Poor Household’s Demand for Cheap Dietary Staples

Ramses Y. Armendariz, Ph.D. ECON 490: Predictive Analytics

Department of Economics Spring 2020 University of Illinois, Urbana-Champaign

ECON 490: Predictive Analytics

Final Project: Testing the Model

The objective of this project is to estimate a structural model of a poor household demand for dietary staples, test the model against the

data, and use the estimated version of the model to extrapolate some predictions. In these notes, I will explain how to use Excel to test

the model by comparing its predictions with the data. As always, you are welcome to use any computer language to solve this part of

the project.

From the previous set of notes, we found that the estimated version of the model is

𝑏(𝑝𝑏; 𝑝𝑚, 𝑖) = 𝑖[0.059𝑝𝑚 − 𝑝𝑏] + 𝑝𝑚𝑝𝑏(0.941)4,951.367

𝑝𝑏(𝑝𝑚 − 𝑝𝑏)

Where the value of 𝑖 for the average household in the experiment is 𝑖 = 8,209.194.

Now, we are going to simulate the model to compare its predictions with the data reported in Jensen and Miller (2008, AER). I have

uploaded the data to Compass, in the project section.

Using the spreadsheet from the data, we will create 6 columns. We will use columns from H to M. We will label the columns as follows:

• H: p_m

• I: b_0

• J: b_1

• K: m_0

• L: HSCS

• M: elasticity

The spreadsheet will look like this:

And we will type the following in each cell:

• H2: 1.855

• I2: We will predict the quantity demanded for bread using the estimated version of the model and evaluated at ▪ 𝑖 = 8,209.194 ▪ 𝑝𝑏 is equal to 1. ▪ 𝑝𝑚 is equal to the value reported in H2.

• J2: We will predict the quantity demanded for bread using the estimated version of the model and evaluated at ▪ 𝑖 = 8,209.194 ▪ 𝑝𝑏 is equal to 1.01. ▪ 𝑝𝑚 is equal to the value reported in H2.

• K2: We will predict the quantity demanded for all the other sources of food using this formula: 𝑚 = (𝑖 − 𝑝𝑏𝑏0) 𝑝𝑚⁄ ▪ 𝑖 = 8,209.194 ▪ 𝑝𝑏 is equal to 1. ▪ 𝑏0 is equal to the value attained in I2. ▪ 𝑝𝑚 is equal to the value reported in H2.

• L2: We will predict the Household Staple Calorie Share following this formula: 𝐻𝑆𝐶𝑆 = 𝑏0 (𝑏0 +𝑚0)⁄ . ▪ 𝑚0 is going to be equal to the value reported in K2. ▪ 𝑏0 is equal to the value attained in I2.

• M2: We will predict the arc-elasticity using the standard formula. ▪ 𝑏1 is going to be the value reported in J2. ▪ 𝑏0 is going to be the value reported in I2.

Ramses Y. Armendariz, Ph.D. ECON 490: Predictive Analytics

Department of Economics Spring 2020 University of Illinois, Urbana-Champaign

▪ 𝑝1 = 1.01 ▪ 𝑝0 = 1.00

• H3: In this cell, we will type “=$H2+0.005”

After feeling all the previous cells, the spreadsheet looks like this:

Next, we will drag all these columns to the raw 1400. The spreadsheet will look like this:

…

Notice that we have predicted plenty of values. Now, we need to compare these predicted values against the data. For these, we will

develop another column, labeled as “model.” We will use columns F. Now, we will type the following:

• In cell F1, we will type “model.”

• In cell F2, we will type “=VLOOKUP($B2,$L$2:$M$1400,2,TRUE)”

• Now, we will drag cell F2 all the way to raw 101.

The spreadsheet will look like this:

…

Ramses Y. Armendariz, Ph.D. ECON 490: Predictive Analytics

Department of Economics Spring 2020 University of Illinois, Urbana-Champaign

Now, we are basically done. We just need to report our results. We will do this with a graph. We will graph columns C, D, E, and F.

Elasticity as a Function of HSCS

*The dashed lines are the 95% confidence intervals from the data.

The pointed line is the point estimate from the data.

The solid line is the model prediction.

The graph we have produced compares the values that the model predicts with the values measured in the experiment. Notice how the

model performs relatively well. For most of the points, its prediction lies inside the 95% confidence interval.

ar DGPs.

-2.000

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

0.330 0.391 0.451 0.512 0.572 0.633 0.694 0.754 0.815 0.875