Demand Estimation & Forecasting 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 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

Empirical Demand Functions Estimated elasticities of demand are computed as

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

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

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

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

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

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

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

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)

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

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

Forecasting Sales for Terminator Pest Control (Figure 7.4)

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

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

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

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

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

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

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

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