Transition Path Functions

Transition Path Functions#

TPI.py modules

ogcore.TPI#

Time path iteration (TPI) module for OG-Core.

This module contains the following functions:

get_initial_SS_values() firstdoughnutring() twist_doughnut() inner_loop() run_TPI()

ogcore.TPI.firstdoughnutring(guesses, r, w, p_tilde, p_i, bq, rm, tr, theta, factor, ubi, j, initial_b, p)[source]#

Solves the first entries of the upper triangle of the twist doughnut. This is separate from the main TPI function because the values of b and n are scalars, so it is easier to just have a separate function for these cases.

Parameters:

  • guesses (Numpy array) – initial guesses for b and n, length 2

  • r (scalar) – real interest rate

  • w (scalar) – real wage rate

  • p_tilde (scalar) – composite good price

  • p_i (Numpy array) – output goods prices

  • bq (scalar) – bequest amounts by age

  • rm (scalar) – remittance amounts by age

  • tr (scalar) – government transfer amount

  • theta (Numpy array) – retirement replacement rates, length J

  • factor (scalar) – scaling factor converting model units to dollars

  • ubi (scalar) – individual UBI credit to household s=E+S of type j in period 0

  • j (int) – index of ability type

  • initial_b (Numpy array) – SxJ matrix, savings of agents alive at T=0

  • p (OG-Core Specifications object) – model parameters

Returns:

errors from first order conditions,

length 2

Return type:

euler errors (Numpy array)

ogcore.TPI.get_initial_SS_values(p)[source]#

Get values of variables for the initial period and the steady state equilibrium values.

Parameters:

p (OG-Core Specifications object) – model parameters

Returns:

initial period and steady state values:

  • initial_values (tuple): initial period variable values,

    (b_sinit, b_splus1init, factor, initial_b, initial_n)

  • ss_vars (dictionary): dictionary with steady state

    solution results

  • theta (Numpy array): steady-state retirement replacement

    rates, length J

  • baseline_values (tuple): (Ybaseline, TRbaseline, Gbaseline,

    D0_baseline), GDP, lump sum transfer, and government spending amounts from the baseline model run

Return type:

(tuple)

ogcore.TPI.inner_loop(guesses, outer_loop_vars, initial_values, ubi, j, ind, p)[source]#

Given path of economic aggregates and factor prices, solves household problem. This has been termed the inner-loop (in contrast to the outer fixed point loop that solves for GE factor prices and economic aggregates).

Parameters:

  • guesses (tuple) – initial guesses for b and n, (guesses_b, guesses_n)

  • outer_loop_vars (tuple) – values for factor prices and economic aggregates used in household problem (r_p, r, w, p_m, BQ, RM, TR, theta)

  • r_p (Numpy array) – real interest rate on household portfolio

  • r (Numpy array) – real interest rate on private capital

  • w (Numpy array) – real wage rate

  • p_m (Numpy array) – output goods prices

  • BQ (array_like) – aggregate bequest amounts

  • TR (Numpy array) – lump sum transfer amount

  • theta (Numpy array) – retirement replacement rates, length J

  • initial_values (tuple) – initial period variable values, (b_sinit, b_splus1init, factor, initial_b, initial_n, D0_baseline)

  • ubi (array_like) – T+S x S x J array time series of UBI transfers in model units for each type-j age-s household in every period t

  • j (int) – index of ability type

  • ind (Numpy array) – integers from 0 to S-1

  • p (OG-Core Specifications object) – model parameters

Returns:

household solution results:

  • euler_errors (Numpy array): errors from FOCs, size = Tx2S

  • b_mat (Numpy array): savings amounts, size = TxS

  • n_mat (Numpy array): labor supply amounts, size = TxS

Return type:

(tuple)

ogcore.TPI.run_TPI(p, client=None)[source]#

Solve for transition path equilibrium of OG-Core.

Parameters:

  • p (OG-Core Specifications object) – model parameters

  • client (Dask client object) – client

Returns:

dictionary with transition path solution

results

Return type:

output (dictionary)

ogcore.TPI.twist_doughnut(guesses, r, w, p_tilde, p_i, bq, rm, tr, theta, factor, ubi, j, s, t, etr_params, mtrx_params, mtry_params, initial_b, p)[source]#

Solves the upper triangle of time path iterations. These are the agents who are alive at time T=0 so that we do not solve for their full lifetime (so of their life was before the model begins).

Parameters:

  • guesses (list) – initial guesses for b and n, length 2s

  • r (Numpy array) – real interest rate

  • w (Numpy array) – real wage rate

  • p_tilde (Numpy array) – composite good price

  • p_i (Numpy array) – output goods prices

  • bq (Numpy array) – bequest amounts by age, length s

  • rm (Numpy array) – remittance amounts by age, length s

  • tr (Numpy array) – government transfer amount

  • theta (Numpy array) – retirement replacement rates, length J

  • factor (scalar) – scaling factor converting model units to dollars

  • ubi (Numpy array) – length remaining periods of life UBI payout to household

  • j (int) – index of ability type

  • s (int) – years of life remaining

  • t (int) – model period

  • etr_params (list) – ETR function parameters, list of lists with size = sxsxnum_params

  • mtrx_params (list) – labor income MTR function parameters, list of lists with size = sxsxnum_params

  • mtry_params (list) – capital income MTR function parameters, lists of lists with size = sxsxnum_params

  • initial_b (Numpy array) – savings of agents alive at T=0, size = SxJ

  • p (OG-Core Specifications object) – model parameters

Returns:

errors from first order conditions,

length 2s

Return type:

euler errors (Numpy array)