[DSGE] NEWS AND NOISE SHOCKS IN HOUSING MARKET

1. ## Basic RBC model with full depreciation
   
2. #
   
3. # Jesus Fernandez-Villaverde
   
4. # Haverford, July 26, 2013
   
5. 
   
6. function main()
   
7. 
   
8.     ##  1. Calibration
   
9. 
   
10.     aalpha = 1/3     # Elasticity of output w.r.t. capital
    
11.     bbeta  = 0.95    # Discount factor
    
12. 
    
13.     # Productivity values
    
14.     vProductivity = [0.9792 0.9896 1.0000 1.0106 1.0212]
    
15. 
    
16.     # Transition matrix
    
17.     mTransition   = [0.9727 0.0273 0.0000 0.0000 0.0000;
    
18.                      0.0041 0.9806 0.0153 0.0000 0.0000;
    
19.                      0.0000 0.0082 0.9837 0.0082 0.0000;
    
20.                      0.0000 0.0000 0.0153 0.9806 0.0041;
    
21.                      0.0000 0.0000 0.0000 0.0273 0.9727]
    
22. 
    
23.     # 2. Steady State
    
24. 
    
25.     capitalSteadyState = (aalpha*bbeta)^(1/(1-aalpha))
    
26.     outputSteadyState = capitalSteadyState^aalpha
    
27.     consumptionSteadyState = outputSteadyState-capitalSteadyState
    
28. 
    
29.     println("Output = ",outputSteadyState," Capital = ",capitalSteadyState," Consumption = ",consumptionSteadyState)
    
30. 
    
31.     # We generate the grid of capital
    
32.     vGridCapital = 0.5*capitalSteadyState:0.00001:1.5*capitalSteadyState
    
33. 
    
34.     nGridCapital = length(vGridCapital)
    
35.     nGridProductivity = length(vProductivity)
    
36. 
    
37.     # 3. Required matrices and vectors
    
38. 
    
39.     mOutput           = zeros(nGridCapital,nGridProductivity)
    
40.     mValueFunction    = zeros(nGridCapital,nGridProductivity)
    
41.     mValueFunctionNew = zeros(nGridCapital,nGridProductivity)
    
42.     mPolicyFunction   = zeros(nGridCapital,nGridProductivity)
    
43.     expectedValueFunction = zeros(nGridCapital,nGridProductivity)
    
44. 
    
45.     # 4. We pre-build output for each point in the grid
    
46. 
    
47.     mOutput = (vGridCapital.^aalpha)*vProductivity;
    
48. 
    
49.     # 5. Main iteration
    
50. 
    
51.     maxDifference = 10.0
    
52.     tolerance = 0.0000001
    
53.     iteration = 0
    
54. 
    
55.     while(maxDifference > tolerance)
    
56.         expectedValueFunction = mValueFunction*mTransition';
    
57. 
    
58.         for nProductivity = 1:nGridProductivity
    
59.         
    
60.             # We start from previous choice (monotonicity of policy function)
    
61.             gridCapitalNextPeriod = 1
    
62.         
    
63.             for nCapital = 1:nGridCapital
    
64.         
    
65.                 valueHighSoFar = -1000.0
    
66.                 capitalChoice  = vGridCapital[1]
    
67.             
    
68.                 for nCapitalNextPeriod = gridCapitalNextPeriod:nGridCapital
    
69. 
    
70.                     consumption = mOutput[nCapital,nProductivity]-vGridCapital[nCapitalNextPeriod]
    
71.                     valueProvisional = (1-bbeta)*log(consumption)+bbeta*expectedValueFunction[nCapitalNextPeriod,nProductivity]
    
72.                
    
73.                     if (valueProvisional>valueHighSoFar)
    
74.                         valueHighSoFar = valueProvisional
    
75.                         capitalChoice = vGridCapital[nCapitalNextPeriod]
    
76.                         gridCapitalNextPeriod = nCapitalNextPeriod
    
77.                     else
    
78.                         break # We break when we have achieved the max
    
79.                     end
    
80.                                  
    
81.                 end
    
82.             
    
83.                 mValueFunctionNew[nCapital,nProductivity] = valueHighSoFar
    
84.                 mPolicyFunction[nCapital,nProductivity] = capitalChoice
    
85.          
    
86.             end
    
87.         
    
88.         end
    
89. 
    
90.         maxDifference  = max(abs(mValueFunctionNew-mValueFunction))
    
91.         mValueFunction    = mValueFunctionNew
    
92.         mValueFunctionNew = zeros(nGridCapital,nGridProductivity)
    
93. 
    
94.         iteration = iteration+1
    
95.         if mod(iteration,10)==0 || iteration == 1
    
96.             println(" Iteration = ", iteration, " Sup Diff = ", maxDifference)
    
97.         end
    
98.            
    
99.     end
    
100. 
     
101.     println(" Iteration = ", iteration, " Sup Diff = ", maxDifference)
     
102.     println(" ")
     
103.     println(" My check = ", mPolicyFunction[1000,3])
     
104. 
     
105. end

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