Poor Household’s Demand for Cheap Dietary Staples
Jingxue
thirdsetofnotes.pdf
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: Simulating Counterfactuals
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 simulate counterfactuals. As always, you are welcome to use any computer language to solve this part of the project. From the first set of notes, we found that the estimated version of the model is
𝑏(𝑝$; 𝑝&, 𝑖) = 𝑖[0.059𝑝& − 𝑝$] + 𝑝&𝑝$(0.941)4,951.367
𝑝$(𝑝& − 𝑝$)
Now, we can employ this model to simulate some counterfactuals. That is, we will use the model to predict what will happen in environments that are not existent (yet) as, for example, plausible changes in policy. We must keep in mind that there are plenty of policies that can be evaluated using this model. In these notes, though, we will only perform 2 simulations:
1. We will extrapolate the whole demand function for the average household in the experiment. 2. We will extrapolate the income elasticity of the staple as a function of price.
Simulation 1: Extrapolating the demand function This simulation is simple. We just need to graph the quantity demanded for bread as a function of price. To generate this graph, it is useful to set a range of prices of the staple that starts at 0.40 and goes to 1.40, with a space between numbers of 0.01.
Quantity Demanded of the Staple as a Function of Its Price
This graph characterizes the demand for bread. In the y-axis, we find the quantity demanded for the staple measured in calories. In the x-axis, we find the price of the staple measured as a proportion of the price of the staple before the experimental treatment was introduced. Notice that the axes are flipped relative to how we usually teach demand in introductory courses. According to this simulation, the demand for the staple satisfies the Law of Demand for all the prices lower than 65% of the price before the treatment. For all the prices that are higher, the demand is Giffen. Simulation 2: Extrapolating the income elasticity as a function of the staple price We will extrapolate the arc-elasticity of income as a function of price in this simulation. Recall that the formula of this arc-elasticity is
𝑏8 − 𝑏9 (𝑏9 + 𝑏8)
2; 𝑖8 − 𝑖9
(𝑖9 + 𝑖8) 2;
3000.000
3200.000
3400.000
3600.000
3800.000
4000.000
4200.000
0. 40
0. 44
0. 48
0. 52
0. 56
0. 60
0. 64
0. 68
0. 72
0. 76
0. 80
0. 84
0. 88
0. 92
0. 96
1. 00
1. 04
1. 08
1. 12
1. 16
1. 20
1. 24
1. 28
1. 32
1. 36
1. 40
Ramses Y. Armendariz, Ph.D. ECON 490: Predictive Analytics
Department of Economics Spring 2020 University of Illinois, Urbana-Champaign
This graph looks like this: Income Elasticity as a Function of Price
Other possible Simulations As I mentioned, there are many other simulations that can be performed. Here, I list some of them:
1. Cross-price elasticity of the staple as a function of income. 2. Income elasticity of the staple as a function of the Household Staple Calorie Share (HSCS) 3. Quantity demanded of calories as a function of the price of the staple
-1.500
-1.400
-1.300
-1.200
-1.100
-1.000
-0.900
-0.800
-0.700
-0.600
0. 40
0. 44
0. 48
0. 52
0. 56
0. 60
0. 64
0. 68
0. 72
0. 76
0. 80
0. 84
0. 88
0. 92
0. 96
1. 00
1. 04
1. 08
1. 12
1. 16
1. 20
1. 24
1. 28
1. 32
1. 36
1. 40
