BM -Demand Estimation

8/12/2019 BM -Demand Estimation

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Demand estimation


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Elasticity estimation is what we want.

To get Arc elasticity, we need discrete data

points

To get point elasticity, we need a demand

function specified.


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How do we get a specific demand function?


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Can specify a relationship as observed inpast data.

With the hypothetical data given earlier, what

kind of a demand function can be specified?


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The specification should explain the data.

How is it done?

- explain with a scatter diagram.


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With many independent variables?

Resort to statistical techniques.

- Regression.


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Steps

STEPS:

Listing of variables

Model specification

Data collection

Run the regression

Check the results


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Demand function

Demand = f( price, income, prices of related goods, etc.)

Functional relationship to be specified and estimated

Linear or non-linear

Linear- Regression technique.

Qx= a + bPx + cI + dPr + ..

Regression helps us estimate the values of a,b,c,d


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An Example

Demand Estimation for Pizzas in the U.S

Variables: Demand for Pizzas-Dependent variable; Independent Variables: Own Price (X1), Avg Annual

Tuition

Fee(X2), Price of Soft drink(X3),Location(X4)

Linear Model: a+bX1+cX2+dX3+eX4

Data: Time series or cross section-Past data


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Results:

Q = 38.50.16X1+ 0.02X2 - 0.05X3 +

2.67X4

Interpretation


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Coefficient of Determination : R2

Tests of Statistical significance


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Results continued

Elasticity estimation

Base values

X1: 1.75; X2: 15000; X3:0.75; X4(urban):0

Q = 7.05

Own Price elasticity: -0.16*175/7=-4

Tution Fee Elasticity: 0.02*15/7=0.04


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Compute the cross price elasticity.


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Valid for what range?

Important because elasticity varies along alinear function.


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More Estimations:

Demand for 45-inch colour TV sets sold by

Computronics

Q=10002P+0.0003A+ 0.001I

+0.000001N+0.1Pr


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Non-Linear Specifications:

Exponential form: aXbYcZd

Linearize using logs

Lg a +b lgX + c lgY + d lgZ

Data to be fed in as logs.

* The coefficients are the elasticities


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Example of Log-Linear estimation:

Demand for ceylon tea in the US.

Log Q = b log Pc+c logPi+ d log Pb + eLog Y

Where, Pc is the price of SriLankan tea; Pi is theprice of indian Tea

Pb is the price of Brazilian coffee; Y is income


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Results:

-1.481Log Pc+1.181 Log Pi+0.186log Pb+0.257 log Y

Interpretation of coefficients as Elasticities.

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BM -Demand Estimation