Chapter 7 Demand Estimation and Forecasting Mc GrawHillIrwin

Chapter 7 Demand Estimation and Forecasting Mc. Graw-Hill/Irwin Copyright © 2013 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

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 7 -2

Direct Methods of Demand Estimation v Consumer interviews ~ Range from stopping shoppers to speak with them to administering detailed questionnaires 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 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 7 -5

Empirical Demand Functions v Demand equations derived from actual market data v Useful in making pricing & production decisions 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 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 7 -8

Empirical Demand Functions v Estimated elasticities of demand are computed as 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 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 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) 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 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 t 7 -14

Forecasting Sales for Terminator Pest Control (Figure 7. 2) 2013 2013 2013 2014 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 7 -16

Sales with Seasonal Variation (Figure 7. 3) 2010 2011 2012 2013 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 7 -18

Effect of Seasonal Variation (Figure 7. 4) Qt Qt = a′ + bt Sales Qt = a + b t a′ c a t Time 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 7 -20

Some Final Warnings v Forecasts are incapable of predicting sharp changes that occur because of structural changes in the market 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 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 7 -23