| auction_model {auctionr} | R Documentation |
Estimates a first-price auction model.
Description
Estimates a first-price auction model.
Usage
auction_model(
dat = NULL,
init_param = NULL,
num_cores = 1,
method = "BFGS",
control = list(),
std_err = FALSE,
hessian_args = list()
)
Arguments
dat |
A data.frame containing input columns in the following order: the winning bids, number of bids, and |
init_param |
Vector of initial values for mu, alpha, sigma, and beta vector, provided in order specified.
Note that the Weibull distribution requires mu and alpha to be positive. The standard deviation of unobserved heterogeneity, sigma, must be positive as well. The Beta vector may take any values.
If |
num_cores |
The number of cores for running the model in parallel. The default value is 1. |
method |
Optimization method to be used in optim() (see ?optim for details). |
control |
A list of control parameters to be passed to optim() (see ?optim for details). |
std_err |
If TRUE, the standard errors of the parameters will also be calculated. Note that it may significantly increase the computation time. |
hessian_args |
A list of arguments passed as the |
Details
This function estimates a first-price auction model with conditionally independent private values. This version of the package estimates a procurement auction, where the winning bid is the amount that a single buyer will pay to the top bidding supplier, and values correspond to costs. The model allows for unobserved heterogeneity that is common to all bidders in addition to observable heterogeneity. The winning bid (Y) takes the form
Y = B * U * h(X)
where B is the proportional winning bid, U is the unobserved heterogeneity, and h(X) controls for observed heterogeneity. The model is log-linear so that log(Y) = log(B) + log(U) + log(h(X)) and log(h(X)) = beta1 * X1 + beta2 * X2 + ...
The (conditionally) independent private costs are drawn from a Weibull distribution with parameters mu (mean) and alpha (shape). The CDF of this distribution is given by
F(c) = 1 - exp(- (c * 1/mu * Gamma(1 + 1/alpha))^(alpha))
The unobserved heterogeneity U is sampled from log-normal distribution with mean 1 and a free parameter sigma representing its standard deviation.
init_params, the initial guess for convergence, must be supplied.
This function utilizes the Rsnow framework within the Rparallel package. If numcores is not specified, this will be run using only
one CPU/core. One can use parallel::detectCores() to determine how many are available on your system, but you are not advised
to use all at once, as this may make your system unresponsive. Please see Rparallel and Rsnow for more details.
Note that the supplied data can not have missing values.
Value
A list returned by optim(). See ?optim for more details. If std_err was set to TRUE and the routine succeeded in inverting
the estimated Hessian, the list will have an additional component:
std_err |
A vector of standard errors for parameter estimates. |
Author(s)
Mackay, Alexander. amackay@hbs.edu, HBS Research Computing research@hbs.edu.
References
Mackay, Alexander. 2020. "Contract Duration and the Costs of Market Transactions." Working paper, Appendix G.
See Also
Examples
###########################################################################
## Estimating parameters and standard errors with custom "control" argument
set.seed(100)
dat <- auction_generate_data(obs = 15, mu = 10, alpha = 2,
sigma = 0.2, beta = c(-1,1),
new_x_mean= c(-1,1),
new_x_sd = c(0.5,0.8))
res <- auction_model(dat, init_param = c(8, 2, .5, .4, .6),
num_cores = 1,
control = list(parscale = c(1,0.1,0.1,1,1)),
std_err = TRUE)
res
## run vignette("auctionr") to view a more detailed example