Assignment 2 (Advanced Theory ECON 8820)
Due 10pm, EST, Tuesday, April 2
Note: This assignment requires you to use Dynare. In addition to submitting the answers, you also need to submit the Dynare mod file and output file. Please submit all files through Brightspace.
Total marks: 40 marks
1) (5 marks) In Table 1, you are given the volatilities of the key labour market variables from two sample periods P1 and P3 calculated from A1. P1: period prior to the Great Recession (2000M12 to 2007M12), and P3: period after the Great Recession (2010M1 to 2020M2). In data, the standard deviation of output (y) time series (logged and HP filtered) is 0.02. Define the relative volatility of a particular time series as the ratio of its standard deviation to the standard deviation of y. Compute the relative volatilities for the variables listed below and fill the results in Table 1, where u is unemployment, v is vacancy, theta is labour market tightness, and f is job finding rate.
Table 1: Standard Deviations for P1 and P3 in Data
    u    v    theta    f
SD: P1     0.12    0.14    0.25    0.08
SD: P3    0.04    0.05    0.08    0.05
Relative SD: P1                
Relative SD: P3                
              Note that all the time series are logged and HP filtered.
2) (10 marks) Use the parameters’ values discussed in class and simulate the simple matching model using Dynare for P1. Construct two tables: one for model predicted relative SDs; one for model predicted correlations. Briefly discuss the model’s performance in terms of generating labor market business cycle properties observed in the data. 

You are given the following correlation info observed in the data (Table 2).

     Table 2: Correlations of Key Labour Market Variables in Data (P1: 2000-07)

    u    v    theta    f
u    1            
v    -0.98    1        
theta    -0.99    0.99    1    
f    -0.89    0.92    0.91    1

3) (5 marks) Use b=0.9 instead of b=0.4 while keeping all the other parameters unchanged. Simulate the model and compute the relative volatilities only for unemployment and vacancies. Does increasing b lead to higher volatilities of these two variables?

4) (20 marks) You are given the following Tables 3 and 4 regarding the period after the Great Recession (P3).

Repeat questions 2) and 3) for P3. Note you will need to re-calibrate lambda (job separation rate in the model), a_w_ss (job finding rate in the model), and theta_ss (labour market tightness in the model) to match the data averages (see Table 3 below)
                                                                                   
                             Table 3: Monthly Data Average for P3 (2010-20)

theta    f    s
0.63    0.28    0.019
 Note -- theta: labour market tightness; f: job finding rate; s: separation rate

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