+ 1. Time Series Models (Week 7) Suppose you want to use time series data to estimate oil demand. To do so, you estimate four different time series models: d d qoilta + Popoilt + d qoilta 19ilt-1+ Popoilt + BPoilt-1+ qoilta qoilt = a + 19ilt-1 + BoPoilt + BPoil,t-1 + d Regression Model Autoregressive (AR) Model Distributed Lag (DL) Model Autoregressive Distributed Lag (ADL) Model where quilt is the U.S. residential quantity demanded of oil and point is the price of oil in the current year and quail,t1 and Poilt-1 are the respective one-year lagged values. The results from these four regressions are shown in the table below. Regression Model AR Model DL Model ADL Model 500 500 500 500 50.50 0.75 -10.25 -7.75 -5.40 1 -2.45 -1.65 1. Using the coefficient estimates from the regression model, if the price of oil increases by $1.00 today, by how much does oil demand decrease today? 2. Would you present robust or Newey-West standard errors with the regression model? 3. Using the coefficient estimates from the autoregressive (AR) model, if the quantity of oil demanded increased by 1 today, by how much does oil demand increase one year from now? 4. Would you present robust or Newey-West standard errors with an autoregressive (AR) model? 5. Using the coefficient estimates from the distributed lag (DL) model, if the price of oil increases by $1.00 today, by how much does oil demand decrease today? Hint: Bo represents the effect of a contemporaneous change in the price of oil. 6. Using the coefficient estimates from the distributed lag (DL) model, if the price of oil increases by $1.00 today, by how much does oil demand decrease in aggregate. Hint: The long-run multiplier in a distributed lag (DL) model is calculated as (o + B). 7. Would you present robust or Newey-West standard errors with a distributed lag (DL) model? 8. Using the coefficient estimates from the autoregressive distributed lag (ADL) model, if the quantity of oil demanded increased by 1 today, by how much does oil demand increase one year from now? 9. Using the coefficient estimates from the autoregressive distributed lag (ADL) model, if the price of oil increases by $1.00 today, by how much does oil demand decrease today? Hint: Bo represents the effect of a contemporaneous change in the price of oil. 10. Using the coefficient estimates from the autoregressive distributed lag (ADL) model, if the price of oil increases by $1.00 today, by how much does oil demand decrease in aggregate. Hint: The long- run multiplier in an autoregressive distributed lag (ADL) model is calculated as (o + B)/(1 - 1). 11. Would you present robust or Newey-West standard errors with an autoregressive distributed lag (ADL) model