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

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

Managerial Economics 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 Dr. Chen’s notes: Market studies (field experiments) are costly and risky. The testing market prices (either high or low) might influence the product image. Lab experiments are inexpensive; however, participants are generally college students who may not represent the population customers. The best (relatively inexpensive and accurate) technique of demand estimation is empirical market data analysis.

Managerial Economics 7-4 Empirical Demand Functions Demand equations derived from actual market data Useful in making pricing & production decisions In linear form, an empirical demand function can be specified as

Managerial Economics 7-5 Empirical Demand Functions In linear form b =  Q/  P (direct impact on Q when  P = 1) c =  Q/  M (direct impact on Q when  M =1) d =  Q/  P R (direct impact on Q when  P R =1) Expected signs of coefficients b is expected to be negative (law of demand) c is positive for normal goods; negative for inferior goods d is positive for substitutes; negative for complements

Managerial Economics 7-6 Empirical Demand Functions Estimated elasticities of demand are computed as

Managerial Economics 7-7 Nonlinear Empirical Demand Specification When demand is specified in log-linear form, the demand function can be written as

Managerial Economics 7-8 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)

Managerial Economics 7-9 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) Q t = a + bt Dr. Chen’s notes: Time-series forecasting is a statistical model by using historical data to project the future trend. It does not attempt to explain underlying causal relationships that produce the observed outcome. Please study the textbook pp. 260~270 for the case of Pest Control. Choosing the correct period number is the key. On the next slide, would you please get the sales forecast for November 2012? t =?

Managerial Economics Forecasting Sales for Terminator Pest Control (Figure 7.2)

Managerial Economics 7-11 Linear Trend Forecasting 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 t-test of b. Dr. Chen’s notes: On textbook pp. 262, the p-value of t is very small (less than  = 0.05) to confirm the significance. Then we may use the time-series model to predict the future periods.

Managerial Economics 7-12 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 1 for observations that occur during the season assigned to that dummy variable Takes value of 0 otherwise Dr. Chen’s notes: On textbook pp. 266, you can see how to set up dummy variables for four quarters (seasons) on Table 7.2. Why three dummy variables for four quarters? The fourth quarter can be denoted by D 1 = 0, D 2 = 0, and D 3 = 0.

Managerial Economics 7-13 Dummy Variables (continued) Dr. Chen’s notes: The applications of dummy variable are also popular in regression for the “qualitative” independent variable. Its value is either 1 or 0; that is, D = 1, if (qualitative character) D = 0, otherwise. For example, if a regression for annual income estimation considers “gender” as one of independent variables, then it can set up the gender dummy as D G = 1, if male D G = 0, otherwise (female) Assume that the regression outcome is Y = 15, ,200S + 2,000D G, where Y= annual income, S= schooling years. How to interpret the coefficient of dummy variable? Is it positive 2,000, right? It implies that gender discrimination exists in annual income because male has an extra $2,000 in estimation. You can see that the setting of dummy variable is very convenient to point out any significant influence of qualitative independent variable.

Managerial Economics 7-14 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 Forecasts are incapable of predicting sharp changes that occur because of structural changes in the market