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Example Demands

Introduction

In our last project we used data to estimate systems of food demand using different datasets. An output from that project was as set of cfe.Regression objects; these bundle together both data and the results from the demand system estimation, and can be used for prediction as well.

Here we’ll explore some of the uses of the cfe.Regression class, using an instance created previously (as in Project 3).

After having estimated a demand system using data from our favorite country, we can imagine different counterfactual scenarios. What if prices were different? What if we give a cash transfer to a household? What if school fees reduce the budget for food? What are the consequences of any of these for diet & nutrition?

If you don’t already have the latest version of the CFEDemands package installed, grab it, along with some dependencies:

!pip install -r requirements.txt

import pandas as pd
import cfe.regression as rgsn

Data

We’ll get data from two places. First, basic data, including a food conversion table and recommended daily intakes table can be found in a google spreadsheet.

Here are addresses of google sheets for different dataframes for the case of Uganda:

InputFiles = {'Expenditures':('1yVLriVpo7KGUXvR3hq_n53XpXlD5NmLaH1oOMZyV0gQ','Expenditures (2019-20)'),
              'Prices':('1yVLriVpo7KGUXvR3hq_n53XpXlD5NmLaH1oOMZyV0gQ','Prices'),
              'HH Characteristics':('1yVLriVpo7KGUXvR3hq_n53XpXlD5NmLaH1oOMZyV0gQ','HH Characteristics'),
              'FCT':('1yVLriVpo7KGUXvR3hq_n53XpXlD5NmLaH1oOMZyV0gQ','FCT'),
              'RDI':('1yVLriVpo7KGUXvR3hq_n53XpXlD5NmLaH1oOMZyV0gQ','RDI'),}

Prices, FCT, RDI

from eep153_tools.sheets import read_sheets
import numpy as np
import pandas as pd

def get_clean_sheet(key,sheet=None):

    df = read_sheets(key,sheet=sheet)
    df.columns = [c.strip() for c in df.columns.tolist()]

    df = df.loc[:,~df.columns.duplicated(keep='first')]

    df = df.drop([col for col in df.columns if col.startswith('Unnamed')], axis=1)

    df = df.loc[~df.index.duplicated(), :]

    return df

# Get prices
p = get_clean_sheet(InputFiles['Prices'][0],
                    sheet=InputFiles['Prices'][1])

if 'm' not in p.columns:  # Supply "market" indicator if missing
    p['m'] = 1

p = p.set_index(['t','m'])
p.columns.name = 'j'

p = p.apply(lambda x: pd.to_numeric(x,errors='coerce'))
p = p.replace(0,np.nan)

fct = get_clean_sheet(InputFiles['FCT'][0],
                    sheet=InputFiles['FCT'][1])

fct = fct.set_index('j')
fct.columns.name = 'n'

fct = fct.apply(lambda x: pd.to_numeric(x,errors='coerce'))

################## RDI, if available (consider using US) #####################
rdi = get_clean_sheet(InputFiles['RDI'][0],
                    sheet=InputFiles['RDI'][1])
rdi = rdi.set_index('n')
rdi.columns.name = 'k'

Pre-estimated Demand Systems

An instance r of cfe.Regression can be made persistent with r.to_pickle('my_result.pickle'), which saves the instance “on disk”, and can be loaded using cfe.regression.read_pickle. We use this method below to load data and demand system previously estimated for Uganda:

r = rgsn.read_pickle('uganda_2019-20.pickle')  # Assumes you've already set this up e.g., in Project 3

Reference Prices

Choose reference prices. Here we’ll choose a particular year, and average prices across markets. If you wanted to focus on particular market you’d do this differently.

# Reference prices chosen from a particular time; average across place.
# These are prices per kilogram:
pbar = p.xs('2019-20',level='t').mean()
pbar = pbar[r.beta.index] # Only use prices for goods we can estimate

Budgets

Get food budget for all households, then find median budget:

import numpy as np

xhat = r.predicted_expenditures()

# Total food expenditures per household
xbar = xhat.groupby(['i','t','m']).sum()

# Reference budget
xref = xbar.quantile(0.5)  # Household at 0.5 quantile is median

Food Quantities

Get quantities of food by dividing expenditures by prices:

qhat = (xhat.unstack('j')/pbar).dropna(how='all')

# Drop missing columns
qhat = qhat.loc[:,qhat.count()>0]

qhat

Finally, define a function to change a single price in the vector $p$:

def my_prices(p0,p=pbar,j='Millet'):
    """
    Change price of jth good to p0, holding other prices fixed.
    """
    p = p.copy()
    p.loc[j] = p0
    return p

Demand functions

import matplotlib.pyplot as plt
%matplotlib notebook

use = 'Millet'  # Good we want demand curve for

# Vary prices from 50% to 200% of reference.
scale = np.linspace(.5,2,20)

# Demand for Millet for household at median budget
plt.plot([r.demands(xref,my_prices(pbar[use]*s,pbar))[use] for s in scale],scale)

# Demand for Millet for household at 25% percentile
plt.plot([r.demands(xbar.quantile(0.25),my_prices(pbar[use]*s,pbar))[use] for s in scale],scale)

# Demand for Millet for household at 75% percentile
plt.plot([r.demands(xbar.quantile(0.75),my_prices(pbar[use]*s,pbar))[use] for s in scale],scale)

plt.ylabel(f"Price (relative to base of {pbar[use]:.2f})")
plt.xlabel(f"Quantities of {use} Demanded")

Engel Curves

fig,ax = plt.subplots()

ax.plot(np.log(scale*xref),[r.expenditures(s*xref,pbar)/(scale*xref) for s in scale])
ax.set_xlabel(f'log budget (relative to base of {xref:.0f}')
ax.set_ylabel(f'Expenditure share')
ax.set_title('Engel Curves')