Introduction to Econometrics

December 20, 2020AdminBusiness

100 marks total

Answers to the exam questions are due. However, any student who requires extra time for ANY reason (registered with Student Accessibility Services, feeling stressed/anxious about this or any other course or life in general, has a job, still combining sunflowers, dog got sick, upset about the US election results, Mom yelled at you to clean your room, went too hard at the Nob last week and still recovering, suffering withdrawal symptoms from the Jets not playing or literally any other reason)

Early this semester, we learned about the five desirable properties of an econometric model. In your own words, fully describe each of these properties and explain why they are desirable in an econometric model. (10 marks)

COVID-19 has provided the single greatest disruption to humanity since the Second World War. Some people have hypothesized that colder weather will result in a significant increase in COVID-19 cases due to the fact that most people will spend more time indoors (and hence in closer contact) as the weather gets colder. Using new daily COVID-19 cases for Manitoba as the dependent variable and daily high temperature for the city of Winnipeg as the independent variable for the period from March 15^th to November 1^st 2020 (approximately 7.5 months), test the hypothesis that colder weather causes more cases of COVID-19. How do your results change if you just use data from September 1^st to November 1^st? What implications, if any, do you think that has for choosing a dataset and drawing conclusions from what you find as an economist? You will have to independently find the data needed to answer this question. (30 marks)

Earlier this semester we learned that if X, Y and Z are random variables and a, b, and c are constants, then the variance of (aX + bY + cZ) = a² var(X) + b² var(Y) + c² var(Z) + 2ab cov(X,Y) + 2ac cov(X,Z) + 2bc cov(Y,Z). Using the algebra of expectations operators (hint: remember from Lecture 2 we said “the variance of ANYTHING can be calculated this way….”, prove this is true. Show all your work. (15 marks)

Recall our “regular” simple regression (SR) model is y_t = β₁ + β₂x_t + e_t. But what if we knew that β₁ = 0 (i.e. that there is no intercept in our model)

(a) algebraically, what would our SR model look like in that case? (3 marks) What about graphically? (2 marks)

(b) using calculus and starting with the sum-of-squares function, derive the LS estimator b₂ given that you know β₁ = 0, similar to what we did in Lecture 3 when we derived our “regular” least-squares estimators. (10 marks)

Using your results from question (2), predict the number of cases that Manitoba could expect if the daily high temperature is negative 35 degrees, using (a) the results from March 15^th to November 1^st, then (b) the results from September 1^st to November 1^st. Which do you think will be closer to the truth, and why? (10 marks)