Parameter Calculation Functions

paramfunctions

ccc.paramfunctions

ccc.paramfunctions.calc_g(g_scg, g_lcg, g_xcg, omega_scg, omega_lcg, omega_xcg, m, E_c)[source]

Calculate the after-tax, annualized, real rate of return on all capital gains

..math::
g = omega_{scg}times g_{scg} + omega_{lcg}times g_{lcg} +

omega_{xcg}times mE

Parameters
  • g_scg (scalar) – the real, after-tax annualized return on short- term capital gains

  • g_lcg (scalar) – the real, after-tax annualized return on long- term capital gains

  • g_xcg (scalar) – the real, after-tax annualized return on capital gains held until death

  • omega_scg (scalar) – the fraction of capital gains that are short-term

  • omega_lcg (scalar) – the fraction of capital gains that are long-term

  • omega_xcg (scalar) – the fraction of capital gains that are held until death

  • m (scalar) – share of equity return retained by the firm and reinvested

  • E_c (scalar) – expected, after-tax return on corporate equity

Returns

the after-tax, annualized, real rate of return on

all capital gains

Return type

g (scalar)

ccc.paramfunctions.calc_g__g(Y_g, tau_cg, m, E_c, pi)[source]

Calculate the real, after-tax annualized return on short or long- term capital gains

..math::
g_{icg} = frac{1}{Y_{icg}}lnbiggl[(1-tau_{icg})e^{(pi+mE)

Y_{icg}}+tau_{icg}biggr] + pi

Parameters
  • Y_g (scalar) – number of years asset held before gains realized

  • tau_cg (scalar) – tax rate on capital gains income

  • m (scalar) – share of equity return retained by the firm and reinvested

  • E_c (scalar) – expected, after-tax return on corporate equity

  • pi (scalar) – inflation rate

Returns

real, after-tax annualized return on capital

gains

Return type

g__g (scalar)

ccc.paramfunctions.calc_s(p)[source]

Compute the after-tax rate of return to savers, s.

\[s = ...\]
Parameters

p (CCC Specification Object) – model parameters

Returns

return to savers and required return to pass-through

entities:

  • s_dict (dict): dictionary of s for investments in

    corporate and pass-through businesses and by type of financing

  • E_nc (scalar): required pre-tax return on pass-through

    investments

Return type

(tuple)

ccc.paramfunctions.calc_s__d(s_d_td, alpha_d_ft, alpha_d_td, alpha_d_nt, tau_int, tau_w, i, pi)[source]

Compute the after-tax return to debt investments.

..math::
s_{j,d} = alpha_{j,d,ft}((1-tau_{int})i - pi) +

alpha_{j,d,td}s_{j,d,td} + alpha_{j,d,nt}(i-pi) - tau_{w}

Parameters
  • s_d_td (scalar) – after-tax return on debt investments made through tax-deferred acounts

  • alpha_d_ft (scalar) – fraction of debt investments held in full-tax accounts

  • alpha_d_td (scalar) – fraction of debt investments held in tax-deferred acounts

  • alpha_d_nt (scalar) – fraction of debt investments held in tax-free accounts

  • tau_int (scalar) – marginal tax rate on interest income

  • tau_w (scalar) – marginal tax rate on wealth

  • i (scalar) – nominal interest rate

  • pi (scalar) – inflation rate

Returns

after-tax return on debt investments

Return type

s__d (scalar)

ccc.paramfunctions.calc_s_c_d_td(sprime_c_td, gamma, i, pi)[source]

Compute the after-tax return on corprate debt investments made through tax-deferred accounts.

..math::

s_{c,d,td} = gamma(i-pi) + (1-gamma)s^{‘}_{c,td}

Parameters
  • sprime_c_td (scalar) – the after-tax return on corporate investments made through tax-deferred accounts

  • gamma (scalar) – Fraction of debt owned through whole-life insurance policies

  • i (scalar) – the nominal interest rate

  • pi (scalar) – the inflation rate

Returns

the after-tax return on corprate debt

investments made through tax-deferred accounts

Return type

s_c_d_td (scalar)

ccc.paramfunctions.calc_s_c_e(s_c_e_ft, s_c_e_td, alpha_c_e_ft, alpha_c_e_td, alpha_c_e_nt, tau_w, E_c)[source]

Calculate the after-tax return on investments in corporate equity

..math::
s_{c,e} = alpha_{c,e,ft}times s_{c,e,ft} + alpha_{c,e,td}

times s_{c,e,td} + alpha_{c,e,nt}times E - tau_{w}

Parameters
  • s_c_e_ft (scalar) – after-tax return on investments in corporate equity in fully-taxable accounts

  • s_c_e_td (scalar) – after-tax return on investments in corporate equity in tax-deferred accounts

  • alpha_c_e_ft (scalar) – fraction of corporate equity investments made through full-taxable accounts

  • alpha_c_e_td (scalar) – fraction of corporate equity investments made through tax-deferred accounts

  • alpha_c_e_nt (scalar) – fraction of corporate equity investments made through tax-exempt accounts

  • tau_w (scalar) – marginal tax rate on wealth

  • E_c (scalar) – expected, after-tax return on corporate equity

Returns

the after-tax return on investments in

corporate equity

Return type

s_c_e (scalar)

ccc.paramfunctions.calc_s_c_e_td(Y_td, tau_td, i, pi, E_c)[source]

Calculate the after-tax return on investmentes in corporate equity in tax-deferred accounts.

..math::
s_{c,e,td} = frac{1}{Y_{td}}ln((1-tau_{td})e^{(pi+E)Y_{td}}

+tau_{td}) - pi

Parameters
  • Y_td (scalar) – years investments are held in tax-deferred accounts

  • tau_td (scalar) – marginal tax rate on investments in tax-deferred accounts

  • i (scalar) – nominal interest rate

  • pi (scalar) – inflation rate

  • E_c (scalar) – expected, after-tax return on corporate equity

Returns

the after-tax return on investmentes in

corporate equity in tax-deferred accounts.

Return type

s_c_e_td (scalar)

ccc.paramfunctions.calc_sprime_c_td(Y_td, tau_td, i, pi)[source]

Compute after-tax rate of return on savings invested in tax-deferred accounts.

\[s^{'}_{c,td} = \frac{1}{Y_{td}}log((1-\tau_{td})*e^{i*Y_{td}}+ \tau_{td}) - \pi\]
Parameters
  • Y_td (scalar) – number of years savings held in tax-deferred retirement account

  • tau_td (scalar) – effective marginal tax rate on investment income from tax-deferred accounts

  • i (scalar) – the nominal interest rate

  • pi (scalar) – the inflation rate

Returns

the after-tax return on corporate

investments made through tax-deferred accounts

Return type

sprime_c_td (scalar)