warp {revpref}R Documentation

Tests consistency with the Weak Axiom of Revealed Preference at efficiency ee

Description

This function allows the user to check whether a given data set is consistent with the Weak Axiom of Revealed Preference at efficiency level ee (eeWARP) and computes the number of eeWARP violations. We say that a data set satisfies WARP at efficiency level ee if qtReDqsq_t R^D_e q_s and qtqsq_t \neq q_s implies epsqs<psqtep_s'q_s < p_s'q_t (see the definition of R^D_e below). The exact WARP, with e=1e = 1, is a necessary and sufficient condition for a data set to be rationalizable by a continuous, strictly increasing, piecewise strictly concave, and skew-symmetric preference function (see Aguiar et al. (2020)). Moreover, Rose (1958) showed that for the case of two goods (N=2N = 2), WARP is equivalent to the Strong Axiom of Revealed Preference (SARP). In other words, when there are only two consumption categories, transitivity has no empirical bite.

Usage

warp(p, q, efficiency = 1)

Arguments

p

A T×NT \times N matrix of observed prices where each row corresponds to an observation and each column corresponds to a consumption category. TT is the number of observations and NN is the number of consumption categories.

q

A T×NT \times N matrix of observed quantities where each row corresponds to an observation and each column corresponds to a consumption category.TT is the number of observations and NN is the number of consumption categories.

efficiency

The efficiency level ee, is a real number between 0 and 1, which allows for a small margin of error when checking for consistency with the axiom. The default value is 1, which corresponds to the test of consistency with the exact WARP.

Value

The function returns two elements. The first element (passwarp) is a binary indicator telling us whether the data set is consistent with WARP at a given efficiency level ee. It takes a value 1 if the data set is eeWARP consistent and a value 0 if the data set is eeWARP inconsistent. The second element (nviol) reports the number of eeWARP violations. If the data set is eeWARP consistent, nviol is 0. Note that the maximum number of violations in an eeWARP inconsistent data is T(T1)/2T(T-1)/2.

Definitions

For a given efficiency level 0e10 \le e \le 1, we say that:

References

See Also

sarp for the Strong Axiom of Revealed Preference and garp for the Generalized Axiom of Revealed Preference.

Examples


# define a price matrix
p = matrix(c(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),
nrow = 10, ncol = 3, byrow = TRUE)

# define a quantity matrix
q = matrix(c( 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),
nrow = 10, ncol = 3, byrow = TRUE)

# Test consistency with WARP and compute the number of WARP violations
warp(p,q)

# Test consistency with WARP and compute the number of WARP violations at e = 0.95
warp(p,q, efficiency = 0.95)


[Package revpref version 0.1.0 Index]