Estimation of Demand

Prof. Ravikesh Srivastava

Lecture-8

From Theory to Practice

What is the true quantitative relationship between demand and the factors that affect it?

How can demand functions be estimated?

How can managers interpret and use these estimations?

Procedures used in marketing research for demand estimation

Consumer Surveys Consumer Clinics Market Experiments Historical Time Series

Experiments Statistical Links Between

National, State, And Regional Performance With Consumer Demand In The Region.

Most common methods used are:

a) consumer interviews or surveysb) market studies and experimentsc) regression analysis

Consumer Surveys

A survey instrument is designed and administered either by mail or by phone or in person. Ask potential buyers how much of the

commodity they would buy at different prices (or with alternative values for the non-price determinants of demand)

Consumer Clinics

Participants know what you are trying to learn and may try to assist the research or support expected findings.

These are also very costly to administer.

Consumer Interviews continued

Problems:1. Selection of a representative sample

what is a good sample!

2. Response bias how truthful can they be?

3. Inability or unwillingness of the respondent to answer accurately

Market Studies and Experiments

More expensive and difficult technique for estimating demand• Displaying the products in several

different stores, generally in areas with different characteristics, over a period of time

• For instance, changing the price, holding everything else constant

Market Studies and Experiments continued

Problems in conducting market studies and experiments:

a) expensiveb) availability of subjectsc) do they relate to the problem, do

they take it seriously

Simple Linear Regression-an effective method to estimate Demand

We assume a two variable case where the form of the

relationship between variables is linear.

Regression Analysis and Demand Estimation

The most frequently used statistical technique in demand estimation

Estimates the quantitative relationship between variables

Quantity demanded being the dependent variable

If only one independent variable (predictor) used: simple regression

If several independent variables used: multiple regression

Think of a demand function of general form:

Qi = + 1Y - 2 pi + 3ps - 4pc + 5Z + e

whereQi = quantity demanded of good i

Y = incomepi = price of good ips = price of the substitute(s)pc = price of the complement(s)Z = other relevant determinant(s) of

demande = error term

and i has to be estimated from historical data

Data used in regression analysis:• Cross-sectional• Time series

Simple Linear Regression Model

In the simplest case, the dependent variable Y is assumed to have the following relationship with the independent variable X:

Y = a + bX + uwhereY = dependent variableX = independent variablea = interceptb = slopeu = random factor

Estimating the Regression Equation

Finding a line that ”best fits” the data• The line that best fits a collection of X,Y

data points, is the line minimizing the sum of the squared distances from the points to the line as measured in the vertical direction

• This line is known as a regression line, and the equation is called a regression equation

Estimated Regression Line:

Y= â + bX

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Skatter Plot

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L

Q

Observed Combinations of Output and Labor input

X Variable 1 Line Fit Plot

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X Variable 1

Y

Y

Predicted Y

Sum of Squares

Sum of Squares cont.

TSS = (Yi - Y)2

RSS = (Ŷi - Y)2

ESS = (Yi - Ŷi)2

This regression line gives the minimum ESS among all possible straight lines.

^^ where Y = mean of Y

The Coefficient of Determination

Coefficient of determination R2 measures how well the line fits the scatter plot (Goodness of Fit)

• R2 is always between 0 and 1 • If it’s near 1 it means that the regression

line is a good fit to the data• Another interpretation: the percentage of

variance ”accounted for”

TSSESS

1TSSRSS

R2

Specification of Regression Model:

Proxy variables• to present some other “real” variable, such

as taste or preference, which is difficult to measure

Dummy variables (X1=0; X2=1)• for qualitative variable, such as gender or

location Linear vs. non-linear relationship

• quadratic terms or logarithms can be used

Y = a + bX1 + cX12

QD=aIb logQD= loga + blogI

Example: Specifying the Regression Equation for Pizza Demand

We want to estimate the demand for pizza by college students in India

What variables would most likely affect their demand for pizza?

What kind of data to collect?

Data: Suppose we have obtained cross- sectional data on college students of randomly selected 30 college campus (by a survey)

The following information is available: average number of slices consumed per

month by students average price of a slice of pizza sold

around the campus price of its complementary product (soft

drink) tuition fee (as proxy for income) location of the campus (dummy variable

is included to find out whether the demand for pizza is affected by the number of available substitutes); 1 urban, 0 for non-urban area

Linear additive regression line:

Y = a + b1pp + b2 ps + b3T + b4L

where Y = quantity of pizza demandeda = the interceptPp = price of pizza

Ps = price of soft drink

T = tuition feeL = locationbi = coefficients of the X variables measuring the

impact of the variables on the demand for pizza