In the question , the formula for utility function, consumption should have time index t. Thank you for help. work out only a part will be fine too!

3. Compute the steady state numerically with Dynare. (N ate: you need to be careful in the way you select the initial guesses, otherwise the procedure Will not converge). Comment on your ndings. We use a stochastic macroeconomic model to account for the aggregate uctuations of the Canadian economy. We extend the model with TFP shocks and rigid labor supply that we have covered in the course. We also consider the same data you worked with in the more recent problem sets. The representative agent's utility function is specied as: 00 017: E0 25* 75:0 1 'Yt Where 7, denotes timevarying risk aversion, with unconditional average it, = 2. The CRRA parameter is stochastic, and its log follows an AR(1) process with normally distributed i.i.d. shocks: ln 'Yt : pry 1n'l'tl + 51,15: amt N N\"): 0-37)' The size of the labor force is normalized to l and it does not change over time. The representative agent has a time endowment of one unit per period, which is devoted entirely to work (Lf = 1). The production function is CobbDouglas: Y, = Zth'Lt1_a. Total Factor Productivity (TFP) is timevarying and its log follows an AR(1) stochastic process with normally distributed i.i.d. shocks: ln Z, 2 pz ln Zt_1 + 62,13, 627,5 N N (0, 022). The two shocks (677,5, 6 2,15) are negatively correlated, with correlation p772. Kt is the capital stock7 which depreciates at rate 6. In this model, there is no government. We consider the HPltered data you constructed in the problem sets. Namely, retrieve the series (in levels) for consumption (Ct) and investment (1,). Compute output (K) as the sum of only these two variables. Take the log of the three series in levels and then apply the HP lter with smoothing parameter A = 1600. Consider the cyclical component of each series