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contraction_mapping.py
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contraction_mapping.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat May 26 16:20:26 2018
@author: errard
This scripts perform the contraction mapping described in BLP (1995) paper.
"""
import numpy as np
import pandas as pd
from BLP_market_share import calculate_n_consumer_market_share as cal_mkt_shr
from BLP_market_share import calculate_utility as cal_uti
import sys
# Read data
# =============================================================================
if sys.platform == 'darwin':
file_path = "/Users/errard/Dropbox/SSQ_Election/RawData20180515.csv"
market_population_file_name = "/Users/errard/Dropbox/SSQ_Election/adj_census_pop_T.csv"
else:
file_path = "C:/SSQ_Election/RawData20180515.csv"
market_population_file_name = "C:/SSQ_Election/adj_census_pop_T.csv"
def read_csv(file_path):
'''
This function read csv files to pandas dataframe.
input:
file_path: str.
output:
dta: pandas dataframe
'''
f = open(file_path)
dta = pd.read_csv(f)
f.close()
return(dta)
dta = read_csv(file_path)
dta['const'] = np.ones((len(dta), 1))
market_population = read_csv(market_population_file_name)
market_population = market_population.drop(columns = ['depcity', 'arrcity'])
dta = pd.merge(dta, market_population,
left_on = ['depcity', 'arrcity'],
right_on = ['depcity_code', 'arrcity_code'],
how = 'left')
# Set up hyper parameters
# =============================================================================
n_consumers = int(1)
estimates = [-5.246357, -.6285018, -.8258803, -1.604927, 1.448219,
0.7957358, 1.093028, -0.2235259, -0.1370856, -6.126835]
sigma = [2.816481]
data = dta[['priced', 'timed', 'pop_dep', 'moninc', 'edu',
'unemploymentrate_arr', 'unemploymentrate_dep',
'poll', 'mayor_arr', 'const']]
mkt = dta['mkt']
end_var = [0]
seed = 654781324
# =============================================================================
#%% Calculate the market share when nothing changes. This calculation costs
# about 3.5 mins.
data = dta[['priced', 'timed', 'pop_dep', 'moninc', 'edu',
'unemploymentrate_arr', 'unemploymentrate_dep',
'poll', 'mayor_arr', 'const']]
mkt_shr = dta['marketshare1'].copy()
mkt_shr[mkt_shr == 0] = 1e-100
mkt_shr = np.array(mkt_shr)
#%%
def contraction_mapping(mkt_shr, estimates, sigma, data, end_var, mkt,
xi = None,
work = 'Calculating the market share...',
congrats = 'Finished!!',
n_consumers = 500, tolerance = 1e-15, max_iter = 500):
"""
input:
mkt_shr: n x 1 numpy ndarray, the observed market share.
output:
"""
difference = 1
n_iter = 1
delta_old = cal_uti(estimates, sigma, data, end_var, np.zeros(len(sigma)))
if type(xi) == type(None):
xi = np.zeros(len(data))
data = data.assign(xi = xi)
est = estimates.copy()
est.append(1)
delta = cal_uti(est, sigma, data, end_var, np.zeros(len(sigma)))
while (difference > tolerance) & (n_iter <= max_iter):
print('*****Contraction Mapping*****')
print('<Iteration: ' + str(n_iter) + '>')
n_iter += 1
diff = np.log(mkt_shr) - np.log(cal_mkt_shr(est,
sigma, data, end_var, mkt, n_consumers,
work, congrats, seed))
delta = delta + diff.reshape(len(delta), 1)
difference = np.max(np.abs(diff))
print('The difference is ' + str(difference))
print('')
xi = delta - delta_old
data = data.assign(xi = xi)
return(delta, xi)
mean_uti, xi = contraction_mapping(mkt_shr, estimates, sigma, data, end_var,
mkt, xi = xi, n_consumers = int(1e4), max_iter = 5)
#%%
np.savetxt(file_path + 'xi.csv', xi, delimiter = ',')