Formal and Informal Choices Given Aprime and cash-on-hand

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FFS_FIBS_MIN_C_COST_INF_BRIDGE combine ffs_fibs_min_c_cost + inf_bridge
Default
Parse Parameters
Compute Consumption given Borrowing and Savings
Compute Utility With Default
Display

function [fl_max_c, fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...
            ffs_fibs_min_c_cost_bridge(varargin)

FFS_FIBS_MIN_C_COST_INF_BRIDGE combine ffs_fibs_min_c_cost + inf_bridge

Given coh and aprime choice, what are the optimal formal and informal joint choices including bridge choices. This function is invoked after optimal a-prime choices have been found. This is invoked so that during solution, do not have to store these choices. This is the same material as what is in ff_abz_fibs_vf.m

@param fl_ap float aprime choice, for example optimal aprime solved

@param fl_coh float cash-on-hand for the aprime choice

@param ar_aprime array N by 1 level of aggregate borrowing excluding bridge loan. Note that bridge loan is needed if coh is negative and households can not pay back principle and interests. This must be negative.

@return fl_max_c float next period consumption cost (bl_b_is_principle == true), or this period consumption gain (bl_b_is_principle == false) based on choosing optimally between formal and informal, borrowing and savings joint categories, given either total borrowing in principles or principles + interest rate from ar_aprime.

@return fl_b_bridge float bridge loan debt to pay for unpaid uncovered cash-on-hand

@return fl_inf_borr_nobridge float informal borrowing choices (Excluding Informal Bridge loans, calculated elsewhere) which could come from informal borrowing only if that minimizes consumption cost, or joint formal and informal borrowing if that is the cost minimizing choice. if bl_b_is_principle == true, then this includes just the principles, no intrest rates. if bl_b_is_principle == false, that means this includes interest rates costs as well as principles costs.

@return fl_for_borr float formal borrowing choice that minimizes consumption costs given fixed ar_aprime. Could come from formal borrowing alone (which shows up as joint formal and something else where the other choice is 0), or formal + informal joint borrow, or formal borrowing and formal savings.

@return fl_for_save float this is the formal savings choice when households are borrowing. Households coulds save just for savings, no borrowing as well, that is not captured here.

@example

bl_input_override = true;
[fl_max_c, fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...
     ffs_fibs_min_c_cost_bridge(fl_ap, fl_coh, ...
         param_map, support_map, armt_map, func_map, bl_input_override);

@seealso

Formal Borrowing Grid: ffs_for_br_block_gen
Informal Interest Rates: ffs_r_inf
Match Borrowing to Formal Grid: ffs_for_br_block_match
Optimize Formal and Informal, Borrowing and Savings Joint Choices: ffs_fibs_min_c_cost
Bridge Loan: ffs_fibs_inf_bridge
Overall Optimization: ffs_fibs_min_c_cost_bridge
Discrete Choices: ffs_fibs_identify_discrete

Default

if (~isempty(varargin))

    % override when called from outside
    [fl_ap, fl_coh, param_map, support_map, armt_map, func_map] = varargin{:};
    bl_display_minccost_bridge = false;

else

    close all

    % Default
    it_param_set = 4;
    bl_input_override = true;
    [param_map, support_map] = ffs_ipwkbz_fibs_set_default_param(it_param_set);

    % principle or p+r
    param_map('bl_bridge') = true;
    param_map('fl_r_inf') = 0.065;

    % Gather Inputs from armt_map
    params_group = values(param_map, ...
        {'fl_r_fbr', 'st_forbrblk_type', 'fl_forbrblk_brmost', 'fl_forbrblk_brleast', 'fl_forbrblk_gap'});
    [fl_r_fbr, st_forbrblk_type, fl_forbrblk_brmost, fl_forbrblk_brleast, fl_forbrblk_gap] = params_group{:};
    [ar_forbrblk, ar_forbrblk_r] = ...
        ffs_for_br_block_gen(fl_r_fbr, st_forbrblk_type, fl_forbrblk_brmost, fl_forbrblk_brleast, fl_forbrblk_gap);

    armt_map = containers.Map('KeyType','char', 'ValueType','any');
    armt_map('ar_forbrblk') = ar_forbrblk;
    armt_map('ar_forbrblk_r') = ar_forbrblk_r;

    % Get Functions
    params_group = values(param_map, {'fl_crra', 'fl_c_min', 'fl_b_bd'});
    [fl_crra, fl_c_min, fl_b_bd] = params_group{:};
    params_group = values(param_map, {'fl_Amean', 'fl_alpha', 'fl_delta'});
    [fl_Amean, fl_alpha, fl_delta] = params_group{:};
    params_group = values(param_map, {'fl_r_fsv', 'fl_w'});
    [fl_r_fsv, fl_w] = params_group{:};
    [~, ~, ~, ~, ~, ~, f_coh_fbis, f_coh_save, ~] = ...
        ffs_ipwkbz_fibs_set_functions(...
        fl_crra, fl_c_min, fl_b_bd, fl_Amean, fl_alpha, fl_delta, fl_w, fl_r_fbr, fl_r_fsv);

    func_map = containers.Map('KeyType','char', 'ValueType','any');
    func_map('f_coh_fbis') = f_coh_fbis;
    func_map('f_coh_save') = f_coh_save;

    % Testing COH and Aprime Vectors
    fl_ap = -10;
    fl_coh = 5;

    % Testing COH and Aprime Vectors
    fl_ap = -10;
    fl_coh = -7;

    % Example where aprime choice can not repay debt.
    fl_ap = -5;
    fl_coh = -10;

    % Set Display Control
    support_map('bl_display_infbridge') = true;
    support_map('bl_display_minccost') = true;

    bl_display_minccost_bridge = true;
end

Parse Parameters

% Gather Inputs from armt_map
params_group = values(armt_map, {'ar_forbrblk', 'ar_forbrblk_r'});
[ar_forbrblk, ar_forbrblk_r] = params_group{:};

% Gather Inputs from param_map
% fl_r_inf is a shock, need to be inserted in
params_group = values(param_map, {'bl_rollover', 'bl_default', 'bl_bridge', 'bl_b_is_principle', 'fl_r_inf', 'fl_r_fsv', 'fl_c_min'});
[bl_rollover, bl_default, bl_bridge, bl_b_is_principle, fl_r_inf, fl_r_fsv, fl_c_min] = params_group{:};

% func_map
if (bl_b_is_principle)
    % when savings is principle: mimizing cost cost tomorrow
    params_group = values(func_map, {'f_coh_fbis', 'f_coh_save'});
    [f_coh_fbis, f_coh_save] = params_group{:};
else
    % when not principle, but principle + interest: maximize c gain today
    params_group = values(func_map, {'f_cons_coh_fbis', 'f_cons_coh_save'});
    [f_cons_coh_fbis, f_cons_coh_save] = params_group{:};
end

% support_map
params_group = values(support_map, {'bl_display_minccost', 'bl_display_infbridge'});
[bl_display_minccost, bl_display_infbridge] = params_group{:};

Compute Consumption given Borrowing and Savings

find the today's consumption maximizing formal and informal choices given a' and coh. The formal and informal choices need to generate exactly a', but depending on which formal and informal joint choice is used, the consumption cost today a' is different. Note here, a is principle + interests. Three areas:

CASE A a' > 0: savings, do not need to optimize over formal and informal choices
CASE B a' < 0 & coh < 0: need bridge loan to pay for unpaid debt, and borrowing over-all, need to first pick bridge loan to pay for debt, if bridge loan is insufficient, go into default. After bridge loan, optimize over formal+informal, borrow+save joint choices.
CASE C $ a' < 0 & coh > 0: do not need to get informal bridge loans, optimize over for+inf save, for+save+borr, inf+borr only, for borrow only.

if (fl_ap < 0)

    % Calculate Bridge Loan Borrowing
    if (fl_coh < 0 && bl_bridge)
        bl_input_override = true;
        [fl_aprime_nobridge, fl_b_bridge, fl_c_bridge] = ffs_fibs_inf_bridge(...
            bl_b_is_principle, fl_r_inf, fl_ap, fl_coh, ...
            bl_display_infbridge, bl_input_override);

    else

        fl_aprime_nobridge = fl_ap;
        fl_b_bridge = 0;
        fl_c_bridge = 0;

    end

    % Find Optimal Formal Informal Borrow Save Combo
    % calculate consumption gain from formal + informal
    % borrowing and savings choices.
    bl_input_override = true;
    [fl_max_c_nobridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = ...
        ffs_fibs_min_c_cost(...
        bl_b_is_principle, fl_r_inf, fl_r_fsv, ...
        ar_forbrblk_r, ar_forbrblk, ...
        fl_aprime_nobridge, bl_display_minccost, bl_input_override);

    % Compute Consumption given Formal and Informal joint
    % consumption with formal borrow menu + bridge loans.
    if (bl_b_is_principle)
        fl_max_c_or_coh_raw = f_coh_fbis(fl_r_inf, fl_for_borr, fl_b_bridge + fl_inf_borr_nobridge, fl_for_save);
    else
        fl_max_c_or_coh_raw = f_cons_coh_fbis(fl_coh, fl_max_c_nobridge + fl_c_bridge);
    end

else

    % consumption with savings
    if (bl_b_is_principle)
        fl_max_c_or_coh_raw = f_coh_save(fl_ap);
    else
        fl_max_c_or_coh_raw = f_cons_coh_save(fl_coh, fl_ap);
    end

    % assign values for formal and informal choices
    % possible that fl_coh < 0, but if then fl_ap > 0 is
    % not valid choice
    [fl_b_bridge, fl_inf_borr_nobridge, fl_for_borr, fl_for_save] = deal(0, 0, 0, fl_ap);

end

bl_b_is_principle:1
fl_r_bridge:0.065
ar_aprime:-5
ar_b_bridge:-10
bl_display_infbridge:1
    ar_coh_today    ar_aprime    ar_b_bridge    ar_c_bridge    ar_aprime_nobridge
    ____________    _________    ___________    ___________    __________________

        -10            -5            -10          -10.65               5         

*ar_coh_today*: cash on hand someone arrives in the period with given debt and current income
*ar_aprime*: func called during finding optimal aprime, this is the current aprime overall choice
*ar_b_bridge*: amount of bridge loan required to cover negative coh (includes interest if bl_b_is_principle = false)
*ar_c_bridge*: consumption gain today from the bridge loan to cover negative coh; or consumption cost tomorrow for debt which increases c today
*ar_aprime_nobridge*ar_aprime_nobridge:aprime = -10, -5 for bridge; -5 left for other borrowing choices;aprime = -10, -11 for bridge (given r), +1 savings left, reduces consumption, back to neg coh, infeasible state;
    ar_aprime_nobridge    mt_max_c_nobridge    ar_average_r    mt_inf_borr_nobridge    mt_for_borr    mt_for_save
    __________________    _________________    ____________    ____________________    ___________    ___________

            5                   5.125             -1.025                0                   0              5

Error using ffs_ipwkbz_fibs_set_functions>@(z,b_with_r,k)(f_prod(z,k)+k*(1-fl_delta)+fl_w+b_with_r)
Too many input arguments.

Error in ffs_fibs_min_c_cost_bridge (line 211)
        fl_max_c_or_coh_raw = f_coh_fbis(fl_r_inf, fl_for_borr, fl_b_bridge + fl_inf_borr_nobridge, fl_for_save);

Compute Utility With Default

assign u(c)

if (~bl_b_is_principle) && ...
        ((fl_max_c_or_coh_raw <= fl_c_min || ( ~bl_rollover && ~bl_bridge && fl_coh < fl_c_min)))

    if (bl_default)
        % Replace Consumption if default cmin
        fl_max_c = fl_c_min;
    else
        % Replace Consumption if no default nan
        fl_max_c = 0;
    end
    % if coh < 0 but aprime > coh, choice not sufficient to pay debt, then
    % fl_for_save ends up > 0, but that is not possible, not a real choice.
    if (fl_for_save > 0)
        fl_for_save = 0;
    end
else
    fl_max_c = fl_max_c_or_coh_raw;
end

Display

if (bl_display_minccost_bridge)

    disp('fl_max_c_raw');
    disp(fl_max_c_or_coh_raw);

    disp('fl_max_c');
    disp(fl_max_c);

    disp('fl_for_save');
    disp(fl_for_save);

end

end