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

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

7-3 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

7-4 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

7-5 Empirical Demand Functions Demand equations derived from actual market data Useful in making pricing & production decisions

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, & P R is the price of some related good R

7-7 Empirical Demand Functions In linear form b =  Q/  P c =  Q/  M d =  Q/  P R 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 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 To estimate a log-linear demand function, covert to logarithms

7-10 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)

7-11 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 (Q t ) are assumed to be linearly related to time (t)

7-12 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 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

7-13 A Linear Trend Forecast (Figure 7.1) Estimated trend line Sales Q t           2007   12

7-14 Forecasting Sales for Terminator Pest Control (Figure 7.2)

7-15 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

7-16 Sales with Seasonal Variation (Figure 7.3)                

7-17 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

7-18 Effect of Seasonal Variation (Figure 7.4) Sales Time QtQt t Q t = a′ + b t a′ a Q t = a + b t c

7-19 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

7-20 Some Final Warnings Forecasts are incapable of predicting sharp changes that occur because of structural changes in the market