revpref 1.0.5

Python Tools for Computational Revealed Preference Analysis

revpref

Python Tools for Computational Revealed Preference Analysis

Synopsis

Our package provides a set of tools to

i) check consistency of a finite set of consumer demand observations with GARP

ii) compute goodness-of-fit indices when the data do not obey the axioms

We implement various method to compute following indices:

CCEI (Critical Cost Efficiency index, Afrait 1972)

• CCEI (also known as the Afriat efficiency index). The CCEI is defined as the maximal value of the efficiency level e at which the data set is consistent with GARP.
• Generally, A is directly prefered to B when $p^Aq^A>p^Aq^B$, and CCEI is the suprema of e under constraint $e p^Aq^A>p^Aq^B$ to satisfy GARP .
• We provide three method to compute CCEI. (Warshall, MTZ and bisection)

HMI (Houtman and Maks index, Houtman and Maks, 1985)

• The Houtman-Maks index gives the relative size of the largest subset of observations that is still consistent with GARP.
• For instance, if we delete the tenth choice from a 10-choice dataset and find it satisfy GARP, then the HMI is (10 - 1)/10 = 0.9
• We provide two methods to compute CCEI. (GrossKaiser, MTZ)

AVI (Average Afrait index, Varian 1990)

• AVI thinks that every choice has its own e. AVI is the maxium of the mean of e-vector.
• We provide only one method to compute AVI. (MTZ)

MPI (Money Pump index, Echenique et al., 2011)

• The MPI is the amount of money one can extract from a consumer who violates the axioms.
• We provide a general algorithm to compute MPI under finite max length of cycles, and we also provide a faster matrix algorithm for max length = 2. (Cycle, Matrix)

MCI (Minimal Cost index, Dean and Martin, 2016)

• MCI is defined as the minimum cost of removing all cycles from the graph.
• We provide two methods to compute MCI. (Optimize, MTZ)

AEE (Average Expenditure Error, Dean and Martin, 2016)

• AEE is defined by relaxing the GARP condition: p^tq^t - r^t >= p^tq^v and finding the minimum sum of r^t that satisfies the condition
• We provide MTZ method to compute AEE.

Installation

You can install our package from PyPI using the following command

pip install revpref

or from github and install it manually

git clone https://github.com/Aliebc/revpref.git
cd revpref
python3 setup.py install

Requirements

Python >= 3.10

numpy, scipy, networkx and pulp are required.

Example

Below we provide some simple examples to illustrate the main class in our package.

import revpref as rp
import numpy as np

p = np.array(
    [[4, 4, 4], 
     [1, 9, 3], 
     [2, 8, 3], 
     [1, 8, 4], 
     [3, 1, 9], 
     [3, 2, 8], 
     [8, 4, 1], 
     [4, 1, 8], 
     [9, 3, 1], 
     [8, 3, 2]]
)

q = np.array(
    [[1.81, 0.19, 10.51], 
     [17.28, 2.26, 4.13], 
     [12.33, 2.05, 2.99], 
     [6.06, 5.19, 0.62], 
     [11.34, 10.33, 0.63], 
     [4.33, 8.08, 2.61], 
     [4.36, 1.34, 9.76], 
     [1.37, 36.35, 1.02], 
     [3.21, 4.97, 6.20], 
     [0.32, 8.53, 10.92]]
)

pref = rp.RevealedPreference(p, q) # Construct the class
# Accelerate if you have Gurobi Optimizer or CPLEX
# pref = rp.RevealedPreference(p, q, lp_solver = 'GUROBI_CMD')
print(pref.check_garp()) # Check if satisfy GARP

print("---CCEI---")
print(pref.ccei()) # Compute the CCEI
print(pref.ccei(method='bisection', tol = 1e-10))
print(pref.ccei(method='mtz')) # Use other methods

print("---AVI---")
print(pref.avi())

print("---MPI---")
print(pref.mpi())
print(pref.mpi(method='matrix'))

print("---MCI---")
print(pref.mci())
print(pref.mci(method='mtz'))

print("---HMI---")
print(pref.hmi())
print(pref.hmi(method='mtz'))

print("---AEE---")
print(pref.aee())

Expected output:

False
---CCEI---
0.9488409272581934
0.9488409272162244
0.94884093
---AVI---
0.9948840929999999
---MPI---
0.0724275724275725
0.0724275724275725
---MCI---
0.0051182597916708365
0.0051182597916708365
---HMI---
0.9
0.9
---AEE---
0.256

References

[1] Afriat, Sidney N."Efficiency estimation of production functions." International economic review (1972): 568-598.

[2] Houtman, Martijn, and Julian Maks. "Determining all maximal data subsets consistent with revealed preference." Kwantitatieve methoden 19, no. 1 (1985): 89-104.

[3] Varian, Hal R. "Goodness-of-fit in optimizing models." Journal of Econometrics 46, no. 1-2 (1990): 125-140.

[4] Echenique, Federico, Sangmok Lee, and Matthew Shum. "The money pump as a measure of revealed preference violations." Journal of Political Economy 119, no. 6 (2011): 1201-1223.

[5] Dean, Mark, and Daniel Martin. "Measuring rationality with the minimum cost of revealed preference violations." Review of Economics and Statistics 98, no. 3 (2016): 524-534.

[6] Demuynck, Thomas, and John Rehbeck. "Computing revealed preference goodness-of-fit measures with integer programming." Economic Theory 76, no. 4 (2023): 1175-1195.

[7] Gross, John, and Dan Kaiser. "Two simple algorithms for generating a subset of data consistent with warp and other binary relations." Journal of Business & Economic Statistics 14, no. 2 (1996): 251-255.