Chapter 7

Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/IrwinManagerial Economics, 9e

Managerial Economics ThomasMauriceninth edition

Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

McGraw-Hill/IrwinManagerial Economics, 9e

Managerial Economics ThomasMauriceninth edition

Chapter 7

Demand Estimation & Forecasting

Managerial EconomicsManagerial Economics

7-2

Direct Methods of Demand Estimation

• Consumer interviews• Range from stopping shoppers to speak with

them to administering detailed questionnaires

• Potential problems Selection of a representative sample, which is a

sample (usually random) having characteristics that accurately reflect the population as a whole

Response bias, which is the difference between responses given by an individual to a hypothetical question and the action the individual takes when the situation actually occurs

Inability of the respondent to answer accurately


7-3

Direct Methods of Demand Estimation• Market studies & experiments

• Market studies attempt to hold everything constant during the study except the price of the good

• Lab experiments use volunteers to simulate actual buying conditions

• Field experiments observe actual behavior of consumers


7-4

Empirical Demand Functions

• Demand equations derived from actual market data

• Useful in making pricing & production decisions

• In linear form, an empirical demand function can be specified as

RQ a bP cM dP where is quantity demanded, is the price of the goodor service, is consumer income, & is the price of somerelated good

R

Q PM P

R


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• In linear form• b = Q/P

• c = Q/M

• d = Q/PR

• Expected signs of coefficients• b is expected to be negative

• c is positive for normal goods; negative for inferior goods

• d is positive for substitutes; negative for complements

RQ a bP cM dP


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• Estimated elasticities of demand are computed as

RQ a bP cM dP

PÊ bQ

PÊ bQ

M

Mˆ Ê cQ

M

Mˆ Ê cQ

RXR

PÊ dQ

RXR

PÊ dQ


7-7

Nonlinear Empirical Demand Specification• When demand is specified in log-linear

form, the demand function can be written as

b c dRQ aP M P

To estimate a log-linear demandfunction, convert to logarithms

To estimate a log-linear demandfunction, convert to logarithms

RlnQ lna b ln P c ln M d ln P In this form, elasticities are constant In this form, elasticities are constant

Êb MÊc XR

ÊdÊb MÊc XR

Êd


7-8

Demand for a Price-Setter

• To estimate demand function for a price-setting firm:• Step 1: Specify price-setting firm’s

demand function• Step 2: Collect data for the

variables in the firm’s demand function

• Step 3: Estimate firm’s demand using ordinary least-squares regression (OLS)


7-9

Time-Series Forecasts

• A time-series model shows how a time-ordered sequence of observations on a variable is generated

• Simplest form is linear trend forecasting

• Sales in each time period (Qt ) are assumed to be linearly related to time (t)

t tQ a b


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Linear Trend Forecasting

• If b > 0, sales are increasing over time

• If b < 0, sales are decreasing over time

• If b = 0, sales are constant over time

a bUse regression analysis to estimatevalues of and

a bUse regression analysis to estimatevalues of and

tˆ ˆˆQ a bt

bˆp b

Statistical significance of a trend is

determined by testing or by examining

the -value for

bˆp b

Statistical significance of a trend is

determined by testing or by examining

the -value for


7-11

Estimated trend line

A Linear Trend Forecast(Figure 7.1)

Sale

s

Time

Q

t

199

7

199

8

199

9

200

0

200

1

200

2

200

3

200

4

200

5

200

6

2004Q

200

7

7

201

2

2009Q 12


7-12

Forecasting Sales for Terminator Pest Control (Figure 7.2)


7-13

Seasonal (or Cyclical) Variation• Can bias the estimation of parameters

in linear trend forecasting• To account for such variation, dummy

variables are added to the trend equation• Shift trend line up or down depending on

the particular seasonal pattern• Significance of seasonal behavior

determined by using t-test or p-value for the estimated coefficient on the dummy variable


7-14

Sales with Seasonal Variation(Figure 7.3)

2004 2005 2006 2007


7-15

Dummy Variables

• To account for N seasonal time periods• N – 1 dummy variables are added

• Each dummy variable accounts for one seasonal time period• Takes value of 1 for observations

that occur during the season assigned to that dummy variable

• Takes value of 0 otherwise


7-16

Effect of Seasonal Variation(Figure 7.4)

Sale

s

Time

Qt

t

Qt = a’ + bt

a’

a

Qt = a + bt

c


7-17

Some Final Warnings

• The further into the future a forecast is made, the wider is the confidence interval or region of uncertainty

• Model misspecification, either by excluding an important variable or by using an inappropriate functional form, reduces reliability of the forecast

• Forecasts are incapable of predicting sharp changes that occur because of structural changes in the market

Chapter 7

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