ARE 212代写、代做CLRM留学生、代写R语言、R编程设计

日期：2019-03-09 10:53

ARE 212 - Problem Set 2

Due March 10th

Part I: Theory (For your practice only. Not required)

1. Derive the sampling error of the GLS estimator by showing that bGLS ?

2. I used concentrated likelihood to derive the ML estimate for the CLRM. We could also set the likelihood

equations (first derivatives of the log likelihood) equal to zero. Confirm that the ML estimator proposed in

class satisfies these first order conditions.

3. Show that V (s2|X) = 2σ4

n?k and indicate which of our assumptions you need to get this result. [Hint: Look up

what the mean and variance of a random variable ～ χ2

m are.]

Part II: Applied - Returns to Scale in Electricity Supply

Read Nerlove’s (1955) paper ”Returns to Scale in Electricity Supply”. The goal of this problem set is to replicate

some of the results from this classic paper. The paper and data are available on the class website.

1. Read the data into R. Print out the data. Read it. Plot the series and make sure your data are read in correctly.

Make sure your data are sorted by size (kwh). [Hint: Check for obvious typos in the data and if you find any

fix them!]

2. Replicate regression I (page 176) in the paper. (You won’t be able to exactly, since the original data contained

an error that has been fixed). Your estimate for the price differences will differ slightly, but the R2 will be the

same.

3. Conduct the hypothesis test using constant returns to scale (βy = 1) as your null hypothesis. What is the pvalue

associated with you test statistic? What is your point estimate of returns to scale? Constant? Increasing?

Decreasing?

4. Plot the residuals against output. What do you notice? What does this potentially tell you from an economic

perspective? Compute the correlation coefficient of the residuals with output for the entire sample? What does

this tell you?

5. Nerlove tried to remedy his ”residual problem” by running separate models for different sized industries. Divide

your sample into 5 subgroups of 29 firms each according to the level of output. Estimate the regression model

again for each group separately. Can you replicate Equations IIA - IIIE? Calculate the point estimates for

returns to scale for each sample. Is there a pattern relating to size of output?

6. Create ”dummy variables” for each industry [which you may have done in the previous part]. Interact them with

the output variable to create five ”slope coefficients”. Run a model, letting the intercept and slope coefficient

on output differ across plants, but let the remainder of the coefficients be pooled across plants. Are there any

noticeable changes in returns to scale from the previous part?

7. Conduct a statistical test comparing the first model you estimate to the last model you estimated. (Hint: Is

one model a restricted version of the other?). Would separate t-test have given you the same results?

8. To see whether returns to scale declined with output, Nerlove tested a nonlinear specification by including

(ln(y))2 as a regressor. Conduct a statistical test you feel is appropriate to test this hypothesis.