TAKEHOME FINAL EXAMINATION
First Semester 2022
NOTE: You are required to answer EIGHT (8) of EIGHT (8) questions.
Marks allocated to each part of the questions are indicated. This paper consists of 6 pages and EIGHT (8) questions.
Please check that your copy is complete. Total Marks: 100 (60% of final grade)
You must complete all the estimations in Microsoft Excel or other approved software and include your answers and computation output in a SINGLE Word file.
Email this Word file with your Student ID in the email’s subject
to
By 1 pm 17 June 2022 NZ Time
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Section A: Crosssectional Analysis
Question 1 (Total 10 Marks).
Consider the model: 𝑙𝑛(𝑤𝑎𝑔𝑒) = 𝛽_{0} + 𝛽_{1}𝑒𝑑𝑢𝑐 + 𝑢 , where 𝑤𝑎𝑔𝑒 is hourly wage in dollars and
𝑒𝑑𝑢𝑐 is the years of education.
 Suppose that you have collected a sample of 20 individuals, comprising information on their wages and years of education, {(𝑤𝑎𝑔𝑒_{𝑖}, 𝑒𝑑𝑢𝑐_{𝑖}), 𝑖 = 1 ⋯ 20}. Write down the expected value of 𝑙𝑛(𝑤𝑎𝑔𝑒) conditional 𝑒𝑑𝑢𝑐. State your
(3 mark)
 Interpret the meaning of 𝛽_{1}. Roughly sketch the relationship between 𝑤𝑎𝑔𝑒 and
𝑒𝑑𝑢𝑐. (3 marks)
 Use appropriate notation to describe a situation whereby the OLS estimators of the model coefficients are still unbiased but not BLUE. (4 marks)
Question 2 (Total 10 Marks).
For a sample of 100 communities in an area, you are interested in estimating a model relating median housing price (𝑝𝑟𝑖𝑐𝑒) in the community to various community characteristics: 𝑛𝑜𝑥 is the amount of nitrogen oxide in the air, in parts per million; 𝑑𝑖𝑠𝑡 is a weighted distance of the community from employment centres, in miles; 𝑟𝑜𝑜𝑚𝑠 is the average number of rooms in houses in the community; and 𝑠𝑡𝑟𝑎𝑡𝑖𝑜 is the average studentteacher ratio of schools in the community;
𝑝𝑟𝑜𝑝𝑡𝑎𝑥 stands for property tax measured by an ordinal number ranging from 1 to 4 (1=lowest and 4 =highest). Use the data in the sheet named after your Student ID in “Question 2 data ECON307 final exam 2022.xlsx” to estimate the following model,
𝑙𝑛( 𝑝𝑟𝑖𝑐𝑒𝑖) = 𝛽0 + 𝛽1 𝑙𝑛( 𝑛𝑜𝑥𝑖) + 𝛽2 𝑙𝑛( 𝑑𝑖𝑠𝑡𝑖 ) + 𝛽3𝑟𝑜𝑜𝑚𝑠𝑖 + 𝛽4𝑠𝑡𝑟𝑎𝑡𝑖𝑜𝑖 + 𝛽5𝑝𝑟𝑜𝑝𝑡𝑎𝑥𝑖 + 𝑢𝑖
where 𝑖 = 1, ⋯ ,100.
 Estimate the model and interpret the ceteris paribus effects of all the
(3 marks)
 Test, at the 5% significance level, if there is heteroscedasticity; if there is, state the consequences in terms of the estimates in 1.
(3 marks)
 Explain any drawbacks of using the ordinal variable to measure the effect of property tax on the house price. Respecify the model so that it can overcome the drawbacks. Estimate the new model and comment on the effect of property tax on the house
(4 marks)
Question 3 (Total 10 Marks).
Use the data in the sheet named after your Student ID in “Question 3 data ECON307 final exam 2022.xlsx” to estimate the following model (assume that all necessary assumptions hold).

𝑡𝑟𝑚𝑔𝑝𝑎_{𝑖} = 𝛽_{0} + 𝛽_{1}𝑐𝑟𝑠𝑔𝑝𝑎_{𝑖} + 𝛽_{2}𝑐𝑢𝑚𝑔𝑝𝑎_{𝑖} + 𝛽_{3}𝑡𝑜𝑡ℎ𝑟𝑠_{𝑖} + 𝛽_{4}𝑡𝑜𝑡ℎ𝑟𝑠^{2} + 𝛽_{5}𝑠𝑎𝑡_{𝑖} + 𝛽_{6}ℎ𝑠𝑝𝑒𝑟𝑐_{𝑖}
+ 𝛽_{7}𝑓𝑒𝑚𝑎𝑙𝑒_{𝑖} + 𝛽_{8}𝑠𝑒𝑎𝑠𝑜𝑛_{𝑖} + 𝑢_{𝑖}
where, trmgpa is term GPA, crsgpa is a weighted average of overall GPA in courses taken, cumgpa is GPA prior to the current semester, tothrs is total credit hours prior to the semester, sat is SAT score, hsperc is graduating percentile in high school class (a ranking measure, eg. a value of 1 = top 1 per cent), female is a gender dummy, and season is a dummy variable equal to unity if the student’s sport is in season.
 What does the basic group represent? (2 marks)
 Are the variables crsgpa and cumgpa jointly significant at the 5% level (show your workings)? (4 marks)
 Calculate the value of 𝑡𝑜𝑡ℎ𝑟𝑠 such that the ceteris paribus effect of 𝑡𝑜𝑡ℎ𝑟𝑠 on 𝑡𝑟𝑚𝑔𝑝𝑎 is 0 (Note: the solution may be unrealistic for some datasets). (4 marks)
Question 4 (Total 10 Marks).
Consider a linear regression model to explain cigarette (cig) consumption:
cigi = b0 + b1incomei + b2 pricei + b3educi + ui
Suppose Assumptions MLR 14 hold and Var(uiincome, price, educ) = 𝜎^{2}𝑖𝑛𝑐𝑜𝑚𝑒_{𝑖} × 𝑝𝑟𝑖𝑐𝑒_{𝑖}
 Write down the transformed model that has a homoscedastic error term and point out if the resulting model has an intercept term. (5 marks)
 Use the data in the sheet named after your Student ID in “Question 4 data ECON307 final exam 2022.xlsx”and estimate the model with WLS. (5 marks)
Question 5 (Total 10 Marks).
The following linear regression model has been specified to model 𝑤𝑎𝑔𝑒 using 𝑒𝑑𝑢𝑐 (education):
wage = b0 + b1educ + u
The model is misspecified because it has failed to include another important variable, ability. Thus, the OLS estimates of the model coefficients are said to suffer from omitted variable bias since educ and ability are likely to be highly correlated. Although this is called the omitted variable error, the effect of ability on wage is actually contained in the u. In other words, it is still in the equation.
Explain the sense in which the word “omitted” is used. Write down two functional forms relating the two variables, one that implies that all the coefficient estimates will be biased, and the other that only the slope coefficient estimate will be biased.
Section B: Time Series Analysis
Question 6 (Total 10 Marks).
Consider an FDL (2) model whereby the dependent variable is inflation rate and the explanatory variables are the current and previous unemployment rate. If the model is estimated by OLS, then an important assumption that is required for the unbiasedness of the OLS estimator is unlikely to hold. Explain what that assumption is and why it is unlikely to hold in this particular setting.
Question 7 (Total 30 Marks).
Climate change is taking place. The Paris Agreement released in 2015 is the latest global agreement on climate change that aims to limit the rise of the global temperature to a certain range over a specified time period. The impact of economic activity on climate change has been studied extensively by associating economic output (GDP) with emissions of the greenhouse gas carbon dioxide (CO2).
Question 7 requires you to use time series econometrics to analyse the relationship between GDP and CO2 within a country as well as between two countries. The data file, “Question 7 data ECON307 final exam 2022.xlsx”, contains annual observations from World Bank on per capita GDP ($USD in 2010 prices, GDP therefore after) and per capita CO2 (metric tons, CO2 therefore after) for 9 countries for period 19602016. Some countries have observations for a shorter time period than the other countries, you may need to remove observations from one country in order to match the available time periods for the other country. Use the data for your allocated countries, which can be found from the “Country allocations” sheet in the data file, to answer the questions below.
 Plot the data and comment on if there is any trend in the
(2 marks)
 Estimate a simple linear regression model for each of the two countries to examine whether GDP can explain CO2. Comment on the regression
(2 marks)
 Augment the model in 7.2 by including a linear trend in the model and estimate the augmented model. Explain whether you expect the linear trend to be significant and the meaning of its
(4 marks)
 Augment the model in 7.2 by including a quadratic GDP term in the model. The resulting model is known as Environmental Kuznets Curve. Solve for the level of GDP which results in the maximum (or minimum) level of CO2.
(5 marks)
 Change the model specification in 7.2 to an FDL of order two model. Estimate and interpret the LRP, and report its standard
(7 marks)
 Test whether all the variables are nonstationary (unit root processes) using an appropriate version of the DickyFuller test. Explain the meaning of the null and alternative hypotheses of the test. Comment on any possible implication of the testing outcomes on the regression analyses performed in 27.5.
(10 marks)
Question 8 (10 Marks).
Crude oil and natural gas have significant impacts on socioeconomic development and social stability. Many studies have found evidence of significant relationships between oil and natural gas prices. The data file, “Question 8 data ECON307 final exam 2022.xlsx”, contains 100 monthly observations on crude oil and natural gas prices. Use the data in the sheet named after your Student ID to test the stationarity of the two variables (specify the null and alternative hypotheses and related models). If they are nonstationary but are integrated of the same order, test if they are cointegrated. Conditional on the outcomes of the cointegration test, specify and estimate an appropriate dynamic model that captures the shortrun relationship between the two variables. Explain the estimated cointegration relationship (if found) and the shortrun dynamic relationship.