1. Suppose that we want to test for the presence of a unit root in the AR(1) model with a drift: (a) Outline the Dickey-Fuller (ADF) test procedure. (b) Suppose that we use data on the logarithm of the Gross Domestic Product (GDP), In(GDP), based on quarterly data from 2000 (Q1) to 2018 (Q4) and we obtain the following OLS estimateS o= 0.442/ 1= 0.217, SE( () = 0.22 and SE( 1) = 0.111 (SE denotes standard error). Does the In(GDP) appear to be stationary? Justify your answer. (You need to look up the critical values) (c) How does the ADF procedure change if you believe that the error sequence ut is serially correlated? 2. Let the vertical axis of a figure indicate the mortality rate. There are two time periods, t = 1 and t = 2, where time period is measured on the horizontal axis. The following table presents average mortality rate for the treatment group and the control group. Treatment |Control Before Treatment 15 17.5 After Treatment 16.5 20.5 (a) Enter the four points in the figure and label them y Treatment, Before y Treatment, After yControl, Before , and Control, After . Connect the points. Finally calculate and indicate the value for the difference-in-difference estimator on the graph. (b) Explain the circumstances under which the fixed effect model with panel data is preferable to this simple difference-in-difference estimator. 3. Describe how you would formulate a model to test Purchasing Power Parity using the cointegration test. You must clearly state the model specification, null hypothesis, variable definition, and test statistics. 4. Suppose that we want to estimate the effect of several variables on annual coon- sumption and that we have a panel data set on individuals collected on January 31, 2017 and January 31, 2018. If we include a year dummy for 2018 and use first differencing, can we also include age in the original model? Explain. 5. The following data examines the effect of social assistance on child mortality rate employing parametric Regression Discontinuity method. The variables are county-level child mortality and poverty rates. The following model is estimated