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Question 2: An RBC model with Investment Adjustment Costs (50 Marks) Consider the following RBC model with investment adjustment costs. The process of accumulation of the capital stock (Kg) is dened as: Kt+1 : (1 7 6)Kt + [1* '1' (It, 115-1\" I: where 6 is the depreciation rate of physical capital, It is gross investment, and \\I1(.) is the adjust- ment costs function. Following a popular assumption in the literature, we assume that the investment adjustment costs are quadratic (r!) is a positive parameter): v..)=(;_:1_.)2 The representative agent derives utility from a standard utility function. In particular, current con- sumption (0:) and leisure (it) a'ect positively the utility. The utility function is specied as: En Zt [7103(Ct) + (1 \"0105001 i=0 The representative agent has a time endowment of one unit per period, which is split between leisure (it) and work (LE) The size of the labor force is normalized to 1 and it does not vary over time. We assume that the households own the capital stock, they undertake the investment decisions, and that their savings are equal to investment in every period (so that St = I: is guaranteed). The budget constraint of the households is: C: + I: : ths + 7'th In this model, there is no government. The production function is Cobb-Douglas: Y} = ZgKf'Lf\4. Now consider the dynamics of the model in the following three cases1 Where we start from the benchmark calibration of point 2, and then we change some parameter values (while keeping all the others at the benchmark calibration). Report, comment and interpret your results, stressing the economic mechanisms at play. Focus on the standard deviations of the endogenous variables and on the IRF's (expressed as deviations from the steady-state). (23.) Benchmark calibration (b) 11) = 0.01 (c) w : 10.0 5. Obtain quarterly time series data on income, consumption, investment, and hours worked for the US. economy. Explain any steps you might have taken to get the data you'll be working with. Assess the t of the model by comparing the IRF's of the model (based on a calibration of your choice), to the IRF's of a VAR(1) on the US. data