Guestion is here

1) [40 points] The index of industrial production (IR ) is a monthly time series that measures the quantity of industrial commodities produced in a given month. a) (10 pts) Explain and write an equation for the behavior of the variables if (IP,) behaves as a random walk model. Will this be stationary? b) (10 pts) A researcher conducted an Augmented Dickey Fuller test on the series, with a drift, time trend and two lagged terms and obtained the following regression: A1(1P,) = 0061+ 0.00004: 0.0181n(IR_1) + 0.333A1n(IP,_1) + 0.162A1n(IR_2) (std. error) (0.024) (0.00001) (0.007) (0.075) (0.055) Using an ADF test, test whether the series is stationary or not. First state the null and the alternative hypothesis. [The critical values are 3.96 for 1%, -3.41 for 5% and 3.13 for 10% signicance level] c) (10 pts) Suppose that variable industrial production (In IP, ) and variable labor input (In Lr ) are integrated of order one, i.e. [(1). Explain the term \"integrated of order one\" and how you will test the order of integration. (:1) (10 pts) Describe, step by step, how you will test whether ln IP, and In L! are cointegrated. Write the equations that you will estimate and the hypothesis that you will need to test