Demand EstimationDemand EstimationDemand EstimationDemand Estimation

&&ForecastingForecasting

Based on Keat & Young, Managerial Economics

• We know how each of the determinants of demand affects the amount of goods people are willing to buy

But, how to put the theory into practice?

• We need to know the true quantitative relationship between demand and the factors that affect it

But, how to find out the ‘quantitative relationship’?

Direct approach

• Consumer Surveys• Focus Group Discussions

Problem: Consumers often cannot be realistic about how they would act in actual market situations

Voluntary participation of people in consumer panel

surveys !!

• High-end technology• Expensive• Only big established market

research firms can do it

Regression Analysis

• The most commonly used procedure used by economists to estimate consumer demand

• Also used to estimate production and cost functions, macroeconomic studies such as international trade etc

Suppose we want to estimate the demand for pizza by college students

1. Which all variables should we analyze?

2. What all variables can be used?

Answer:

1. All variables that are believed to have an impact on demand

2. Based on the availability of data and the cost of generating new data

Classification of data• Cross-Sectional Data: Information on

variables for a GIVEN PERIOD OF TIME.

• Time Series Data: Information about the

variables over a number of periods of time

• Panel Data: Combination of the above two

We have collected cross-sectional data of college

students@!!!

By Random survey of 30 colleges

We have information for each campus on

1. Average number of slices of pizza consumed/month

by students

2. Average prices of a slice of pizza in places selling

pizza in and around the campus

3. Annual course fee

4. Average price of a soft drink sold in pizza places

5. Location of the campus [urban vs. semi-urban vs.

rural] – DUMMY VARIABLE

Creativity in research:

• Why annual course fees introduced in the

model?

• Why the price of soft-drinks used?

• Why is the location dummy variable used?

Answer:• Difficulty in getting the average income

of students or their families

• A soft-drink can be thought of as a good compliment for pizza

• The location dummy is a proxy for the effect of substitutes: Colleges in urban areas may have more eating establishments from which to choose and this might adversely effect the students demand for pizza

Using these data we express the regression

equation in the following linear, additive

fashion

Y = a + b1X1 + b2X2 + b3X3 + b4X4

Y = Quantity of pizza demand

a = the constant value or Y-intercept

X1 = Average price of a slice of pizza

X2= Annual tuition fees

X3 = Average price of soft drink

X4= Location of campus [ =1 if located in urban area, and 0 if otherwise]

b1, b2, b3, b4 = the coefficients of the X-variables measuring the impact of the variables in the demand for pizza

Hypothesis about the anticipated relationships:

1. Price is inversely related: Coefficient of price

should be negative [ b1 should be -ve]

2. Assuming tuition to be a proxy for income,

pizza could be “normal” or “inferior”. Cannot

say anything about the sign beforehand.

3. The price of soft drink also inversely related

being a compliment [b3 should be negative]

4. Location in an urban setting is expected to be

an inverse determinant for the demand for

pizza

• ..\Regression - pizza example.xls

We have obtained the following

estimates:

Y = 26.67 – 0.088 X1 + 0.138 X2 - 0.076 X3 - 0.0544 X4

(0.018) (0.087) (0.020) (0.884)

R2 = 0.717 Adjusted R2 = 0.67 F= 15.8

Std Error of the Y-estimate = 1.64

(The standard errors of the coefficients are listed in parenthesis)

• b1 = -0.088 indicates that:

If the price rises by 1 unit. Then the quantity

demanded of pizza decrease by (1)x(0.088)=0.8. If

the price rises by 100 units, it will result in a

decrease of quantity demanded by

(100)x(0.088)=8.8

• b2 = +0.138 indicates that:

If the fee increase by 1 unit, it results in quantity

demanded of Pizza by 0.138. Since fees the proxy for

our income, it indicates that pizza is “normal” good

b3 = -0.076 indicates that:

As the price of soft drink goes students tend to buy

less pizza. Soft Drink is a “Compliment” good to pizza

b4 = -0.544 indicates that:

Those students who attend colleges in urban areas

will buy about half a slice of pizza per month less than

their counterparts in the suburbs or rural areas!!

Assuming that:

Price of pizza = 100

Annual college fees = 14 (in thousands)

Price of soft drink = 110 (in Cents)

Location of campus = Urban area [i.e., X4 = 1]

Inserting these values in our equation, we get:

Y = 26.67 – 0.088 (100) + 0.1238 (14) – 0.076 (110) – 0.544 (1)

= 10.898 [approximately 11]

Computing elasticity

Price elasticity:[-0.088 (100/10.898)] = -0.807

Income elasticity: [0.1328 (14/10.898)] = 0.177

Cross price elasticity: [-0.076 (110/10.898)] = -0.767

E = (dQ/dP) / ( P/Q)

Since less than 1, Price Inelastic

Statistical evaluation of the regression

results

Is the regression result from a SAMPLE, of students true for the whole population

of college students?

In other words, is it statistically

significant.

Significance implies:

1. Is the result truly reflective of the

population

2. How truly the coefficient explains the

relationship between variables

T-test: The basic test of statistical significance

T = Divide the estimated coefficient by

its standard error = bi/ std error of bi

If the absolute value is greater than 2, then it is

significant, 95% of the times. There is 5%

chance that we are mistaken. This is called

the level of significance

In our example b2 and b4 are not significant

Coefficient of determination or R2

It shows the % of variation in Y accounted for by the variation in all Xs in the equation.

R2= 0: indicates that variations in Y are not due to the variations in the Xs

R2= 1 : all of the variation in Y are accounted or by the Xs

In our pizza examples;R2 = 0.717.72% of the variation in the demand for pizza by college students is accounted for by the variation in the independent variables we have considered

F-test:It measures the statistical

significance of their regression equation rather than each individual coefficients as the t-test do.

In effect it is a test of the statistical significance of the R2

Implications for management decision:

Inelastic price:it implies that they can expect price decreases to lead to a fall in revenue.

Do not try lowering prices to increase sales

2. Significant Cross-Price elasticity: Lowering the price of soft drinks can be thought of,

Being compliments, it can attract people to buy more pizza

3. Fees and location are not statistically significant and their magnitudes very small:

For Chains such as Pizza Hut or Domino’s, this would indicate that they would not have to be concerned about the type of college or its location in deciding where to open the pizza franchise