Time Series and Auto correlation EC 421: Introduction to Econometric Due before midnight (11:59pm) on Sunday, 17 November 2019 DUE Your solutions to this problem set are due before midnight on Sunday, 17 November 2019. Your les must be uploaded to Canvas—including (1) your responses/answers to the question and (2) the R script you used to generate your answers. Each student must turn in her/his own answers. OBJECTIVE This problem set has three purposes: (1) reinforce the econometrics topics we reviewed in class; (2) build your R toolset; (3) start building your intuition about causality and time series within econometrics. Problem 1: Time Series Imagine that we are interested in estimating the effect of monthly oil prices on monthly gasoline prices. The dataset price_oil_gasoline.csv contains these prices—the monthly average oil price (the price in dollars per barrel of Brent Crude oil, as measured by the US EIA) and the monthly average price of all gades gasoline, as measured by the US EIA). The table on the last page describes the variables in this dataset. 1a. Plot the evolution of prices of Oil or Gasoline over time. Make sure your axis, labels and title are clear. 1b. consider that (the price of gasoline in month ) only depends upon a constant , (the price of oil in month ), and a random disturbance . Estimate this model with OLS. What is the estimate of ? Is it statistically signicant? 1c. Does the price of oil explain a lot of the variation in the price of gasoline? Hint: What is the R 2? (In R, you can nd R 2 using summary() applied to a model you estimated with lm().) 1d. The model that we estimated in (1b) is a static model—meaning it does not allow previous periods' prices to affect the current price of gasoline. Suppose we think that the previous two months' oil prices also affect the price of gasoline, i.e., Estimate this model and compare your new estimate for to your previous estimate (from model 1b). Hint: Use the function lag(x, n) from the dplyr package to take the nth lag of variable x. P Gasoline t t β0 P Oil t t ut P Gasoline t = β0 + β1P Oil t + ut (1a) β1 P Gasoline t = β0 + β1P Oil t + β2P Oil t−1 + β3P Oil t−2 + ut (1d) β1 2 / 5 1e. Interpret your estimated coefcients for and . Are they statistically signicant?

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