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Chapter 7

Chapter 7. Demand Estimation & Forecasting. 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. Empirical Demand Functions. In linear form b = Q/P

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Chapter 7

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  1. Chapter 7 Demand Estimation & Forecasting

  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. Empirical Demand Functions • 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

  4. Empirical Demand Functions • Estimated elasticities of demand are computed as

  5. Nonlinear Empirical Demand Specification • When demand is specified in log-linear form, the demand function can be written as

  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. 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. 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. 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. 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. 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. 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 (Qt ) are assumed to be linearly related to time (t)

  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. Estimated trend line   2004 2009 A Linear Trend Forecast(Figure 7.3) Q    Sales        t 2000 2003 2002 2001 1994 1997 1996 1995 1998 1999 Time

  15. Forecasting Sales for Terminator Pest Control(Figure 7.4)

  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.                Sales with Seasonal Variation(Figure 7.5) 2001 2002 2003 2004

  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. Qt = a’ + bt Qt = a + bt c a’ a Effect of Seasonal Variation(Figure 7.6) Qt Sales t Time

  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. 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. 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. 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

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