## 经济代写|EC212 Econometrics

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## EC212 Econometrics课程简介

The objective of this course is to provide the basic knowledge of econometrics that is essential equipment for any serious economist or social scientist. The course introduces statistical tools including regression analysis and its application using cross-sectional data.

The second week onwards will be focused on how various technical problems inherent in economic analysis, including heteroskedasticity, autocorrelation, and endogeneity should be handled. This section of the course will pay special attention to the application of the regression model to time-series data – both stationary and non-stationary.

Using the theories and their application in economics, you will participate in daily workshops to get hands-on experience implementing the various estimators and testing procedures in Stata using real-world data. As a result, you will consider how the theory can be applied to a wide range of questions of economic interest (For example, modelling long-term relationships between prices and exchange rates).

By the end of the course, you will be able to provide proof of the unbiasedness or biasedness and consistency or inconsistency of least squares, and instrumental variable estimators using simple models.

## PREREQUISITES

It seems like you are describing a course in econometrics that aims to equip students with basic knowledge and skills in statistical analysis, with a focus on regression analysis and its application to cross-sectional and time-series data in economics. The course also covers various technical problems that can arise in econometric analysis, such as heteroskedasticity, autocorrelation, and endogeneity, and how to address them.

In addition to theoretical instruction, the course provides practical workshops to give students hands-on experience using statistical software (such as Stata) to implement various estimators and testing procedures on real-world data. The course aims to help students apply econometric theory to a wide range of economic questions, such as modelling long-term relationships between prices and exchange rates.

By the end of the course, students should be able to evaluate the unbiasedness or biasedness and consistency or inconsistency of least squares and instrumental variable estimators using simple models.

## EC212 Econometrics HELP（EXAM HELP， ONLINE TUTOR）

1 What is autocorrelation? Which assumption of the CLRM is violated, and why?

Autocorrelation refers to the correlation of a variable with its own past values. In other words, autocorrelation occurs when the error terms in a regression model are not independent of each other, but instead are correlated with one another.

Autocorrelation violates the assumption of the classical linear regression model (CLRM) that the error terms are independently and identically distributed (i.i.d.). When autocorrelation is present in a regression model, it means that the error terms are not independent of each other, which violates the “independence” part of the i.i.d. assumption.

Autocorrelation can arise in time series data, where the observations are taken at regular intervals over time. For example, stock prices or GDP data are typically collected over time, and autocorrelation can occur if the error terms in a regression model are correlated with the previous time periods’ error terms.

Autocorrelation can also arise in cross-sectional data if there are unobserved factors that are correlated across observations. For example, if a regression model tries to explain the test scores of students in a class, and some students have a common unobserved factor such as the quality of the teacher, the error terms in the model could be correlated with each other.

When autocorrelation is present in a regression model, the estimated coefficients can still be unbiased, but the standard errors of the coefficients will be underestimated. This can lead to incorrect inferences about the significance of the coefficients and incorrect hypothesis testing. Therefore, it is important to detect and correct for autocorrelation in regression analysis.

Describe the steps of the DW test for autocorrelation. What are its disadvantages and which alternative tests can you suggest?

The Durbin-Watson (DW) test is a statistical test used to detect the presence of autocorrelation in the residuals of a regression model. The DW test statistic ranges from 0 to 4, with values close to 2 indicating no autocorrelation, values less than 2 indicating positive autocorrelation, and values greater than 2 indicating negative autocorrelation.

The steps of the DW test for autocorrelation are as follows:

- Estimate the regression model and obtain the residuals.
- Calculate the sum of squared differences between adjacent residuals, denoted as e(i) – e(i-1).
- Calculate the sum of squared residuals, denoted as SSE.
- Calculate the DW test statistic using the formula: DW = (sum of squared differences) / SSE.
- Compare the calculated DW test statistic to the DW critical values, which depend on the sample size, the number of independent variables, and the desired significance level. If the calculated DW test statistic is greater than the upper critical value or less than the lower critical value, then there is evidence of autocorrelation.

The DW test has several disadvantages. First, it can only detect first-order autocorrelation, which means that it cannot detect higher-order autocorrelation. Second, it assumes that the error terms are normally distributed, which may not be true in practice. Third, it assumes that the regression model is correctly specified, which means that all relevant variables are included in the model and that the functional form is correctly specified.

Alternative tests for autocorrelation include the Breusch-Godfrey test, the Ljung-Box test, and the runs test. The Breusch-Godfrey test is a general test for higher-order autocorrelation, while the Ljung-Box test is a test for autocorrelation in time series data. The runs test is a non-parametric test for randomness in the residuals.

## Textbooks

• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely

available through the university library here)

• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through

the university library here)

To reiterate, the textbooks are freely available through the university library. Note that

you must be connected to the university Wi-Fi or VPN to access the ebooks from the library

links. Furthermore, the library links take some time to populate, so do not be alarmed if

the webpage looks bare for a few seconds.

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