Econometrics

Problem 3 . Long-term interest rates, such as the US 10-year Treasury rates, are believed to be random walk. That is, the best forecast of future rates is today's rate. Here, you are asked to evaluate the one-quarter-ahead (consensus) forecasts of the 10-year Treasury rates from a panel of professional forecasters. More specifically, let quarter t be the quarter in which the forecasters report their forecasts of the 10-year Treasury rate for quarter t+1. As such, let At+1 be the actual rate in quarter t+1, and Pt+1 be the professional (consensus) forecast of At+1 made in quarter t. In addition, let Rt+1 be the random walk forecast of At+1. Using the results from Eviews (given below) to answer the following questions: a. Find and interpret the bias proportion and the variance proportion. b. Are the professional forecasts unbiased? Write down the test equation, the null and alternative hypotheses, the decision rule, and your conclusion. c. Are the professional forecasts free of systematic bias? Write down the test equation, the null and alternative hypotheses, the decision rule, and your conclusion. d. Are the professional forecasts more informative than the random walk forecasts? Write down the test equation, the null and alternative hypotheses, the decision rule, and your conclusion. e. Calculate Theil's U coefficient and explain what it implies. f. Are the professional forecasts more accurate than the random walk forecasts in terms of MSE? Write down the test equation, the null and alternative hypotheses, the decision rule, and your conclusion.

Exercice 4 ACF/PACF of AR/MA/ARMA models You can simulate trajectories from ARIMA models with functions. In this exercise, you will look at correlograms arima.sim in R, and you can produce correlograms with the acf and pacf and try to identify (as best as you can) whether they might correspond to AR, to MA or to full ARMA models.

Exercice 3 Random walk with drift Consider the model X₁ = 8 + Xt-1 + Wt, where Wt are independent Normal (0, 1) variables, for all t > 1, and assume that X₁ = 0.

Exercice 2 Mean squared prediction errors Consider the problem of predicting Y using a function g of X, where X and Y are (possibly dependent) random variables. We want to minimize the mean squared error (MSE): E [(Y − 9(X))²] . We will look at various choices of g, in the particular case where Y = X³ + Z², where X and Z are independent Normal variables with mean 0 and variance 1

price A= ßo + ß1nox + ß₂rooms + ß3dist + ß4 (rooms x dist) + u Variable price refers to the price of a house, regressor rooms refers to the number of rooms in the house and dist to distance of the house from the city centre. What is the expected effect of variable dist for houses with 7 bedrooms? How would you find out whether the variable dist is statistically significant?

Consider the following regression that examines the wages of graduating economists: wage₁ = 𝛽o + 𝛽1ranki + u¡ where rank is the rank of the school the student graduated from (lower is better) and wage is the wage in dollars per hour. A random sample of recent graduates was taken. a) What is the predicted sign on 𝛽₁? Explain. b) Suppose that the R² of the model is very poor: R² = 0.01. What does this say about the potential to interpret causality in the model? c) Suppose that a government experiment sent students to schools of different ranks: that is, rank; is randomly assigned. Is the estimate of ₁ unbiased? Explain.

a) Consider a dataset of 2000 people, 1000 chosen randomly in 2010 and another 1000 chosen randomly in 2011. In both years, the same questions were asked. What kind of dataset is this? b) A test preparation company advertises that the average student can raise their scores in ECON 101 by spending $120 on their course. One of your fellow students in ECON 399 takes a random sample of past ECON 101 students and finds using an OLS regression that those who have taken the course score 15 points lower on the final exam on average compared to those that did not take the course. Does this mean the test preparation course for ECON 101 is ineffective? Explain. c) Consider the simple linear regression model. What is the expression for 𝛽o? d) In words, what is Assumption SLR 2?

Which variable in Question 2 would be considered as the dependent variable? O Theft O Cameras

Interpret the correlation between Theft and Cameras there is strong, negative correlation. There is a moderate, positive correlation

Compare the two models below, which one has a better prediction power and is a better model?