, \text { s.t. } F_{t+1}=r F_t+Y_t-I_t-C_t,$$

$$\begin{gathered} C_t=\frac{r-1}{r}\left(F_t+E_t \sum_{s=0}^{\infty} \frac{Y_{t+s}-I_{t+s}}{r^s}\right)=\frac{r-1}{r} F_t+\bar{Y}t-\bar{I}t \ \Delta C_t=\left(E_t-E{t-1}\right) \frac{r-1}{r}\left(E_t \sum{s=0}^{\infty} \frac{Y_{t+s}-I_{t+s}}{r^s}\right)=\left(\bar{Y}t-\bar{I}_t\right)-E{t-1}\left(\bar{Y}_t-\bar{I}_t\right) \end{gathered}$$

$$\Delta C A_t=(r-1) \Delta F_t+\Delta Y_t-\Delta I_t-\Delta C_t$$

## 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。

Posted on Categories:Financial Econometrics, 经济代写, 计量经济学

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## 经济代写|计量经济学代写Introduction to Econometrics代考|Time-Varying Betas with Interaction Variables

Rolling OLS and ‘realized betas’ do not rely on a parametric model to specify the dynamics of the time-varying betas. Shanken (1990) and Schadt (1996) introduce the hypothesis that the dynamics of the betas depends on a set of exogenous variables. This leads to an alternative way of modeling conditional betas, via the use of interaction variables (see also Gagliardini et al. 2016).

Indeed, interaction variables can be used to introduce dynamics in $\beta_{n, t}$ in the following way:
$$\beta_{n, t}=\beta_n+\sum_{k=1}^K \theta_{n, k} Z_{k, t-1}$$
where each $Z_{k, t-1}$ variable $(k=1, \ldots, K)$ is an observable state variable, predetermined at the end of period $t-1$, and assumed to drive the dynamics of the beta of the $n$ ‘th factor, and where $\theta_{n, k}$ is its associated coefficient. The above model can be rewritten as
$$\tilde{r}{i, t}=\alpha+\beta \tilde{r}{M, t}+\sum_{k=1}^K \theta_k Z_{k, t-1} \tilde{r}_{M, t}+\varepsilon_t$$
and, therefore, corresponds to a multiple linear regression model with $k$ interaction variables when the conditional variance is constant or a GARCH model with $k$ interaction variables in the conditional mean when the conditional variance is assumed to follow a GARCH dynamics.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Indirect Dynamic Conditional Betas

As we have seen, the theoretical conditional CAPM expresses the conditional market beta as follows:
$$\beta_{i, t}=\frac{\operatorname{cov}t\left(R{M, t+1}, R_{i, t+1}\right)}{\operatorname{var}t\left(R{M, t+1}\right)} .$$

This expression opens up the possibility of obtaining time-varying betas from the estimation of conditional variances and covariances obtained, for instance, by a multivariate GARCH model (see for instance Bali 2010 for an application and Bauwens et al. 2006 for a survey on MGARCH models). In this case, the model imposes a minimal structure on the time-varying process, apart from the modeling of conditional variances and covariances in an autoregressive form. However, Eq. (39) does not apply in the multi-factor model when the factors are correlated.

Engle (2016) recently extended the multivariate GARCH approach to the case of a multi-factor model. Following Engle’s (2016) methodology, the conditional betas are inferred from an estimate of the conditional covariance matrix $\Sigma_t$ of $\left(\mathbf{x}_t, y_t\right)^{\prime}$.
For ease of exposition, we assume in this section that $\mathbf{x}$ and $y$ have been centered so that $\mathbf{x}$ does not contain a vector of ones (corresponding to $\alpha$ ) and, therefore, one does not need to estimate the intercept in (31).

In order to obtain the coefficients of the multivariate regression of $y_t$ (asset returns) on $\mathbf{x}t$ (factors), Engle (2016) assumes that $\left(\mathbf{x}_t, y_t\right)^{\prime}$ follows an $(N+1)$-dimensional normal distribution (conditional on the information set at time $t-1$, denoted $\mathcal{F}{t-1}$ ), i.e.
$$\left(\begin{array}{c} \mathbf{x}t \ y_t \end{array}\right) \mid \mathcal{F}{t-1} \sim N\left(\left(\begin{array}{c} \mathbf{0}{m-1} \ 0 \end{array}\right), \Sigma_t \equiv\left(\begin{array}{cc} \Sigma{\mathbf{x x}, t} & \Sigma_{\mathbf{x} y, t} \ \Sigma_{y \mathbf{x}, t} & \Sigma_{y y, t} \end{array}\right)\right),$$
where subscripts embody natural partitions.
In order to derive an estimate of the conditional betas, Engle (2016) relies on the fact that the conditional distribution of $y_t$ on $\mathbf{x}t$ is $$y_t \mid \mathbf{x}_t \sim N\left(\Sigma{y \mathbf{x}, t} \Sigma_{\mathbf{x x}, t}^{-1} \mathbf{x}t, \Sigma{y y, t}-\Sigma_{y \mathbf{x}, t} \Sigma_{\mathbf{x x}, t}^{-1} \Sigma_{\mathbf{x} y, t}\right) .$$
In more details, estimates of the time-varying coefficients inferred from the regression of $y_t$ on $\mathbf{x}t$ can be retrieved from $\Sigma_t$ as follows: $$\widehat{\boldsymbol{\beta}}_t^{\mathrm{DCB}} \equiv\left(\hat{\beta}{1, t}^{\mathrm{DCB}}, \ldots, \hat{\beta}{N, t}^{\mathrm{DCB}}\right)^{\prime}=\Sigma{\mathbf{x x}, t}^{-1} \Sigma_{\mathbf{x} y, t} .$$

## 经济代写|计量经济学代写Introduction to Econometrics代考|Time-Varying Betas with Interaction Variables

$$\beta_{n, t}=\beta_n+\sum_{k=1}^K \theta_{n, k} Z_{k, t-1}$$

$$\tilde{r}{i, t}=\alpha+\beta \tilde{r}{M, t}+\sum_{k=1}^K \theta_k Z_{k, t-1} \tilde{r}_{M, t}+\varepsilon_t$$

## 经济代写|计量经济学代写Introduction to Econometrics代考|Indirect Dynamic Conditional Betas

$$\beta_{i, t}=\frac{\operatorname{cov}t\left(R{M, t+1}, R_{i, t+1}\right)}{\operatorname{var}t\left(R{M, t+1}\right)} .$$

Engle(2016)最近将多元GARCH方法扩展到多因素模型的情况。根据Engle(2016)的方法，条件贝塔是从$\left(\mathbf{x}_t, y_t\right)^{\prime}$的条件协方差矩阵$\Sigma_t$的估计中推断出来的。

## 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。

Posted on Categories:Financial Econometrics, 经济代写, 计量经济学

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## 经济代写|计量经济学代写Introduction to Econometrics代考|How to Measure Financialization

Few datasets are available to study the evolution of the share of financial commodity investors in the markets. The semi-annual BIS dataset on OTC derivative commodity contracts does not provide a breakdown by types of investors.

The US Commodity Futures Trading Commission (CFTC) on the contrary provides on a weekly basis reports that contribute to identifying different categories of investors. The Disaggregated Commitments of Traders (COT) covers 22 major physical commodity markets and reports the open interest positions by separating traders into the following four categories of traders: producer/merchant/processor/user; swap dealers; managed money; and other reportables. There are mainly two limits to these data. First, the breakdown does not inform on whether positions are taken on a speculation or hedging basis (Fattouh et al. 2013). Second, the rising role of institutional investors is not visible directly as such investors are split into the swap dealers, managed money, and other reportables categories.

As a response, the CFTC provides a report since January 2009 called the COT Supplement that covers 13 selected agriculturals with a breakdown now identifying explicitly the so-called Commodity Index Traders (CIT). This dataset has been widely used in the empirical literature and used to infer CIT positions on other commodities (Singleton 2013), despite the critics on the validity and representativeness of such inferred positions (Irwin and Sanders 2011).

Other papers go more granular by relying on specific proprietary data, such as Brunetti et al. (2016) who used individual daily positions of large market participants data from CFTC’s large trader reporting system.

Finally, few papers rely on alternative data providers, as Henderson et al. (2015) that used commodity-linked notes issued by, and obligations of, financial institutions. Such notes are filed with the U.S. Securities and Exchange Commission (SEC) and made publicly available through the EDGAR database. These notes are typically purchased by non-informed traders and hedged via long positions on futures markets.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Indirect Measures

Although financialization relies on the inflow of financial investors, some studies do not use explicit dataset on investors’ positions, but rather take 2003/2004 as an implicit break date where financialization takes effect. These papers provide evidence supporting a rise in comovement within commodity markets and with equity markets by relying on rolling window correlation (Bhardwaj et al. 2015), on variants of dynamic conditional correlation model (Silvennoinen and Thorp 2013; Zhang et al. 2017) or on the time-varying explanatory power of multifactor models (Christoffersen et al. 2019).

Whether direct measures dominate indirect measure remains an open question. The direct measures have a richer information set on the time-varying intensity of financial investor pressure. The indirect ones instead isolate from discussions on the relevant direct measures (CIT, swap dealers, and/or money managers) capturing financial investors’ pressure and by taking the simple, clear, but arbitrary, view of a break in 2004.

Financial investors are mainly active on the paper market. Most empirical studies therefore assess the impact of financialization on the futures prices. However, as discussed in Cheng and Xiong (2014), measuring the impact of financialization on futures is an intermediate step, as what ultimately matters is its impact on the spot market. There is then a second strand of literature that studies the mechanisms whereby the paper market (futures prices) impacts the real market (spot prices).
According to Cheng and Xiong (2014), futures prices are related to spot prices via three mechanisms. First, the theory of storage relates the futures and spot prices via an equilibrium relationship, as documented in Basak and Pavolva (2016). Second, the risk-sharing mechanism relates the futures and the expected future spot price via risk premia depending on the hedging pressure, as documented Acharya et al. (2013). Third, the informational role of futures markets takes futures prices as signals to guide commodity demand and thus spot prices, as documented in Dimpfl et al. 2017.

What the data providers call spot prices are not always spot prices, but often the nearest maturity futures contracts. Indeed, most spot trades occur over the counter and are not reported in harmonized datasets. Moreover, commodity spot prices are subject to substantial heterogeneity in data quality and commodity grades. Spot prices also reflect locations and specific transportation costs.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Indirect Measures

Cheng and Xiong(2014)认为，期货价格与现货价格通过三种机制相互关联。首先，存储理论通过均衡关系将期货和现货价格联系起来，如Basak和Pavolva(2016)所述。其次，风险分担机制通过风险溢价将期货和预期的未来现货价格联系起来，这取决于对冲压力，如Acharya等人(2013)所述。第三，期货市场的信息作用将期货价格作为引导商品需求的信号，从而引导现货价格，如Dimpfl等人2017年所述。

## 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。

Posted on Categories:Financial Econometrics, 经济代写, 计量经济学

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## 经济代写|计量经济学代写Introduction to Econometrics代考|Commodity Dependence Definitions

Commodity dependence is typically measured by the share of commodity-export earnings in total exports (IMF), in total merchandise exports (UNCTAD), and in GDP. Alternatively, commodity dependence can be measured by the percentage of people engaged in the production of commodities or by the share of government revenues due to commodity production and exports.

Part of the commodity currency literature picks some specific countries, without requiring any criterion, thereby presuming their commodity dependence, such as Russia, Saudi Arabia, and Norway in Habib and Kalamova (2007), or Australia, Canada, New Zealand, and South Africa in Chen and Rogoff (2003), Algeria in Koranchelian (2005) or Peru in Tashu (2015).

Another part of the literature casts the net wider by considering more systematically groups of countries specialized in commodities (Cashin et al. 2004; Bodart et al. 2015), or sub-groups such as energy (Coudert et al. 2011; Dauvin 2014). The main criterion used in this category of studies is the one originally set by the IMF where a country is classified as a commodity exporter when its primary commodity exports (categories SITC4 0, 1,2,3,4, and 68 of the Standard International Trade Classification) account for at least $50 \%$ of the value of total exports of goods and services on average over a given time window. The list of countries accordingly established in Cashin et al. (2004) has been used in many subsequent studies.

A new IMF definition from Aslam et al. (2016) sets a dual criterion that commodity exporters are emerging market and developing economies for which gross exports of commodities constitute at least $35 \%$ of total exports and net exports of commodities constitute at least $5 \%$ of exports-plus-imports on average. This new criterion of net export is certainly relevant as it helps in excluding the commodity-exporting countries that are large commodity importers. We expect indeed the export commodity price fluctuations to be offset by the import ones when the net export of commodities is not positive and large enough.

The literature is divided on the way to build the relevant commodity price series. The least relevant approach in our context would be to relate the real exchange rates to a world commodity price index. Such approach would be appropriate if countries were dependent on the same commodities (which is not the case) or if the commodity prices were highly correlated (which is not the case). The commodity currency literature then only considers country-specific commodity price indices based on the country-specific commodity exports.

The first approach, followed by Chen and Rogoff (2003), Cashin et al. (2004) and Coudert et al. (2011), considers a country-specific commodity price index, $\mathrm{CToT}{i t}$, constructed as follows $$\mathrm{CToT}{i t}=\sum_{h=1}^H w_{i h_i} P_{h_i t}$$
where $P_{h_i t}$ is the logarithm of the price of the commodity that ranks at the $h$-th position in commodity exports of country $i$, where $w_{i h_i}$ is the weight of that commodity in commodity exports (Cashin et al. 2004) or home production (Chen and Rogoff 2003) of country $i$, normalized such that the weights sum to one, where $\mathrm{H}$ is the number of most exported commodities considered for the formula $[H=3$ in Cashin et al. (2004) and $H=5$ in Coudert et al. (2011)].

## 经济代写|计量经济学代写Introduction to Econometrics代考|Commodity Dependence Definitions

Aslam等人(2016)的IMF新定义设定了双重标准，即商品出口国是新兴市场和发展中经济体，其商品出口总额至少占出口总额的$35 \%$，商品净出口平均至少占出口加进口的$5 \%$。这种净出口的新标准当然是相关的，因为它有助于排除大宗商品进口国中的大宗商品出口国。当商品净出口不是正值和足够大时，我们确实期望出口商品价格波动被进口商品价格波动所抵消。

Chen和Rogoff(2003)、Cashin等人(2004)和Coudert等人(2011)采用的第一种方法考虑了一个特定国家的商品价格指数$\mathrm{CToT}{i t}$，其构造如下$$\mathrm{CToT}{i t}=\sum_{h=1}^H w_{i h_i} P_{h_i t}$$

## 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。

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## 经济代写|计量经济学代写Introduction to Econometrics代考|Deflators

The PSH refers to a relative price where the denominator is expected to capture the evolution of import prices in developing countries. Three proxies are usually considered: the manufacturing unit values index, the U.S. manufacturing price index, and the consumer price indices.

The manufacturing unit values, or MUV, is a trade-weighted index of developed countries’ (24 countries in the current version) exports of manufactured goods to developing countries. It is built from UNCTAD’s Handbook of Statistics database and from IMF’s World Economic Outlook database (Spatafora and Tytell 2009). It covers the period after 1900 with some gaps for 1914-1920 and 1939-1947 that have been filled by interpolation by Grilli and Yang (1988) and updated notably by Pfaffenzeller et al. (2007). This proxy is by far the most frequently used (see for example, Aslam et al. 2016).

The US manufacturing price index was derived by Grilli and Yang (1988) as an index of domestic prices of manufactured products in the U.S. netting out energy, timber, and metal prices from the U.S. wholesale price index of industrial commodities. The key weakness of this indicator is that it only considers the mix of manufactured goods exports of one sole industrial country and also relies on the, strong, assumption of the law of one price whereby manufactured products prices in the US reflect the international prices.

The consumer price indices from major economies is a widely available alternative deflator. However, this proxy includes non-tradables, which unduly distort the terms of trade flavor that we want to capture.

As an alternative, commodity terms of trade could be measured against a price index of service sector outputs rather than manufacture, given the growing economic importance of the service sector. This suggestion certainly gains relevance as the weight of services reaches $23 \%$ of total world trade, growing by more than $7 \%$ in 2018 , with the US and EU accounting together for $44 \%$ of world service trade.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Datasets

The most widely-used dataset is the one developed by Grilli and Yang (1988). Their indices are mainly based on World Bank commodity price data. Grilli and Yang considered 24 non-fuel individual commodities: aluminum, bananas, beef, cocoa, coffee, copper, cotton, hides, jute, lamb, lead, maize, palm oil, rice, rubber, silver, sugar, tea, timber, tin, tobacco, wheat, wool, and zinc. They construct an all commodities price index and three sub-indices for agricultural food commodities, non-food agricultural commodities, and metals. The indices are base period trade-weighted arithmetic averages of the commodity prices concerned. They also provide an alternative geometric average version of the same (sub-) indices. Grilli and Yang’s original series ran from 1900 to 1986 but has been updated by a number of researchers (Pfaffenzeller et al. 2007).

For studying long-run price trends, the longer the series, the better. The Economist commodity price index goes back further to 1845, as used by Cashin and McDermott (2002). Harvey et al. (2010) assemble some data series back as far as 1650. Ensuring consistency and continuity over such a long period remains of course inexorably subject to cautious interpretations. Given the long-term perspective of the PSH, most researchers deal with annual frequency. Relying on monthly commodity price series of the World Bank, available as from 1960, would not bring additional relevant information.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Deflators

PSH指的是一种相对价格，其分母有望反映发展中国家进口价格的演变。通常考虑三个代理指标:制造业单位价值指数、美国制造业价格指数和消费者价格指数。

## 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。

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## 经济代写|计量经济学代写Introduction to Econometrics代考|Data and Model Specification

We use quarterly data from 1991 to 2016 for advanced and developing countries. There are 18 countries in the sample, divided into four groups. (1) The EU group consists of seven countries including Belgium, France, Germany, Italy, Netherlands, Switzerland, and the UK. ${ }^6$ (2) The non-OECD group consists of all the countries in the sample that are not part of OECD. It includes Brazil, China, Hong Kong, India, Mexico, Russia, and Taiwan. (3) Countries in the sample that do not fall into the above two categories are included in the ‘Others’ group. These are Canada, Japan,and Korea. (4) The USA is considered separately, as we are primarily interested in investigating spillover effects from the USA to other countries.

Regional variables for the groups ‘EU,’ ‘Non-OECD,’ and ‘Others’ were constructed by aggregating country-specific variables over $N$ countries.
$$y_t=\sum_{i=1}^N \omega_i y_{i, t}$$
where $y_t$ denotes a regional variable, $y_{i, t}$ is the value of that variable for country $i$, and $\omega_i$ represents the relative importance of a country $i$ within the region. Following Dees et al. (2007), $\omega_i$ is computed by dividing the PPP-GDP figure of each country by the total sum across the $N$ countries of the region, such that their weights add up to unity.

Spillover effects may be related to the level of trade with the rest of the world. Therefore, a country’s openness to other countries is calculated as (Import + Export)/GDP. Table 1 shows the openness of each country vis-a-vis the USA. This table shows the ratio being often greater than one. It follows that the majority of countries are indeed more open than the USA. Only two countries exhibit evidence of lesser openness than the USA, but even in these cases, the ratios are close to the US level.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Weak Exogeneity Test

As mentioned earlier, one of the main assumptions of the GVAR model is the weak exogeneity of the country-specific foreign variables $y_{i, t}^$. In general, a variable in a VARX model is considered weakly exogenous if it is not dependent on contemporaneous values of endogenous variables, but is likely to depend on the lagged values of these endogenous variables. More formally, $y_{i, t}^$ is considered weakly exogenous if $y_{i, t}$ does not affect $y_{i, t}^$ in the long run, but $y_{i, t}^$ is said to be ‘long-run forcing’ for $y_{i, t}$. As shown in Johansen (1992), this assumption allows proper identification of the cointegration relations. In the formal test, the joint significance of the estimated error-correction terms in auxiliary equations for the country-specific foreign variables $y_{i, t}^$ is tested. Specifically, for each $l$ th element of $y_{i, t}^$, a regression of the following form is conducted:
$$\Delta y_{i, t, l}^=a_{i, l}+\sum_{j=1}^{r_i} \delta_{i, j, l} \widehat{E C M}{i, j, t-1}+\sum{s=1}^{p_i^} \phi_{i, s, l}^{\prime} \Delta y_{i, t-s}+\sum_{s=1}^{q_i^} \Psi_{i, s, l} \Delta \tilde{y}{i, t-s}^+\eta{i, t, l}$$
where $\widehat{E C M}{i, j, t-1}$, for $j=1,2, \ldots, r_i$ are the estimated error-correction terms corresponding to the $r_i$ cointegrating relations found for the $i$ th country, and $p_i^$ and $q_i^$ are the orders of the lagged changes for the domestic and foreign variables, respectively. The test for the weak exogeneity is an $F$-test of the joint hypothesis that $\delta{i, j, l}=0$ for $j=1,2, \ldots, r_i$ in the above equation. It is not necessary that lag orders of $p_i^$ and $q_i^$ are the same for the underlying country-specific model. They are selected using the SB criterion.

The results are shown in Table 5. As can be seen, all the variables pass the weak exogeneity test, as the assumption of exogeneity cannot be rejected at the $5 \%$ level. This is a very desirable result, as it confirms the suitability of the GVAR model for this region. Based on the eigenvalues, the model was also found to be stable.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Data and Model Specification

“欧盟”、“非经合组织”和“其他”组的区域变量是通过汇总$N$国家的具体国家变量来构建的。
$$y_t=\sum_{i=1}^N \omega_i y_{i, t}$$

## 经济代写|计量经济学代写Introduction to Econometrics代考|Weak Exogeneity Test

$$\Delta y_{i, t, l}^=a_{i, l}+\sum_{j=1}^{r_i} \delta_{i, j, l} \widehat{E C M}{i, j, t-1}+\sum{s=1}^{p_i^} \phi_{i, s, l}^{\prime} \Delta y_{i, t-s}+\sum_{s=1}^{q_i^} \Psi_{i, s, l} \Delta \tilde{y}{i, t-s}^+\eta{i, t, l}$$

## 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。

Posted on Categories:Financial Econometrics, 经济代写, 计量经济学

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## 经济代写|计量经济学代写Introduction to 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 $(\mathrm{FW})$, housing wealth $(\mathrm{HW})$ 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.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Threshold ECM Specification for Wealth Effects

In a second time, we consider potential thresholds into the ECM framework and we extend the LECM by introducing nonlinearity in the adjustment and consideration of a Nonlinear ECM. In particular, we propose two different regressions for the wealth-consumption short-term adjustment dynamics: TAR-ECM and M-TARECM models in order to capture different forms of nonlinearities in the adjustment. This extension aims to capture further asymmetry and nonlinearity in the wealthconsumption adjustment relationship that may escape the LECM. It is thus a more flexible methodology to investigate cointegration. The difference between the TAR and MTAR models is in the definition of the Heaviside indicator function, which is based on the level value of the threshold of the indicator variable in the TAR model, while it is based on the difference of the indicator variable for the MTAR model.
In practice, TAR-ECM and M-TAR-ECM are estimated using the Enders and Siklos (2001) methodology which generalized the Engle and Granger procedure to allow for nonlinear adjustments. Indeed, the estimation of the TAR-ECM and M-TAR-ECM processes is based on the estimated residuals from the long-run relationship between the two variables, consumption and wealth [models (1) and (2)]. This also requires the existence of a single cointegration relationship (see for instance Marquez et al. 2013 for the UK case).
The M-TAR-ECM model can be written as:
$$\Delta \hat{u}t=I_t \rho_1 \hat{u}{t-1}+\left(1-I_t\right) \rho_2 \hat{u}{t-1}+\sum{i=1}^k \gamma_i \Delta \hat{u}{t-1}+\varepsilon_t$$ with the indicator function $I_t$ defined as: $I_t=\left{\begin{array}{l}1 \text { if } \Delta \hat{u}{t-1} \geq 0 \ 0 \text { if } \Delta \hat{u}{t-1}<0\end{array}\right}$. A TAR-ECM corresponds to: $$\Delta \hat{u}_t=I_t \rho_1 \hat{u}{t-1}+\left(1-I_t\right) \rho_2 \hat{u}{t-1}+\sum{i=1}^k \gamma_i \Delta \hat{u}{t-1}+\varepsilon_t$$ with the indicator function $I_t$ defined as: $I_t=\left{\begin{array}{l}1 \text { if } \hat{u}{t-1} \geq 0 \ 0 \text { if } \hat{u}_{t-1}<0\end{array}\right}$.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Linear Cointegration Specification for Wealth Effects

$$\begin{gathered} c_t=\alpha+\beta_1 T W_t+\beta_2 y_t+\varepsilon_t \ c_t=\alpha+\beta_1 F W_t+\beta_2 H W_t++\beta_3 y_t+\varepsilon_t \end{gathered}$$

## 经济代写|计量经济学代写Introduction to Econometrics代考|Threshold ECM Specification for Wealth Effects

M-TAR-ECM模型可以写成:
$$\Delta \hat{u}t=I_t \rho_1 \hat{u}{t-1}+\left(1-I_t\right) \rho_2 \hat{u}{t-1}+\sum{i=1}^k \gamma_i \Delta \hat{u}{t-1}+\varepsilon_t$$，其中指标函数$I_t$定义为:$I_t=\left{\begin{array}{l}1 \text { if } \Delta \hat{u}{t-1} \geq 0 \ 0 \text { if } \Delta \hat{u}{t-1}<0\end{array}\right}$。一个TAR-ECM对应:$$\Delta \hat{u}t=I_t \rho_1 \hat{u}{t-1}+\left(1-I_t\right) \rho_2 \hat{u}{t-1}+\sum{i=1}^k \gamma_i \Delta \hat{u}{t-1}+\varepsilon_t$$，其中指标函数$I_t$定义为:$I_t=\left{\begin{array}{l}1 \text { if } \hat{u}{t-1} \geq 0 \ 0 \text { if } \hat{u}{t-1}<0\end{array}\right}$。

## 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。

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## 经济代写|计量经济学代写Introduction to 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:
$$\underset{(n \times t)}{y}=\underset{(n \times n * k)}{\mathbf{A}^{\top}} \times \underset{(n * k \times t)}{x}+\underset{(n \times r)}{\mathbf{H}^{\top}(x)} \times \underset{(r \times t)}{\xi}+\underset{(n \times t)}{w}$$
representing the measurement equation for $\mathrm{a} y_t \in \mathbb{R}^n$ 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.

## 经济代写|计量经济学代写Introduction to 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 balances 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 $\left(Y{\mathrm{pc}_t}^p\right)$ 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.

## 经济代写|计量经济学代写Introduction to Econometrics代考|A Panel Time-Varying State-Space Extension

$$y_{i, t}=x_{i, t}^{\top} \bar{\beta}+x_{i, t}^{\top} \xi_{i, t}+\omega_t$$

$$\underset{(n \times t)}{y}=\underset{(n \times n * k)}{\mathbf{A}^{\top}} \times \underset{(n * k \times t)}{x}+\underset{(n \times r)}{\mathbf{H}^{\top}(x)} \times \underset{(r \times t)}{\xi}+\underset{(n \times t)}{w}$$

## 经济代写|计量经济学代写Introduction to Econometrics代考|A Time-Varying Parameter Model for the M3 Velocity

$$\log V_{i, t}=\beta_{0, i}+\xi_{i, t}+\lambda_i f_t+\beta_{1, i} i_t+\beta_{2, i} \pi_t^e+\beta_{3, i} \log Y_{p c_{i, t}}+\beta_{4, i} \log Y_{p c_{i, t}}^p+\varepsilon_{i, t}$$

## 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。

Posted on Categories:Financial Econometrics, 经济代写, 计量经济学

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## 经济代写|计量经济学代写Introduction to 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
$$\Delta y_t=a+c y_{t-1}+\boldsymbol{b} \boldsymbol{x}{t-1}+\sum{i=1}^{p-1} \boldsymbol{d}i^{\prime} \Delta \boldsymbol{z}{t-i}+\boldsymbol{f}^{\prime} \Delta \boldsymbol{x}t+u_t$$ 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 $\left(u_t \sim N\left(0, \sigma^2\right)\right)$. $\boldsymbol{x}$ 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.

## 经济代写|计量经济学代写Introduction to Econometrics代考|Data

We obtain quarterly data on housing price-to-rent ratios from the OECD for the Euro area, Japan, the UK, and the USA (Table 1). The maximum sample period is from 1968 to 2018 (nearly 200 observations for each country), and the base year of the data is 2015. Here, the Euro area consists of 15 countries: Greece, France, the Slovak Republic, Italy, Spain, Belgium, Luxembourg, Germany, Portugal, the Netherlands, Finland, Ireland, Austria, Slovenia, and Estonia. (Hereafter, we refer to the Euro area as a country for convenience.) Because financial bubbles are traditionally considered infrequent phenomena, we chose countries with more than 195 observations. In terms of the standard deviations of this ratio, the US housing market is most stable, and the Japanese market is most volatile.
We also obtain housing price indices from the OECD. Housing prices appear to have a positive relationship with the price-to-rent ratios for all countries and exhibit more stable movements compared to prices (Fig. 1). Furthermore, while there are some similarities in the ratios across four countries, they have a declining trend in Japan during the “Lost Decades” (i.e., after 1990). This trend indicates relatively higher inflation in rental properties than houses in Japan and is indeed attributable to the deflation in housing prices according to this figure. This result indicates a weak demand for house purchases during the weak economic conditions of this period. In contrast, there is an increasing trend in the UK ratio from the late 1990s, indicating a housing market boom.

## 经济代写|计量经济学代写Introduction to Econometrics代考|T-ARDL Model

Pesaran et al.(2001)提出了五种不同确定性术语组合的ARDL规范。在这里，我们使用金融研究中最流行的模型，不受限制的常数，没有趋势。对于资产价格$(y)$，我们可以表示为

## 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。