Inverse Optimal Tax Class Object

inverse_optimal_tax.py Class

iot.inverse_optimal_tax

class iot.inverse_optimal_tax.IOT(data, income_measure='e00200', weight_var='s006', eti=0.25, dist_type='log_normal', kde_bw=None, mtr_smoother='kreg', mtr_smooth_param=3)

Constructor for the IOT class.

This IOT class can be used to compute the social welfare weights across the income distribution given data, tax policy parameters, and behavioral parameters.

Parameters:

• data (Pandas DataFrame) – micro data representing tax payers. Must include the following columns: income_measure, weight_var, mtr

• income_measure (str) – name of income measure from data to use

• weight_var (str) – name of weight measure from data to use

• eti (scalar) – compensated elasticity of taxable income w.r.t. the marginal tax rate

• bandwidth (scalar) – size of income bins in units of income

• lower_bound (scalar) – minimum income to consider

• upper_bound (scalar) – maximum income to consider

• dist_type (None or str) – type of distribution to use if parametric, if None, then non-parametric bin weights

• mtr_smoother (None or str) – method used to smooth our mtr function, if None, then use bin average mtrs

Returns:

IOT

Return type:

class instance

compute_income_dist(data, income_measure, weight_var, dist_type, kde_bw=None)

Compute the distribution of income (parametrically or not) from the raw data.

This method computes the probability density function and its derivative.

Parameters:

• data (Pandas DataFrame) – micro data representing tax payers. Must include the following columns: income_measure, weight_var, mtr

• income_measure (str) – name of income measure from data to use

• weight_var (str) – name of weight measure from data to use

• dist_type (None or str) – type of distribution to use if parametric, if None, then non-parametric bin weights

Returns:

• z (array_like): mean income at each bin in the income

  distribution

• f (array_like): density for income bin z

• f_prime (array_like): slope of the density function for

  income bin z

Return type:

tuple

compute_mtr_dist(data, weight_var, income_measure, mtr_smoother, mtr_smooth_param)

Compute marginal tax rates over the income distribution and their derivative.

Parameters:

• data (Pandas DataFrame) – micro data representing tax payers. Must include the following columns: income_measure, weight_var, mtr

• weight_var (str) – name of weight measure from data to use

• mtr_smoother (None or str) – method used to smooth our mtr

• function

• None (if)

• mtrs (then use bin average)

Returns:

• mtr (array_like): mean marginal tax rate for each income bin

• mtr_prime (array_like): rate of change in marginal tax rates

  for each income bin

Return type:

tuple

df()

Return all vector attributes in a DataFrame format

Parameters:

None

Returns:

DataFrame with all inputs/outputs

for each income bin

Return type:

df (Pandas DataFrame)

sw_weights()

Returns the social welfare weights for a given tax policy.

See Jacobs, Jongen, and Zoutman (2017) and Lockwood and Weinzierl (2016) for details.

\[g_{z} = 1 + \theta_z \varepsilon^{c}\frac{T'(z)}{(1-T'(z))} + \varepsilon^{c}\frac{zT''(z)}{(1-T''(z))^{2}}\]

Parameters:

None

Returns:

vector of social welfare weights across the income distribution

Return type:

array_like