Write the solution using python.

Exercise: Stochastic Growth 1. Consider the measure of technology Zt for years 19772018 you computed in the previous question. Decompose this series a trend component Zttrend and a cyclical component Ztcycle. 2. Calculate the average growth rate (years 1977-2018) of the trend component Zttrend. Call it g. Then assume that the trend component of TFP Ztrend grows smoothly at the constant rate g : Zttrend=(1+g)Zt1trend where Z0=Z2018 is given. For t=0,1,T,T=101, compute Zt+1trend using equation (1). 3. Assume the log-deviations of actual TFP Z from trend TFP are determined according to an AR(1) process: log(Zt/Zttrend)=log(Zt1/Zt1trend)+t where Z0 is given and tN(0,2). Estimate for years 1977-2018. 4. Solve equation (2) for Zt to get an expression for Zt in terms of Zt1,Zttrend,Zt1trend, and t : Zt=Zttrendelog(Zt1/Zt1trend)+t 5. For t=0,1,..T,T=101, compute compute Zt+1 using equation (3) 6. For t=0,1,..T,T=101, contruct a well-labeled plot of the simulated values of Z and Ztrend 7. Compute the mean and standard deviation of log(Z/Ztrend)