University : | Others UniLearnO is not sponsored or endorsed by this college or university. |
---|---|

Country : | Mauritius |

**Task**

**1. GMM**

In the dataset hw data.csv, you have a time series which comes from the Moving Average process with q lags, MA(q) process. The MA(q) process is defined as follows:

y_{t} = µ + ϵ_{t} + θ_{1}ϵ_{t} −1 + ... + θ_{q}ϵ_{t }− q

You will need libraries ’gmm’ and ’tseries’ to answer the following questions. Note that if you do not answer correctly point a), all consecutive questions will be wrong, hence no points can be earned.

(a) How would you identify the lag q? Identify the lag q.

(b) Derive the moment conditions function for the process you identified previously and write a corresponding function in R. Use more moment conditions than the number of coefficients that you want to estimate.

(c) Estimate the model using ’gmm’ with an identity weighting matrix. Provide the output and interpret the coefficient significance and the J-test statistic.

(d) Estimate the model using ’gmm’ with an optimal weighting matrix. Provide the output and interpret the coefficient significance and the J-test statistic.

(e) Compare the results from c) and d).

**2. Delta method**

Let us model the variables X1 and X2 as follows

X1 = 0.2V1 + 0.7V2 + 0.3V3 X2 = 4V2 − 3V3 V1 ∼ N(0, 1), V2 ∼ χ 2 (3), V3 ∼ U[1, 2]

The linear model is defined as:

Y = β_{0 }+ β_{1}X_{1 }+ β_{2}X_{2} + ϵ

Let us assume, that we are interested in quantity Φ:

Φ = ln(β_{0} + β _{2} 1 ) − (β _{1} 2 _{1} )

Estimate the value of Φ and also the variance of Φ, V ar(Φ). To estimate V ar(Φ) use the next methods:

(a) Delta method (by hand)

(b) Delta method (using ’deltamethod’ function)

(c) Bootstrap (with 1000, 10000 replications)

(d) Compare the results.

**3. Bootstrap **

Assume a random sample from Exponential distribution. X ∼ exp(λ). (a) Generate 200 observations from the exponential distribution for λ = 2.

(b) Check the sample mean and variance and compare them to the theoretical values. (c) Plot the histogram of generated data, kernel density approximation, theoretical density of exponential distribution and exponential Q-Q plot. Discuss.

(d) Use brute force bootstrapping to obtain the Bootstrap mean, standard errors and bias-reduced estimate of the mean. Use 100,000 bootstrap replications.

(e) Now, use the ’boot’ function with 100,000 bootstrap replications.

(f) Obtain the confidence intervals, use different types and compare the results. Which type is appropriate to use in this case?

(g) Plot the bootstrapped mean. Discuss.

**4. Endogeneity**

(a) Discuss the nature of the endogeneity problem in the system above. You might check important correlations and you should explain the difference between x1 and x3. Do you expect to observe any bias within the OLS estimation? Explain why and discuss the source of possible bias. What solutions do you suggest?

(b) Estimate the model by OLS and interpret.

This Econometrics Assignment Help has been solved by our **Econometrics Experts **at **Unilearno**. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.

Eureka! You've stumped our genius minds (for now)! This exciting new question has our experts buzzing with curiosity. We can't wait to craft a fresh solution just for you!

Flat 50% Off
Order New Solution

Hire A Tutor