Chapter 7 Demand Estimation and Forecasting Mc GrawHillIrwin

Chapter 7: Demand Estimation and Forecasting Mc. Graw-Hill/Irwin Copyright © 2011 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

Direct Methods of Demand Estimation • Consumer interviews • Range from stopping shoppers to speak with them to administering detailed questionnaires 7 -2

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 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 7 -5

Simple regression analysis • Simple linear regression assumes oneway 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 7 -6

Empirical Demand Functions • In linear form, an empirical demand function can be specified as 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 7 -7

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 7 -8

Empirical Demand Functions • Estimated elasticities of demand are computed as 7 -9

Nonlinear Empirical Demand Specification • When demand is specified in log-linear form, the demand function can be written as • To estimate a log-linear demand function, covert to logarithms • In this form, elasticities are constant 7 -10

Demand for a Price-Setter • To estimate demand function for a pricesetting 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 -11

Checkers Pizza 7 -12

Linear Regression 7 -13

Time-Series Forecasts • A time-series model shows how a timeordered 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) 7 -14

Linear Trend Forecasting • Use regression analysis to estimate values of a and b • If b > 0, sales are increasing over time • If b < 0, sales are decreasing over time • If b = 0, sales are constant over time • Statistical significance of a trend is determined by testing or by examining the p-value for 7 -15

A Linear Trend Forecast (Figure 7. 1) Q Estimated trend line 12 Sales 7 2012 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 t 7 -16

Linear Trend Estimation 7 -17

Forecasting Sales for Terminator Pest Control (Figure 7. 2) 7 -18

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 -19

Sales with Seasonal Variation (Figure 7. 3) 2004 2005 2006 2007 7 -20

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 7 -21

Effect of Seasonal Variation (Figure 7. 4) Qt Qt = a′ + bt Sales Qt = a + b t a′ c a t Time 7 -22

Quarterly Sales Data 7 -23

Dummy Variable Estimates 7 -24

Dummy Variable Specification 7 -25

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 7 -26

Some Final Warnings • Forecasts are incapable of predicting sharp changes that occur because of structural changes in the market 7 -27

Confidence Intervals 7 -28