Chapter 7: Demand Estimation and Forecasting

McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

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Direct Methods of Demand Estimation

• Consumer interviews• Range from stopping shoppers to speak with

them to administering detailed questionnaires

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Direct Methods of Demand Estimation

• Potential problems with consumer interviews• 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

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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

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Empirical Demand Functions

• Demand equations derived from actual market data

• Useful in making pricing & production decisions

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Simple regression analysis

• Simple linear regression assumes one-way causation

• Inappropriate for competitive markets

• Price and output are simultaneously determined in competitive markets

• Advanced regression techniques are available for estimating demand in competitive markets

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Empirical Demand Functions

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

RQ a bP cM dP

where Q is quantity demanded, P is the price of the good or service, M is consumer income, & PR is the price of some

related good R

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Empirical Demand Functions

• 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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Empirical Demand Functions

• Estimated elasticities of demand are computed as

RQ a bP cM dP

ˆˆ PE b

Q

ˆ ˆMM

E cQ

ˆˆ RXR

PE d

Q

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• In this form, elasticities are constant

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 demand function, covert to logarithms

RlnQ lna b ln P c ln M d ln P

M XRˆ ˆˆ ˆ ˆˆE b E c E d

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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)

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Checkers Pizza

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Linear Regression

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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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• If b > 0, sales are increasing over time

• If b < 0, sales are decreasing over time

• If b = 0, sales are constant over time

Linear Trend Forecasting

tˆ ˆˆQ a bt

• Use regression analysis to estimate values of a and b

• Statistical significance of a trend is determined by testing or by examining the p-value for

b̂b̂

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A Linear Trend Forecast(Figure 7.1)

Estimated trend line

Sale

s

Q

t

199

7

199

8

199

9

200

0

200

1

200

2

200

3

200

4

200

5

200

6

2004Q̂

200

7

7

201

2

2009Q̂ 12

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Linear Trend Estimation

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Forecasting Sales for Terminator Pest Control (Figure 7.2)

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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

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Sales with Seasonal Variation(Figure 7.3)

2004 2005 2006 2007

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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 one (1) for observations that

occur during the season assigned to that dummy variable

• Takes value of zero (0) otherwise

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Effect of Seasonal Variation(Figure 7.4)

Sale

s

Time

Qt

t

Qt = a′ + bt

a′

a

Qt = a + bt

c

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Quarterly Sales Data

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Dummy Variable Estimates

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Dummy Variable Specification

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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

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Some Final Warnings

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

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Confidence Intervals

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