bronars {revpref}

Computes the Bronars power index for a given axiom at a given efficiency level

Description

The power of the revealed preference test of a given axiom captures the probability of rejecting the axiom if the data set is generated by irrational behavior. Following Bronars' (1987) approach, we measure power using Becker's (1962) notion of irrational behavior. More specifically, we generate irrational behavior by simulating a consumer who makes consumption choices randomly from his or her budget set such that the budget set is exhausted. The Bronars power index captures the probability of rejecting the null hypothesis that the random choices are utility maximizing. Essentially, Bronars' power index is the number of times a violation is detected in the simulated data sets divided by the number of repetitions.

Usage

bronars(p, q, simulation = 1000, model = "GARP", efficiency = 1)

Arguments

p

A T X N matrix of observed prices where each row corresponds to an observation and each column corresponds to a consumption category. T is the number of observations and N is the number of consumption categories.

q

A T X N matrix of observed quantities where each row corresponds to an observation and each column corresponds to a consumption category.T is the number of observations and N is the number of consumption categories.

simulation

Specifies the number of repetitions required of the simulated random data. The default value is 1000.

model

Specifies which axiom (GARP, SARP, or WARP) should be used to compute the power. The default option is "GARP".

efficiency

The efficiency level e is a real number between 0 and 1 and allows for a small margin of error. The default value is 1.

Value

The function returns the power of a given axiom against uniformly random behavior at a given efficiency level.

References

• Becker, Gary S. "Irrational behavior and economic theory." Journal of political economy 70, no. 1 (1962): 1-13.

• Bronars, Stephen G. "The power of nonparametric tests of preference maximization." Econometrica: Journal of the Econometric Society (1987): 693-698.

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)

# compute Bronars power index for GARP at full efficiency
bronars(p,q)

# compute Bronars power index for SARP at e = 0.99
bronars(p,q, model = "SARP", efficiency = 0.99)