Set Model Functions One Asset Borrowing and Savings

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Contents

function [f_util_log, f_util_crra, f_util_standin, f_coh, f_cons_coh, f_cons_checkcmin] = ...
    ffs_abz_set_functions(varargin)

FFS_ABZ_SET_FUNCTIONS setting model functions

define functions here to avoid copy paste mistakes

@param fl_crra float crra utility

@param fl_c_min float minimum consumption

@param fl_r_save float savings interest rate, the borrowing interest rate is a paramter for the coh and inc functions, not a parameter for the overall function here.

@param fl_w float wage rate

@return f_util_log handle log utility

@return f_util_crra handle crra utility general

@return f_util_standin handle log utility with coh for testing graphing codes

@return f_inc income handle equation wage and interests

@return f_coh handle cash on hand equation given current period shock

@return f_cons handle consumption equation given coh and asset choice

@example

[f_util_log, f_util_crra, f_util_standin, f_inc, f_coh, f_cons_coh, f_cons, f_cons_checkcmin] = ...
     ffs_abz_set_functions(fl_crra, fl_c_min, fl_r_save, fl_w);

@seealso

Default

[fl_crra, fl_c_min] = deal(1, 0.001);
[fl_r_save, fl_w] = deal(0.02, 1.23);
default_params = {fl_crra fl_c_min fl_r_save fl_w};

Parse Parameters

% numvarargs is the number of varagin inputted
[default_params{1:length(varargin)}] = varargin{:};
[fl_crra, fl_c_min, fl_r_save, fl_w] = default_params{:};

Equations if Choice is Principle

Choice is principle does not work in this structure with variation in borrowing interest rate.

% utility
f_util_log = @(c) log(c);
f_util_crra = @(c) (((c).^(1-fl_crra)-1)./(1-fl_crra));

% COH and C
f_coh = @(z, b) (z*fl_w + b);
f_cons_coh = @(coh, fl_r_borr, bprime) (coh - (bprime.*(1./(1+fl_r_save)).*(bprime>0) + bprime.*(1./(1+fl_r_borr)).*(bprime<=0)));

% Support
f_coh_princ = @(fl_r_borr, z, b) (z*fl_w + (b.*(1+fl_r_save).*(b>0) + b.*(1+fl_r_borr).*(b<=0)));
f_cons_coh_princ = @(coh, bprime) (coh - bprime);

% f_cons_checkcmin is not used in main solution, but at the end of solution file to
% get consumption based on optimal choices. Here we add conditioning based
% on cmin, so that consumption is not negative. If do not do this, for
% defaulters, next period a'=0, would seem like they have large negative
% consumption.
f_cons_checkcmin = @(fl_r_borr, z, b, bprime) ((f_cons_coh(f_coh(z, b),fl_r_borr,bprime)).*((f_cons_coh(f_coh(z, b),fl_r_borr,bprime)) >= fl_c_min) + ...
                                               fl_c_min.*((f_cons_coh(f_coh(z, b),fl_r_borr,bprime)) < fl_c_min));
% Simple Consumption b and k
f_util_standin = @(fl_r_borr, z, b) f_util_log(f_coh_princ(fl_r_borr,z,b).*(f_coh_princ(fl_r_borr,z,b) > 0) + ...
                                    fl_c_min.*(f_coh_princ(fl_r_borr,z,b) <= 0));

end

ans =

  function_handle with value:

    @(c)log(c)

Published with MATLAB® R2019a