Merge pull request #447 from QuantEcon/add-shorrock

FEAT: Add Shorrocks mobility index

docs/source/inequality.rst

@@ -0,0 +1,7 @@
+Inquality
+==========
+
+.. automodule:: quantecon.inquality
+    :members:
+    :undoc-members:
+    :show-inheritance:

quantecon/__init__.py

@@ -23,7 +23,7 @@
 # from .game_theory import <objects-here> 							#Place Holder if we wish to promote any general objects to the qe namespace.
 from .graph_tools import DiGraph, random_tournament_graph
 from .gridtools import cartesian, mlinspace, simplex_grid, simplex_index
-from .inequality import lorenz_curve, gini_coefficient
+from .inequality import lorenz_curve, gini_coefficient, shorrocks_index
 from .kalman import Kalman
 from .lae import LAE
 from .arma import ARMA

quantecon/inequality.py

@@ -84,3 +84,40 @@ def gini_coefficient(y):
     return np.sum(i_sum) / (2 * n * np.sum(y))
 
 
+def shorrocks_index(A):
+    """
+    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
+    -----------
+    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)

quantecon/tests/test_inequality.py

@@ -6,7 +6,7 @@
 
 import numpy as np
 from numpy.testing import assert_allclose
-from quantecon import lorenz_curve, gini_coefficient
+from quantecon import lorenz_curve, gini_coefficient, shorrocks_index
 
 
 def test_lorenz_curve():
@@ -63,4 +63,28 @@ def test_gini_coeff():
 
     y = np.random.weibull(a, size=n)
     coeff = gini_coefficient(y)
-    assert_allclose(expected, coeff, rtol=1e-01)
+    assert_allclose(expected, coeff, rtol=1e-01)
+
+
+def test_shorrocks_index():
+    """
+    Test Shorrocks mobility index function against the example used in 'Wealth
+    distribution and social mobility in the US: A quantitative approach'
+    (Benhabib, Bisin, Luo, 2017).''
+    https://www.econ.nyu.edu/user/bisina/RevisionAugust.pdf
+    """
+
+    # Construct the mobility matrix from Benhabib et al.
+    P = [[0.222, 0.222, 0.215, 0.187, 0.081, 0.038, 0.029, 0.006],
+         [0.221, 0.220, 0.215, 0.188, 0.082, 0.039, 0.029, 0.006],
+         [0.207, 0.209, 0.210, 0.194, 0.090, 0.046, 0.036, 0.008],
+         [0.198, 0.201, 0.207, 0.198, 0.095, 0.052, 0.040, 0.009],
+         [0.175, 0.178, 0.197, 0.207, 0.110, 0.067, 0.054, 0.012],
+         [0.182, 0.184, 0.200, 0.205, 0.106, 0.062, 0.050, 0.011],
+         [0.123, 0.125, 0.166, 0.216, 0.141, 0.114, 0.094, 0.021],
+         [0.084, 0.084, 0.142, 0.228, 0.170, 0.143, 0.121, 0.028]]
+
+    expected = 0.98  # result from paper
+    index = shorrocks_index(P)
+    assert_allclose(expected, index, rtol=1e-2)
+