# Econometrics

Question 1-10 MCQ

In the model in Question 11, (1) what is the Standard Error of the Estimate? (2) What is the 95% Confidence Interval of the errors? (3) How do you interpret the 95% Confidence Interval of the errors? (4) We get the Lower/Upper 95% Indiv Performance values as follows. How do you interpret this range when Cameras = 7?

\text { 1. For the Linear Model } Y-X \beta+c \text {, define } X \text { and } \beta \text { as: } (a) Find the least squares estimator of ß. (b) Find the mean, variance, and distribution of the least squares estimator from part(₂) (c) Find the estimator of o². \text { (d) Give the formula for the }(1-\alpha) \% \text { confidence interval for } \beta_{1} \text {. }

1. Consider the following regression: \text { InGDPpC }=\beta_{0}+\beta_{1} \text { Institutions } 1+u_{1} where the dependent variable is In of GDP per capita, the explanatory variable is a measure of institutional quality (a higher value implies better quality institutions),and the subscript i represents countries. [7 marks] a) Draw a scatter plot that demonstrates how this regression would be biased and explain how your scatter plot demonstrates the bias. For simplicity, assume that there are no other sources of bias when creating your scatter plot. Your scatterplot should be clearly labelled and easy to understand. [2 marks] b) Suppose you estimate the above equation using OLS and the estimated value ofB₁ is 0.23. Interpret this coefficient. [1 mark] c) Now, suppose you have a valid instrumental variable. Do you expect the TSL Sestimate to be greater than, less than, or the same as the OLS estimate of B₁?Explain your answer. [2 marks] d) Explain whether or not panel data would be useful for addressing simultaneous causality bias in this context. [2 marks]

2. For the Linear Model Y-XB+c, define Y, X, ß, and (a) Find the least squares estimator of B. (b) Find the mean, variance, and distribution of your least squares estimator from part (a).1 (c) Find the estimator of o². (d) Find the formulas for SST, SSM, and SSE for this particular model. (e) Give the ANOVA Table for this particular model. (f) Determine the appropriate null and alternative hypotheses for this particular model using the F-test statistic from the ANOVA Table.

Question 1 5 marks A boutique beer brewery produces 2 types of beers, Dark-ale and Light-ale daily with a total cost function: TC = 3QD + QD X QL + 4QL where: QD is the quantity of the Dark-ale beer (in kegs) and Q₁ is the quantity of the Light-ale beer (in kegs). The prices that can be charged are determined by supply and demand forces and are influenced by the quantities of each type of beer according to the following equations: PD = 32 QD + QL for the price (in dollars per keg) of the Dark-ale beer and P₁ = 42+2QD - -QL for the price (in dollars per keg) of the Light-ale beer. The total revenue is given by the equation:TR = PD XQD + PL X QL and the profit given by the equation Profit = TR - TC First, use a substitution of the price variables to express the profit in terms of QD and Q₁ only. Using the method of Lagrange Multipliers find the maximum profit when total production (quantity)is restricted to 192 kegs. Note Qp or Q₁ need not be whole numbers. Question 25 marks A farmer discovers that his land has been targeted as a chemical dumping ground with a chemical that is dangerous for growing any crops. It is known that the chemical concentration decays according to the exponential decay process. At the time of discovery, the concentration of the chemical was 15% of the original. One week later, the chemical content reduced to 14%. The police have two suspects, who were both in prison for 15 weeks each at different times for other offences but providing them with alibis (proof of innocence). Suspect A served his sentence ending 35 weeks before the time of the discovery and Suspect B was released from prison 40 weeks before the time of the discovery. Use the exponential decay model to determine whether any of the suspects are innocent.