#### Transcript CHAPTER 7: Demand Estimation and Forecasting

Chapter 7: Demand Estimation and Forecasting McGraw-Hill/Irwin Copyright © 2011 by the McGraw-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 7-6 Empirical Demand Functions • In linear form, an empirical demand function can be specified as Q a bP cM dPR 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 Q a bP cM dPR • 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 Q a bP cM dPR • Estimated elasticities of demand are computed as P ˆ ˆ Eb Q M ˆ ˆ EM c Q PR ˆ ˆ E XR d Q 7-9 Nonlinear Empirical Demand Specification • When demand is specified in log-linear form, the demand function can be written as Q aP M P b c d R • To estimate a log-linear demand function, covert to logarithms lnQ lna b ln P c ln M d ln PR • In this form, elasticities are constant ˆ bˆ E ˆ cˆ E M ˆ dˆ E XR 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 7- Linear Regression 7-13 7- 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) Qt a bt 7-14 Linear Trend Forecasting • Use regression analysis to estimate values of a and b ˆ aˆ bt ˆ Q t • 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 b̂ or by examining the p-value for b̂ 7-15 A Linear Trend Forecast (Figure 7.1) Q Estimated trend line Q̂ 2009 12 Q̂ 20047 Sales t 2012 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 7-16 Linear Trend Estimation 7-17 7- 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 + bt a′ c a t Time 7-22 Quarterly Sales Data 7-23 7- Dummy Variable Estimates 7-24 7- Dummy Variable Specification 7-25 7- 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 7-