2. Is this how it’s done?
Last This %
Year Year Change Change
Price $4 $5 $1 +25%
Q 8 10 2 +25%
Ep = +25% / +25% = + 1
Questions:
1) Is Ep = + 1?
2) What’s the right way to do it?
3. Estimation of Demand
I. The Direct Methods
Interviews and Surveys
Market Experimentations and
Simulations
II. The indirect Methods
Regression Estimation of Consumer
Demand
4. Interviews and Surveys
Ask buyers or potential buyers about their likely
reactions to a change in each of the demand
determinants.
Practical Issues:
Randomness of the sample
Interviewer bias
The best-of-intentions problem
Confusing questions and confusing answers
6. Regression Analysis
of Consumer Demand
A statistical technique that attempts
to "explain" or "predict" movements
in one economic variable, the
dependent variable, as a function of
the movements of a set of
independent (explanatory)
variables.
7. Desirable Characteristics
It shows explicitly the association between the
dependent variable and the independent
variables.
It also provides statistical reliability allowing
the researchers to measure the reliability of the
prediction.
In Econometrics, the economists call it:
‘BLUE’ property.
8. Procedure of Regression Analysis
1. Specifying the variables
2. Obtaining data on the variables
3. Specifying the form of the
estimation equation
4. Estimate the regression parameters
using the method of least squares.
9. Demand and Elasticity Estimation
Step 1 - The model:
Q = f(A, Px, and Pq), where
Q = Number of 2-year contracts sold
A = Advertising expenditures (in dollars)
Px = Price of 1-year contract (in dollars)
Pq = Price of 2-year contract (in dollars)
10. The Data
Time-series data for 1986-97 and the
effect of inflation
Time-series data and the effect of
serial correlation
N=12, K=4, 8 degrees of freedom
11. Estimation of 2 Equations
The 1st Equation - Linear
Q = a + b1 A + b2 Px + b3 Pq
The 2nd Equation - multiplicative
Q = aAb1
Px
b2
Pq
b3
12. The Estimated 1st Equation
Q = 4,589.08 + 0.01015 A + 16.40334 Px - 10.82852 Pq
s.e. (0.00410) (5.35702) (3.77846)
t stat 2.47576 3.06202 -2.86586
p-value 0.00384 0.01553 0.02096
Adj R2 = 0.69127, F=9.20976 (p=0.00566)
SEE=52.98, N=12, K=4
13. Evaluation of Regression Estimation
1. The coefficient of determination (R2
) -
How well does the regression line fit the data?
2. The F-Test - Does the estimated equation
have sufficient explanatory power?
3. The t-Test - Is each of the independent
variables statistically significant?
4. The Standard Error of the Estimate (SEE) -
Can the confidence interval of the predicted
value for the dependent variable be
estimated?
14. The Standard Error of the
Estimate (SEE)
How accurate is the predicted sales?
The SEE can be used to construct prediction intervals
If SEE = 53, then and approximate 95% prediction
interval for the sales of 2-year contracts is equal to
Q’ + 2(53)
15. Uses of the 1st Equation
The demand curve for explaining demand
relationships and for predicting demand
Estimation of the arc elasticities of demand
using
Q1-Q2 Pq1 - Pq2
Ep = ----------- ---------------
Q1+Q2 Pq1+ Pq2
Estimation of the point elasticities of demand
using ep = (dQ/dPq)(Pq/Q)
16. The Multiplicative Equation
Q = aAb1Pxb2Pqb3
Two key questions:
What are the advantages of the multiplicative
form over the linear form
How to go about estimating this non-linear
equation?
See pp. 154-56 of McGuigan/Moyer/Harris,
10th ed. for details
17. The Advantages of the
Multiplicative Form
Q = a Ab1Pxb2 Pqb3
dQ/dPq = (b3) (aAb1Pxb2 Pqb3 -1)
Since epq = (dQ/dPq)(Pq/Q),
epq = (b3)(aAb1Pxb2 Pqb3 -1)(Pq/Q)
= (b3)[(aAb1Pxb2 Pqb3)/Q]
= b3
18. How to estimate the parameters of
the multiplicative equation?
Converting the multiplicative equation
Q = a Ab1Pxb2 Pqb3
into the natural-log form, we have:
Ln Q = Ln a + b1 Ln A + b2 Ln Px + b3 Ln Pq
