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# 经济代写|计量经济学代写ECONOMETRICS代考|ECON345 UNITS OF MEASUREMENT AND FUNCTIONAL FORM

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## 经济代写|计量经济学代写ECONOMETRICS代考|THE STRUCTURE OF ECONOMIC DATA

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: $$\text { salârdol }=963,191+18,501 \text { roe } .$$ ## 经济代写|计量经济学代写ECONOMETRICS代考|Incorporating Nonlinearities in Simple Regression So far we have focused on linear relationships between the dependent and independent variables. As we mentioned in Chapter 1, linear relationships are not nearly general enough for all economic applications. Fortunately, it is rather easy to incorporate many nonlinearities into simple regression analysis by appropriately defining the dependent and independent variables. Here we will cover two possibilities that often appear in applied work. In reading applied work in the social sciences, you will often encounter regression equations where the dependent variable appears in logarithmic form. Why is this done? Recall the wage-education example, where we regressed hourly wage on years of education. We obtained a slope estimate of$0.54$[see equation (2.27)], which means that each additional year of education is predicted to increase hourly wage by 54 cents. Because of the linear nature of (2.27), 54 cents is the increase for either the first year of education or the twentieth year; this may not be reasonable. Suppose, instead, that the percentage increase in wage is the same given one more year of education. Model (2.27) does not imply a constant percentage increase: the percentage increases depends on the initial wage. A model that gives (approximately) a constant percentage effect is $$\log (\text { wage })=\beta_0+\beta_1 e d u c+u,$$ where$\log (\cdot)$denotes the natural logarithm. (See Appendix A for a review of logarithms.) In particular, if$\Delta u=0$, then $$\% \Delta \text { wage } \approx\left(100 \cdot \beta_1\right) \Delta d u c .$$ Notice how we multiply$\beta_1$by 100 to get the percentage change in wage given one additional year of education. Since the percentage change in wage is the same for each additional year of education, the change in wage for an extra year of education increases as education increases; in other words, (2.42) implies an increasing return to education. By exponentiating (2.42), we can write wage$=\exp \left(\beta_0+\beta_1 e d u c+u\right)$. This equation is graphed in Figure 2.6, with$u=0$. ## 金融计量经济学代写 ## 经济代写|计量经济学代写ECONOMETRICS代考|经济数据的结构 应用经济学中有两个重要的问题:(1)理解因变量和/或自变量的测量单位的改变如何影响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。全面理解函数形式问题所需的数学知识见附录a。 改变计量单位对OLS统计的影响 在示例2.3中，我们选择以数千美元衡量年薪，股本回报率以百分数衡量(而不是小数)。在这个例子中，了解如何衡量工资和roe是至关重要的，以便理解公式(2.39)中的估计 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发生变化。在示例$2.3$中，假设我们不是用几千美元来衡量工资，而是用美元来衡量。让salardol是美元工资(salardol$=845,761$会被解释为$\$845,761$。)当然，salardol与以千美元计的工资有一个简单的关系:salardol $=1,000 \cdot$ salary。我们不需要实际运行salardol对roe的回归，就知道估计方程为:
$$\text { salârdol }=963,191+18,501 \text { roe } .$$

## 经济代写|计量经济学代写ECONOMETRICS代考|在简单回归中合并非线性

$$\log (\text { wage })=\beta_0+\beta_1 e d u c+u,$$
，其中$\log (\cdot)$表示自然对数。(参见附录A对对数的回顾。)特别地，如果$\Delta u=0$，那么
$$\% \Delta \text { wage } \approx\left(100 \cdot \beta_1\right) \Delta d u c .$$

## 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。