revealPref {ramchoice}

Revealed Preference Analysis in Random Limited Attention Models

Description

Given a random sample of choice problems and choices, revealPref returns test statistics, critical values and p-values against a collection of preferences. Five methods for choosing critical values are available: (i) GMS: generalized moment selection (plug-in (estimated) moment conditions with shrinkage); (ii) PI: critical values based on plug-in estimated moment conditions (this is not uniformly valid); (iii) LF: critical values based on the least favorable model (plug-in 0 for the moment conditions); (iv) 2MS: two-step moment selection; and (v) 2UB: refined moment selection (plug-in upper bound of moment inequalities).

sumData is a low-level function that generates summary statistics, and genMat can be used to construct the constraint matrices. The simulated dataset ramdata is also provided for illustration. For revealed attention analysis, see revealAtte.

Usage

revealPref(
  menu,
  choice,
  pref_list = NULL,
  method = "GMS",
  nCritSimu = 2000,
  BARatio2MS = 0.1,
  BARatio2UB = 0.1,
  MNRatioGMS = NULL,
  RAM = TRUE,
  AOM = TRUE,
  limDataCorr = TRUE,
  attBinary = 1
)

Arguments

menu

Numeric matrix of 0s and 1s, the collection of choice problems.

choice

Numeric matrix of 0s and 1s, the collection of choices.

pref_list

Numeric matrix, each row corresponds to one preference. For example, c(2, 3, 1) means 2 is preferred to 3 and to 1. When set to NULL, the default, c(1, 2, 3, ...), will be used.

method

String, the method for constructing critical values. Default is GMS (generalized moment selection). Other available options are LF (least favorable model), PI (plug-in method), 2MS (two-step moment selection), 2UB (two-step moment upper bound), or ALL (report all critical values).

nCritSimu

Integer, number of simulations used to construct the critical value. Default is 2000.

BARatio2MS

Numeric, beta-to-alpha ratio for two-step moment selection method. Default is 0.1.

BARatio2UB

Numeric, beta-to-alpha ratio for two-step moment upper bound method. Default is 0.1.

MNRatioGMS

Numeric, shrinkage parameter. Default is sqrt(1/log(N)), where N is the sample size.

RAM

Boolean, whether the restrictions implied by the RAM of Cattaneo et al. (2020) should be incorporated, that is, their monotonic attention assumption (default is TRUE).

AOM

Boolean, whether the restrictions implied by the AOM of Cattaneo et al. (2024) should be incorporated, that is, their attention overload assumption (default is TRUE).

limDataCorr

Boolean, whether assuming limited data (default is TRUE). When set to FALSE, will assume all choice problems are observed. This option only applies when RAM is set to TRUE.

attBinary

Numeric, between 1/2 and 1 (default is 1), whether additional restrictions (on the attention rule) should be imposed for binary choice problems (i.e., attentive at binaries).

Value

sumStats

Summary statistics, generated by sumData.

constraints

Matrices of constraints, generated by genMat.

Tstat

Test statistic.

critVal

Critical values.

pVal

P-values (only available for GMS, LF and PI).

method

Method for constructing critical value.

Author(s)

Matias D. Cattaneo, Princeton University. [e-mail].

Paul Cheung, University of Maryland. [e-mail]

Xinwei Ma (maintainer), University of California San Diego. [e-mail]

Yusufcan Masatlioglu, University of Maryland. [e-mail]

Elchin Suleymanov, Purdue University. [e-mail]

References

M. D. Cattaneo, X. Ma, Y. Masatlioglu, and E. Suleymanov (2020). A Random Attention Model. Journal of Political Economy 128(7): 2796-2836. doi:10.1086/706861

M. D. Cattaneo, P. Cheung, X. Ma, and Y. Masatlioglu (2024). Attention Overload. Working paper.

Examples

# Load data
data(ramdata)

# Set seed, to replicate simulated critical values
set.seed(42)

# list of preferences
pref_list <- matrix(c(1, 2, 3, 4, 5,
                      2, 1, 3, 4, 5,
                      2, 3, 4, 5, 1,
                      5, 4, 3, 2, 1), ncol=5, byrow=TRUE)

# revealed preference using only RAM restrictions
result1 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = TRUE, AOM = FALSE)
summary(result1)

# revealed preference using only AOM restrictions
result2 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = FALSE, AOM = TRUE)
summary(result2)

# revealed preference using both RAM and AOM restrictions
result3 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = TRUE, AOM = TRUE)
summary(result3)

# revealed preference employing additional restrictions for binary choice problems
result4 <- revealPref(menu = ramdata$menu, choice = ramdata$choice, method = "GMS",
  pref_list = pref_list, RAM = TRUE, AOM = TRUE, attBinary = 2/3)
summary(result4)