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

4. Simulate the model economy for a number of periods equal to the length of the data series +100 periods. (a) (b) Consider the following statistics for aggregate output, investment and consumption: the stan- dard deviation, the relative standard deviation With respect to output, the rst order autocor relation, the contemporaneous correlation with output. Compare the statistics generated by the model (discarding the rst 100 periods) with their data counterparts. Comment on your results. Estimate a VAR(1) model on the Canadian data. Are the (orthogonalized) impulse responses of the economic model similar to the VAR ones? If not, explain Why the economic model might be failing. Can you suggest how the model could be modied to obtain a better t (you don't need to solve your proposed variant of the model)? 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