Demonstrate basic concepts related to to selection bias, regression, and instrumental variables

Regression_and_IV.py

# *-----------------------------------------------------------------
# | PROGRAM NAME: Regression_and_IV.py
# | DATE: 12/31/20
# | CREATED BY: MATT BOGARD 
# | PROJECT FILE:      
# *----------------------------------------------------------------
# | PURPOSE: demonstrate basic concepts related to to selection bias, regression, and instrumental variables
# *----------------------------------------------------------------

import pandas as pd
import numpy as np

#
# basic utilities
#

pd.set_option('display.float_format', '{:.2f}'.format) # suppress sci notation

# generate some data
data = {'treat' :[1,1,1,1,1,1,0,1,1,0,0,0,0,0],
        'lifestyle':['H','H','H','H','H','H','H','N','N','N','N','N','N','N'],
		'wtchg':[-12,-10,-9,-11,-12,-10,-8,-8,-2,5,8,10,-5,-2],
		'calories':[2000,2000,3000,3000,2000,2000,2000,3000,3000,5000,5000,5000,3000,3000],
        'push':[1,0,0,1,1,0,0,1,1,0,0,1,0,0],
}

# convert to a data frame
df = pd.DataFrame(data,columns=['treat','lifestyle','wtchg','calories','push'])
print(df)

import statsmodels.api as sm # import stastmodels
import statsmodels.formula.api as smf # this allows us to use an explicit formulation
 
# raw comparisons
results = smf.ols('wtchg ~ treat', data=df).fit()
results.params



# hypothetical - what if we could control for lifestyle?

results = smf.ols('wtchg ~ treat + lifestyle', data=df).fit()
results.params


# regression controlling for historical calorie intake
results = smf.ols('wtchg ~ treat + calories', data=df).fit()
results.params

# 
# manual IV estimation
#


stage1 = smf.ols('treat ~ push', data=df).fit()
stage1.params


stage2 = smf.ols('wtchg ~ push', data=df).fit()
stage2.params

stage2.params[1]/stage1.params[1] # estimate our treatment effect


#
# using the IV2SLS estimator from statsmodels
#

from statsmodels.sandbox.regression.gmm import IV2SLS 

# fit IV2SLS model 
# syntax: IV2SLS(endogenous, exogenous, instrument)
# we can think of this as: IV2SLS(outcome, treatment, insgrument) 
# note: when stats models runs these models under the hood it expects a constant term that we have to add to get the correct result
resultIV = IV2SLS(df['wtchg'], sm.add_constant(df['treat']), sm.add_constant(df['push'])).fit()
resultIV.summary()