Chapter 7 Demand Estimation Forecasting 2016 by Mc

Chapter 7 Demand Estimation & Forecasting © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -1

Learning Objectives v Explain strengths and weaknesses of direct methods of demand estimation v Specify an empirical demand function v Employ linear regression methodology to estimate the demand function for a single price-setting firm v Forecast sales and prices using time-series regression analysis v Use dummy variables in time-series demand analysis to account for cyclical or seasonal variation in sales v Discuss and explain several important problems that arise when using statistical methods to forecast demand © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -2

Direct Methods of Demand Estimation v Consumer interviews ~ Range from stopping shoppers to speak with them to administering detailed questionnaires © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -3

Direct Methods of Demand Estimation v 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 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -4

Direct Methods of Demand Estimation v 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 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -5

Empirical Demand Functions v Demand equations derived from actual market data v Useful in making pricing & production decisions © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -6

Empirical Demand Functions v 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, and N is the number of buyers © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -7

Empirical Demand Functions v In linear form ~ b = Q/ P ~ c = Q/ M ~ d = Q/ PR v 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 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -8

Empirical Demand Functions v Estimated elasticities of demand are computed as © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -9

Nonlinear Empirical Demand Specification v When demand is specified in log-linear form, the demand function can be written as v To estimate a log-linear demand function, covert to logarithms v In this form, elasticities are constant © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -10

Demand for a Price-Setter v 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 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -11

Time-Series Forecasts v A time-series model shows how a timeordered sequence of observations on a variable is generated v Simplest form is linear trend forecasting ~ Sales in each time period (Qt ) are assumed to be linearly related to time (t) © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -12

Linear Trend Forecasting v 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 v Statistical significance of a trend is determined by testing or by examining the p-value for © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -13

A Linear Trend Forecast (Figure 7. 1) Q Estimated trend line 12 2018 Sales 20137 2018 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. t 7 -14

Forecasting Sales for Terminator Pest Control (Figure 7. 2) 2013 2013 2013 2014 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -15

Seasonal (or Cyclical) Variation v Can bias the estimation of parameters in linear trend forecasting v 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 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -16

Sales with Seasonal Variation (Figure 7. 3) 2010 2011 2012 2013 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -17

Dummy Variables v To account for N seasonal time periods ~ N – 1 dummy variables are added v 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 © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -18

Effect of Seasonal Variation (Figure 7. 4) Qt Qt = a′ + bt Sales Qt = a + b t a′ c a t Time © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -19

Some Final Warnings v The further into the future a forecast is made, the wider is the confidence interval or region of uncertainty v Model misspecification, either by excluding an important variable or by using an inappropriate functional form, reduces reliability of the forecast © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -20

Some Final Warnings v Forecasts are incapable of predicting sharp changes that occur because of structural changes in the market © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -21

Summary v Consumer interviews and market studies are two direct methods of demand estimation ~ Problems can include: (1) selection of a representative sample; (2) response bias; and (3) inability of the respondent to answer accurately v Empirical demand functions are demand equations derived from actual market data and are extremely useful in making pricing and production decisions v The first step to estimating a single price-setting firm’s demand is to specify the demand function; the second step is to collect data; the third step is to estimate the parameters using the linear regression © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -22

Summary v A time-series model shows how a time-ordered sequence of observations on a variable is generated ~ The simplest form of time-series forecasting is linear trend forecasting v Seasonal or cyclical variation can bias results in linear trend models; to account for this, dummy variables are added to the trend equation ~ Dummy variables take a value of 1 for those observations that occur during the season assigned to that dummy variable, and a value of 0 otherwise v When making forecasts, analysts must recognize the limitations that are inherent in forecasting © 2016 by Mc. Graw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part. 7 -23