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Description of programs for Hopenhayn-Nicolini's optimal unemployment 
insurance model:

hugo.m: the main program which calculates the replacement ratio for 
        unemployment scheme without wage tax

valhugo.m: the function file defining the value function of planner

Note: A small function file named hugofoc1.m will be written when main
      program is executed.

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hugo.m
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Output:

a table of replacement ratios for three different initial promised values

(Note: We do not know the exact initial promised value which produces column
       4 of Table 1 in the paper. The second initial value given by us, 16942,
       produces quite similar result as column 4.)


Procedure:

Part 1: Iterate to get vuaut(autarky Vu) and determine r given the calibration
        restriction p(aaut) = 0.1, where aaut is the optimal search effort under
        autarky.

        Iteration algorithm: 1. Initialize vuaut;
                             
                             2. Given P(aaut)=0.1, we can express aaut as a function
                                of r. Given vuaut, we can write first order condition
                                of autarky problem as a function of r;
                             
                             3. Use fsolve to get optimal r;
                             
                             4. Given r in step 3, calculate optimal search effort and
                                use it to update vuaut;
                             
                             5. Iterate until convergence. The final result satisfies
                                p(aaut) = 0.1,

Part 2: Parameterize vmax and vmin and construct chebyshev polynomials. Note that vmax
        ~= Ve to guarantee convergence of coefficients.(as pointed out by Eva)

Part 3: 1. Initialize Chebyshev coefficients,  
        
        2. Approximate value function with initial coefficients. I substitute away both 
           consumption and search effort, so future state variable(promised value) is 
           our control variable( the same case as capital);
        
        3. Given value function, use fmin to get vuprime, next period promised value. 
           Evaluate valhugo.m at optimal vuprime to get value function;
        
        4. Regress value function Cv on Chebyshev polynomials to update coefficients;
        
        5. Iterate till coefficients converge.  

Part 4: Replicate column 4 of Table 1.

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valhugo.m
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The only thing to note is cinv, which equals max(0,inverse of utility function), a point
made by Eva.