Source code for quantecon.inequality

"""
Implements inequality and segregation measures such as Gini, Lorenz Curve

"""

import numpy as np
from numba import njit, prange


[docs]@njit def lorenz_curve(y): """ Calculates the Lorenz Curve, a graphical representation of the distribution of income or wealth. It returns the cumulative share of people (x-axis) and the cumulative share of income earned Parameters ---------- y : array_like(float or int, ndim=1) Array of income/wealth for each individual. Unordered or ordered is fine. Returns ------- cum_people : array_like(float, ndim=1) Cumulative share of people for each person index (i/n) cum_income : array_like(float, ndim=1) Cumulative share of income for each person index References ---------- .. [1] https://en.wikipedia.org/wiki/Lorenz_curve Examples -------- >>> a_val, n = 3, 10_000 >>> y = np.random.pareto(a_val, size=n) >>> f_vals, l_vals = lorenz(y) """ n = len(y) y = np.sort(y) s = np.zeros(n + 1) s[1:] = np.cumsum(y) cum_people = np.zeros(n + 1) cum_income = np.zeros(n + 1) for i in range(1, n + 1): cum_people[i] = i / n cum_income[i] = s[i] / s[n] return cum_people, cum_income
[docs]@njit(parallel=True) def gini_coefficient(y): r""" Implements the Gini inequality index Parameters ----------- y : array_like(float) Array of income/wealth for each individual. Ordered or unordered is fine Returns ------- Gini index: float The gini index describing the inequality of the array of income/wealth References ---------- https://en.wikipedia.org/wiki/Gini_coefficient """ n = len(y) i_sum = np.zeros(n) for i in prange(n): for j in range(n): i_sum[i] += abs(y[i] - y[j]) return np.sum(i_sum) / (2 * n * np.sum(y))
[docs]def shorrocks_index(A): r""" Implements Shorrocks mobility index Parameters ----------- A : array_like(float) Square matrix with transition probabilities (mobility matrix) of dimension m Returns -------- Shorrocks index: float The Shorrocks mobility index calculated as .. math:: s(A) = \frac{m - \sum_j a_{jj} }{m - 1} \in (0, 1) An index equal to 0 indicates complete immobility. References ----------- .. [1] Wealth distribution and social mobility in the US: A quantitative approach (Benhabib, Bisin, Luo, 2017). https://www.econ.nyu.edu/user/bisina/RevisionAugust.pdf """ A = np.asarray(A) # Convert to array if not already m, n = A.shape if m != n: raise ValueError('A must be a square matrix') diag_sum = np.diag(A).sum() return (m - diag_sum) / (m - 1)