# Household Functions#

household.py modules

## ogcore.household#

### Household functions.#

ogcore.household.FOC_labor(r, w, p_tilde, b, b_splus1, n, bq, factor, tr, ubi, theta, chi_n, etr_params, mtrx_params, t, j, p, method)[source]#

Computes errors for the FOC for labor supply in the steady state. This function is usually looped through over J, so it does one lifetime income group at a time.

$w_t e_{j,s}\bigl(1 - \tau^{mtrx}_{s,t}\bigr) \frac{(c_{j,s,t})^{-\sigma}}{ \tilde{p}_{t}} = \chi^n_{s} \biggl(\frac{b}{\tilde{l}}\biggr)\biggl(\frac{n_{j,s,t}} {\tilde{l}}\biggr)^{\upsilon-1}\Biggl[1 - \biggl(\frac{n_{j,s,t}}{\tilde{l}}\biggr)^\upsilon\Biggr] ^{\frac{1-\upsilon}{\upsilon}}$
Parameters:
• r (array_like) – the real interest rate

• w (array_like) – the real wage rate

• p_tilde (array_like) – composite good price

• b (Numpy array) – household savings

• b_splus1 (Numpy array) – household savings one period ahead

• n (Numpy array) – household labor supply

• bq (Numpy array) – household bequests received

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

• tr (Numpy array) – government transfers to household

• ubi (Numpy array) – universal basic income payment

• theta (Numpy array) – social security replacement rate for each lifetime income group

• chi_n (Numpy array) – utility weight on the disutility of labor supply

• e (Numpy array) – effective labor units

• etr_params (list) – parameters of the effective tax rate functions

• mtrx_params (list) – parameters of the marginal tax rate on labor income functions

• t (int) – model period

• j (int) – index of ability type

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

• method (str) – adjusts calculation dimensions based on ‘SS’ or ‘TPI’

Returns:

error from FOC for labor supply

Return type:

FOC_error (Numpy array)

ogcore.household.FOC_savings(r, w, p_tilde, b, b_splus1, n, bq, factor, tr, ubi, theta, rho, etr_params, mtry_params, t, j, p, method)[source]#

Computes Euler errors for the FOC for savings in the steady state. This function is usually looped through over J, so it does one lifetime income group at a time.

$\frac{c_{j,s,t}^{-\sigma}}{\tilde{p}_{t}} = e^{-\sigma g_y} \biggl[\chi^b_j\rho_s(b_{j,s+1,t+1})^{-\sigma} + \beta_j\bigl(1 - \rho_s\bigr)\Bigl(\frac{1 + r_{t+1} \bigl[1 - \tau^{mtry}_{s+1,t+1}\bigr]}{\tilde{p}_{t+1}}\Bigr) (c_{j,s+1,t+1})^{-\sigma}\biggr]$
Parameters:
• r (array_like) – the real interest rate

• w (array_like) – the real wage rate

• p_tilde (array_like) – composite good price

• b (Numpy array) – household savings

• b_splus1 (Numpy array) – household savings one period ahead

• b_splus2 (Numpy array) – household savings two periods ahead

• n (Numpy array) – household labor supply

• bq (Numpy array) – household bequests received

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

• tr (Numpy array) – government transfers to household

• ubi (Numpy array) – universal basic income payment

• theta (Numpy array) – social security replacement rate for each lifetime income group

• rho (Numpy array) – mortality rates

• etr_params (list) – parameters of the effective tax rate functions

• mtry_params (list) – parameters of the marginal tax rate on capital income functions

• t (int) – model period

• j (int) – index of ability type

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

• method (str) – adjusts calculation dimensions based on ‘SS’ or ‘TPI’

Returns:

Euler error from FOC for savings

Return type:

euler (Numpy array)

ogcore.household.constraint_checker_SS(bssmat, nssmat, cssmat, ltilde)[source]#

Checks constraints on consumption, savings, and labor supply in the steady state.

Parameters:
• bssmat (Numpy array) – steady state distribution of capital

• nssmat (Numpy array) – steady state distribution of labor

• cssmat (Numpy array) – steady state distribution of consumption

• ltilde (scalar) – upper bound of household labor supply

Returns:

None

Raises:

Warnings – if constraints are violated, warnings printed

ogcore.household.constraint_checker_TPI(b_dist, n_dist, c_dist, t, ltilde)[source]#

Checks constraints on consumption, savings, and labor supply along the transition path. Does this for each period t separately.

Parameters:
• b_dist (Numpy array) – distribution of capital at time t

• n_dist (Numpy array) – distribution of labor at time t

• c_dist (Numpy array) – distribution of consumption at time t

• t (int) – time period

• ltilde (scalar) – upper bound of household labor supply

Returns:

None

Raises:

Warnings – if constraints are violated, warnings printed

ogcore.household.get_bq(BQ, j, p, method)[source]#

Calculate bequests to each household.

$bq_{j,s,t} = \zeta_{j,s}\frac{BQ_{t}}{\lambda_{j}\omega_{s,t}}$
Parameters:
• BQ (array_like) – aggregate bequests

• j (int) – index of lifetime ability group

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

• method (str) – adjusts calculation dimensions based on ‘SS’ or ‘TPI’

Returns:

Return type:

bq (array_like)

ogcore.household.get_ci(c_s, p_i, p_tilde, tau_c, alpha_c, method='SS')[source]#

Compute consumption of good i given amount of composite consumption and prices.

$c_{i,j,s,t} = \frac{c_{s,j,t}}{\alpha_{i,j}p_{i,j}}$
Parameters:
• c_s (array_like) – composite consumption

• p_i (array_like) – prices for consumption good i

• p_tilde (array_like) – composite good price

• tau_c (array_like) – consumption tax rate

• alpha_c (array_like) – consumption share parameters

• method (str) – adjusts calculation dimensions based on ‘SS’ or ‘TPI’

Returns:

consumption of good i

Return type:

c_si (array_like)

ogcore.household.get_cons(r, w, p_tilde, b, b_splus1, n, bq, net_tax, e, p)[source]#

Calculate household consumption.

$c_{j,s,t} = \frac{(1 + r_{t})b_{j,s,t} + w_t e_{j,s} n_{j,s,t} + bq_{j,s,t} + tr_{j,s,t} - T_{j,s,t} - e^{g_y}b_{j,s+1,t+1}}{1 - \tau^{c}_{s,t}}$
Parameters:
• r (array_like) – the real interest rate

• w (array_like) – the real wage rate

• p_tilde (array_like) – the ratio of real GDP to nominal GDP

• b (Numpy array) – household savings

• b_splus1 (Numpy array) – household savings one period ahead

• n (Numpy array) – household labor supply

• bq (Numpy array) – household bequests received

• net_tax (Numpy array) – household net taxes paid

• e (Numpy array) – effective labor units

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

Returns:

household consumption

Return type:

cons (Numpy array)

ogcore.household.get_tr(TR, j, p, method)[source]#

Calculate transfers to each household.

$tr_{j,s,t} = \zeta_{j,s}\frac{TR_{t}}{\lambda_{j}\omega_{s,t}}$
Parameters:
• TR (array_like) – aggregate transfers

• j (int) – index of lifetime ability group

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

• method (str) – adjusts calculation dimensions based on ‘SS’ or ‘TPI’

Returns:

Return type:

tr (array_like)

ogcore.household.get_y(r_p, w, b_s, n, p, method)[source]#

Compute household income before taxes.

$y_{j,s,t} = r_{p,t}b_{j,s,t} + w_{t}e_{j,s}n_{j,s,t}$
Parameters:
• r_p (array_like) – real interest rate on the household portfolio

• w (array_like) – real wage rate

• b_s (Numpy array) – household savings coming into the period

• n (Numpy array) – household labor supply

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

• method (str) – adjusts calculation dimensions based on ‘SS’ or ‘TPI’

ogcore.household.marg_ut_cons(c, sigma)[source]#

Compute the marginal utility of consumption.

$MU_{c} = c^{-\sigma}$
Parameters:
• c (array_like) – household consumption

• sigma (scalar) – coefficient of relative risk aversion

Returns:

marginal utility of consumption

Return type:

output (array_like)

ogcore.household.marg_ut_labor(n, chi_n, p)[source]#

Compute the marginal disutility of labor.

$MDU_{l} = \chi^n_{s}\biggl(\frac{b}{\tilde{l}}\biggr) \biggl(\frac{n_{j,s,t}}{\tilde{l}}\biggr)^{\upsilon-1} \Biggl[1-\biggl(\frac{n_{j,s,t}}{\tilde{l}}\biggr)^\upsilon \Biggr]^{\frac{1-\upsilon}{\upsilon}}$
Parameters:
• n (array_like) – household labor supply

• chi_n (array_like) – utility weights on disutility of labor

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

Returns:

marginal disutility of labor supply

Return type:

output (array_like)