1. Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Managerial Economics Thomas Maurice eighth edition Chapter 7 Demand Estimation & Forecasting

2. Managerial Economics 2 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 2 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

3. Managerial Economics 3 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 3 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

4. Managerial Economics 4 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 4 Empirical Demand Functions Estimated elasticities of demand are computed as

5. Managerial Economics 5 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 5 Nonlinear Empirical Demand Specification When demand is specified in log-linear form, the demand function can be written as

6. Managerial Economics 6 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 6 Market-Determined vs. Manager- Determined Prices Method of estimating parameters of an empirical demand function depends on whether price of the product is market- determined or manager-determined Price-taking firms do not set the price of their product Prices are endogenous, or market-determined by the intersection of demand & supply For price-setting firms Prices are manager-determined, or exogenous

7. Managerial Economics 7 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 7 Simultaneity Problem When estimating industry demand for price-taking firms, simultaneity problem must be addressed Arises because output & price are determined jointly by forces of demand & supply Two econometric problems arise Identification problem Simultaneous equations bias problem

8. Managerial Economics 8 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 8 Identification Problem Industry demand is identified when It is possible to estimate the true demand function from a sample of observations of equilibrium output & price Demand is identified when supply includes at least one exogenous variable that is not also in the demand equation

9. Managerial Economics 9 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 9 Simultaneous Equations Bias When price is endogenous, price will be correlated with random error term in demand equation This causes simultaneous equations bias if OLS is applied To avoid this bias, two-stage least- squares (2SLS) can be applied if industry demand is identified

10. Managerial Economics 10 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 10 Industry Demand for a Price-Taker To estimate industry demand function for a price-taking firm: Step 1: Specify industry demand & supply equations Step 2: Check for identification of industry demand Step 3: Collect data for the variables in demand & supply Step 4: Estimate industry demand using 2SLS

11. Managerial Economics 11 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 11 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 demand function Step 3: Estimate firm’s demand using OLS

12. Managerial Economics 12 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 12 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)

13. Managerial Economics 13 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 13 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

14. Managerial Economics 14 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 14 Estimated trend line A Linear Trend Forecast (Figure 7.3) Sales Time Q t 1994 1995 19961997 19981999 2000 20012002 2003           2004  2009 

15. Managerial Economics 15 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 15 Forecasting Sales for Terminator Pest Control (Figure 7.4)

16. Managerial Economics 16 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 16 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

17. Managerial Economics 17 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 17 Sales with Seasonal Variation (Figure 7.5)                 2001200220032004

18. Managerial Economics 18 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 18 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

19. Managerial Economics 19 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 19 Effect of Seasonal Variation (Figure 7.6) Sales Time QtQt t Q t = a’ + b t a’ a Q t = a + b t c

20. Managerial Economics 20 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 20 Econometric Models Statistical models that uses an explicit structural model to explain underlying economic relations Technique of forecasting with simultaneous equations employs an estimated demand & supply functions to produce forecasted values for sales & price

21. Managerial Economics 21 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 21 Forecasting with Simultaneous Equations Step 1: Prevailing demand & supply functions are estimated using current data Both equations must be identified & are estimated using 2SLS Step 2: Future values of exogenous variables are obtained by estimation or forecasting models Forecast values are substituted into demand & supply equations

22. Managerial Economics 22 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 22 Forecasting with Simultaneous Equations Step 3: Intersection of future demand & supply equations is found Values of P & Q at the intersection are the forecast values of sales & price for that future period

23. Managerial Economics 23 Copyright © 2005 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin 23 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