EC306 Econometrics Assignment Example Maynooth University Ireland

This course aims to introduce the fundamental concepts and methods of econometrics, with a focus on their application to the analysis of economic data. We will emphasize the role of econometric research in understanding and predicting economic behaviour, and help you to develop your skills in applying statistical tools to empirical problems. The course is entirely project-based; you will work on a collaborative assignment with other students (in teams of two or three) throughout the semester.

Get Assignment Solutions of EC306: Econometrics

In this course, there are many types of assignments given to students like individual assignments, group-based assignments, continuous assessments, reports, case studies, final year projects, skills demonstrations, learner records, and other solutions given by us.

On successful completion of the module, students should be able to:

Assignment Task 1: Describe the key components of a statistical model

A statistical model is a set of assumptions that makes it possible to analyze data and use those results for prediction or explanation. A model is typically expressed in an equation that relates a dependent variable to one or more independent variables, together with assumptions about the likely behaviour of these variables. The goal is often predictive – for example, to use the information on the current values of the independent variables to predict future values of the dependent variable (or vice versa). However, it may also be explanatory – for example, to use a statistical model to help understand why something happens, by identifying the factors that are most important in causing it.

The key components of a statistical model are the explanatory variables, the dependent variable, and the error term.

• The explanatory variables are the factors that we believe are responsible for the variation in the dependent variable.
• The dependent variable is the quantity that we are trying to explain.
• The error term represents all of those variables other than the explanatory variables that affect the dependent variable but which we cannot measure, such as unmeasured effects and measurement errors.

Assignment Task 2: Explain the criteria used to evaluate the performance of an estimator

There are several criteria that can be used to evaluate the performance of an estimator, including:

• The bias of the estimator: This is how far the estimate deviates from the true value. A biased estimator will consistently produce estimates that are either too high or too low, relative to the true value.
• The variance of the estimator: This measures the amount of variability in the estimates produced by the estimator. A high variance means that the estimates are widely dispersed, while a low variance indicates that they are clustered around the true value.
• The efficiency of the estimator: This measures how well the estimator exploits all of the information available in the sample. Stochastic efficiency means that the estimator is consistent, while Semi-parametric efficiency means that it uses all of the information unobserved by the model in an optimal way.
• The asymptotic relative efficiency: This compares the variance of two estimators when n becomes large. It provides a consistent measure of how efficiently two estimators use the information in the sample.

Assignment Task 3: Discuss the motivation behind the least-squares estimator

The least-squares estimator is the most popular method of estimation because it provides a simple way to calculate an estimate that minimizes the difference between the observed values of Y and our predictions based on the model.

When the explanatory variables are deterministic (i.e., they have no error term), then there can be no deviation between the observed values of Y and the predictions. This motivates the model with deterministic variables; however, in practice, we often use stochastic variables (which have an error term).

The least-squares method provides a way to calculate an estimator for these cases by minimizing the sum of squared errors (SSE) between what is predicted by the model and what is observed.

Assignment Task 4: Estimate a linear regression model using ordinary least squares

The linear regression model is:

Y = β0 + β1X1 + β2X2 + ε

Where:

Y is the dependent variable (in our example, the amount of rainfall)

β0 is the intercept (i.e., the value of Y when X1 = 0)

β1 is the coefficient on X1

β2 is the coefficient on X2

ε is a random error term with mean 0 and variance σ2.

The least-squares estimator for β0, β1, and β2 are:

β0 = (X1^TX1)^{-1}X1^TY

β1 = (X1^TX1)^{-1}Y

β2 = (X2^TX2)^{-1}X2^TY

Note: X is the mean of all of the explanatory variables, and Y is their mean when Y is included in the model. https://www.youtube.com/watch?v=D9-2xnKfNbg

The linear regression model is a way of using observations about a dependent variable (in our example, the amount of rainfall) to estimate the values of some explanatory variables (in our example, the temperature, and humidity). The model allows us to predict the value of the dependent variable without actually having to observe it. The model contains one or more explanatory variables which are thought to be related to the dependent variable, and an error term is added to the model to capture all of the factors which affect our predictions but are not included in the model.

The linear regression model represents a dependent relationship between two random variables: one representing the explanatory variables (referred to as an explanatory variable) and one representing the dependent variable (referred to as a response variable). The relationship between these two variables is typically linear, but it can be non-linear.

Assignment Task 5: Outline the conditions required for the Gauss-Markov theorem to hold

The Gauss-Markov theorem states that the least-squares method is both unbiased and efficient under certain conditions.

Some of these are:

1. There are no perfect multicollinearity problems in the model, which means that there cannot be any perfect linear relationships between different explanatory variables within the model (i.e., if two or more explanatory variables within the model are correlated, then their estimate will be biased).
2. The error term in the model has zero mean (i.e., the average value of the difference between predicted and observed values is 0).
3. The variance of the error term must be constant for all observations (i.e., heteroscedasticity must not be present).
4. The explanatory variables must be linearly independent (i.e., the set of explanatory variables cannot be reduced to a smaller set without including some error term).

Under these conditions, the least-squares estimator is both unbiased and efficient.

Assignment Task 6: Conduct hypothesis tests on the linear regression model

The null hypothesis is that the coefficient on the explanatory variable is equal to 0 (i.e., β1 = 0). The alternative hypothesis is that it is not equal to 0 (i.e., β1 ≠ 0).

For each of these tests, we can calculate a p-value which tells us how likely it is that the null hypothesis is true (i.e., that β1 = 0). If the p-value is less than 0.05, then we can reject the null hypothesis and say that there is evidence that the coefficient on the explanatory variable is not equal to 0.

If the p-value is greater than or equal to 0.05, then we cannot say with 95% confidence that the explanatory variable does not have a significant effect on the dependent variable.

To carry out these hypothesis tests, you need to use SPSS and run a linear regression analysis. You can then view this in SPSS, which will show you the coefficient on each explanatory variable. You can then go on to run the test by doing an output command in SPSS to get the p-value for each test.

Assignment Task 7: Examine the linear regression model when the assumptions needed for the Gauss-Markov theorem fail

When the assumptions needed for the Gauss-Markov theorem fail, the least-squares estimator is no longer unbiased or efficient. This means that the estimates generated by the model are not accurate and that different explanatory variables may be more or less important in predicting the dependent variable.

In particular, if heteroscedasticity is present in the model (i.e., the variance of the error term is not constant for all observations), then the least squares estimator will be biased. This means that the estimate for β1 will be different depending on which observations are used to calculate it. If multicollinearity is present in the model (i.e., if there are perfect linear relationships between different explanatory variables), then the least squares estimator will be inefficient. This means that the estimate for β1 will be very close to the value of 0, regardless of which observations are used to calculate it.

Buy EC306 Econometrics Assignment Solutions at reasonable prices from experts of Irelandassignmenthelp.com!

The assignment example discussed above is based on EC306 Econometrics Assignment.

Ireland Assignment Help is a well-known and trusted brand that provides quality assignment writing services to students. We have a team of experienced and qualified writers who can help students with all their academic projects. Our essay writing services are popular among students as we provide high-quality work without taking too much time. You can also get assignments done online and our team of professionals will ensure that the work is delivered before the deadline.

If you’re looking for assignment writers who can provide quality work, then we can be your number one choice. We have a team of writers who are responsible and dedicated to providing high-quality work in the shortest possible time. Our team of professionals understands that students want custom papers written in a certain format and that is why our writers always deliver just that.