ETF2100 - Introductory Econometrics - Questions and Answers - Economics Assessment Answer

Assessment Task:

Question 1  
(a) Estimate the following regression model by least squares. Report the result in full. No need to provide Eviews output here. 
ln(price)i = β1 + β2bedi + ei (A1)
(b) Interpret the estimated slope coe?cient. Be careful about the unit in your interpretation. Is the sign of the slope coe?cient what you expected? Why? 
(c) Your friend commented on your result above that your model might incorrectly leave out the size of each house (sqft) and that can have consequences on your estimate of β2. Do you agree with your friend’s comment? Why or why not? What would be the consequence of omitting the variable sqft? 
(d) Now estimate the following model where we add in house size. Report the result in full AND provide Eviews output here.
ln(price)i = β1 + β2bedi + β3sqfti + ei (A2)
(e) Interpret b2, your estimate for β2 from part (d). How does this interpretation di?er from the interpretation in part (b) 
(f) Using model in (A2), is there evidence that the number of bedroom has an e?ect on ln(price)? Note: p-value approach is su?cient for this part. 
(g) Compare the coe?cient for bed that you got from estimating model (A1) and from model (A2). Which one of these two estimates is more reliable? If you think one of these estimates is biased, explain which one and why. In that case, what is the direction of the bias based on your comparison of the two estimates? 

(h) Using Eviews, ?nd and report the (Pearson) correlation coe?cient between bed and sqft. Is the sign what you expected? 
(i) Does what you ?nd in part (h) and any other previous parts support your answer in part (g), in particular with regard to the direction of the bias? Explain 
Question 2 
(a) Now consider the following model. Explain the reason why we include the variables age and age squared in the model.
ln(price)i = β1 + β2sqfti + β3agei + β4age2 i + ei (A3)
(b) Report the result in full and provide Eviews output
(c) Using the F-test at 5% signi?cance level, test whether age helps explain variation in house prices. You must write out the test in full including null and alternative hypotheses stated in terms of the parameters. Compute the F-statistic manually by estimating both the restricted and unrestricted model. 
(d) What do the estimates for β3 and β4 tell you about the relationship between house price and house age, keeping size constant? Hint: Think about the signs of these coe?cients and what they say about the shape of the quadratic function. Make sure to explain your answer in the context of the question.

 (e) Write down the expressions for ∂ \ E(ln(price)|X) ∂age where X denotes all observations on sqft and age. Interpret this expression for a house with age equal to a particular level, say age0. Be careful about the use of units and percentages. Note, there is no need to put in any numbers here and you can use bk to denote estimate for βk. 
(f) Using the F-test at 5% signi?cance level, test the null hypothesis that houses start becoming more expensive with age when they are 50 years old. You must write out the test in full including null and alternative hypotheses stated in terms of the parameters. Compute the F-statistic manually by estimating both the restricted and unrestricted model. 
(g) Find point prediction (using the corrected predictor) AND 95% prediction interval for the price of a 45-year old house with 2000 square feet living area. 

Question 3 
(a) Now estimate the following model using least squares. Report the result in full AND provide Eviews output.
price = β1 + β2sqfti + β3agei + β4bathsi + ei (A4)
(b) Interpret the estimated coe?cient for sqft, age and baths. Is the sign of each coe?cient what you expected? Why? 
(c) Construct a 99% interval estimate for β4. Interpret this interval estimate. 
(d) Test at the 5% level of signi?cance the null hypothesis that an increase in the total living area by 100 square feet has the same e?ect on house price as a 10-year decrease in the house age, other things being constant. Use at-statistic approach and write down all the steps used to conduct your test.
(e) You suspect that the change in price associated with extra square feet of house size depends on how old the house is. Extend the model in (A4) to allow for this (write the new model down). Estimate this model and include your Eviews output.
(f) Comment on the signi?cance of all the coe?cients in the extended model you estimate in part (e) using the p-value approach.
(g) Using this extended model, write down the expressions for the marginal e?ect ∂ \ E(price|X) ∂sqft where X denotes all observations on sqft and age. Interpret this expression for a house with age equal to a particular level, say age0. Note, there is no need to put in any numbers here and you can use bk to denote estimate for βk. 
(h) Find point estimates AND 95% interval estimates for the marginal e?ect of an extra hundred square feet of total living area on house price for houses that are (i) 2 years old, and (ii) 45 years old. How do these estimates change as age increases?
(i) Using model in (A4), perform RESET tests with one and two terms. Do the tests suggest that the model is a reasonable one? 

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