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)

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

\[g = \omega_{scg}\times g_{scg} + \omega_{lcg}\times g_{lcg} + \omega_{xcg}\times mE\]

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)

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

\[g_{icg} = \frac{1}{Y_{icg}}\ln\biggl[(1-\tau_{icg})e^{(\pi+mE) Y_{icg}}+\tau_{icg}\biggr] + \pi\]

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)

Compute the after-tax rate of return to savers, s. Calls other calc_s_x_y functions to compute various rates of return.

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_pt (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)

Compute the after-tax return to debt investments.

\[s_{j,d} = \alpha_{j,d,ft}((1-\tau_{int})i - \pi) + \alpha_{j,d,td}s_{j,d,td} + \alpha_{j,d,nt}(i-\pi) - \tau_{w}\]

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)

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

\[s_{c,d,td} = \gamma(i-\pi) + (1-\gamma)s^{'}_{c,td}\]

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)

Calculate the after-tax return on investments in corporate equity

\[s_{c,e} = \alpha_{c,e,ft}\times s_{c,e,ft} + \alpha_{c,e,td} \times s_{c,e,td} + \alpha_{c,e,nt}\times E - \tau_{w}\]

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)

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

\[s_{c,e,td} = \frac{1}{Y_{td}}\ln((1-\tau_{td})e^{(\pi+E)Y_{td}} +\tau_{td}) - \pi\]

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)

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)