simple-fpa 1.1

Simple nonparametric inference for sealed first-price auctions.

A package for the "Nonparametric inference on counterfactuals in sealed first-price auctions" paper by Pasha Andreyanov and Grigory Franguridi.

It contains a class that fits the auction data using a symmetric first-price auction model with either additive or multiplicative heterogeneity, and predicts latent valuations and counterfactuals.

The interface of the package consists of 4 steps.

• pass a dataframe with auctionid and bid column names
• pass covariate (continuous and discrete) column names and create bid residuals and fitted values
• fit the non-parametric model
• predict latent bids, and also expected total surplus, potential bidder surplus and revenue, as functions of exclusion level

Arxiv and Github repository

https://arxiv.org/abs/2106.13856

https://github.com/pandreyanov/pashas_simple_fpa

Sample code

Package can be installed via pip from terminal

pip install simple_fpa

Import typical auction data

from simple_fpa import Model
import pandas as pd
import numpy as np

import matplotlib.pyplot as plt
from pylab import rcParams

rcParams.update({
    "text.usetex": True,
    "font.family": "serif",
    "font.serif": ["Arial"],
    "figure.dpi": 200
})

df = pd.read_csv('../_data/haile_data_prepared.csv', index_col=0)

Residualize the bids, print summary

model = Model(data = df, auctionid_columns = ['auctionid'], bid_column = 'actual_bid')
cont_covs = ['adv_value', 'hhi', 'volume_total_1']
disc_covs = ['year', 'forest']
model.residualize(cont_covs, disc_covs, 'multiplicative')

model.summary()

# # we can simulate artificial data, of course
# model.data._resid = np.sort(np.random.uniform(0,1,size = len(model.data)))

Trim the residuals, fit the model and predict latent valuations

model.trim_residuals(10)
model.fit(smoothing_rate = 0.2, trim_percent = 5, reflect = True)
model.predict()

Make confidence intervals and confidence bands

model.make_ci(99, hyp = 'twosided')
model.make_cb(99, draws = 1000, hyp = 'twosided')
model.make_cicb_for_ts(99, draws = 1000, hyp = 'twosided')
model.plot_stats()

Find optimal exclusion level and plot counterfactuals

model.find_optimal_u()
model.plot_counterfactuals()

Inspect the data

model.data.sample(5)

Predictions

The counterfactuals are populated into the original dataset, ordered by the magnitude of bid redisuals. Some observations will not have a prediction, as they will be ignored (trimmed) in the non-parametric estimation. I use underscore in front of all variables created by the package.

• _resid : bid residuals

• _fitted : bid fitted values

• _trimmed : variable takes 1 if observations were omitted (trimmed) and 0 otherwise

• _u : u-quantile levels, takes values between 0 and 1

• _hat_q : estimate of quantile density of bid residuals

• _hat_v : estimate of quantile function of value residuals

• _latent_resid : same as _hat_v

• _hat_ts : total surplus as function of exclusion level u

• _hat_bs : (one) potential bidder surplus as function of exclusion level u

• _hat_rev : auctioneer revenue as function of exclusion level u

• q_ci, v_ci, _bs_ci, _ts_ci, _rev_ci : respective asymptotic confidence intervals

• q_cb, v_cb, _bs_cb, _ts_cb, _rev_cb : respective asymptotic confidence bands