rpmpopulationpmf {rpm}

Compute the population distribution of pairs and singles from a Revealed Preference Matchings Model

Description

rpmpopulationpmf computes the probability mass function for a population of the pairs and singles from a Revealed Preference Matchings Model based on arbitary availability distribution and preferences. It is typically based on the estimate from a rpm() call.

Usage

rpmpopulationpmf(
  object,
  N = 2000,
  num_women = NULL,
  num_men = NULL,
  pmfW = NULL,
  pmfM = NULL,
  verbose = FALSE
)

Arguments

object

list; an object of classrpm that is typically the result of a call to rpm().

N

integer; The total population size. This must be set. The number of women and men are derived from the (weighted) data.

num_women

integer; (Optional) The number of women in the population.

num_men

integer; (Optional) The number of men in the population.

pmfW

vector; (Optional) The population proportions of the numbers of women of each type. This should be compatible with the type in the object.

pmfM

vector; (Optional) The population proportions of the numbers of men of each type. This should be compatible with the type in the object.

verbose

logical; Should verbose messages be printed out.

Details

The function rpm is used to fit a revealed preference model for men and women of certain characteristics (or shared characteristics) of people of the opposite sex. The model assumes a one-to-one stable matching using an observed set of matchings and a set of (possibly dyadic) covariates to estimate the parameters for linear equations of utilities. It does this using an large-population likelihood based on ideas from Dagsvik (2000), Menzel (2015) and Goyal et al (2023).

The model represents the dyadic utility functions as deterministic linear utility functions of dyadic variables. These utility functions are functions of observed characteristics of the women and men. These functions are entered as terms in the function call to rpm. This function simulates from such a model.

Value

A list of data.frame, each a simulation from the population.

References

Goyal, Shuchi; Handcock, Mark S.; Jackson, Heide M.; Rendall, Michael S. and Yeung, Fiona C. (2023). A Practical Revealed Preference Model for Separating Preferences and Availability Effects in Marriage Formation, Journal of the Royal Statistical Society, A. doi:10.1093/jrsssa/qnad031

Dagsvik, John K. (2000) Aggregation in Matching Markets International Economic Review,, Vol. 41, 27-57. JSTOR: https://www.jstor.org/stable/2648822, doi:10.1111/1468-2354.00054

Menzel, Konrad (2015). Large Matching Markets as Two-Sided Demand Systems Econometrica, Vol. 83, No. 3 (May, 2015), 897-941. doi:10.3982/ECTA12299

Examples

library(rpm)
data(fauxmatching)

fit <- rpm(~match("edu") + WtoM_diff("edu",3),
          Xdata=fauxmatching$Xdata, Zdata=fauxmatching$Zdata,
          X_w="X_w", Z_w="Z_w",
          pair_w="pair_w", pair_id="pair_id", Xid="pid", Zid="pid",
          sampled="sampled")
a <- rpmpopulationpmf(fit)